INVITED RESEARCH REPORT
© August 1987
Lambert T. Dolphin
Senior Research Physicist
That a major revolution in nuclear physics, astronomy and cosmology is underway these days is perhaps not obvious to the general public, or even perhaps to the average research scientist who is not working directly in one of these fields. It was but 300 years ago this year that Sir Isaac Newton published his "Principia," launching the western world boldly forward towards the era of modern physics. An explosive increase in the body of knowledge about our physical universe has resulted. The most rapid changes in this body of knowledge, however, seem to have occurred just in the past few years and appear to be taking place even now at an accelerated rate.
As startling and profound as Albert Einstein's Special and General Theories of Relativity were when they first appeared, shortly after the turn of this century, advances in particle physics and in astronomy in the past three or four decades have been even more radical in their implications.
It is now known that certain atomic constants governing the atom and its inner workings are the very same constants that likewise describe phenomena in space-time on the largest scale of observables in the universe. Thus, for some as yet unexplained reasons, the realm of the smallest physical observables is coupled to the grandest scale of events and happenings amongst the stars and galaxies.
All science rests upon some form of philosophical presupposition, or upon basic assumptions made at the start of a hypothesis. Good science means questioning basic assumptions from time to time, or altering one's weltanschaung in the light of new findings. Today's scientific theories are built on the foundations laid by the previous generation, and a good many of our theories are certainly valid because they work so well and have stood the test of time. But old theories do give way to new, and hopefully a net gain in understanding follows.
The progress of science occurs mostly by observation and experiment, though some scientific discoveries are the result of pure mathematical studies later tested and found to fit observable data in the universe. Scientific instruments extend the range of the five senses by orders of magnitude in all directions. Observations and experimental data are used to fit the data to a curve and to find an equation that will allow extrapolation into uncharted waters. It is an unwritten law, known as Occam's Razor, that the simpler equation (or theory) is to be preferred to the complex, even if both fit the data. This principle propels the scientist to look for "Grand Unified Theories" and to find simpler models to replace the too-complex. Often a new scientific theory is found to fit the experimental data very well --- at first, and everyone rejoices. Then more precision measurements are made. When the new data are in small differences between theory and experiment are frequently discovered. Whenever this happens concerted efforts (often by many research groups) are launched spontaneously to find the reasons for the discrepancies and to revise the older theory. Growth in science also depends on new ways at looking at old data, at carefully looking for the exceptions to the rule, or by following hunches, intuition or "leaps of faith" to see where they lead.
Choosing to study observational anomalies that apparently run counter to the prevailing assumptions of the day is not guaranteed to prove popular with all scientists. Many scientists have never taken a class in the history of science so as to be aware of how the body of scientific evidence has developed over time, or they would be, perhaps, less afraid of change. Some researchers may be so engrossed in the excitement of their current studies that they fail to take into account new evidence from other disciplines, or to question the assumptions upon which prevailing models rest. Everyone tends to forget that much of today's scientific orthodoxy came out from yesterday's unpopular heresies. It is the mark of a good scientist to not be afraid to question what has been taken for granted (perhaps for decades), by others. The authors of this report raise a scientific discussion, which, if true, has profound implications not only for physics but also for philosophy as well. As far as I can discern, their arguments are sound, their homework has been done, and they "have done their sums correctly."
The authors of this report discuss the possibility that the velocity of light is not a constant. This notion is not so unreasonable when one considers the history of "c". When the Danish Astronomer Roemer, (Philosophical Transactions, June 25, 1677), announced to the Paris Academie des Sciences in September 1676 that the anomalous behavior of the eclipse times of Jupiter's inner moon, Io, could be accounted for by a finite speed of light, he ran counter to the current wisdom espoused by Descartes and Cassini. It took another quarter century for scientific opinion to accept the notion that the speed of light was not infinite. Until then it had never been the majority view that this physical quantity was finite.
The Greek philosophers generally followed Aristotle in the belief that the speed of light was infinite. However there were exceptions such as Empedocles of Acragas (c. 450 B.C.) who spoke of light, "traveling or being at any given moment between the earth and its envelope, its movement being unobservable to us," (The Works of Aristotle translated into English, W.D. Ross, Ed., Vol. III, Oxford Press 1931: De Anima, p4l8b and De Sensu, pp446a-447b). Around 1000 A.D. the Moslem scientists Avicenna and Alhazen both believed in a finite speed for light, (George Sarton, "Introduction to the History of Science," Vol.I, Baltimore, 1927, pp709-12). Roger Bacon (1250 A.D.) and Francis Bacon (1600 A.D.) accepted that the speed of light was finite though very rapid. The latter wrote, "Even in sight, whereof the action is most rapid, it appears that there are required certain moments of time for its accomplishment...things which by reason of the velocity of their motion cannot be seen--as when a ball is discharged from a musket," (Philosophical Works of Francis Bacon, J.M. Robertson, ed., London, 1905, p363). However, in 1600 A.D. Kepler maintained the majority view that light speed was instantaneous, since space could offer no resistance to its motion, (Johann Kepler, "Ad Vitellionem paralipomena astronomise pars optica traditur," Frankfurt 1804).
It was Galileo in his "Discorsi...î published in Leyden in 1638, who proposed that the question might be settled in true scientific fashion by an experiment over a number of miles using lanterns, telescopes and shutters. The Academia del Cimento of Florence reported in 1667 that such an experiment over a distance of one mile was tried, "without any observable delay," ("Essays of Natural Experiments made in the Academie del Cimento," translated by Richard Waler, London, 1684, p157). However, after reporting the experimental results, Salviati, by analogy with the rapid spread of light from lightning, maintained that light velocity was fast but finite.
Descartes, who died in 1650, strongly held to the instantaneous propagation of light and accordingly influenced Roemer's generation of scientists who accepted his arguments. He pointed out that we never see the sun and moon eclipsed simultaneously. However if light took, say, one hour to travel from earth to moon, the point of co-linearity of the sun, earth, and moon system causing the eclipse would be lost and visibly so, (Christiaan Huygens, "Traite de la Lumiere...î Leyden, 1690, pp4-6, presented in Paris to the Academie Royale des Sciences in 1678). It was Christiaan Huygens in 1678 who demolished Descartes' argument by pointing out, on Roemer's measurements, that light took of the order of seconds to get from moon to earth, maintaining both the co-linearity and a finite speed. However it was only Bradley's independent confirmation published January 1, 1729 that caused the opposition to a finite value for the speed of light to cease. Roemer's work, which had split the scientific community, was at last vindicated. After 53 years of struggle, science accepted the observational fact that light traveled at a finite speed. Until recently that finite speed has been generally been taken to be a fixed and immutable constant of the universe in which we live.
I first became aware of the research investigations of Trevor Norman and Barry Setterfield four years ago. I had stumbled across, almost by accident, a short technical paper in which they described an analysis of the known experimental measurements to date of the velocity of light. Their data seemed to show that a small (but statistically significant) decrease in "c" had occurred during the past 400 years. I followed the subsequent printed responses solicited from scientists around the world on the issues raised by the original paper and found Norman and Setterfield competently answered the questions raised by critics of their theory. I knew from experience that major changes in scientific theories often start out from just this kind of beginning. I have learned to sort out new ideas such as these when they appear in print and to pay close attention to a few of them, for it is out of papers like this one that change and progress in science often come.
At first I was both cautious and skeptical, though interested. I remember speculations when I was an undergraduate in physics at San Diego State University (near the famous 200 inch Hale Telescope on Mt. Palomar), concerning the red shift of light from distant galaxies, and the apparent expansion of the universe outwards from a point of singularity. These ideas were not, I recalled, well received by all when they were first propounded. I had heard of the possibility of "tired light," but always assumed the speed of light had been dependably constant for billions of years. So out of curiosity I wrote to Barry Setterfield soon after reading their article. I received a prompt and courteous reply. There followed a lengthy exchange of comments, articles and references between the three of us. I have since talked to several other respected and competent scientific colleagues in the United States and abroad who also take Norman and Setterfield's work seriously and this has given me increased confidence that they are onto something new and important. Last year Trevor Norman was instrumental in establishing an electronic mail connection between our two organizations to facilitate discussions between the three of us.
In all honesty I can say that it has taken me four years to get comfortable (and enthused about) their findings. It has been very good for me to do my homework in the process of evaluating what they have written. I have had to dig out my Quantum Mechanics, Nuclear Physics, Relativity and Cosmology textbooks from graduate school at Stanford University, and get up to date a bit by reading more recent works. When I learned recently that Norman and Setterfield had now carried their work to the stage where a thorough report had been drafted, I offered my assistance in hopes their findings could be better known.
If indeed the velocity of light has changed or is changing, a certain set of related other physical "constants" have changed as well. The authors have not set out to "prove" that this is indeed the case. They have however amassed and carefully studied a great body of data that suggests that the some of most "sacred" of the physical constants are not constant after all. Their report is written in accord with perfectly orthodox scientific standards. That is, they have collected and analyzed the available data and formed a hypothesis. This hypothesis (that the velocity of light has decreased with time) is testable. It is a perfectly valid hypothesis until further data proves otherwise. I believe it is timely and appropriate to call wider attention to this hitherto little known investigation. This report is therefore presented to invite discussion, comment, rebuttal, and hopefully to provoke researchers to look for further evidence which could support or refute the authors' conclusions.
The authors and I have agreed that papers and comments should be solicited so that a follow on report might be published by us on this important subject. The reader, whether scientist or layman, is welcome therefore to contact either of the authors or myself in this regard. Norman and Setterfield also have available a small supplement to this report which addresses some of the ramifications of different universal timescales, which logically follow from possible real changes in such basic constants as the velocity of light. I recommend that those readers with interests in the latter area write the authors directly for a copy of this supplement. I myself found it most helpful and stimulating.
Lambert T. Dolphin
Senior Research Physicist
Geoscience and Engineering Center
II. C DECAY PROPOSAL HISTORICALLY.
(A). Dynamical c variation discussed.
(B). The speed of Light and relativity.
(C). Reactions and arguments.
III. MEASURED VALUES OF C.
(A). The Roemer-type determinations.
(B). The Bradley-type observations.
(C). Toothed wheel experiments.
(D). Rotating mirror results.
(E). Kerr Cell results.
(F). The six methods used 1945-1960.
(G). The post-1960 results.
(H). The ratio ESU/EMU and waves on wires.
(I). Conclusions from collective data.
IV. PHYSICAL QUANTITIES AFFECTED BY C DECAY.
(A). Maxwell's Laws and the electronic charge.
(B). Atomic rest-masses.
(C). The atom and Planck's constant.
(D). Atomic orbits and related quantities.
(E). Radioactive decay.
V. TIME AND GRAVITATION.
(A). Atomic time.
(C). Length, time and c.
(D). Lasers and a test for c decay.
VI. DATA CONCLUSIONS AND ULTIMATE CAUSES.
(A). General conclusions from all data.
(B). Conclusions from c data.
(C). Conclusions from refined atomic data.
(D). Ultimate causes and the c equation.
(A). Radioactive radiation intensities.
(B). Stellar radiation intensities.
(C). The red-shift.
(D). The Doppler formula.
(E). The missing mass.
(F). Superluminal jets.
(G). Final comments.
APPENDIX I: Non-technical summary.
SELECTED PROFESSIONAL COMMENT
TABLE 1. Roemer method values.
TABLE 2. Results of Bradley's observations.
TABLE 3. Bradley aberration method values.
TABLE 4. Toothed wheel experimental values.
TABLE 5. Rotating mirror experiments.
TABLE 6. Kerr cell values of c.
TABLE 7. Results by six methods 1945-1960.
TABLE 8. Results 1960-1983 - mainly Laser.
TABLE 9. C values by the ratio of ESU/EMU.
TABLE 10. C values by waves on wires.
TABLE 11. Refined List of c data.
TABLE 12. Options with changing c.
TABLE 13. Values of the electronic charge, e.
TABLE 14. Values of the specific charge e/(mc).
TABLE 15. Experimental values of h/e, 2e/h, h/e².
TABLE 16. The Rydberg constant, R.
TABLE 17. The proton gyromagnetic ratio.
TABLE 18. Other c independent quantities.
TABLE 19. Half-lives of the main heavy radio-nuclides.
TABLE 20. The Newtonian gravitational constant G.
TABLE 21. Comparison of curves fitted to Table 11 data.
TABLE 22. Results of analysis of speed of light data.
TABLE 23. Summary of behavior of atomic quantities.
TABLE 24. Consistent trends in 7 atomic quantities.
FIGURE I. Pulkova aberration results. (note: the first two measurements on this graph are from earlier abberation results and not from Pulkova. The labeling of the graph has caused some confusion)
FIGURE II. Best 23 c values by 8 methods 1740-1940.
FIGURE III. Typical curve fit on table 11 c data.
FIGURE IV. Typical curve fit detail 1870-1983.
FIGURE V. Probable atomic clock behavior all curves.
Acknowledgements: We are indebted to Flinders University, South Australia, for the use of facilities, and for the patience and help of Ron, Kai, Judy and Ian at the I.L.L. desk. Thanks also to Dr. R.O. Hampton (biologist, Waite Research Institute) for his impressions and valued comments as an 'outsider' in the fields addressed. The comments and suggestions of Professor P.P. Martins Jr., CETEC, Brazil, Professors D.H. Kenyon and D. Meredith, San Francisco State University, along with Dr. G. Mortimer, Adelaide University, South Australia, and Drs. J. Rice and M. Murray of Flinders University, are deeply appreciated. The very useful discussions with Dr. D.R. Humphreys, Sandia National Labs., Albuquerque, U.S.A. and Col.(ret.) Dr. W.T. Brown, (formerly Chief of Science and Technology Studies, Air War College, Assoc. Professor, U.S. Air Force Academy), and the late Dr. Brian Daily, (formerly Dean of the Faculty of Science, Adelaide University), have made a major contribution to the form and content of this presentation.
THE ATOMIC CONSTANTS, LIGHT, AND TIME.
by Trevor G. Norman* and Barry Setterfield**
*School of Mathematical Sciences, Flinders University, South Australia 5042.
**Present address: P.O. Box 318, Blackwood, S.A., 5051, Australia.
The behavior of the atomic constants and the velocity of light, c, indicate that atomic phenomena, though constant when measured in atomic time, are subject to variation in dynamical time respectively. Electromagnetic and gravitational processes govern atomic and dynamical time respectively. If conservation laws hold, many atomic constants are closely linked with c. Any change in c affects the atom. For example, electron orbital speeds are proportional to c, meaning that atomic time intervals are proportional to 1/c. Consequently, the time dependent constants are affected. Therefore, Planck's constant, h, may be predicted to vary in proportion to 1/c as should the half-lives of radioactive elements. Conversely, the gyromagnetic ratio, g, should be proportional to c. Any variation in c, macroscopically, therefore reflects changes in the microcosm of the atom.
A systematic, non-linear decay trend is revealed by 163 measurements of c in dynamical time by 16 methods over 300 years. Confirmatory trends also appear in 475 measurements of 11 other atomic quantities by 25 methods in dynamical time. Analysis of the most accurate atomic data reveals that the trend has a consistent magnitude in all quantities. Lunar orbital data indicate continuing c decay with slowing atomic clocks. A decay in c also manifests as a red-shift of light from distant galaxies. These variations have thus been recorded at three different levels of measurement: the microscopic world of the atom, the intermediate level of the c measurements, and finally on an astronomical scale. Observationally, this implies that the two clocks measuring cosmic time are running at different rates.
Relativity can be shown to be compatible with these results. In addition, gravitational phenomena are demonstrably invariant with changes in c and the atom. Observational evidence also demands consistent atomic behavior universally at any given time, t. This requires the permeability and metric properties of free space to be changing. In relativity, these attributes are governed by the action of the cosmological constant, L, proportional to c2, whose behavior can be shown to follow an exponentially damped form like L = a + ekt(b + dt). This is verified by the c data curve fits.
DEFINITION: A dynamical second is defined as 1/31,556,925.9747 of the earth's orbital period and was standard until 1967. Atomic time is defined in terms of one revolution of an electron in the ground state orbit of a hydrogen atom. The atomic standard by the caesium clock is accurate to limits of ±8 x 10-14.
THE ATOMIC CONSTANTS, LIGHT, AND TIME
There are two basic clocks by which cosmic time is commonly measured. One is atomic time that is governed by the period taken for an electron to move around once in its orbit. In essence, it is electromagnetic in character. The other is dynamical time whose units are subdivisions of the period that the earth takes to make one complete orbit of the sun. Obviously, this clock is governed by gravitation. Dynamical time was kept universally until 1967 when the atomic standard was introduced using the caesium clock. Dirac and Kovalevsky have pointed out360 that if the two clock rates were different, 'then Planck's constant as well as atomic frequencies would drift'.
The observational evidence suggests that these two clocks do run at different rates. The lunar and planetary orbital periods, which comprise the dynamical clock, have been compared with atomic clocks from 1955 to 1981 by Van Flandern and others1. Assessing the evidence in 1984, T.C. Van Flandern came to a conclusion, with a dilemma. He stated that1 ëthe number of atomic seconds in a dynamical interval is becoming fewer. Presumably, if the result has any generality to it, this means that atomic phenomena are slowing down with respect to dynamical phenomena ... (though) we cannot tell from the existing data whether the changes are occurring on the atomic or dynamical level.í In either event, atomic quantities bearing units that involve time should show the same correlated variation when measured in dynamical time. Among those quantities would be Planck's constant, h, the gyromagnetic ratio, g', radioactive decay constants, l, and the speed of light, c. The electron rest-mass, m, should also vary from energy considerations and by the definition of force/acceleration.
Dimensionless constants and those with mutually canceling time dependent terms remain invariant if conservation laws are to be upheld. The observational limits set for the 'cosmological variation' of many constants are actually limits on energy conservation. In these cases, a ratio of atomic quantities with mutually canceling time units, such as hc, is usually measured. No conclusion can thus be drawn about any variability in c or h separately. The only statement that is valid is that ' h must vary precisely as 1/c within the observational limits. Those limits are absolutely upheld here.
Theory and experimentally observed effects agree only if distances remain unaffected by the difference in the run-rate between the two clocks. Wavelengths and atomic orbit radii are thus invariant along with the Avogadro Number, N0. As electron orbital velocities are time dependent, it follows that higher velocities produce shorter time intervals on the atomic clock, seen dynamically. Slowing atomic clocks thus imply slowing electron velocities seen from the dynamical time-frame. In addition, those atomic quantities with time units on the denominator should decay while those with time units on the numerator should increase. The measured values of a number of quantities are examined first, confirming the atomic slow-down in dynamical time. Van Flandern's dilemma as to which clock varies is investigated later. For conservation laws to be valid, the atom and dynamical processes will act in completely consistent ways in their own time-frames leaving all quantities invariant there, no matter which clock is in fact varying. However, when dynamically constant orbital periods are measured atomically, the different clock rates will appear as a variation in the gravitational constant, G, seen atomically. This is what Van Flandern observed originally1. The reverse, or dynamical observation of atomic phenomena, is examined here.
Light is produced by atomic processes and its velocity, c, has been measured for 300 years. The subsequent analysis concentrates on this basic quantity initially. It is found that there is a statistically significant decay when c is measured in dynamical time. All 16 methods of c measurement give a decay both individually and collectively. The main points raised in the discussion on c decay in the scientific literature are reviewed.
If conservation laws are valid, a slow-down in c, measured dynamically, should be matched by a proportional change in electron orbit velocities and other atomic processes. Conservation laws require that the time dependent atomic quantities should also be c dependent. An atomic interval, dt, is thus proportional to 1/c, being longer when c is lower. This is precisely the effect that Van Flandern has noted. Consequently, changes in c are either the cause, or the result, of changes in the atom. Light speed thus emerges as a key factor interlinking the atomic constants. The values of these atomic constants, measured dynamically, are found to vary in a way that is consistent with c decay and slowing atomic clocks. Observationally, 16 methods of measurement of various atomic quantities show a statistically significant atomic slow-down. It is also implied in 3 other cases.
The data from all 16 methods of measuring c, and 25 methods of measuring the atomic constants, are treated uniformly. All readily available data have been tabulated, comprising 194 atomic, 281 radio-nuclide, and 163 c values. They include those results rejected by the experimenters themselves or their immediate peers and their reasons for rejection are quoted. The rejected data are often used, but are omitted from refined analysis. Data are treated by a standard least-squares linear fit to discover trends. The slope of this fit decreases with time for all c-dependent quantities. The students t-distribution is applied to the least-squares data mean and to the correlation coefficient, r, to find the confidence interval in the data trend and linear fit.
Note that for the sake of convenience in presentation, all methods of measuring a particular atomic quantity are tabulated together, including the best adjusted values. Some of these methods may not measure the quantity directly. However, the different systems of measurement are indicated in the column marked 'Method'. In these cases, an analysis is made of each method individually and the trend confirmed. This indicates that the trend is not unique to a particular system of measurement but is a genuine effect. This is also the case with the best adjusted values. Indeed, it is in just those cases where an atomic constant has been found varying that the earlier data were gradually omitted from adjusted analysis as more 'correct' newer values were found. The adjusted value was thus determined on the 'best' data that was then available and so long-term changes in this value also indicate a slowing atomic clock.
A summary of the measured trends in 12 atomic quantities is presented in Table 23. The results from all data are given first for each quantity, then those for the most accurate measurements. More details of the speed of light data are given in Table 22 and Figures III and IV. Since it covers a greater time range, the decreasing decay rate from the c data is more readily apparent than with other quantities. In Table 23, the rate of change in an atomic quantity per year is divided by the value of that quantity for all the most accurate data. This allows a cross-comparison of results. In Table 24 the non-linear slow-down is evident and is shown to be concordant in magnitude from the measurements of 7 atomic quantities. It should be noted that the measured rate of slowing is tapering off very rapidly. Future monitoring will be required to discern which of several possibilities will be followed. The full analysis summarized by Tables 22-24 therefore shows that the slowing of atomic processes in dynamical time has formal statistical significance, which upholds Van Flandern's statements. This then raises some issues which are mainly associated with c decay.
The issue of relativity with c variation was essentially addressed with recent papers by Breitenberger6, Mermin7 and Singh8. They show constancy of c was not essential as relativity theory can be deduced without c at all. On a neo-Newtonian level, a variation in c as the limit velocity for energy propagation suggests that a gravitational permeability term should be included in equations. When this is done, a resemblance to relativistic terms is noted. Gravitational potentials on both approaches are then proportional to Gm/c2, which is constant for all c because of mutually canceling, c-dependent terms. For the same reason, the basic equation E=mc2 is also completely valid. Under these circumstances, gravitational terms in general relativity hold dynamically. Furthermore, all gravitational phenomena are thus shown to be invariant with changes in the atom or c, leaving the dynamical clock unaffected. However, in its own time-frame, the atom acts in a completely consistent way leaving all atomic constants without variation. This suggests that relativity also holds when considered by the atomic standard. A constant dynamical interval, dt, could also be written as c.dt. The general relativistic equations involving time intervals written as (c2.dt2) would thus be valid dynamically if the time interval were measured atomically. An equation in dynamical time results that is independent of c.
In other words, from relativistic and neo-Newtonian theory, the dynamical clock is completely invariant with any change in c or atomic behavior. The implication is that the behavior of the atomic clock is variable intrinsically, or is subject to c-dependent external factors, such as the permeability of free space, which leave the dynamical clock unaffected. Furthermore, conservation laws seem violated if gravitational phenomena were causing these data trends. It seems that the atomic clock is slowing down rather than the dynamical clock speeding up. Van Flandern's dilemma thus appears to be solved and relativity is upheld.
One final constraint appears necessary. Light speed must have the same value at any instant in all dynamical frames throughout the universe. This constraint has recently been upheld experimentally by Barnet et al. 9. They demonstrated that light from distant quasars arrived here with the same velocity as light from more local astronomical sources. That means consistent atomic behavior universally at any given time t. This requires the permeability, or energy density, and metric properties of free space to be changing. This option is favored by general relativity where these properties are controlled57 by the action of the cosmological constant, L. A change in L therefore seems to be the root cause of the observed variations.
In the Schwarzschild metric, the term L/c2 appears which requires L to be proportional to c2 for energy conservation. This also follows as L there has dimensions of time-2. We can thus write L = kc2, with k a true constant of about 10-66 cm-2. This allows a L/k substitution for c2 in electromagnetic and other equations. A universe under the action of L, essentially exhibits a form of simple harmonic motion with L varying as the radius89. An exponentially damped sinusoid would be typical L behavior90. This is born out by the c observations which follow the equation c = [a + ekt(b + dt)]1/2, where one solution gives k = - 0.0048, a = 9.029 x 1010, b = 4.59 x 1013, d = -2.60 x 1010, t is the year. However, most properties of this complex expression are closely reproduced by a much simpler polynomial c = a + bt2 + dt8, where a = 299792, b = 0.01866 and d = 3.8 x 10-19. This equation also has a superior fit to the c data.
In conclusion, theory and observation indicate that electromagnetic wave amplitude energies, and hence photon intensities, are proportional to 1/c. Consequently, although stellar and radioactive processes were more vigorous in the past, proportional to c, the net radiation intensity remained unchanged with temperatures unaffected. The latter follows since thermal conductivity is proportional to c. This approach receives observational support since light from distant objects is undimmed by c decay. However, for light in transit, increasing amplitude energy is made at the expense of wavelength energy. Wavelengths are thus proportional to 1/c giving a red-shift to light from distant galaxies. Note that the observed red-shift, z, is a net result since the action of L causes galactic motion towards the observer. This research thus holds the potential to resolve some perplexing problems of science.
II. THE C DECAY PROPOSAL HISTORICALLY:
(A). DYNAMICAL C VARIATION DISCUSSED:
In October 1983 the speed of light, c, was declared a universal constant of nature defined as 299,792.458 Km/s and as such is now used in the definition of the meter. However, in a recent article on this subject, Wilkie² points out that ëmany scientists have speculated that the speed of light might be changing over the lifetime of the universeí and concludes that ëit is still possible that the speed of light might vary on a cosmic timescale.í Van Flandern1 agrees. He states that ëAssumptions such as the constancy of the velocity of light ... may be true in only one set of units (atomic or dynamical), but not the other.í
Historically, the literature, particularly from the 1920's to the 1940's, amplifies this conclusion and indicates that if c is varying it is doing so in dynamical units, not atomic. Thus, the values for c obtained by Michelson alone were as follows in Table A (with full details in Table 5).
|DATE||VALUE OF C (km/s)|
These results are not typical of a normal distribution about today's fixed value. However, the 1882.8 result is confirmed by the values from two other experiments. One by Newcomb in 1882.7 yielded a c value of 299,860 ±30 Km/s, while Nyren using another method in 1883 obtained a definitive value of 299,850 ±90 Km/s (see discussion below for details). In other words, Michelson's 1882.8 result was completely consistent with the other values obtained that year. The mean of these three values (299,854 Km/s) lies above today's value by 61.8 Km/s, though the standard deviation of these three values is only ±5 Km/s. The quoted probable errors thus seem to be conservative.
Assuming no c variation, the least squares mean for all these data show they are distributed about a point 53 Km/s above today's value. The mean error is ±45.8 Km/s, which places today's value beyond its lower limit. If the students t-distribution is applied to these data, the hypothesis that c has been constant at its present value from 1879.5 to 1926.5 can be rejected with a confidence interval of 98.2%. One would expect that other results from this type of experiment would lie below today's value by a similar amount to restore the normal distribution. This is not observed.
Assuming, then, that the variation is real, it represents a measured decay of 112 Km/s in 47 years. A linear, least squares fit to these data gives a drop of 1.62 Km/s per year. The resulting correlation coefficient r = -0.879, and this decay correlation is significant at the 98.9% confidence level from the t-statistic. This is not an isolated instance: similar trends occur with all methods of c measurement, individually and collectively, involving 163 data points. Some are illustrated in Figures I and II. Despite a preference for the constancy of atomic quantities, Dorsey3 did concede that 'As is well known to those acquainted with the several determinations of the velocity of light, the definitive values successively reported...have, in general, decreased monotonously from Cornu's 300.4 megameters per second in 1874 to Anderson's 299.776 in 1940...' In fact, even Dorsey's reworking of the original data left c values generally above those currently prevailing.
The continuing drop in the measured value of c with each new determination elicited further remarks on the topic until the mid 1940's. By then the wealth of comment can be gauged by the representative sample in the final reference (360) given below. The listing includes 18 from Nature alone. A variety of possible decay curves for c was espoused, and the resulting experiments invalidated some proposals. The effects of c variation on some other quantities were discussed, and a number of scenarios eliminated by experiment.
(B). THE SPEED OF LIGHT AND RELATIVITY:
De Bray4, after listing the four most recent determinations of c commented 'If the velocity of light is constant, how is it that, INVARIABLY, new determinations give values which are lower than the last one obtained, ...There are twenty-two coincidences in favor of a decrease of the velocity of light, while there is not a single one against it' (his emphasis). De Bray then made a key point in stating that 'Vrkljan has shown (Zeits. fur Phys., Vol.63, pp 688-691; 1930) that a decrease in the velocity of light is not in contradiction with the general theory of relativity.'
Again, Canuto and Hsieh5 point out that the gravitational field equations in general relativity contain a single factor M = Gm/c2 as a constant of integration. All the equations demand is that the net result, M, is constant without saying anything about compensating variations in individual terms. Likewise, a recent paper by Breitenberger6 states that 'The special theory of relativity is shown to be independent of the assumption that the velocity of light, c, is a universal constant. ...Existing theory-dependent arguments purporting to demonstrate the constancy of c are shown to be inadequate.' Furthermore, 'natural units furnished by atomic standards' should replace length and time intervals, in line with Van Flandern's option if c is changing dynamically. The proposals advocated by Mermin7 and Singh8 are also relevant. They show that relativity theory can be deduced without introducing c at all. In IV (B) below, mention is made of the fact that the basic equation, E = mc2;, may be deduced without relativity theory, and that it, too, is valid in a changing c scenario.
The constancy of c in the atomic frame implies the validity of relativity there. From the above, and statements below in V (A) and IV (B), c decay and relativity seem compatible dynamically. Additionally, Einstein's base for relativity also appears valid dynamically provided that c (1) remains independent of the motion of the source and (2) has the same value at any instant in all dynamical frames throughout the universe. Point (2) has been experimentally verified by Barnet et al.9. Using the aberration method, they reported that light from distant quasars arrived here with the same velocity as light from nearby stars. They concluded that c had remained constant to within 0.4% throughout the life of the universe. These results do not necessarily set limits on a cosmological variation of c at all. Rather, they completely affirm the principle that c has a universal value at any given time t. This is also confirmed by the 1976 results of Baum and Florentin-Nielsen10. A further comment on this point occurs in the final discussion.
(C). REACTIONS AND ARGUMENTS:
Three reactions to the decrease in the measured value of c were summarized by Dorsey3, after admitting that the idea of c decay had 'called forth many papers.' He stated that 'Not a few of their authors seem to be very favorably impressed by the idea of a secular variation, some seem to be favorable to it but unwilling to commit themselves, and some are strongly critical.' Dorsey himself was in the last category as eventually was R.T. Birge. Nevertheless, in 1941 even Birge11 acknowledged that 'these older results are entirely consistent among themselves, but their average is nearly 100 km/s greater than that given by the eight more recent results'. In this, history repeated itself. In 1886, Newcomb12, who had obtained some of those 'older results' mentioned by Birge, stated that the still older results around 1740 were also consistent but placed c about 1% higher than in his own time.
This persistent trend was countered by three arguments. Initially, it was deemed contrary to Einsteinian theory, but, as indicated above, the truth appears to be otherwise. The second argument recognized, as Newcomb and Birge's statements do, that the measured values of c were differing with time. Dorsey3 proposed in 1944 that perhaps the measuring equipment was at fault or that it was an artifact of more sophisticated procedures. However, his lengthy analysis still left the early c values above c now. He concluded that all measurements prior to 1928 were unreliable, extended their error limits, and claimed that c decay could be rejected on these grounds.
However, Dorsey did not address the main problem. He failed to demonstrate why the measured values of c should show a systematic trend with the mutual unreliability of the equipment. Indeed, if c was constant, error theory indicates that there should have been a random scatter about a fixed value. This is not observed. Instead, the analysis below shows a statistical decay trend for c measured by 16 different methods, individually as well as collectively. This tends to negate Dorsey's contention since it represents one chance in 43 million of being the coincidence that he might have implied (trends could be increasing, decreasing or static). Furthermore, in the seven instances where the same equipment was used in a later series of experiments, a lower c value has always resulted at the later date. Dorsey had no satisfactory explanation for this phenomenon.
Birge13 gave a third reason for rejecting c decay. After noting that wavelengths and length standards were experimentally invariant over time, he stated that 'if the value of c...is actually changing with time, but the value of (wavelength) in terms of the standard meter shows no corresponding change, then it necessarily follows that the value of every atomic frequency...must be changing. Such a variation is obviously most improbable....' Ironically, this is the very effect that Van Flandern observed experimentally. Indeed, the analysis below shows that when the basic equations are worked through with energy conservation in mind, the conclusion emerges that the emitted frequency of light from atoms is the quantity varying with c and wavelengths do remain unchanged. The constraint of energy conservation based on constant length standards (including dynamical and atomic distances) alone appears to give predicted trends in the values of other atomic constants that are consistent with measurement and observation. As Birge pointed out in his article, invariant length and wavelength standards are upheld experimentally.
More recently, it has been suggested that measured values became 'locked' around some canonical value, an effect called 'intellectual phase locking'. This hardly accounts for the confirmatory trends in other atomic constants, nor the lower values obtained when the same c-measuring equipment was used for a later experiment. Dorsey's reworked results also deny it. Furthermore, when many of the measurements were being made, c behavior was still a matter for debate and appropriate descriptive curves were discussed.
However, since the 1940's, a different attitude to the value of c has prevailed which may itself be a form of intellectual phase-locking. As one reviewer pointed out, Aslakson's measurements with the 'SHORAN' navigation system in 1949 required a higher value for c than was currently accepted to agree with geodetic distances. He delayed publication for several years while he sought for supposed errors in his system. As it turned out, his experimental value was correct, within its error limits, and the accepted c value was too low for reasons discussed later. The importance of experimental results compared with accepted norms is thereby well illustrated.
Accordingly, it seems appropriate to re-examine all experimental determinations of c and related atomic quantities to establish what these results actually reveal. The initial results of the investigation are hereby presented.
III. MEASURED VALUES OF C:-
(A). THE ROEMER-TYPE DETERMINATIONS:
The Roemer-type measurements are based on the eclipse times of Jupiter's satellite Io. These fall behind schedule as the earth in its orbit draws away from Jupiter and pick up again as the earth approaches Jupiter. Light travel time across the earth's orbit radius (1.4959787 x 108 Km) delays the eclipses and allows a calculation of c.
Initially these results differed. Observations by Cassini14 (1693 and 1736) gave the orbit radius delay as 7 minutes 5 seconds. Roemer in 1675 gave it as 11 minutes from selected observations15. Halley16 in 1694 noted that Roemer's 1675 figure for the time delay was too large while Cassini's was too small. Newton17 listed the delay as 'seven or eight minutes' in 1704 and 1713. All but Roemer suggested a delay shorter than today's value, yet estimates of Roemer's c value range18 from 193,120 to 327,000 Km/s. Roemer's selective procedure and time for Io's period affects his c value.
An examination of the best 50 Roemer values was undertaken by Goldstein19 in 1975 after initial work20 in 1973. The correction21 of a procedural error, only recently noted, 'gave a light travel time 2.6% lower than the presently accepted value. The formal uncertainty is ±1.8%' Roemer's value thus becomes 307,600 ±5400 Km/s. The investigations are continuing22.
Table 1 lists the results obtained by this method that have been found in the literature to date. If the uncertain 1675 and 1693 values are omitted, the data mean is 1701 Km/s above c now. On this basis, the hypothesis that c has been constant at its present value during these experiments can be rejected at the 96.5% confidence interval. If the other alternative is explored, a least squares linear fit to the data gives a decay of 25.9 Km/s per year, with r = - 0.982. The decay correlation is significant at the 99.97% confidence interval. In view of initial uncertainties, only the Glasenapp and Harvard values are included in the final analysis of Table 11.
TABLE 1 - ROEMER METHOD VALUES
|AUTHORITY||MEDIAN DATE||ORBIT RADIUS DELAY (sec)||C (Km/s)|
|1. Roemer||1675||-||307,600 ±5400|
|3. Delambre||1738 ±71||493.2||303,320|
|6. Glasenapp||1861 ±13||498.57||300,050|
|7. Sampson||1876.5 ±32||498.64||300,011|
|7. Harvard||1876.5 ±32||498.79 ±0.02||299,921 ±13|
1. Provisional correction only (see text).
2. Uncorrected observations by Cassini94.
3. Mean of 1000 observations from 1667-1809. Delambre95 and Newcomb96.
4. Value deduced by Martin97.
5. Generally accepted value98.
6. Reduction of 320 eclipses 1848-1873 by Glasenapp99 using 5 methods. Result mean of 4 as method 1 comprehensively covered in method 5. See also Kulikov100 and Newcomb96.
7. Reduction of Harvard observations 1844-1909 done in 1909. Official Harvard reductions, and those by Sampson (see Whittaker101).
TABLE 2 - RESULTS OF BRADLEY'S OBSERVATIONS
|LOCATION||STARS||DATE||AUTHORITY||ABERRATION ANGLE (arc-seconds)|
|1. Kew||8 stars||1726-27||Bradley||20.25|
|2. Kew||g Draconis||1726-27||Busch||20.2495|
|2. Kew||g Draconis||1726-27||Auwers||30.3851 ±0.0725|
|3. Kew||g Draconis||1726-27||Newcomb||20.53 ±0.12|
|2. Wanstead||23 stars||1727-47||Busch||20.205|
|2. Wanstead||23 stars||1727-47||Auwers||20.460 ±0.063|
|4. Greenwich||g Draconis||1750-54||Bessel||20.475|
|4. Greenwich||g Draconis||1750-54||Peters||20.522 ±0.079|
1. Bradley's102 observational mean was 20.2 arc-seconds. However, he took the mean of the two extreme limits to get 20.25 (see also Sarton103).
2. Busch's reworkings were disputed by Auwers who also corrected for collimation and screw errors104.
3. Auwer's reworking corrected for a theoretical latitude variation by Newcomb105.
4. Bessel and Peters both rejected Bradley's observations of Feb. 20, 21, and 23 in 1754 as disagreeing with all others and giving large remainders. Their values above omit these observations106.
(B). THE BRADLEY-TYPE OBSERVATIONS:
To illustrate this technique, consider a drop of rain falling vertically. The rain has an aberration angle towards a car moving with constant speed, the angle depending on the rain's velocity. Similarly, a star's aberration angle (K) can be measured due to c and the essentially constant orbital speed of the earth. A constant value Kc = 6144402 has been adopted from the current I.A.U. value of K = 20.49552 arc-seconds.
Table 2 gives the results from Bradley's observations from 1726 to 1754 on 24 stars. The final average value omitting both of Busch's disputed reworkings was 20.437 arc-seconds. The average date is 1740 for a c value of 300,650 Km/s, just 858 Km/s above the present value for c. If Busch's reworkings are accepted, this mean figure increases to 1632 Km/s above c now.
Table 3 lists 63 aberration determinations from 1740 to 1930 given by Kulikov23 and Newcomb24. Only the dated values are included and repeats are omitted. Basically the same type of equipment was used during this time with basically the same error margins, while observational methods were substantially unaltered. The mean of all data is 76.2 Km/s above c now. The t-statistic thus indicates that the hypothesis that c equaled c today during these experiments can be rejected at the 93.9% confidence interval. Figure I presents the results from the Pulkova Observatory. That mean is 88 Km/s above c now for a mean date of 1879.
However, one mean value does not give the full picture. If Table 3 is split into 50 year segments, and the mean c value in each segment is taken, and the difference of the mean from c now is noted, the results become:
|DATE||C MEAN (Km/s)||DIFFERENCE (Km/s)|
The difference column indicates the trend for the mean to become successively higher further back in time. This suggests that the above statistical rejection of a constant c proposal is all the more justified for these experiments.
A least squares linear fit to all data also supports the likely alternative proposition, as it gives a decay of 4.83 Km/s per year. The Pulkova results in Fig. I indicate a decay of 6.27 Km/s per year with an acceptance of the decay correlation r = - 0.947 at the 99.9% confidence level. Newcomb24 quotes errors for all these data as approximately three times the size of those for the following observations. Consequently, only the definitive values of Nyren (1883) and Struve (1841) and the comprehensively treated Bradley value with Lindenau are used in the final discussion.
TABLE 3 - BRADLEY ABERRATION METHOD: PULKOVA VALUES MARKED * - SEE FIG. I
|AV.YR.||TIME OF OBS.||OBSERVER||K (Arc Seconds)||C VALUE (Km/s)|
|1740||1726-1754||Bradley: Reworked Average||20.437||300,650|
|1783||1750-1816||Lindenau: ±fr. weights||20.450 ±0.011||300,460 ±170|
|*1841||1840-1842||Struve: corrected 1853||20.463 ±0.017||300,270 ±250|
|*1841||1840-1842||Folk-Struve||20.458 ±0.008||300,340 ±120|
|*1843||1842-1844||Struve: ±fr. mean error||20.480 ±0.011||300,020 ±170|
|1843||1842-1844||Lindhagen-Schweizer||20.498 ±0.012||299,760 ±180|
|1858||1842-1873||Nyren-Peters||20.495 ±0.013||299,800 ±190|
|1864.5||1862-1867||Newcomb: weighted av.||20.490||299,870|
|1868||1863-1873||Nyren and Gylden||20.52||299,440|
|1870||1861-1879||Nyren-Wagner||20.483 ±0.003||299,980 ±50|
|1880.5||1879-1882||Nyren||20.517 ±0.009||299,480 ±130|
|*1883||1883-1883||Nyren: wtd. av. all obs.||20.491 ±0.006||299,850 ±90|
|1889.5||1889-1890||Kustner||20.490 ±0.018||299,870 ±260|
|1889.5||1889-1890||Marcuse||20.490 ±0.012||299,870 ±180|
|1889.5||1889-1890||Doolittle||20.450 ±0.009||300,460 ±130|
|1890.5||1890-1891||Comstock||20.443 ±0.011||300,560 ±170|
|1891.5||1891-1892||Batterman||20.507 ±0.011||299,630 ±170|
|1891.5||1891-1892||Marcuse||20.506 ±0.009||299,640 ±130|
|1891.5||1891-1892||Chandler||20.507 ±0.011||299,630 ±170|
|1892.5||1891-1894||Becker||20.475 ±0.012||300,090 ±180|
|1894.5||1894-1895||Rhys-Davis||20.452 ±0.013||300,430 ±190|
|1896||1893-1899||Rhys-Jacobi-Davis||20.470 ±0.010||300,170 ±150|
|1896.5||1896-1897||Rhys-Davis||20.470 ±0.011||300,170 ±170|
|1897||1897-1897||Grachev-Kowalski||20.471 ±0.007||300,150 ±100|
|1898.5||1898-1899||Rhys-Davis||20.470 ±0.011||300,170 ±170|
|1898.5||1898-1899||Grachev||20.524 ±0.007||299,380 ±100|
|1899||1899-1899||Grachev||20.474 ±0.007||300,110 ±100|
|1900.5||1900-1901||Internat. Lat. Serv.||20.517 ±0.004||299,480 ±60|
|1901.5||1901-1902||Doolittle||20.513 ±0.009||299,540 ±130|
|1901.5||1901-1902||Internat. Lat. Serv.||20.520 ±0.004||299,440 ±60|
|1903||1903-1903||Doolittle||20.525 ±0.009||299,360 ±130|
|1904.5||1904-1905||Ogburn||20.464 ±0.011||300,250 ±170|
|1905||1905-1905||Doolittle (wtd. av.)||20.476 ±0.009||300,080 ±130|
|1905||1904-1906||Bonsdorf||20.501 ±0.007||299,710 ±100|
|1906||1906-1906||Doolittle (wtd. av.)||20.498 ±0.009||299,760 ±130|
|1906.5||1904-1909||Bonsdorf et. al.||20.505 ±0.008||299,650 ±120|
|1907||1907-1907||Doolittle||20.504 ±0.009||299,670 ±130|
|1907||1906-1908||Bayswater||20.512 ±0.007||299,550 ±100|
|*1907.5||1907-1908||Orlov||20.491 ±0.008||299,860 ±120|
|1907.5||1907-1908||Internat. Lat. Serv.||20.525 ±0.004||299,360 ±60|
|1908||1908-1908||Doolittle||20.507 ±0.012||299,630 ±180|
|*1908.5||1908-1909||Semenov||20.518 ±0.010||299,460 ±150|
|1908.5||1908-1909||Internat. Lat. Serv.||20.522 ±0.004||299,410 ±60|
|1909||1909-1909||Doolittle||20.520 ±0.009||299,440 ±130|
|*1909.5||1909-1910||Semenov||20.508 ±0.013||299,610 ±190|
|1910||1910-1910||Doolittle||20.501 ±0.008||299,710 ±120|
|1922||1915-1929||Kulikov||20.512 ±0.003||299,550 ±50|
|1923.5||1911-1936||Spencer-Jones||20.498 ±0.003||299,760 ±50|
|1928||1928-1928||Spencer-Jones||20.475 ±0.010||300,090 ±150|
|1930.5||1930-1931||Spencer-Jones||20.507 ±0.004||299,630 ±60|
|1933||1915-1951||Sollenberger||20.453 ±0.003||300,420 ±50|
|*1935||1929-1941||Romanskaya||20.511 ±0.007||299,570 ±100|
|1935.5||1926-1945||Rabe (gravitational)||20.487 ±0.003||299,920 ±50|
Whittaker101, Kulikov107, suggest K = 20.511: c is then above c(now) for most values.
CLICK HERE TO SEE FIGURE I
TABLE 4 - TOOTH WHEEL EXPERIMENTAL VALUES
|EXPERIMENTER||DATE||NUMBER||BASE (meters)||C VALUE (Km/s)|
|4. Fizeau (?)||1855||-||8633||298000|
|5. Cornu||1872||658||10310||298500 ±300|
|6. Cornu||1874.8||624||22910||300400 ±300|
|7. Cornu-Helmert||*1874.8||624||22910||299990 ±200|
|8. Cornu-Dorsey||*1874.8||624||22910||299900 ±200|
|10. Perrotin/Prim||1900.4||1540||11862.2||300032 ±215|
|11. Perrotin||*1900.4||1540||11862.2||299900 ±80|
|12. Perrotin||1901.4||-||-||299880 ±50|
|13. Perrotin||*1902.4||2465||45950.7||299860 ±80|
|14. Perrotin/Prim||*1902.4||2465||45950.7||299901 ±84|
1. Fizeau108 journal value - base too short for accuracy. Wheel of 720 teeth at 12.6 revs/sec gave minimum intensity.
2. Textbook value109. Difference arising from interpretation of Fizeau's length measure of 70,948 leagues of 25 to the degree.
3. Values 2, 3, and 4 appeared110 in 1927 but were omitted in all more comprehensive discussions. Dorsey111 pointed out that further values were promised, but none are extant.
4. It is probable that this may be a bad citation for Foucault's result of 1862.
5. Cornu112. Rejected by Cornu113 due to systematic errors. Crude apparatus with low precision114.
6. Cornu115. Working to 4 figures only. Newcomb116 gives the wrong years for these determinations. This error copied by Preston117.
7. Result corrected by Helmert118, discussed, verified119 despite Cornu's protest. Accepted by Birge120. Newcomb121, Preston117 and Michelson122 incorrectly attribute this value to Listing123. Michelson124 also misquoted the value. Probable error assessed by Todd125.
8. Cornu's result re-analyzed by Dorsey126.
9. No probable error given and spread of results attributed to c varying with wavelength in vacuo127. Criticized severly by Newcomb128 and Cornu129. Aluminum wheel of 150 teeth used.
10. Prim's analysis of after Perrotin's death - treatment method unsatisfactory - completely discarded by Prim130.
12. Perrotin's132 mean of the 1900.4 and 1902.4 determinations.
14. Prim's130 analysis of the 1902.4 determination after Perrotin's death.
(C). TOOTHED WHEEL EXPERIMENTS:
In this method, an intense beam of light is chopped by a rotating toothed wheel, traverses a distance of several miles, returns via a mirror and is viewed between the teeth of the wheel. At certain speeds of rotation, the returning light will be blocked by the teeth, at other speeds it will be visible. From those measured speeds and the known distance, c is derived. This is often called the Fizeau method after its pioneer.
Table 4 lists 14 results from this method. Those results marked (*) are usually considered reliable. The values obtained by Fizeau and Young / Forbes reflected problems with short baselines. Fizeau's pioneering experiments have been described as25 'admittedly but rough approximations...intended to ascertain the possibilities of the method.' Newcomb26 pointed out that the performance of Young and Forbes' apparatus did not do justice to their method since the 12 experimental results27 varied by over 4,000 Km/s.
The mean of the best data alone indicates that c was 117.7 Km/s above the current value for a mean date of 1891. This gives a confidence interval of 99.4% that c was not constant at its current value during these experiments. Additionally, a least squares linear fit to all 14 data points gives a decay of 164 Km/s per year, while the best data alone give a decay of 2.17 Km/s per year. These data all suggest a decay in c.
This conclusion is reinforced by the fact that Perrotin obtained his value essentially using Cornu's equipment some 27 years later28. Perrotin's mean is 65 Km/s below the mean of Cornu's reworked results, indicating that the decay effect was not primarily due to equipment limitations.
(D). ROTATING MIRROR RESULTS:
For this method, a beam of light is reflected from a rotating mirror to a distant fixed mirror and returned. The rotating mirror has meanwhile moved through an angle which results in the returned beam undergoing a measurable deflection from which c may be calculated knowing the path length and mirror rotation rate. This is often called the Foucault method.
Table 5 lists the rotating mirror results. The pioneer experiments by Foucault29 were hampered by trouble with the screw of the micrometer and diffraction distortion30, leaving his value uncertain. In 1880, Michelson31 discarded his exploratory value of 1878. Newcomb also rejected his own 1880.9 and 1881.7 values (299,627 and 299,694 Km/s in air respectively) due to systematic errors from vibrations of an unbalanced mirror and irregular pivots. Two pairs of images were seen in the micrometer. As a consequence, Newcomb32 insisted that his 'results should depend entirely on the measures of 1882.' To avoid criticism, these two values were included in the 1881.8 in vacuo mean with the 1882 result. If these uncertain values are omitted, the mean value is 40.3 Km/s above c today with a confidence level of 93.9% that c did not have its present value during those experiments. This is supported as a least squares linear fit to the six data points gives a decay of 1.85 Km/s per year with r = -0.932 and a confidence interval in the decay correlation of 99.6%.
TABLE 5 - ROTATING MIRROR EXPERIMENTS
|EXPERIMENTER||DATE||NUMBER||BASE (meters)||C VALUE (Km/s)|
|1. Foucault||1862.8||80||20.0||298,000 ±500|
|2. Michelson||1878.0||10||152.4||300,140 ±480|
|3. Michelson||*1879.5||100||605.40||299,910 ±50|
|5. Newcomb||*1882.7||66||3,721.21||299,860 ±30|
|6. Michelson||*1882.8||563||624.65||299,853 ±60|
|7. Michelson||*1924.6||80||35,426.23||299,802 ±30|
|8. Michelson||*1926.5||1600||35,426.23||299,798 ±15|
|9. Pease/Pearson||*1932.5||2885||1,610.4||299,774 ±10|
* Values generally accepted as reliable.
1. Foucault134 obtained a deflection of 0.7 mm with 500 revs/sec from a one-faced mirror with 'very unfavorable limitations' experimentally (Todd135).
2. Michelson136 obtained a deflection of 7.5 mm with 130 revs/sec from a one-faced mirror and a 'crude piece of apparatus' (Michelson137). De Bray138 has incorrect baseline and probable error.
3. Michelson139 obtained a deflection of 133.2 mm with 257.3 revs/sec from one-faced mirror. Corrected result in Michelson140. Newcomb141 misquotes the corrected value. Todd135 quoted erroneous figures from an incorrect Abstract142 that someone had prepared from Michelson143.
4. Mean of 2 rejected values and accepted final value. Average deflection 18 cm from 4-faced mirror speeds of 114-268 revs/sec. The three series comprised 255 experiments. The shorter path length of series 1 is quoted.
5. Newcomb144. Accepted result of 3rd series.
6. Michelson145. Average deflection of 138 mm from 1-faced mirror speeds pf 129-259 revs/sec.
7. Michelson146. Polygonal mirror method combining features of the toothed wheel and rotating mirror. Measurements on the undisplaced image. Glass octagon used at 528 revs/sec. The corrected value for the series in Michelson147 is omitted from the Birge148 list but appears in Froome and Essen149 and Table 11 below.
8. Michelson150 used polygonal mirrors of 8, 12, 16 faces. Zero deflection at 264-528 revs/sec used. Result corrected for group velocity by Birge151. Final values from the 5 mirrors agreed within ±1 Km/s. Michelson152 and others153 make misleading statements and quote incorrect values.
9. Michelson/Pease/Pearson154. Michelson died as series began. Mirror speeds of 585-730 revs/sec for 32 faces used. Null position not used. Convenient speeds gave deflections near 0.01 mm. Micrometer problems noted155. Unstable baseline156 gave regular and irregular variations in c values hourly, daily, and in periods up to 1 year.
For Pease and Pearson, a long baseline on unstable alluvial soil seemed to cause varying c values with33 'A correlation between fluctuations in the results and the tides on the sea coast' and lunar phases34. Omitting their final result gives a mean value 52.1 Km/s above c now in 1899. This gives a confidence interval of 95.6% that c did not equal c now during that time. In addition, a decay of 1.74 Km/s per year results, with r = -0.905 and a confidence level of 98.2% in the decay correlation.
It is also worthy of note that Michelson's determinations 1879.5 and 1882.8 were both with the same equipment, as were the 1924.6 and 1926.5 pair35. On both occasions a lower value for c was recorded at the later date, ruling out equipment variation as the cause and enhancing the suspicion that a decay in c itself was responsible. As mentioned above, the concordance of Newcomb's 1882.7 result with Michelson's 1882.8 value and the definitive aberration value of Nyren in 1883 lends credence to the notion that c was actually higher at the time of those measurements.
(E). KERR CELL RESULTS:
This method is similar to the toothed wheel, but the light beam is chopped electrically. The transit times of electrons in detection tubes, light passing through glass, liquids, and air, all systematically result in an estimate of c below the real value. Birge11 applied uniform corrections to four results by this method. In so doing he noted that 'The base line in each case was about 40 meters' and gives the probable error for each as about 10 Km/s indicating similar experimental conditions. Any trend should not be an instrumental effect.
The results are given in Table 6. The linear fit of data gives a decay of 1.03 Km/s per year with r = -0.81 at the 90.5% confidence level. The systematic errors give low values for c, but a decay is still apparent. These systematic errors seem not to be the cause of the decay trend, therefore, but shift this trend into a lower range of c values.
(F). THE SIX METHODS USED 1945-1960:
Froome and Essen36 and Taylor et al. supply 23 data points as the evidence from these six new methods which are listed in Table 7. Three radar values are omitted as they did not measure atmospheric moisture, which critically affects the radio refractive index. Under these circumstances the final c value is somewhat spurious37. Also omitted on the basis of Mulligan and McDonald's statements38 are two early spectral line results with errors due to imperfect wavelength measurements. Results spread over 180 and 500 Km/s also disqualify two quartz modulator values39 of 1950.
The linear fit gives a decay of 0.19 Km/s per year with a confidence level of 99.0% in the data showing c as higher than now during those 15 years. Five of the six methods gave a decay individually, radar being the exception due to the removal of a signal intensity error in the later results40.
TABLE 6 - KERR CELL VALUES* OF C
|EXPERIMENTER||DATE||NUMBER||VALUE OF C (Km/s)|
|1. Mittelstaedt||1928.0||775||299,786 ±10|
|2. Anderson||1936.8||651||299,771 ±10|
|3. Huttel||1937.0||135||299,771 ±10|
|4. Anderson||1940.0||2895||299,776 ±10|
* Uniform corrections applied to all experiments by Birge157.
1. Preliminary report by Karolus and Mittelstaedt158 with a final report by Mittelstaedt159. De Bray has incorrect base length160.
2. Initial report by Anderson161 and final corrections including the phase velocity given by Anderson162.
3. Report by Huttel163. Uncorrected original value 299,768 ±10 Km/s.
4. Improved techniques removed glass from the light path. Other variables also altered. Dorsey164 stated the precision essentially as for his earlier experiment at ±14 Km/s. However, Birge165 puts it at ±6. Average again ±10 Km/s.
TABLE 8 - RESULTS 1960-1983 - MAINLY LASER
|DATE||EXPERIMENTER||REFERENCE||VALUE OF C (Km/s)|
|2.||1967||Simkin et. al.||191||299,792.56 ±0.11|
|6.||1973||Evenson et. al.||195||299,792.4574 ±0.0011|
|8.||1974||Blaney et. al.||196||299,792.4590 ±0.0008|
1. Modulated light. Baseline error corrected 1967 (see Froome and Essen200).
2. Microwave interferometer.
4-11. Laser methods. Discussion in Mulligan201.
6. Result corrected for new definition by Blaney et. al.196.
TABLE 7 - RESULTS* BY SIX METHODS 1945-1960
|DATE||EXPERIMENTER||REFERENCE||MEASUREMENT METHOD||VALUE OF C (Km/s)|
|1.||1947||Essen,Gordon-Smith||166||Cavity Resonator||299,798 ±3|
|2.||1947||Essen,Gordon-Smith||166||Cavity Resonator||299,792 ±3|
|5.||1950||Essen||169||Cavity Resonator||299,792.5 ±1|
|6.||1950||Hansen and Bol||170||Cavity Resonator||299,794.3 ±1.2|
|10.||1951||Froome||174||Radio Interferometer||299,792.6 ±0.7|
|11.||1953||Bergstrand (av. date)||175||Geodimeter||299,792.85 ±0.16|
|12.||1954||Froome||176||Radio Interferometer||299,792.75 ±0.3|
|13.||1954||Florman||177||Radio Interferometer||299,795.1 ±3.1|
|15.||1955||Plyler,Blaine,Connor||179||Spectral Lines||299,792 ±6|
|18.||1956||Rank,Bennett,Bennett||181||Spectral Lines||299,791.9 ±2|
|22.||1958||Froome||183||Radio Interferometer||299,792.5 ±0.1|
|23.||1960||Kolibayev (av. date)||184||Geodimeter||299,792.6 ±0.06|
Geodimeters (8 values): Decay of 0.22 Km/s per year
Cavity Resonators (4 values): Decay of 0.53 Km/s per year
Radio Interferometers (4 values): Decay of 0.04 Km/s per year
Tellurometers (3 values): Decay of 0.20 Km/s per year
Spectral lines (2 values): Decay of 0.10 Km/s per year
Radar (2 values): Error removal gave higher c value in 2nd result
* Data as discussed by Froome and Essen185 and Taylor et. al.186.
1. Mean preliminary value from the two modes used in the final experiment. See Froome and Essen, Table III, p.61.
6. Reference in the name of Bol only. This value by DuMond and Cohen187 is corrected for the 'skin effect' mentioned by Froome and Essen188.
11. Weighted mean result189 for period 1949-1957.
Froome and Essen41 made an important statement, reiterating that 'As with the unit of length, errors in the unit of time have never yet presented a limitation in the accuracy of measuring the velocity of light.' A variation in c cannot be attributed to these causes, therefore. It also becomes apparent that the linear fit decay rate is decreasing with time. Table C lists the mean decay rates in Km/s per year and the date. The first value is derived by taking the two most conservative individual values by the Roemer method rather than the means. One was the 1877 official Harvard reductions. The other was Roemer's 1675 value. Here, for comparison purposes only in Tables C and D, the minimum point in the quoted error limit was used. Roemer's value thus became 302,200 Km/s.
This would seem to indicate that any decay is following a non-linear pattern. These two facts have a bearing on the post 1960 results. A tapering rate of decay may get to the stage where it is undetectable or ceases, depending on the decay pattern. The significance of this is enforced by the results of equation (34) and the remarks pertaining thereto.
(G). THE POST 1960 RESULTS:
Table 8 lists 11 values of c that were obtained between 1960 and 1983. Eight of these used laser techniques.
A linear fit of all 11 data points gives a decay of 0.0026 Km/s per year. The eight laser values alone give a decay of 0.00013 Km/s per year. The last six give a 0.00004 Km/s per year INCREASE, while the last five and four values give c as constant, or decaying at 0.000097 Km/s per year respectively. The first seven data points 1966-1973 show a decay of 0.0058 Km/s per year. Confidence intervals for c not constant were about 50% in all cases. Minimum laser values were recorded in 1973.
The only conclusion to be drawn from these figures of low statistical confidence is that any decay during this period would have occurred at a very slow rate, perhaps may have ceased altogether, or c may have begun to increase at some time in this period. The reason for these inconclusive observations becomes apparent later. A method used to overcome the problem is mentioned below, and the results indicate continuing decay at a rate lower than that prior to 1960.
CLICK HERE TO SEE FIGURE II
TABLE 9 - C VALUES BY THE RATIO OF ESU/EMU
|EXPERIMENTERS||DATE||MEAN VALUE (Km/s)||RANGE ERROR OR PRECISION||REFERENCE|
|1. Weber/Kohlrausch||1856||310,700||±20,000 Km/s||202|
|2. Maxwell||1868||284,000||±20,000 Km/s||203|
|6. Ayrton/Perry||1879||296,000||Errors of 1/100||207|
|8. Shida||1880||295,500||Precision of 1%||209|
|10. Exner||1882||287,000||Errors up to 8/100||211|
|11. J.J.Thomson||1883||296,400||±20,000 Km/s||212|
|13. Colley||1886||301,500||Errors up to 2/100||214|
|15. Thomson et. al.||1888||292,000||Precision of 1.75%||216|
|18. J.Thomson/Searle||*1890||299,600||Errors of 1/500||218|
|19. Pellat||*1891||300,920||Errors of 1/500||219|
|21. Hurmuzescu||*1897||300,100||Errors of 1/1000||221|
|22. Perot/Fabry||*1898||299,730||Errors of 1/1000||222|
|23. Webster||1898||302,590||Precision of 1%||223|
|24. Lodge/Glazebrook||1899||300,900||Errors up to 4/100||224|
|25. Rosa/Dorsey||*1906||299,803||±30 Km/s||225|
NOTE:- All Table 9 values from uniform treatment by Abraham43. Froome and Essen226 applied a uniform correction of 95 Km/s to these results for air to bring them to c in vacuo.
Numbers 3, 4, and 11. Mean value from Froome and Essen212.
14. Mean date of 3 experiments.
25. Recently corrected value to vacuum conditions etc. (see text).
TABLE 10 - C VALUES BY WAVES ON WIRES
|EXPERIMENTER||DATE||No.||C VALUE (Km/s)||RANGE OR ERROR (Km/s)||REFERENCE|
|6. Mercier||1923||5 sets||299,795||±30||232|
NOTE:- Table 10 values in air from discussion by Blondlot43.
Number 5: MacLean used a free space technique.
Number 6: Mercier value corrected to in vacuo (see text).
(H). THE RATIO ESU/EMU AID WAVES ON WIRES:
The charge on a capacitor is measured in electrostatic and electromagnetic units in the first of these methods. The wavelength and frequency of a radio wave transmitted along a pair of parallel wires are measured in the second. The values of c obtained by these two methods did not achieve high accuracy except in two cases. A glance at Tables 9 and 10 tells the story. The variation in c values obtained during a determination by these method could go as high as 16,000 Km/s or more. In the cases of numbers 1, 2, and 11 in Table 9, Fowles42 estimated the error as ±20,000 Km/s. In general the spread of values of the velocity in any one determination ranged from 1% to 5%. This is in marked contrast to the 0.02% or lower obtained by the optical methods. These values have thus been omitted from the main analysis.
Despite this, the waves on wires experiments listed in Table 10 still exhibit a decay trend of 7.47 Km/s per year. After a lengthy treatment of the esu/emu ratio experiments, Abraham43 concluded that the values marked with an asterisk in Table 9 were the most accurate. Although the errors of these eight experiments vary up to about 0.5%, they, too, exhibit a decay trend of about 24 Km/s per year with a mean about 189 Km/s above c now.
The two shining exceptions to the low precision are the Rosa/Dorsey value from the ratio of electrostatic to electromagnetic units, and that of Mercier from the waves on wires. Both of these values have recently been reassessed44: the first with the best value for the unit of resistance and air humidity (see also Florman45), the second for atmospheric conditions. Froome and Essen46 also point out that these experiment were the only ones by those two methods that were 'as accurate as the direct measurements of the speed of light at that time...'. Accordingly, these two alone from Tables 9 and 10 are included in the following analysis.
(I). CONCLUSION FROM COLLECTIVE DATA:
When all 163 values involving 16 different methods are used, the linear fit to the data gives a decay of 38 Km/s per year. If only the best data from Table 9, chosen by Abraham43, are coupled with all other figures, then 146 values indicate a decay of 43 Km/s per year. The data mean is 753 Km/s above c now and the hypothesis that c has been constant at today's value over the last 300 years can be rejected with a confidence interval of 97.2%. Nevertheless, if we summarize from the above discussion the difference of the best data means from c now in Km/s at the mean date, we obtain the following:
TABLE 11 - REFINED LIST OF C DATA (See Figs. II, III, IV)
|NO.||DATE||OBSERVER||METHOD||VALUE OF C (Km/s)|
|5||1874.8||Cornu (Helmert)||Toothed Wheel||299,990 ±200|
|6||1874.8||Cornu (Dorsey)||Toothed Wheel||299,900 ±200|
|7||1876.5||Harvard Observat.||Jupiter Satellite||299,921 ±13|
|8||1879.5||Michelson||Rotating Mirror||299,910 ±50|
|9||1882.7||Newcomb||Rotating Mirror||299,860 ±30|
|10||1882.8||Michelson||Rotating Mirror||299,853 ±60|
|12||1900.4||Perrotin||Toothed Wheel||299,900 ±80|
|13||1902.4||Perrotin||Toothed Wheel||299,860 ±80|
|14||1902.4||Perrotin/Prim||Toothed Wheel||299,901 ±84|
|15||1906.0||Rosa and Dorsey||Electromag. Units||299,803 ±30|
|16||1923||Mercier||Waves on Wires||299,795 ±30|
|17||1924.6||Michelson||Polygonal Mirror||299,802 ±30|
|18||1926.5||Michelson||Polygonal Mirror||299,798 ±15|
|19||1928.0||Mittelstaedt||Kerr Cell||299,786 ±10|
|20||1932.5||Pease/Pearson||Polygonal Mirror||299,774 ±10|
|21||1936.8||Anderson||Kerr Cell||299,771 ±10|
|22||1937.0||Huttel||Kerr Cell||299,771 ±10|
|23||1940.0||Anderson||Kerr Cell||299,776 ±10|
|24||1947||Essen,Gordon-Smith||Cavity Resonator||299,798 ±3|
|25||1947||Essen,Gordon-Smith||Cavity Resonator||299,792 ±3|
|28||1950||Essen||Cavity Resonator||299,792.5 ±1|
|29||1950||Hansen and Bol||Cavity Resonator||299,794.3 ±1.2|
|33||1951||Froome||Radio Interferom.||299,792.6 ±0.7|
|35||1954||Froome||Radio Interferom.||299,792.75 ±0.3|
|36||1954||Florman||Radio Interferom.||299,795.1 ±3.1|
|38||1955||Plyler et. al.||Spectral Lines||299,792 ±6|
|41||1956||Rank et. al.||Spectral Lines||299,791.9 ±2|
|45||1958||Froome||Radio Interferom.||299,792.5 ±0.1|
|47||1966||Karolus||Modulated Light||299,792.44 ±0.2|
|48||1967||Simkin et. al.||Microwave Interf.||299,792.56 ±0.11|
|51||1972||NBS (Boulder)||Laser||299,792.460 ±0.006|
|52||1973||Evenson et. al.||Laser||299,792.4574 ±0.0011|
|53||1973||NRC, NBS||Laser||299,792.458 ±0.002|
|54||1974||Blaney et. al.||Laser||299,792.4590 ±0.0008|
|55||1978||Woods et. al.||Laser||299,792.4588 ±0.0002|
|56||1979||Baird et. al.||Laser||299,792.4581 ±0.0019|
|57||1983||NBS (US)||Laser||299,792.4586 ±0.0003|
The Roemer method is again represented by two individual values as in Table C.
However, it is desirable to use only the most reliable values to determine the true situation. Birge11 summarized the best 13 values by six methods in the period 1874.8 to 1940, including those of Rosa/Dorsey and Mercier. Let us take Birge's basic list as definitive, as did Huttel47, Bergstrand48, and Cohen and DuMond49. These same data were advocated by de Bray50,51, and Mittelstaedt52. If the Table 7 and 8 values are added with the remaining starred data from Table 4, then a core of 51 of the most reliable results by 14 methods emerges. The most conservative estimates by the Roemer method are the official 1876.5 ±32 value and the 1861 ±13 result. Newcomb26 lists Nyren's 1883 treatment as the most definitive value by the Bradley method. Its best conservative early data are Lindenau's and Struve's 1843 value with Bradley's reworked average. These total an extra six points from two other methods. Thus, 57 best possible data by 16 methods can be listed as in Table 11 and associated Figures II, III, IV.
These Table 11 data give a mean c value at 52.5 Km/s above c now. Statistically, these data give a confidence interval of 99.46% that c was above its present value. A least squares linear fit indicates a decay of 2.79 Km/s per year with r = - 0.878 and a confidence of 99.99% in the decay correlation. Non linear fits give an improvement on the value of r. Initial independent analyses of these data at Newcastle University53 concluded that 'Any two stage curve fit gives a highly significant improvement over the assumption of a constant c value. Residuals reduced from 22,000 to under 2000.'
Thus 16 different methods of measurement by almost 50 different instruments all exhibit the decay trend. The only values that went against the trend were all rejected by the experimenters themselves or their peers. If this were simply the result of equipment unreliability and improved measurement techniques as Dorsey implied in 1944, then it would be a most unusual phenomenon in itself. Yet historically the measurements and past equipment have only been called into question because their values for c differed from those currently prevailing. This itself argues against any 'intellectual phase-locking'. The other option is that all 16 methods were registering c correctly within their error margins, but that c itself has changed. The above results are typical of a decaying quantity. The atom and atomic constants now need to be examined to see if they support the idea and answer Birge's criticism.
TABLE 12 - OPTIONS WITH CHANGING C
|OPTION I||OPTION II||OPTION III|
|e0 = CONST: m0µ 1/c2||m0 = CONST: e0µ 1/c2||e0 µ 1/c: m0 µ 1/c|
|V = m2/(4pm0r) = C-IND*||V = q2/(4pe0r) = C-IND*||From Options Iand II|
|m2/m0 = C-IND*||q2/e0 = C-IND*||m2/m0 = C-IND* = q2/e0|
|magnetic pole m µ 1/c||unit charge q µ 1/c||m µ 1/Öc:q µ 1/Öc|
NOTE:- The symbol (µ) is taken to mean 'proportional to' throughout this article.
* C-IND means that the expression is independent of variation in c.
N.B. For observed results of wavelength and frequency to hold, atomic and dynamical length standards and distances remain unchanged. Potentials V are thus taken over constant distance r.
IV. PHYSICAL QUANTITIES AFFECTED BY C DECAY:-
(A). MAXWELL'S LAWS AND THE ELECTRONIC CHARGE:
If energy is to be conserved as c decays, then Maxwell's Laws must hold. Therefore if the electric permittivity is e0 and the magnetic permeability is m0 for free space, then as
e0m0 = [1/c2]1/2 (1)
there will be three valid possibilities as illustrated in Table 12. In each case the electric and magnetic potential, V, is conserved. An additional requirement is that wavelengths and atomic or dynamical distances must be invariant from the experimental results mentioned in Birge's assessment13 of the c decay proposal. Atomic orbit radii are thus required to be invariant and consequently also N0, the Avogadro Number, if these experimental results are to be upheld. From the point of view of Table 12, the key requirement is the constancy of q2/e0. This has been demonstrated over astronomical time by Dyson54, Peres55, Bahcall and Schmidt56 and Wesson57 on the basis of experiment and also by the observed abundances of radioactive elements. This cosmological constancy is an important result.
Conservation also requires that the volt V = hf/2e, of measured potential V, is c independent, along with the energy hf. The Josephson frequency is f and h is Planck's constant. This definition by Cohen and Taylor58 and Finnegan et al.59, demands the constancy of the electronic charge, e, quite independently of e0. Theory therefore favors Option I from Table 12.
The value of e has been measured by the oil-drop and X-ray methods. The former obtains a value of e in association with e0, while the latter obtains e via the Avogadro Number, N0. Table 13 lists the results from both methods along with the best adjusted values. The Avogadro Number, N0, is experimentally implied as invariant as noted above. The X-ray method essentially measures N0, and then, from the relation F = N0e, where F is the Faraday, the electronic charge is determined. A linear fit to the X-ray data yields a decay of 0.0000148 x 10-10 ESU/year with a confidence in e not constant at the last X-ray value (31) of 63.72%. Given the invariance of N0, this measured constancy of e also establishes the constancy of F from the above equation. Furthermore, this constancy of e is completely independent of e0.
A least squares linear fit to the oil-drop data gives an increase of 0.000383 x 10-10 ESU per year with a confidence interval of 76.8% in e not constant at the final oil-drop value. The adjusted value results are similar. Given the experimental constancy of e independent of e0, from the X-ray results, these oil drop results indicate the constancy of e0 also. An increase of 0.000026 x 10-10 ESU per year results from the analysis of all data in Table 13. A confidence level of 55.4% in e not constant at its 1973 value is obtained. Theory and experiment thus combine to validate the invariance of e, e0, F and N0.
TABLE 13 - VALUES OF THE ELECTRONIC CHARGE e
|AUTHORITY||DATE||VALUE OF e x 10-10 ESU||METHOD||REF.|
|1. Millikan||1913||4.8049 ± 0.0022||OD||233|
|2. Millikan||1917||4.8071 ± 0.0038||OD||234|
|3. Millikan||1917||4.8059 ± 0.0052||OD||234|
|4. Millikan||1920||4.803 ± 0.005||OD||235|
|5. Wadlund#||1928||4.7757 ± 0.0076||XR||236|
|6. Backlin#||1928||4.794 ± 0.015||XR||237|
|7. R.T.Birge||1929||4.801 ± 0.005||AV||238|
|9. Soderman||1935||4.8026 ± 0.003||XR||240|
|11. Bearden||1935||4.8036 ± 0.0005||XR||242|
|12. DuMond/Bollman||1936||4.799 ± 0.007||XP||243|
|13. R.T.Birge||1936||4.8029 ± 0.0005||AV||244|
|15. Backlin/Flemberg||1936||4.7909 ± 0.0114||OD||246|
|16. Ishida et. al.||1937||4.8453 ± 0.0030||OD||247|
|17. Dunnington||1938||4.8025 ± 0.0004||XM||248|
|18. Dunnington||1938||4.8036 ± 0.0048||OM||248|
|20. R.T.Birge||1939||4.8022 ± 0.0010||AV||250|
|21. Miller/DuMond||1939||4.801 ± 0.002||XR||251|
|22. Miller/DuMond||1939||4.8005 ± 0.0004||XM||251|
|24. Hopper and Laby||1940||4.8137 ± 0.0030||OD||253|
|25. R.T.Birge||1941||4.8025 ± 0.0010||XM||254|
|26. R.T.Birge||1944||4.8030 ± 0.0021||AV||255|
|27. R.T.Birge||1944||4.8021 ± 0.0006||XM||255|
|28. DuMond and Cohen||1947||4.80193 ± 0.0006||XM||256|
|29. DuMond and Cohen||1947||4.8024 ± 0.0005||AV||257|
|30. Bearden and Watts||1950||4.80217 ± 0.00006||AV||258|
|31. DuMond and Cohen||1952||4.80220 ± 0.0001||XM||259|
|32. DuMond and Cohen||1952||4.80288 ± 0.00021||AV||259|
|33. Cohen et. al.||1955||4.80286 ± 0.00009||AV||260|
|34. Cohen and DuMond||1963||4.80298 ± 0.00020||AV||261|
|35. Cohen and DuMond||1965||4.80313 ± 0.00014||AV||262|
|36. Taylor et. al.||1969||4.80325 ±0.0000021||AV||263|
|37. Cohen and Taylor||1973||4.803242 ±0.0000014||AV||264|
NOTE:- # Pioneer results 'not as accurate as the oil drop value' and 'likely to contain various unsuspected sources of systematic error' (Birge238). Omitted from analysis as did Birge238 and Bearden242.
OD = oil drop: OM = oil-drop mean: XR = X-ray: XM = X-ray Mean: XP = X-ray powder method (imprecise): AV = best adjusted value.
OD values 2, 15, 16, 24, by Birge255. Value 1 used the Birge 1944 air viscosity and his 1929 corrections as for 2. Value 3 by Dunnington248. XR values 8-10 by DuMond252. XR method gives e independent of e0.
These above data indicate that Option I from Table 12 is upheld, and will be followed here, despite the advantages of the symmetry of Option III. The permeability of free space, m0, is thus proportional to 1/c2. Variation in this permeability is also one possible cause of the time-dependence of c. Wesson57 has already noted this suggestion for other reasons by Creer. The systematic variation of c under these conditions may be indicative of a systematic alteration of the physical character of the universe due to expansion or contraction under, perhaps, the action of the cosmological constant.
(B). ATOMIC REST-MASSES:
Chemical and nuclear reactions obey the standard equation
E = mc2 (2)
which O'Rahilly60 has demonstrated can be derived non-relativistically and without any assumptions about c behavior. For energy E to be conserved in all chemical and nuclear reactions requires that
m ~ 1/c2 (3)
The symbol ~ means 'proportional to' throughout this report. That this result is not unexpected for charged particles follows from the classical relation for their effective mass m as given by French6l where
m = q2/(6pe0rc2) (4)
and the particle has charge q and radius r.
An experimental check of this proposal that atomic rest-masses should increase with time is given by Table 14. Here e/(mc) is listed for electrons, rather than just m, in order to eliminate the effects of other measured quantities, namely e and c, and the result is in EMU/gm. In the majority of early cases, m was determined by conversion from this same ratio. The fine structure method (marked FS in Table 14) used the Faraday to obtain e/(mc). However, F has already been demonstrated as invariant in the previous section, leaving a valid result. A least-squares linear fit to all data gives a decay of 679.9 EMU/gm. per year, with a confidence interval for e/(mc) not being constant at the 1973 value of 99.17%. However, eight different methods were used to determine e/(mc). The results of each method individually still show a decay (except for the two methods that are represented by single observations) and results are listed with Table 14. This reinforces the conclusion that the quantity m is actually varying as the result is completely independent of the method used in the measurement.
Note that the issue of mass and gravitation is dealt with later in V (B). From this it becomes apparent that rest-masses are invariant when measured in their own time-frames, whether dynamical or atomic. However, when atomic rest-masses are measured dynamically the above variation is noted.
TABLE 14 - VALUES OF THE SPECIFIC CHARGE e/(mc)
|AUTHORITY||DATE||e/(mc) x 107 EMU/gm||METHOD||REF|
|1. J.J.Thomson||1900||1.7591 ±0.0005||CF||265|
|2. Bestelmeyer||1910||1.76 ±0.02||MM||238|
|3. Paschen||1916||1.768 ±0.003||FS||266|
|4. Babcock||1923||1.761 ±0.001||ZE||267|
|6. Wolf*||1927||1.7690 ±0.0018||CF||268|
|7. Houston*||1927||1.7617 ±0.0008||FS||269|
|8. Babcock||1929||1.7606 ±0.0012||ZE||270|
|9. Perry/Chaffee*||1930||1.7611 ±0.0010||DV||271|
|10. Campbell/Houston||1931||1.7579 ±0.0025||ZE||272|
|11. Dunnington||1932||1.7592 ±0.0015||MD||273|
|12. Kirchner*||1932||1.7590 ±0.0009||DV||274|
|13. Kinsler/Houston*||1934||1.7570 ±0.0007||ZE||275|
|14. Shane/Spedding*||1935||1.75815 ±0.0006||FS||276|
|15. Houston#||1937||1.7590 ±0.0005||FS||277|
|16. Dunnington*||1937||1.75982 ±0.0004||MD||278|
|17. Williams*||1938||1.75797 ±0.0005||FS||279|
|18. Shaw*||1938||1.7582 ±0.0013||CF||280|
|19. Bearden*||1938||1.76006 ±0.0004||XR||281|
|20. Chu*||1939||1.76048 ±0.00058||FS||282|
|21. Robinson*||1939||1.75914 ±0.0005||FS||283|
|22. Goedicke*||1939||1.7587 ±0.0008||CF||284|
|23. Drinkwater et. al.*||1940||1.75913 ±0.00027||FS||285|
|24. Birge||1941a||1.7592 ±0.0005||MM||254|
|25. DuMond/Cohen||1947||1.75920 ±0.00038||MM||256|
|26. Bearden and Watts||1951||1.758912 ±0.00005||IM||258|
|27. Bearden and Watts||1951||1.758896 ±0.000028||MM||259|
|28. Gardner||1951||1.75890 ±0.00005||MD||286|
|29. DuMond/Cohen||1952||1.75888 ±0.00005||MM||259|
|30. Cohen et. al.||1955||1.75890 ±0.00002||MM||260|
|31. Cohen/DuMond||1965||1.759796 ±0.000006||MM||262|
|32. Taylor et. al.||1969||1.7588028 ±0.0000054||MM||263|
|33. Cohen and Taylor||1973||1.7588047 ±0.0000049||MM||264|
MM. Mean of Methods etc.(10): Decay = 630.5 EMU/gm/year
FS. Fine Structure (8): Decay = 3620 EMU/gm/year
ZE. Zeeman Effect (4): Decay = 3756 EMU/gm/year
CF. Crossed Fields (4): Decay = 61.61 EMU/gm/year
MD. Magnetic Deflection (3): Decay = 265.9 EMU/gm/year
DV. Direct Velocity (2): Decay = 10500 EMU/gm/year
XR. X-ray Refraction (1): IM. Indirect Method (1):
* Corrected by Birge287: # Corrected in DuMond252.
Conversely, when dynamical phenomena are measured atomically, a variation in the gravitational constant, G, is noted.
(C). THE ATOM AND PLANCK'S CONSTANT:
For energy to be conserved in atomic orbits, the electron kinetic energy must be independent of c and obey the standard equation as given by Wehr and Richards62
Ek = mv2/2 = (Ze2)/(8pe0a) = C-IND (5)
where the expression C-IND represents independence of c throughout this report. From Table 12 the term e2/e0 is also c independent as are atomic and dynamical orbit radii. Thus, the atomic orbit radius, a, in (5) may be described as
a = C-IND (6)
However, from (5) as a result of (3), there comes the conclusion that for atomic particles
v ~ c (7)
Now from Bohr's first postulate (the Bohr Model is used for simplicity throughout as it gives correct results to a first approximation61) comes the relation62
mva = nh/2p (8)
where h is Planck's constant. As a result of (3), (6) and (7) and remembering that n is an integer, we have from (8) that
h ~ 1/c (9)
The value of h is thus expected to increase with time if c is decaying. An experimental check with the data in Table 15A does not negate the proposition. Again, h/e is tabulated as h was determined from this ratio in the majority of cases. A linear fit to the data gives an increase in h/e of 0.00014 x 10-17 erg-sec/ESU per year with a confidence level in h/e not being constant at its 1973 value of 99.99%.
It may be objected that the continuous X-ray data (CX in Table 15A) may be expected to show an increase in h/e with time. This results since the X-ray spectrum does not fall linearly to zero. Up to 1937, the exact position of the short-wave cutoff in the spectrum was estimated by the 'projected tangent method'. In 1936, DuMond and Bollman used a spectrometer with better resolution and found the exact cutoff was not where the projected tangent predicted. In 1943, Ohlin, using even more sensitive equipment noted 'knees' and 'valleys', which further changed the estimated position of the cutoff. In the period 1936-1943 the value of h/e jumped 1.376 to 1.379 x 10-17 erg-sec/ESU due to better resolution by the CX method.
TABLE 15A - EXPERIMENTAL VALUES OF h/e
|AUTHORITY||DATE||h/e x 10-17 erg-sec/ESU||METHOD||REF|
|2. Lawrence*||1926||1.3753 ±0.0027||CP||289|
|6. Van Atta#||1931||1.3753 ±0.0025||CP||293|
|7. Kirkpatrick/Ross*||1934||1.37541 ±0.0001||CX||294|
|9. Whiddington/Woodroofe#||1935||1.3737 ±0.0018||CP||295|
|10. Schaitberger*||1935||1.3775 ±0.0004||CX||296|
|11. DuMond/Bollman*||1936||1.37646 ±0.0003||CX||245|
|12. Dunnington||1938||1.3763 ±0.0003||XM||248|
|13. Wensel||1939||1.3772 ±0.0006||OP||297|
|15. R.T. Birge||1940||1.37929 ±0.00040||IV||250|
|16. R.T. Birge||1941||1.37933 ±0.00023||IV||254|
|18. Panofsky et. al.||1942||1.3786 ±0.0002||CX||300|
|19. DuMond/Cohen||1947||1.3786 ±0.0004||CX||256|
|20. DuMond/Cohen||1947||1.37926 ±0.00009||AV||257|
|21. Bearden et. al.||1951||1 .37928 ±0.00004||XM||301|
|22. Bearden and Watts||1951||1.379300 ±0.000016||AV||258|
|23. DuMond/Cohen||1952||1.37943 ±0.00005||AV||259|
|25. Cohen et. al.||1955||1.37942 ±0.00002||AV||260|
|26. Cohen/DuMond||1965||1.379474 ±0.000013||AV||262|
|27. Taylor et. al.||1969||1.3795234 ±0.0000046||JE||263|
|28. Cohen and Taylor||1973||1.3795215 ±0.0000036||JE||264|
CX = continuous X-ray: CP = critical potentials:
PE = photoelectric effect: XM = X-ray Mean:
OP = optical pyrometry: IV = indirect value:
AV = best adjusted value: JE = ac Josephson effect.
* Values corrected by DuMond252 or Dunnington248.
# These results 'much less accurate' than the X-ray values (DuMond303). They are tabulated for completeness, but omitted from analysis.
TABLE 15B - 2e/h FROM THE ac JOSEPHSON EFFECT (ref. 264)
|LAB.||DATE||2e/h (GHz/V)||ERROR (ppm)|
NOTE:- The NBS 1968 value was 483597.6 ±1.2, (2.4 ppm). Ref. 186.
The argument goes that the increasing value of h is entirely attributable to better equipment. This ignores the fact that the CX method is only one of eight used to determine h/e. Furthermore, Sanders64 has pointed out that the increasing value of h can only partly be accounted for by the improvements in instrumental resolution and changes in the accepted values of other constants. Indeed, a reviewer who had a preference for the constancy of atomic quantities noted that instrumental resolution 'may in part explain the trend in the figures, but I admit that such an explanation does not appear to be quantitatively adequate.'
This point is amplified by the post 1947 results, which largely avoid the problem. Even these values give h/e increasing at 0.0000115 X 10-17 erg-sec/ESU per year, with a confidence in h/e not constant at the 1973 value of 96.7%, or 99.3% if the indirect Birge values of 1940 and 1941 are included. As the best adjusted values generally only included the most recent data and omitted the more 'aberrant' early data, the trend noted in those figures alone reflect the general situation and may be validly used.
However, Sanders' statement is verified by two other considerations. Firstly, the measurements of 2e/h by the ac Josephson effect for 1970-1972. The results are more accurate than those of h/e and are listed in Table 15B. When the results from each of the four laboratories are considered individually, a decay in the value of 2e/h is recorded, with NBS giving the greatest. Treatment of all 11 values of 2e/h gives a decay of 0.0936 GHz/V/year with a confidence of 96.2% that this quantity was not constant at the 1972.38 value. Since the minute drifts in voltage standards are positive as well as negative168, these unidirectional results are the more noteworthy. Furthermore, they were predicted by Dirac and Kovalevsky360 if the atomic clock run-rate differed from the dynamical clock. Secondly, in Table 15 C., the Hall resistance, h/e2, affirms these conclusions with an increase of 0.0159 ohms/year and a confidence in Rh not constant at the 1985 value of 92.9%.
As this approach predicts that h must vary precisely as 1/c, it follows that for all values of h and c
hc = CONSTANT (10)
Experiments by Bahcall and Salpeter65, Baum and Florentin-Nielsen10, and Solheim et al.66 indicate that this holds over astronomical time. Indeed, with a redshift z of distant astronomical objects, Noerdlinger67 obtained the result that d[ln(hc)]/dz £ 3 x 10-4. These cosmological results upholding (10) experimentally, have often been interpreted as setting limits on the variability of either h or c on a universal time-scale. However, in each case an assumption is made about the constancy of the other term. The results that uphold (10) within the experimental limits say only that h must vary precisely as 1/c, which also upholds (9).
Since the standard relations hold for energy E that
E = hc/l = hf (11)
where l is the wavelength of light emitted by the atom and f is the frequency, it follows for energy conservation that from (9) and (10) substituted in (11)
TABLE 15C - THE QUANTIZED HALL RESISTANCE Rh = h/e2
|IDENTIFICATION||DATE||Rh (ohms WBI85)||ERROR (ppm)|
|1. Klitzing et. al.||1980||25812.776 ±0.036||1.39|
|2. Klitzing et. al.||1981||25812.79 ±0.04||1.55|
|3. NBS (US)||1983.5||25812.8495 ±0.0031||0.12|
|4. ETL, NPL, VSL mean||1984.0||25812.8418 ±0.0044||0.17|
|5. LCIE (France)||1984.5||25812.8502 ±0.0039||0.15|
|6. PTB (FRG)||1935.0||25812.8469 ±0.0048||0.18|
NOTE: 1, 2 in REF. 336 p.519-537. 3-6 in CODATA Bulletin 63, 1986, E.R. Cohen and B.N. Taylor p.9, The 1986 Adjustment of the Constants.
TABLE 16 - THE RYDBERG CONSTANT R¥
|AUTHORITY||DATE||R¥ VALUE (cm-1)||REF|
|3. Paschen||1916||109737.35 ±0.06||266|
|4. Birge||1921||109737.36 ±0.2||306|
|5. Pickering/Fowler||1925||109737.36 ±0.06||305|
|6. Houston||1927||109737.335 ±0.016||269|
|7. Houston||1927||109737.313 ±0.060||269|
|8. Birge||1929||109737.42 ±0.06||238|
|9. Chu||1939||109737.314 ±0.020||282|
|10. Drinkwater et. al.||1940||109737.311 ±0.009||285|
|11. Birge||1941||109737.303 ±0.017||287|
|12. DuMond and Cohen||1947||109737.30 ±0.05||256|
|13. Bearden and Watts||1951||109737.323 ±0.024||258|
|14. Cohen||1952||109737.311 ±0.012||307|
|15. DuMond and Cohen||1952||109737.309 ±0.012||259|
|16. Cohen et. al.||1955||109737.309 ±0.012||260|
|17. Cohen and DuMond||1963||109737.31 ±0.03||261|
|18. Cohen and DuMond||1965||109737.31 ±0.01||262|
|19. Csillag||1966||109737.307 ±0.007||308|
|20. Taylor et. al.||1969||109737.312 ±0.011||263|
|21. Cohen, Taylor||1973||109737.3177 ±0.0083||264|
|22. Hansch et. al.||1974||109737.3141 ±0.0010||309|
|23. Weber/Goldsmith||1978||109737.3149 ±0.00032||310|
|24. Petley et. al.||1979||109737.31513 ±0.00085||311|
|25. Amin et. al.||1981||109737.31521 ±0.00011||312|
NOTE:- Values 3-5 and 8 are corrected using Birge238 constants. Values 7 and 11 corrected by Birge287. Values 6, 9, 10, 18, 19 corrected by Taylor et. al.263. Values 20-24 as discussed in Hansch313.
TABLE 18 - OTHER C INDEPENDENT QUANTITIES
|Bohr Magneton||m0* = he/(4pmc)|
|Zeeman Displacement/gauss||Z* = (e/mc)/(4pc)|
|Schrodinger constant (fixed nucleus)||S = 8p2m/h2|
|Compton wavelengths||lc = h/mc|
|de Broglie wavelengths||ld = h/(mv) = hc/E|
|Faraday||F = N0e|
|Volt||V = hf/2e|
f ~ c (12)
l = C-IND (13)
The result in (12) and (13) was supported by experimental evidence at a time when c was measured as varying13. This treatment of the atom based on conservation thus overcomes Birge's objection. Atomic frequencies should vary as c, as in (12), even though Birge13 considered that 'Such a variation is obviously moat improbable.' Therefore, unchanging length standards, in both atomic and dynamical units, along with energy conservation, give results which are concordant with theory and experiment. Varying length standards would nullify (12).
In keeping with invariant wavelengths for emitted light, de Broglie wavelengths of moving particles, ld, are given by h/(mv) = hc/E, and from (3), (7), (9), (10) and (11), this quantity is independent of c. Likewise the Compton wavelength, lc, given as h/(mc), will also be c-independent.
(D). ATOMIC ORBITS AND RELATED QUANTITIES:
The expression for the energy of a given electron orbit n is given by Wehr and Richards62 and French68 as
En = -2p2e4m/(h2n2) (14)
which from (3) and (9) is independent of c. With orbit energies unaffected by c decay, electron sharing between two atomic orbits results in the 'resonance energy' that forms the covalent bond being c independent (see Brown69). A similar argument also applies to the dative bond between co-ordinate covalent compounds. Since the electronic charge is taken as constant, the ionic or electrovalent bond strengths are not dependent on c.
Related to orbit energy is the Rydberg constant R. An application of (3) and (9) to the standard definition62,68 of R results in
R = 2p2e4m/(ch3) = CONSTANT (15)
as the variable quantities mutually cancel. Experimental evidence listed in Table 16 agrees with (15). Omitting the 1890 value, which was not corrected to vacuo or for the infinite nucleus, the linear data fit gives an increase of 0.000495 cm-1 per year, with a confidence in R not constant at the 1981 value of 56.01%. This strongly suggests that the Rydberg constant has not varied. Its measured stability to 7 figures contrasts markedly with c values.
The Fine Structure constant, a, appears in combination with the Rydberg constant in defining some other quantities. An application of (10) to the definition70 of a gives
a = 2pe2/(hc) = CONSTANT (16)
Bahcall and Schmidt56 determined that for distant astronomical sources, a was (1.001 ±0.002) times its current value. Thus (16) is in accord with observation and holds on a cosmological time-scale.
TABLE 17 - THE PROTON GYROMAGNETIC RATIO g'
|1. Thomas/Driscoll/Hipple||+1949||26752.31 ±0.26||314|
|2. DuMond and Cohen||1952||26752.70 ±0.80||259|
|3. Cohen et. al.||1955||26753.00 ±0.40||260|
|4. Wilhelmy*||1957||26755.00 ±1.20||315|
|5. Driscoll and Bender||1958||26751.465 ±0.08||316|
|6. Yanovskii et. al.||1959||26752.00 ±1.50||317|
|7. Capptuller||+1960||26752.50 ±7 0.99||318|
|8. Vigoreaux||1962||26751.440 ±0.070||319|
|9. Yagola/Zingerman/Sepetyi||1962||26751.20 ±0.20||320|
|10. Yanovskii and Studentsov||1962||26750.60 ±0.50||321|
|11. Cohen and DuMond||1963||26751.92 ±0.07||262|
|12. Driscoll and Olsen||1964||26751.555 (mean)||322|
|13. Yagola/Zingerman/Sepetyi||+1966||26751.05 ±0.20||323|
|14. Driscoll and Olsen||1968||26751.526 ±0.099||322|
|15. Hara et. al.||1968||26751.384 ±0.086||324|
|16. Studentsov et. al.||1968||26751.349 ±0.045||325|
|17. Taylor/Parker/Langenberg||1969||26751.270 ±0.082||263|
|18. Olsen and Driscoll||1972||26751.384 ±0.054||326|
|19. Cohen and Taylor||1973||26751.301 ±0.075||264|
|20. Olsen and Williams||1975||26751.354 ±0.011||327|
|21. Wang (Chiao, Liu, Shen)||1977||26751.481 ±0.048||328|
|22. Vigoureaux and Dupuy||1978||26751.178 ±0.013||329|
|23. Kibble and Hunt||+1979||26751.689 ±0.027||330|
|24. Williams and Olsen||1979||26751.3625 ±0.0057||331|
|25. Chiao, Liu and Shen||+1980||26751.572 ±0.095||332|
|26. Chiao and Shen||1980||26751.391 ±0.021||332|
|27. Forkert and Schlesok||+1980||26751.32 ±0.41||333|
|28. Forkert and Schlesok||1980||26751.55 ±0.13||333|
|29. Tarbeyev||1981||26751.257 ±0.040||334|
|30. Tarbeyev||1981||26751.228 ±0.016||334|
* Included in Table for completeness but omitted from trend analysis.
NOTE:- Values 1-17 as corrected by Taylor et. al.335 except for the best adjusted values 2, 3, 11 and 19. Values 18, and 20-30 as discussed by Williams, Olsen and Phillips336 except 21 from p.507 and 29 from p.484 of the same publication.
+ High field values: a decay of 0.0312 rad/sec/gauss per year, similar to the trend from all values.
It may be thought from (8) that orbital angular momentum is not conserved. However, the rate of precession of the orbital angular momentum vectors about their resultant is given by French72 as
PRECESSION = DW/h (17)
where DW is the magnetic potential energy, which from Table 12 is c independent. As this quantity DW also defines the doublet fine structure splitting in ergs, it follows that this, too, is c independent. Applying this and (9) to (17) results in angular momentum being conserved in atomic orbits as
PRECESSION ~ c (18)
The gyromagnetic ratio, g, as defined by French72 also appears to be c-dependent as
g = e/(2mc) ~ c (19)
Table 17 suggests a decay of 0.0294 rad/sec/gauss per year in g, with a 99.9% confidence interval that g was not constant at the 1981 value. Table 18 summarizes some quantities that are c independent through mutually canceling c dependent terms.
(E). RADIOACTIVE DECAY:
As (3) and (7) apply to nucleons as well as electrons, the velocity, v, at which nucleons move in their orbitals seems to be proportional to c. As atomic radii are c independent, and if the radius of the nucleus is r, then the alpha particle escape frequency l* (the decay constant) as defined by Glasstone73 and Von Buttlar74 is given as
l* = Pv/r (20)
where P is the probability of escape by the tunneling process. Since P is a function of energy, which, from the above approach is c independent, then
l* ~ c (21)
For b decay processes, Von Buttlar75 defines the decay constant as
l* = Gf = mc2g2|M|2f/(p2h) (22)
where f is a function of the maximum energy of emission and atomic number Z, both c independent. M, the nuclear matrix element dependent upon energy, is unchanged by c, as is the constant g. Planck's constant is h, so for b decay,
l* ~ c (23)
An alternative formulation by Burcham76 leads to the same result.
TABLE 19: HALF-LIVES OF THE MAIN HEAVY RADIO-NUCLIDES
|Thallium 207||-||3.47||4.71||4.71||4.76||4.76||4.79||4.78*||4.77||m||+ 1.5 x 10-2||+ 3.1 x 10-3|
|Thallium 208||-||3.1||3.1||3.2||3.1||3.1||3.10||3.10*||3.053||m||- 8.4 x 10-4||- 2.7 x 10-4|
|Thallium 210||-||1.4||1.32||1.32||1.32||1.32||1.32||1.30*||1.30||m||- 1.2 x 10-3||- 9.2 x 10-4|
|Lead 210||-||16.5||22||16||22||22||19.4||21||22.3||y||+ 7.0 x 10-2||+ 3.1 x 10-3|
|Lead 211||#38*||36.0||36.0||36.0||36.1||36.1||36.1||36.1*||36.1||m||+ 2.0 x 10-3||+ 5.5 x 10-5|
|Lead 212||#11.3*||10.6||10.6||10.6||10.6||10.6||10.64||10.64*||10.64||h||+ 8.1 x 10-4||+ 7.6 x 10-5|
|Lead 214||21.4*||26.8||26.8||26.8||26.8||26.8||26.8||26.8||26.8||m||+ 4.4 x 10-2||+ 1.6 x 10-3|
|Bismuth 210||-||5.0||4.9||4.85||5.00||5.0||5.01||5.0||5.01||d||+ 1.2 x 10-3||+ 2.4 x 10-4|
|Bismuth 211||-||2.10||2.16*||2.15||2.16||2.16||2.16||2.15*||2.15||m||+ 5.4 x 10-4||+ 2.5 x 10-4|
|Bismuth 212||55||60.0||60.5||60.8||60.5||60.5||60.5||60.6*||60.60||m||+ 4.8 x 10-2||+ 7.9 x 10-4|
|Bismuth 214||#28||19.5||19.7||19.7||19.7||19.7||19.7||19.9||19.7||m||+ 3.5 x 10-3||+ 1.7 x 10-4|
|Polonium 210||-||136||136.3*||136.5||140||140||140*||138.4||138.38||d||+ 5.1 x 10-2||+ 3.6 x 10-4|
|Polonium 216||-||0.14||0.145*||0.14||0.158||0.160||0.158||0.15*||0.15||s||+ 2.0 x 10-4||+ 1.3 x 10-3|
|Polonium 218||3.0||3.0||3.05||3.05||3.05||3.05||3.05||3.05||3.05||m||+ 7.2 x 10-4||+ 2.3 x 10-4|
|Radon 219||4.0*||3.90||3.92||3.92||3.92||3.92||3.92||4.00*||3.96||s||+ 1.8 x 10-4||+ 4.5 x 10-5|
|Radon 220||60||54.0||54.5||54.5||54.5||54.5||(54.5)||55.0*||55.6||s||- 3.0 x 10-2||- 5.4 x 10-4|
|Radon 222||3.65*||3.85||3.823||3.825||3.825||3.82||3.823||3.825||3.8235||d||+ 1.2 x 10-3||+ 3.1 x 10-4|
|Radium 223||-||10.5||11.2||11.2||11.2||11.2||11.7||11.43*||11.435||d||+ 1.3 x 10-2||+ 1.1 x 10-3|
|Radium 224||4.0||3.64||3.64||3.64||3.64||3.64||3.64||3.64*||3.66||d||- 2.7 x 10-3||- 7.3 x 10-4|
|Radium 226||732*?||2000?||1590||1580||1590||1620||1622||1620||1600||y||+ 4.8 x 100||+ 3.0 x 10-3|
|Radium 228||-||5.5||6.7||6.7||6.70||6.7||6.70||5.77*||5.76||y||- 2.1 x 10-3||- 3.6 x 10-4|
|Actinium 227||-||-||20.0||20||-||21.7||21.6||21.6*||21.773||y||+ 4.1 x 10-2||+ 1.8 x 10-3|
|Actinium 228||-||6.2||6.13||6.13||6.13||6.13||6.13||6.13*||6.13||h||- 7.8 x 10-4||- 1.2 x 10-4|
|Thorium 227||-||19.5||18.9||18.9||18.9||18.9||18.2||18.5*||18.718||d||- 1.3 x 10-2||- 6.9 x 10-4|
|Thorium 228||-||2||1.90||1.90||1.90||1.90||1.91||1.91||1.9131||y||- 8.8 x 10-4||- 4.6 x 10-4|
|Thorium 230||-||?||7.6*||7.6||8.30||8.0||8.30*||8.00||8.00 E4||y||+ 8.4 x 10-3||+ 1.0 x 10-3|
|Thorium 231||-||36?||24.6||24.5||24.6||24.6||25.6||25.5*||25.52||h||- 1.0 x 10-1||- 3.9 x 10-3|
|Thorium 232||-||3?||1.65*||1.65||1.39||1.39||1.39||1.41||1.41 E10||y||- 2.0 x 10-2||- 1.7 x 10-2|
|Thorium 234||22.3||24.6||23.8||24.5||24.1||24.1d||24.5*||24.1||24.10||d||+ 1.3 x 10-2||+ 5.4 x 10-4|
|Protact. 231||-||-||1.25||1.20||3.2||3.2||3.43||3.25*||3.28 E4||y||+ 4.5 x 10-2||+ 1.3 x 10-2|
|Protact. 234||-||-||6.7||-||6.7||6.7||-||6.66||6.75||h||+ 5.1 x 10-4||+ 7.5 x 10-5|
|Protact. 234m||-||-||1.14||1.15||1.14||1.14||1.18||1.17*||1.1725||m||+ 8.4 x 10-4||+ 7.1 x 10-4|
|Uranium 234||-||-||3.0?||-||2.69||2.35||2.48||2.50||2.45 E5||y||- 1.0 x 10-2||- 4.0 x 10-3|
|Uranium 235||#7.3||-||-||-||7.07||7.07||(7.13)||7.1||7.038 E8||y||- 6.5 x 10-4||- 9.2 x 10-5|
|Uranium 238||-||6?||4.40||4.5||4.51||4.5||(4.56)||4.51||4.468 E9||y||- 1.6 x 10-2||- 3.5 x 10-3|
# For 1904: Several decaying elements involved, increasing half-life: Ommited from analysis.
? Approximate values - retained in analysis. Seconds = s: Minutes = m: Hours = h: Days = d: Years = y.
NOTE:- Behavior/Year from least squares linear fit to data. Trend/Unit = (Behavior/Year)/(1978 value).
REFERENCES: 1904: Rutherford337, *values Soddy338. 1913: Rutherford339. 1930: Curie et. al.340, *values from Rutherford341. 1936: Crowther342. 1944: Seaborg343. 1950: Glasstone344. 1958: Strominger et. al.345, *values US Navy346, bracketed values Korsunsky347. 1966: Gregory348, *values Goldman349. 1978: Lederer and Shirley350 in Friedlander et. al.351.
For electron capture, the relevant equation from Burcham77 is
l* = K2|M|2f/(2p3) (24)
where f is here a function of the fine structure constant, the atomic number Z, and total energy, all c independent. M is as above. K2 is defined by Burcham78 as
K2 = g2m5c4/(h/2p) (25)
With g independent of c, application of (3) and (9) to m, h and c results in K2 proportional to c so that for electron capture
l* ~ c (26)
This approach thus gives l* proportional to c for all radioactive decay. Table 19 lists the experimental evidence for slowing decay rates of the main naturally occurring heavy radio-nuclides which, generally, were the first to be noted and have their half-lives recorded. They support the contention of increasing half-lives by an almost two-thirds majority, despite increasing efficiencies of particle counters which tend to reverse the trend. The most pessimistic conclusion is that they do not invalidate the proposal.
The b decay coupling constant, g, used above, also called the Fermi interaction constant, bears a value57 of 1.4 x 10-49 erg-cm3. Conservation laws therefore require it to be invariant with changes in c. The weak coupling constant, gw, is a dimensionless number that includes g. Wesson57 defines gw = [gm2c/(h/2p)3]2 where m is the pion mass. From (3) and (9) and constant g, this equation also leaves gw as invariant with changes in c. This is demonstrable in practice since any variation in gw would result in a discrepancy between the radiometric ages for a and b decay processes57. That is not usually observed. The fact that gw is also dimensionless hinted that it should be independent of c for reasons that become apparent shortly. Similar theoretical and experimental evidence also shows that the strong coupling constant, gs has been invariant over cosmic time57. Indeed, the experimental limits that preclude variation in all three coupling constants also place comparable limits on any variation in e or vice versa57. The indication is, therefore, that they have remained constant on a universal time scale. The nuclear g-factor for the proton, gp, also proves invariant from astrophysical observation57. Generally, therefore, the dimensionless coupling constants may be taken as invariant with changing c.
V. TIME AND LENGTH:-
(A). ATOMIC TIME:
If the above list of constants is examined, it is discovered that those which are measured as varying all have units involving time. These include electron velocities, c itself, Planck's constant h, frequencies f, precession rates, the gyromagnetic ratio g, and radioactive decay rates. Even rest-mass involves time from its definition of force/acceleration. It is noticeable that the constants which remain invariant with mutually canceling c-dependent terms are those whose units are time independent. They include the fine structure constant a, the Rydberg constant R¥ , wave-lengths l, energy per unit wavelength hc, the volt, and the electronic charge. The dimensionless constants are also invariant if conservation is to be upheld.
TABLE 20 - MEASUREMENTS OF THE NEWTONIAN GRAVITATIONAL CONSTANT, G
|NO.||EXPERIMENTER||DATE||METHOD||VALUE OF G x 108 dyne-cm2/gm2||REF|
|1.||Cavendish||1798||static torsion||6.754 ±0.041||352|
|2.||Reich||#1838||static torsion||6.64 ±0.06||353|
|3.||Baily||#1843||static torsion||6.63 ±0.07||353|
|4.||Cornu/Baille||1872||static torsion||6.618 ±0.017||354|
|5.||Jolly||#1873||Jolly balance||6.447 ±0.11||353|
|6.||Eotvos||1886||static torsion||6.657 ±0.013||353|
|7.||Richarz/K-Menzel||1888||Jolly balance||6.683 ±0.011||353|
|8.||Wilsing||#1889||Jolly balance||6.594 ±0.15||353|
|9.||Poynting||1891||Jolly balance||6.6984 ±0.004||355|
|10.||Boys||1895||static torsion||6.658 ±0.007||353|
|11.||Braun||1895||dynamic torsion||6.658 ±0.002||355|
|12.||Richarz/K-Menzel||1896||Jolly balance||6.685 ±0.011||356|
|13.||Braun||1897||dynamic torsion||6.649 ±0.002||353|
|15.||Heyl||1930||dynamic torsion||6.6721 ±0.0073||357|
|16.||Zahradnicek||1933||dynamic torsion||6.659 ±0.004||355|
|17.||Heyl/Chrzanowski||1942||dynamic torsion||6.6720 ±0.0049||357|
|18.||Rose et. al.||1969||rotating table||6.674 ±0.003||357|
|19.||Pontikis||1972||resonance torsion||6.6714 ±0.0006||357|
|20.||Renner||1973||dynamic torsion||6.670 ±0.008||353|
|21.||Karagioz||1976||dynamic torsion||6.668 ±0.002||353|
|22.||Rose et. al.||1976||rotating table||6.6699 ±0.0014||355|
|23.||Sagitov||1977||dynamic torsion||6.6745 ±0.003||353|
|24.||Stacey et. al.||1978||geophysical||6.712 ±0.037||358|
|25.||Luther/Towler||1981||dynamic torsion||6.6726 ±0.0005||359|
# Omitted from analysis since data (a) only given to 3 figures, or (b) has high error, or no error given, or (c) aberrant compared with other values.
Summarizing the above approach, we may say that the atom sees no change in c! Atomic time is based on the time an electron takes to travel its orbit once. Seen dynamically then, atomic time intervals, dt, vary as 1/c. For the atom, light has always traveled the same distance in one of its seconds, its light emitting frequency has always been constant, Planck's constant never varies and radioactive decay rates remain unchanged. It is only as we look at the atom from our dynamical time frame that any change is noted. A constant dynamical interval, dt, may thus be written c.dt. This implies that general relativistic equations hold as their time intervals, written as (c2.dt2, would be valid dynamically if time, t, was measured atomically. Since both c and t are invariant in the atomic frame, the equations are automatically valid there.
The change observed in c macroscopically is thus an indication of a variation occurring on the atomic level, with the run rate of the atomic clock being affected. This atomic variation with c answers the key criticism made by Birge in 1934. He stated19 that 'if the value of c...is actually changing with time, but the value of (wavelength) in terms of the standard meter shows no corresponding change then it necessarily follows that the value of every atomic frequency...must be changing. Such a variation is obviously most improbable. Unfortunately,' he lamented13, 'it is not possible to make a direct test, since one cannot compare directly an atomic frequency with any macroscopic standard of time.'
Today, however, evidence comes from analysis of lunar occultations and planetary orbital data. The moon and planets all appear from the measurements to have different angular acceleration rates in atomic time compared with dynamical time. On these results, Van Flandern concludes that1 'the number of atomic seconds in a dynamical interval is becoming fewer. Presumably, if the result has any generality to it, this means that atomic phenomena are slowing down with respect to dynamical phenomena...(though) we cannot tell from existing data whether the changes are occurring on the atomic or dynamical level.' The above analysis verifies these conclusions, and the dilemma seems to dissolve by considering gravitation.
[REVISED IN LATER REPORT ]
(C). LENGTH, TIME AND C:
The atomic unit of time is given by one revolution of an electron in the ground state orbit of a hydrogen atom (see Roxburgh82). Froome and Essen83 note that there was a consistent standard from 1820 to 1955 for the dynamical second as 1/86,400 of the earth's rotational period checked by stellar transit times. Goudsmit et al.84 point out that from 1956 the same standard was redefined as 1/31,556,925.9747 of the earth's orbital period. Atomic clocks became available in 1955 (see Morrison85 and Van Flandern1) and Wilkie2 notes that our time became regulated by atomic seconds in 1967. At that date the old standard interval was redefined as 9,192,631,770 periods of radiation of caesium 133 in the ground state86. The above work suggests that the number of caesium transitions per dynamical second are becoming fewer. However, up to 1967, timing of events in the measurement of c were not affected by this.
Furthermore, there has been a consistent meter length standard since 1798, formalized in 1875 and redefined in 1960 as 1,650,763.73 vacuum wavelengths of the Krypton 86 orange line (see Froome and Essen87). In 1983 it was redefined as the distance light travels in 1/299,792,458 seconds as noted by Wilkie2. There will be no difference in the length standard if c varies provided measurements are done in atomic seconds. If c was to increase and measurements were in dynamical time for the new definition of the meter, then fewer wavelengths of a given spectral line would fit in the interval and the meter would have to be lengthened to restore the definition.
(D). LASERS, AND A TEST FOR C DECAY:
TABLE 21 - COMPARISON OF CURVES FITTED TO ALL TABLE 11 DATA
NOTE:- Typical dates only reproduced from the full Table 11 analysis to avoid a lengthy table.
|DATE t||OBSERVED C VALUE (Km/s)||LINEAR DECAY, EXPON. or LOG.||POWER CURVE||PARABOLA, and COSEC2||CRITICAL, OVER, UNDER DAMPED||SQ. ROOT OF CRITICALLY DAMPED||POLYNOMIAL APPROX. TO ROOT DAMPED|
ALL TABLE 11 DATA RESIDUALS: 2.883 2.813 910 924 **1013 911
= ±(Observed - Predicted):
(Sum of Residual squares)/n: 657 866 **1058 660
|Linear decay:-||r2 = 0.7704:
c = a + bt
|With a = 305242||b = -2.79495|
|Exponential:-||r2 = 0.7705:
e = aebt
|With a = 305285||b = -9.3131 x10-6|
|Logarithmic:-||r2 = 0.7705:
c = a10bt
|With a = 305285||b = -4.0446x 10-6|
|Power Curve:-||r2 = 0.7863:
c = atb
|With a = 342871||b = -0.0177239|
|*Parabola:-||r2 = 0.9704:
c = aT2 + bT + d
|With a = 0.018679||b = 0||d= 299787.23|
|*Cosec2:-||r2 = 0.9703:
c = a cosec2 bT
|With a = 299787.23||b = 2.494912x 10-4|
|*Critical Damping:-||c = a + (d + ft)ebt||With a = 301924||b = -0.00308||d= 4.733 x 106||f = -2870|
|Root Damped:-||c =
Ö[a + ekt(b + dt)]
|a = 9.029 x 1010||b = 4.59 x1013||d = -2.6 x 1010||k = -0.0048|
aT8 + bT2 + d
|With a = 3.8 x 10-19||b = 0.01866||d= 299787.23|
* Maximum r2 left minimum values unadjusted. These curves essentially unaffected by post 1967 values.
For parabolas etc., T = (1961 - t): for cosec2 curves, T = (4335 + t). Minima In 1961 result for each.
** Higher residuals for the preferred curve mainly result from the 1740 value compared with the others.
It is significant that the eight laser values from 1972 to 1983 were using the atomic time and frequency standards. It is therefore inevitable that the constancy of c in the atomic time frame will be reflected in the measurements. It is for this reason that no statistically significant trend was revealed in that period. If any trend was occurring, and the figures up to 1967 indicated a rapidly flattening decay rate, it could only be picked up by a comparison between clock rates. Van Flandern did this1 with lunar orbit data from 1978 to 1981. Though c was not considered, the results give
nï/n = -Pï/P = -cï/c = (3.2 ±1.1) x 10-11/yr (34)
where (ï) indicates a time derivative, P is the moon's orbital period, n is the mean motion and c is light speed. This yields the result that the mean decay rate for c by time comparisons around 1980 was 0.0096 m/s per year. Planetary ranging techniques93 gave initial results in 1978 of nï/n equal to (12.4 ±6.6) x 10-11 per year or a c decay rate of 0.037 m/s per year. However, the combined average for Mercury, Venus and Mars was 30 x 10-11 per year in 1978. This gives a c decay rate of 0.089 m/s per year at that date. By 1983, Canuto et al. (item 30, Table 24) gave tï/t at (1 ±8) x 10-12 /yr.
These results suggest that cï/c is flattening out fast (see Table 24). Two possibilities now exist. The decay rate may either taper rapidly to zero, or bottom out and become an increase. The preferred curve forms on page 55 also allow both options. However the coefficients used in the specific example require the second option to be followed. Minor adjustment would give the first. Van Flandern's clock comparisons over an ever increasing period thus hold the key to discerning the precise behavior of c, cross-checked by data from the gyromagnetic ratio, g', the Hall resistance, h/e2 and 2e/h.
VI. DATA CONCLUSIONS AND ULTIMATE CAUSES:-
(A). GENERAL CONCLUSIONS FROM ALL DATA:
The proposal of c decay and slowing atomic clocks has been examined using 638 values of the relevant atomic quantities measured by 41 methods. This has comprised 194 atomic, 281 radio-nuclide, and 163 c values. Of these, the 16 different methods of measurement of c all individually show a decay. Again, the 15 methods employed for the 104 atomic values predicted to vary and the method used for the 281 radio-nuclides, all confirm the expected trend. This means that 32 methods of measurement and 548 values support c decay and slowing atomic clocks directly. The remaining 9 methods and 90 values give indirect support to the proposal. This can hardly be the result of intellectual phase locking. Further, the odds against 32 methods showing this trend by coincidence are about one in 1015, assuming that some would be expected to show an increase, others a decrease, and some no trend at all. These odds also seem to stretch Dorsey's explanation of equipment unreliability, systematic errors, and improved techniques too far.
If c and associated atomic quantities were true constants, measurements should produce results similar to those for all values of e in Table 13. There, a random fluctuation about a fixed value occurs, regardless of the size of the error limits. The alternative example is R¥ from Table-16, which is stable to seven figures, despite error limits. Both e and R¥ also have low statistical probabilities of any change compared with the modern values. All this is in sharp contrast with the c values and related atomic quantities. These contrasts indicate that the data do not support constant c, but instead favor slowing atomic processes compared with dynamical phenomena as Van Flandern concluded.
TABLE 22 - RESULTS OF ANALYSIS OF SPEED OF LIGHT DATA
|REF.||MEAN DATE||DATA||C MEAN Km/s||C VALUE c.f. NOW Km/s||DECAY RATE Km/s/yr||CONF|
1, 6: Results from the Roemer eclipse method. The four most conservative values used in 1. Item 6 represented by a single value based on a large number of observations.
2, 3, 5, 7, 13: All used the Bradley aberration method. Item 13 had a large scatter of points rendering the decay value unreliable.
4: Best results from seven methods (aberration, eclipse, toothed wheel, rotating mirror, polygonal mirror, waves on wires, ratio of ESU/EMU).
8: Most reliable values from the Fizeau toothed wheel method.
9: Summary of the best data available based on the Birge list (reference 11).
10, 12: The Foucault rotating mirror method was used to obtain these values.
11: Summary of Michelson's 4 prime values. The first two used a rotating mirror. In the second two, a polygonal mirror technique allowed an adjustment to a null position. Each of Michelson's determinations was lower than the previous one. In 7 instances by different experimenters the same equipment was used and always resulted in a lower c value at the later date.
14: The Kerr Cell chopped the light beam electrically like a toothed wheel. A built-in defect in the method gave systematically low results. The decay was still observed, but shifted to a lower range of c values. The confidence interval in this case refers to the decay trend and not the mean value.
15 - 19: Combined results from six modern methods in item 15. Each gave a decay individually as well as collectively. Item 16 used 9 methods, with c values from 1954-1967 inclusive. Item 17 had 4 methods with the first 7 values from Table 8. Item 18 includes all 11 data points from Table 8 with 4 methods involved. The last 4 laser results in Table 8 give Item 19.
CLICK HERE TO SEE FIGURE III
CLICK HERE TO SEE FIGURE IV
(B). CONCLUSIONS FROM C-DATA:
Table 21 makes a comparison with observed values of c for eight types of curve based on the Table 11 data. If all 163 c data points are used, then least squares analyses give higher decay rates than with the Table 11 data. Decay for all data ranges around 40 Km/s per year, but only 2.5 Km/s per year for Table 11 data. Again, measured trends of all related atomic constants do serve to confirm c decay and points do not exhibit a normal distribution about today's values. However, the fewer values involved for each quantity, and their shorter time range, do not allow the same formulation of the decay's precise nature that the c data does. Nevertheless, a cross-comparison of the best atomic results not only endorses the non-linear slow-down in atomic processes, but their values give consistent magnitudes for all 7 varying quantities. This is demonstrated in the next section. A summary of all results of the c data analysis appears in Table 22. Note that in the case of item 18 in Table 22, the dynamical measurements of c are compared with the atomic standard using all data in Table 8 to obtain an estimate of the decay rate for a mean date of 1975. The results from Table 22 are used in Table 24 as outlined in the next section.
(C). CONCLUSIONS FROM REFINED ATOMIC DATA:
Thus far, the atomic data for Tables 13 - 19 have generally been treated as a whole without refinement. Table 23 overcomes this difficulty. The observed trend for all data is maintained in refined analysis, though less extreme in form, as the scatter of points is reduced and the true trend becomes more closely defined experimentally. Items 1-3 in Table 23 are the c data which has already been dealt with. Items 4-6 and 24 were also handled when the electronic charge was considered.
Items 7-11 consider the specific charge e/(mc) with item 7 summarizing all results. These items derive from a consideration of Table 14 where e/(mc) is listed. Item 8 gives the most conservative early results by a single method, namely the crossed-fields values from Table 14 numbers 1, 6, 18, and 22 for a mean date of 1926. Item 9-11 (Table 23) treats the most conservative values by 6 methods. All excessively high or low values were omitted. This gives a range from Dunnington's maximum of 1.7592 in 1932 to the low in 1965 of 1.758796. The values so treated thus become numbers 1, 11, 12, 15, 21, 23-33. To obtain a mean date of 1938, 11 points were used omitting numbers 27, 29, and 31-33. For a mean date of 1945 all 16 points were used, while a mean date result for 1952 was obtained using all values between 1951 and 1955 inclusive. The decay rate in parts per million at these dates closely corresponds with that of the c data as evidenced by Table 24.
Items 12 and 13 in Table 23 consider h/e from Table 15A with item 12 summarizing all results. The best modern data all have values prefixed by 1.379 and until 1940 there was deviation from this. For a mean date of 1947 all 6 data of the above prefix between 1940-1952 inclusive were used. As the 2e/h results from Table 15B were more accurate than h/e for later dates, they were considered instead in items 14 and 15. Item 14 in Table 23 is the summary. The refined data was considered in the range greater than or equal to the prefix 483593.6 and less than or equal to 483593.8. This gave 5 points with a mean date of 1971. For both h/e and 2e/h the trend rate in parts per million closely approximate to that for the c data (see Table 24).
TABLE 23 - SUMMARY OF BEHAVIOR OF ATOMIC QUANTITIES
|2.||c||146||16||1675-1983||-||- 43||97.2 %|
|3.||c||57||16||1740-1983||-||- 2.79||99.99 %|
|4.||*e||37||2||1913-1973||4.803242||+ 0.000026||55.4 %|
|5.||*e||8||1||1913-1940||-||+ 0.000383||76.8 %|
|6.||*e||15||1||1928-1952||-||- 0.0000148||63.7 %|
|7.||e/(mc)||33||7||1900-1973||1.7588047||- 0.0000679||99.2 %|
|8.||e/(mc)||4||1||1900-1939||-||- 0.00000616||77.7 %|
|9.||e/(mc)||11||6||1900-1955||-||- 0.00000303||99.99 %|
|10.||e/(mc)||16||6||1900-1973||-||- 0.00000592||99.98 %|
|11.||e/(mc)||5||3||1951-1955||-||- 0.00000067||99.98 %|
|12.||h/e||28||5||1921-1973||1.3795215||+ 0.00014||99.99 %|
|13.||h/e||6||3||1940-1952||-||+ 0.00000324||99.50 %|
|14.||2e/h||13||1||1966-1973||483593.606||- 0.535||95.5 %|
|15.||2e/h||5||1||1970-1973||-||- 0.0239||66.5 %|
|16.||g'||30||2||1949-1981||26751.228||- 0.0294||99.9 %|
|17.||g'||12||2||1958-1973||-||- 0.0131||93.6 %|
|18.||g'||7||2||1968-1980||-||- 0.00109||99.92 %|
|19.||l||281||35||1904-1978||1 unit||- 0.0001129||85.5 %|
|21.||*R¥||25||1||1890-1981||109737.31521||+ 0.000495||56.01 %|
|22.||*G||25||6||1798-1981||6.6726||- 0.000114||57.83 %|
|23.||hc||cosmologically proven constant - time terms mutually cancel.|
|24.||a||cosmologically proven constant - time terms mutually cancel.|
|25.||**e2/e0||measured as constant cosmologically - time independent.|
REF. = reference number. CONST. = atomic quantity. DATA = number of data used.
METH. = number of methods. DATES = years of observations. VALUE = last value by experiment (not the same as the current best adjusted value). TREND/YR = the trend per year from the least squares linear fit in units of the atomic quantity.
CONF. = confidence interval that the data mean is not equal to the current value.
NOTE:- Items 1-3, 7-20 list all data first, then treat the best data only in each quantity. Items 1, 8, 15, 20 have low confidence intervals due to small data numbers and/or large standard deviations.
1, 2, 3: c = light speed in Km/s. For 2, values with errors 3 0.5% are omitted. For 3, refined data only, based on Birge (see reference 11) plus post 1945 values. For 1, all data are used.
4, 5, 6: e = electronic charge in ESU x 10-10. For 4, all data used. For 5, only oil-drop data employed. For 6, X-ray data only.
7-11: m = electron rest mass. Specific charge e/(mc) in EMU/gm x 107.
12. 13: h = Planck's constant. h/e in units of (erg-sec/ESU) x 10-17.
14, 15: 2e/h in units of GHz/V. Values from ac Josephson effect.
16-18: g' = gyromagnetic ratio in units of rad/sec/gauss.
19, 20: l = radioactive decay constants. All units reduced to unity. In this case METH. column refers to the number of elements only.
21: R¥ = Rydberg constant for infinite nucleus in units of cm-1. It combines variables c, h, and m so that time terms cancel.
22: G = Newtonian gravitational constant in units of dyne-cm2/gm2 x 108.
23-25: see listing under references 10, 54-57 and 65-67 at end of report. a = fine structure constant, e0 = permittivity of free space,
* The statistical treatment indicates these quantities to be absolute constants. The values of R¥ are stable to 7 figures. The values of e and G have a normal distribution about today's value. This is in sharp contrast to the other constants discussed.
** From 4-6 and 25, e0 must be an absolute constant. As e0m0 = 1/c2, free space permeability m0 is implied as proportional to 1/c2.
Items 16-18 give the gyromagnetic ratio results, g', with 16 being the already given summary. Table 17 shows that all recent data are prefixed by 26751. Those data outside that prefix were rejected. For a mean date of 1966, all 12 data of the correct prefix were used from 1958 to 1973. For a mean date of 1974 values between 1968-1980 were used with the prefix narrowed to 26751.3 which had a clear majority over other values for the decimal. The refined results are again in accord with the c data trend in parts per million.
The radioactive decay constant, l, appears in items 19 and 20 in Table 23. Here, for the purposes of comparison, each decay constant has been reduced to unity and an overall general result obtained for item 19. The best data is taken as being those that show a trend of less than 7 x 10-5 per year when the 1904 value is omitted. The relevant elements become Pb211, Bi211 Bi212 (which also omits the 1913 value), Ra224, Th234 (which also omits the 1913 value), and finally U235. The latter was included as the best result from the long-lived nuclides. The mean date for these 6 elements is 1951, and again the results are largely in accord with the refined c data trend.
The consistent trend in 7 atomic quantities, including c, is listed in Table 24. The non-linear nature of the trend is clearly revealed. In 1700 the rate of change per quantity for c (or cï/c) was -4.16 x 10-5. By 1905 it had dropped to about -6.1 x 10-6. Around 1945 two other atomic quantities placed it about -2 x 10-6. In the period 1952-1966, c and two other quantities placed it in the order of -1 to -6 x 10-7. From 1970-1974 the decay measured by three quantities ranged from 2 to 5 x 10-8. In the mid 1970's it was about 10-9, while the late 1970's saw it drop to 10-10. The slowing announced by Van Flandern in the early 1980's were of the order of 10-10 to 10-11. It is important to continue the measurements to discover whether the trend will drop to zero rate of change, taper off slowly, or perhaps reverse and become an increase.
(D). ULTIMATE CAUSES AND THE C EQUATION:
The above data presentation indicates strongly that both light speed and atomic processes, including atomic time, are undergoing a uniform decay process. Furthermore, experiments mentioned above indicate that all atomic clocks are ticking in unison for light speed to have some universal value at any instant. Rather than invoke some property of light or the atom that might suggest they have an intrinsic notion of time, it would seem more logical to search for properties of free space that uniformly affect both. The place to commence would seem to be equation (1) as light speed and atomic behavior are both affected by the permeability of free space. Put into a context of general relativity, this implies that the energy density of free space, and consequently its metric properties, are altering. Wesson and others57 have pointed out that these properties are under the control of the cosmological constant, L. This immediately links atomic variations with the behavior of the cosmos.
TABLE 24 - CONSISTENT TRENDS IN 7 ATOMIC QUANTITIES
|REF||MEAN DATE||ATOMIC QUANTITY||DATA POINTS||RATE OF CHANGE PER QUANTITY|
|1.||1700||c||4||-4.16 x 10-5|
|2.||1740||c||4||-3.31 x 10-5|
|3.||1812||c||6||-1.73 x 10-5|
|4.||1833||c||18||-1.55 x 10-5|
|5.||1865||c||16||-1.65 x 10-5|
|6.||1880||c||63||-1.61 x 10-5|
|7.||1887||c||5||-7.24 x 10-6|
|8.||1890||c||57||-9.31 x 10-6|
|9.||1899||c||5||-5.80 x 10-6|
|10.||1903||c||4||-6.13 x 10-6|
|11.||1905||c||6||-6.17 x 10-6|
|12.||1926||e/(mc)||4||-3.50 x 10-6|
|13.||1934||c||4||-3.43 x 10-6|
|14.||1938||e/(mc)||11||-1.72 x 10-6|
|15.||1945||e/(mc)||16||-3.37 x 10-6|
|16.||1947||h/e||6||+2.34 x 10-6|
|17.||1951||l||6||-2.02 x 10-6|
|18.||1952||e/(mc)||5||-3.79 x 10-7|
|19.||1953||c||23||-6.33 x 10-7|
|20.||1961||c||15||-1.00 x 10-7|
|21.||1966||g'||12||-4.89 x 10-7|
|22.||1970||c||7||-1.94 x 10-8|
|23.||1971||2e/h||5||-4.96 x 10-8|
|24.||1974||g'||7||-4.08 x 10-8|
|25.||1975||c||11||-8.73 x 10-9|
|26.||1978||t||-||-3.00 x 10-10|
|27.||1978||t||-||-1.24 x 10-10|
|28.||1979||c||4||-3.25 x 10-10|
|29.||1980||t||-||-3.20 x 10-11|
|30.||1983||t||-||-1.00 x 10-12|
Symbols as in Table 23. Atomic time = t. The value of e is invariant, while g', l, and t are proportional to c. Since m is proportional to 1/c2, and h to 1/c, then e/(mc) is also proportional to c as is 2e/h. But h/e increases as c decays. The data for items 26, 27, 29 come from ref. 1 and 93. Item 30 in Physical Review Letters, 51:18, p.1609, Oct. 31, 1983, since no evidence of 'orbit stretching' (New Scientist, Nov. 17, 1983, p.494) with Gï/G essentially = 0. But orbit distances are invariant atomically and dynamically as is Gï/G on our approach. Item 30 may thus be spurious.
Data from items 25-30 suggest cï/c and tï/t is rapidly tapering to a zero rate of change. The critically damped curve form on page 55 (and the overdamped case) accommodates this behavior with a minor change in the values of the coefficients, tapering rapidly to the time axis. The underdamped case is clearly invalidated by these and other results. The polynomial will be valid only to its turning point under these conditions. However, CODATA Bulletin 63 for November 1986 gives values for g' and 2e/h which support the curve as presented, exhibiting a slight increase after its minimum point just below the time axis. A choice between the options can only be made by continuing measurement of t, g, 2e/h, and h/e2.
In the Schwarzschild metric, the term L/c2 appears which requires L to be proportional to c2 for energy conservation. This also follows as L there has dimensions of time-2, and as pointed out above it is those time-dependent quantities which are varying. We can thus write L = kc2, with k a true constant of dimensions cm-2. Once the value for k is established, then a L/k substitution may be made for c2 in electromagnetic and other equations. Now a universe under the control of L essentially exhibits some form of simple harmonic motion with L varying as the radius of the cosmos89. An exponentially damped sinusoid would thus be typical L behavior90. This form is typical of the behavior of many electrical, mechanical, and other systems88. Taking the square root of this exponentially damped sinusoid equation immediately gives us the behavior of c.
Table 21 makes it clear that c could well be following this type of curve as it provides an extremely good fit to the data. The exact form that was chosen was c = Ö[(a + ekt(b + dt)], which is the critically damped example88. In the overdamped case, where the equations explicitly contain the sinusoid term, the curve form that fits the data is virtually indistinguishable from this one88. The underdamped case fitting the data also has a similar form, but the predicted future behavior is vastly different. As a consequence, the above example may be considered typical of the other data fits. One solution gives k = -0.0048, a = 9.029 x 1010, b = 4.59 x 1013, d = -2.60 x 1010, and t is the year AD. Residuals are reduced somewhat by taking the coefficients to a higher number of significant figures. This example is fitted to the data in Figures III and IV.
However, most properties of this complex formula for c are reproduced by a simpler polynomial, c = a + bT2 + dT8, where a = 299792, b = 0.01866 and d = 3.8 x 10-19, where T = (1961 - t). This equation also has a superior fit to the c data. The only region where this expression differs from the more complex one is the future reaction of c, as a rapid rise is predicted. By contrast, the exponentially damped form, as it stands, suggests a small rise in c over a long period, although minor adjustments to the coefficients allow cï/c to taper to zero. This latter result is supported by the Table 24 data. The former result may be supported by the 3 standard deviation increase in 2e/h reported by Cohen and Taylor in CODATA Bulletin 63 for November 1986. Their gï'/g' shows a similar increase of about 6 x 10-7/yr like the curve cï/c. Clock comparisons and Rh data are needed to cross-check.
(A). RADIOACTIVE RADIATION INTENSITIES:
The energy of a photon, E, is constant in both time systems and is related to the kinetic energy so that E may be written, as in equation (11),
E = hf = mc2 = C-IND (35)
where m is the effective mass of the photon. This means that the photon momentum, mc, is proportional to 1/c as a result of (3). Now photon momentum is related to light pressure and energy density361 such that if electromagnetic energy density is W, we can write
W ~ 1/c (36)
For an electromagnetic wave, where E0 and H0 are the maximum amplitudes of the electric and magnetic components respectively, the energy density is362
eE02/ 8p = W = mH02 / 8pm l/c (37)
where e is the permittivity and m the permeability of free space. Thus the amplitude energies of electromagnetic waves increase as c decreases. The flux of energy denoted by the Poynting Vector, S, is therefore given by362
S = Wc = C-IND (38)
Some consider the intensity to be given by the square of the electric amplitude, E02, but we will call this quantity the relative energy along with Ditchburn363, and denote the flux, S, as the intensity of radiation.
Consider the decay of a radioactive atom in which a gamma ray is emitted. When the speed of light is 10 times higher than now, that gamma ray has a relative energy or energy density that is 1/10th of its current value in accord with (37). If it is composed of only one wavecrest now, it was composed of only one wavecrest then. Therefore, it requires 10 radioactive atoms to decay in unit time back then to give the same total energy flux, S, or intensity, equal to that now. This is precisely the situation outlined above with decay rates proportional to c. Thus (38) takes into account the higher production rate of photons by radioactive decay. This means that radioactivity in all its forms was intrinsically less of a problem with higher c.
(B) STELLAR RADIATION INTENSITIES:
[REVISED IN LATER PAPER].
(C). THE RED SHIFT:
[REVISED IN LATER REPORT]
(D). THE DOPPLER FORMULA:
[REVISED IN LATER REPORT]
(E). THE MISSING MASS:
The discussion concerning the 'missing mass' needed to hold clusters of galaxies together as well as that within galaxies themselves has elicited a number of possible solutions over the last decade. This c-decay proposal has the potential to overcome the problem in several ways. Firstly, the fact that the proposal requires the sign of L and k (in L = kc2) to be negative is in contrast to the usually assumed positive sign for an expanding cosmos on the basis of the red-shift. However, as Landsberg and Evans point out, it is in ideal agreement with a straight mathematical approach to Cosmology375, a fact hitherto ignored. Furthermore, they state that its acceptance would virtually solve the missing mass problem375. This is certainly the case as negative L acts as a form of gravity over large distances since the acceleration is given by376 a = -rL/3. This contrasts with normal gravity , which diminishes over large distances. The missing mass problem may also be enhanced by misleading red-shift. and Doppler information due to c decay across a cluster of galaxies.
(F). SUPERLUMINAL JETS:
If an event occurred at exactly the speed of light when c was 10 times its present value, and we received the signal with c equal to c now, then that event would appear to occur at exactly c now.
(G). FINAL COMMENTS:
The evidence given by the c, atomic, and astronomical data is therefore seen to lead on a trail that gives new insight into the behavior of the universe. One advantage has been the potential solution to a number of problems that science has faced. This report has dealt with some, mainly in the area of astronomy. However, others requiring further investigation lie in the fields of geology and paleontology. Some outlines are already apparent. It seems possible that the decay in the speed of light may yet be shown to have supplied a driving mechanism for some natural selection and observed preponderances in the fossil record. Other aspects of astronomy are also in view. It is hoped to deal with these questions in detail in the second report. In the meantime, Van Flandern's final comment after discussing the slow-down in atomic time seems appropriate1: 'The implications of this result for our understanding of the origin and ultimate fate of the universe are profound, although not yet fully elaborated.'
1. Van Flandern, T.C., Is the Gravitational Constant Changing? Precision Measurements and Fundamental Constants II, pp. 625-627, B.N. Taylor and W.D. Phillips (Eds.), National Bureau of Standards (U.S.), Special Publication 617 (1984).
2. Wilkie, T., Time to Remeasure the Metre, New Scientist, 100, No. 1381, 258-263, Oct. 27, 1983.
3. Dorsey, N.E., The Velocity of Light, Transactions of the American Philosophical Society, 34, (Part 1), 1-110, Oct. 1944.
4. de Bray, M.E.J. Gheury, The Velocity of Light, Nature, 127, 522, Apr. 4, 1931
5. Canuto, V., and S. Hsieh, Cosmological Variation of G and the Solar Luminosity, Astrophysical Journal. 237, 613, Apr. 15, 1980.
6. Breitenberger, E., The Status of the Velocity of Light in Special Relativity, Precision Measurements and Fundamental Constants II, pp. 667-670, B.N. Taylor and W.D. Phillips (eds.), National Bureau of Standards (U.S.), Special Publication 617, (1984).
7. Mermin, N.D., Relativity without light, American Journal of Physics, 52(2), 119-124, Feb. 1984.
8. Singh, S., Lorenz transformations in Mermin's Relativity without light, American Journal of Physics, 54(2), 183-184, Feb. 1986.
9. Barnet, C., R. Davis, and W.L. Sanders, The Aberration Constant For QSOs, Astrophysical Journal, 295, 24-27, Aug. 1, 1985.
10. Baum, W.A., and R. Florentin-Nielsen, Cosmological Evidence Against Time Variation Of The Fundamental Atomic Constants, Astrophysical Journal, 209, 319-329, Oct. 15, 1976.
11. Birge, R.T., The General Physical Constants, Reports on Progress in Physics, 8, 90-101, 1941.
12. Newcomb, S., The Velocity of Light, Nature, pp.29-32, May 13, 1886.
13. Birge, R.T., The Velocity of Light, Nature, 134, 771-772, 1934.
14. Cassini, G.D., Memoires de l'Academie Royale des Sciences, VIII, 430-431, Paris, 1693 reprinting Les Hypotheses et les Tables des Satellites de Jupiter, Reformees sur de Nouvelles Observations, Paris, 1693. Also Cassini, G.D., Divers ouvrages d'astronomie, p.475, Amsterdam, 1736.
15. Cohen, I.B., Roemer and the first determination of the velocity of light (1676), Isis, 31, 327-379, 1939.
16. Halley, E., Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London, Philosophical Transactions, XVIII, No.214, p. 237-256, Nov.- Dec., 1694.
17. Newton, I., Opticks, Book 2, Part III, Proposition XI, London 1704. Also Newton, I., Philosophiae Naturalis Principia Mathematica, Scholium to Proposition XCVI, Theorem L, 2nd edition, Cambridge, 1713.
18. Boyer, C.B., Early Estimates of the Velocity of Light, Isis 33, 26, 1941.
19. Goldstein, S.J., On the secular change in the period of Io, 1668-1926, Astronomical Journal, 80, 532-539, July 1975.
20. Goldstein, S.J., J.D. Trasco and T.J. Ogburn III, On the velocity of light three centuries ago, Astronomical Journal, 78(1), 122-125, Feb. 1973.
21. Goldstein, S.J., private communication, Feb. 25, 1986.
22. Hecht, J., Io spirals towards Jupiter, New Scientist, No. 1492, p.33, Jan. 23, 1986.
23. Kulikov, K.A., Fundamental Constants of Astronomy, 81-96, 191-195, Translated from Russian and published for N.A.S.A. by the Israel Program for Scientific Translations, Jerusalem. Original dated Moscow, 1955.
24. Newcomb, S., The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy, Supplement to the American Ephemeris and Nautical Almanac for 1897, pp.1-155, Washington, 1895.
25. Fizeau, H.L., Sur une experience relative a la vitesse de propogation de la lumiere, Comptes Rendus, 29, 90-92, 132, 1849. See also comments by de Bray, M.E.J. Gheury, The Velocity of Light, Nature, 120, 602-604, Oct. 22, 1927.
26. Newcomb, S., The Velocity of Light, Nature, pp.29-32, May 13, 1886.
27. Young, J., and G. Forbes, Experimental Determination of the Velocity of White and of Coloured Light, Philosophical Transactions, 173, Part 1, pp.231-289, 1883. Relevant page 269.
28. Dorsey, op. cit., p.37.
29. Foucault, J.L., Determination experimentale de la vitesse de la lumiere: parallaxe du Soleil, Comptes Rendus, 55, 501-503, 792-796, 1862.
30. Dorsey, op. cit., p.12.
31. Michelson, A.A., Experimental Determination of the Velocity Of Light, Astronomical Papers for the American Ephemeris and Nautical Almanac, Vol.1, Part 3, pp. 109-145, 1880. Relevant pages, 115-116.
32. Newcomb, S., Measures of the Velocity Of Light, Astronomical Papers for the Americam Ephemeris and Nautical Almanac, Vol.2, Part 3, 107-230, 1891. Relevant pages, 201-202.
33. Cohen, E.R., and J.W.M. DuMond, The Fundamental Constants of Physics, p. 108, Interscience Publishers, New York, 1957.
34. Michelson, A.A., F.G. Pease, and F. Pearson, Measurement Of The Velocity Of Light In A Partial Vacuum, Astrophysical Journal, 82, 26-61, 1935. Relevant pages 56-59.
35. Dorsey, op. cit., pp. 64, 69.
36. Froome, K.D., and L. Essen, The Velocity of Light and Radio Waves, Academic Press, London, 1969. Data from p. 136-137.
37. Ibid., p.79.
38. Mulligan, J.F., and D.F. McDonald, Some Recent Determinations of the Velocity of Light II, American Journal of Physics, 25, 180-192, 1957. Relevant pages 182-183. Also Froome and Essen, op. cit., pp. 81-82.
39. Froome and Essen, op. cit., pp. 84, 137.
40. Ibid., pp. 76, 78.
41. Ibid., pp. 23, 57.
42. Fowles, G.R., Introduction to Modern Optics, p. 6, Holt, Rinehart and Winston, New York, 1968.
43. Abraham, H., Les Mesures De La Vitesse v. Also R. Blondlot and C Gutton, Sur La Determination De La Vitesse De Propagation Des Ondulations Electromagnetiques. Both articles in Congres International De Physique Paris, 1900, Vol. 2, pp. 247-267 and 268-283.
44. Froome and Essen, op. cit., pp. 45, 48.
45. Florman, E.F., A Measurement of the Velocity of Propogation of Very-High--Frequency Radio Waves at the Surface of the Earth, Journal of Research of the National Bureau of Standards, 54, 335-345, 1955. Relevant page 342.
46. Froome and Essen, op. cit., pp.8, 9, 41.
47. Huttel, A., Ein Methode zur Bestimmung der Lichtgeschwindigkeit unter Anwendung des Kerreffektes und einer Photozelle als phasenabhangigen Gleichrichter, Annalen der Physik. series 5, Vol.37, 365-402, 1940.
48. Bergstrand, L.E., A preliminary determination of the velocity of light, Arkiv For Matematik Astronomi Och Fysik, A36, No.20, 1-11, 1949.
49. Cohen and DuMond, 1957, op. cit., p. 111.
50. de Bray, M.E.J.Gheury, The Velocity of Light, Nature, 120, 602-604, Oct. 22, 1927.
51. de Bray, M.E.J.Gheury, The Velocity of Light, Isis, 25, 437-448, 1936.
52. Mittelstaedt, 0., Uber die Messung der Lichtgeschwindigkeit, Physikalische Zeitschrift, 30, 165-167, 1929.
53. Malcolm, D., Lecturer in Computing, personal communication, August 23, 1982.
54. Dyson, F.J., Time Variation of the Charge of the Proton, Physical Review Letters, 19, 1291-1293, Nov. 27, 1967.
55. Peres, A., Constancy Of The Fundamental Electric Charge, Physical Review Letters, 19, 1293-1294, Nov. 27, 1967.
56. Bahcall, J.N., and M. Schmidt, Does The Fine-Structure Constant Vary With Cosmic Time?, Physical Review Letters, 19, 1294-1295, Nov. 27, 1967.
57. Wesson, P.S., Cosmology and Geophysics. Monographs on Astronomical Subjects: 3, pp. 65-66, 115-122, 207-208, Adam Hilger Ltd., Bristol, 1978. In the case of Creer, K.M., see Discovery, 26, 34-39, 1965 and Wesson, op. cit., p.182.
Note that in the case of the coupling constants, the following also apply: Broulik, B. and J.S. Trefil, Variation of the Strong and Electromagnetic Coupling Constants over Cosmological Times, Nature, 232, 246-247, July 23, 1971. Also, A.I. Shlyakhter, Direct test of the constancy of fundamental nuclear constants, Nature, 264, p.340, Nov. 25, 1976. Also, P.C.W. Davies Time variation of the coupling constants, Journal of Physics, A: General Physics, Vol. 5, pp.1296-1304, Aug. 1972. Also Wesson, op. cit., p.88-89, and Eisberg, op. cit., p.628, 635, 640, 698, 701.
58. Cohen, E.R., and B.N. Taylor, The 1973 Least-Squares Adjustment of the Fundamental Constants, Journal of Physical and Chemical Reference Data, 2 (4), 663-718, 1973. Relevant page, 668.
59. Finnegan, T.F., A. Denenstein, and D.N. Langenberg, Progress Towards the Josephson Voltage Standard: a Sub-Part-Per-Million Determination of 2e/h, Precision Measurement and Fundamental Constants I, p.231-237, D.N. Langenberg and B.N. Taylor editors, National Bureau of Standards Special Publication 343, Aug. 1971.
60. O'Rahilly, A., Electromagnetic Theory, pp.304-323, Dover, New York, 1965.
61. French, A.P., Principles of Modern Physics, Wiley, New York, 1959. The relevant pages are 64-66.
62. Wehr, M.R., and J.A. Richards Jr., Physics of the Atom, Addison-Wesley, Reading, Massachusetts, 1960. Pages used are 86-89.
63. Eisberg, R.M., Fundamentals of Modern Physics, p.137, Wiley, New York, 1961.
64. Sanders, J.H., The Fundamental Atomic Constants, p.13, Oxford University Press, Oxford, 1965.
65. Bahcall, J.N., and E.E. Salpeter, On The Interaction Of Radiation From Distant Sources With The Intervening Medium, Astrophysical Journal, 142, 1677-1681, 1965.
66. Solheim, J.E., T.G. Barnes III, and H.J. Smith, Observational Evidence Against A Time Variation In Planck's Constant, Astrophysical Journal, 209, 330-334, Oct. 15, 1976.
67. Noerdlinger, P.D., Primordial 2.7° Radiation as Evidence against Secular Variation of Planck's Constant, Physical Review Letters, 30, 761-762, April 16, 1973.
68. French, op. cit., p.109.
69. Brown, G.I., Modern Valence Theory, p. 74-75, Longmans, London, 1959.
70. Eisberg, op. cit., p.134.
71. French, op. cit., p.213, 235.
72. Ibid., p.235.
73. Glasstone, S., Sourcebook on Atomic Energy, p. 158. 1st Edition, Macmillan, London, 1950
74. Von Buttlar, H., Nuclear Physics, p.448-449, Academic Press, New York, 1968.
75. Ibid., p.485, 492.
76. Burcham, W.E., Nuclear Physics, p.606, McGraw-Hill, New York, 1963.
77. Ibid., p.609.
78. Ibid., P.604.
79. Martin, S.L., and A.K. Connor, Basic Physics, Vol. 1-3, p.728, Whitcombe Tombs, Melbourne, 8th edition, 2nd printing. No date given - about 1955 to 1960.
80. Ibid., p.725
81. Anonymous, Diminishing Gravity Is No Joke, New Scientist, 63, 711, 1974.
82. Roxburgh, I.W., The Laws and Constants of Nature, Precision Measurement and Fundamental Constants II, pp. 1-9, B.N. Taylor and W.D. Phillips (Eds), National Bureau of Standards (U.S.), Special Publication 617, (1984).
83. Froome and Essen, op. cit., p.22.
84. Goudsmit, S.A., R. Claiborne, and the Editors of Life, Life Science Library: Time, p. 106, Time-Life International, Nederland N.V., 1967.
85. Morrison, L. The day time stands still, New Scientist, p.20-21, June 27, 1985.
86. Froome and Essen, op. cit., p.23.
87. Ibid., p.20-21.
88. Wylie, C.R., Advanced Engineering Mathematics, second edition, pp.194-244, McGraw-Hill, New York, 1960.
89. Landsberg, P. T., and D.A. Evans, 'Mathematical Cosmology', pp.105-114, Oxford University Press, 1979.
90. Kreyszig, E., 'Advanced Engineering Mathematics', third edition, pp.62-69, Wiley international, 1980. Also, D'Azzo, J.J., and C.H. Houpis, 'Feed-back Control System Analysis & Synthesis', second edition, pp.69-
85, McGraw-Hill, Kogakusha, 1980.
93. Van Flandern, T.C., Is The Gravitational Constant Changing? Astrophysical Journal, 248 (2), 813-816, Sept.1, 1981.
94. Cassini, G.D., Memoires de l'Academie Royale des Sciences, VIII, 430-431, Paris, 1693 reprinting Les Hypotheses et les Tables des Satellites de Jupiter, Reformees sur de Nouvelles Observations, Paris, 1693. Also Cassini, G.D., Divers ouvrages d'astronomie, p.475, Amsterdam, 1736.
95. Delambre, J.B.J., Tables ecliptiques des satellites de Jupiter, Paris, 1817. Also Delambre, J.B.J., Histoire de l'astronomie moderne, Vol.II, p.653, Paris, 1821.
96. Newcomb, S., The Velocity of Light, Nature, pp.29-32, May 13, 1886,
97. Martin, B., Philosophia Britannica: or a New and Comprehensive System of the Newtonian Philosophy, Vol. 2, p.273, 2nd edition in 3 Volumes, London, 1759.
98. Anonymous, Encyclopaedia Britannica, Vol.1, p.457, 1771.
99. Glasenapp, S.P., (Glazenap), A Comparative Study of the Observations of the Eclipses of Jupiter's Satellites (Sravnenie nablyudenii zatmenii sputnikov Yupitera), Sankt-Petersburg, 1874.
100. Kulikov, K.A., Fundamental Constants of Astronomy, 81-96, 191-195, Translated from Russian and published for N.A.S.A. by the Israel Program for Scientific Translations, Jerusalem. Original dated Moscow, 1955.
101. Whittaker, E.T., History of Theories of Aether and Electricity, Vol.1, p.23, 95, Dublin, 1910.
102. Bradley, J., A letter from the Reverend Mr. James Bradley, Savilian Professor of Astronomy at Oxford, and F.R.S. to Dr. Edmond Halley, Astronom. Reg. etc., giving an Account of a new discovered Motion of the Fix'd Stars. Philosophical Transactions, Vol.35, No.406, pp.637-661, Dec. 1728.
103. Sarton, G., Discovery of the aberration of light, Isis, 16, 233-265, 1931.
104. Kulikov, K.A., op. cit., pp. 81-82.
105. Newcomb, S., The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy, Supplement to the American Ephemeris and Nautical Almanac for 1897, pp.1-155, relevant p. 137, Washington, 1895.
106. Kulikov, K.A., op. cit., pp. 82-83.
107. Ibid, p. 92.
108. Fizeau, H.L., Sur une experience relative a la vitesse de propogation de la lumiere, Comptes Rendus, 29, 90-92, 132, 1849.
109. Jenkins, F.A., and H.E. White, Fundamentals of Optics, p.386, Third Edition, McGraw-Hill, New York, 1957. See also, The Velocity of Light, Science, 66 Supp. X, Sept. 30, 1927.
110. Anonymous, The Velocity of Light, Science, 66 Supp. X, Sept. 30, 1927, (quoting an article from l'Astronomie - no exact reference).
111. Dorsey, N.E., op. cit., p.13.
112. Cornu, A., Determination de la vitesse de la lumiere et de la parallaxe du Soleil, Comptes Rendus, 79, 1361-1365, 1874. See also Cornu, A., Determination Nouvelle de la Vitesse de la Lumiere, Journal de l'Ecole Polytechnique, 27 (44), 133-180, 1874.
113. Cornu, A., Determination De La Vitesse De La Lumiere Entre L'Observatoire Et Montlhery, Annales de l'Observatoire de Paris, 13, A293, 298, 1876.
114. Dorsey, N.E., op. cit., p. 15.
115. See A. Cornu, references 112, 113.
116. Newcomb, S., Measures of the Velocity Of Light, Astronomical Papers for the Americam Ephemeris and Nautical Almanac, Vol.2, part 3, 107-230, 1891.
117. Preston, T., The Theory of Light, p.511, Macmillan and Co. Ltd., London, 1901.
118. Helmert, Ueber eine Andeutung constanter Fehler in Cornu's neuester Bestimmung der Lichtgeschwindigkeit, Astronomische Nachrichten, 87 (2072), 123-126, 1876.
119. Cornu, A., Sur La Vitesse De La Lumiere, Rapports presentes au Congres International de Physique de 1900, Vol.2, pp.225-246.
120. Birge, R.T., The General Physical Constants, Reports on Progress in Physics, 8, 90-101, 1941.
121. Newcomb, S., see reference 116, p.202.
122. Michelson, A.A., The Velocity Of Light, Decennial Publications of the University of Chicago, Vol.9, p.6, 1902.
123. Listing, J.B., Einige Bemerkungen die Parallaxe der Sonne betreffend, Astronomische Nachrichten, 93, (2232), 367-376. Relevant p. 369, 1878.
124. Michelson, A.A., Preliminary Measurement Of The Velocity Of Light, Journal of the Franklin institute, p.627-628, Nov. 1924. Also, Michelson, A.A., New Measurement of the Velocity of Light, Nature, 114, No. 2875, p.831, Dec. 6, 1924.
125. Todd, D.P., Solar Parallax from the Velocity of Light, American Journal of Science, series 3, Vol. 19, 59-64. Relevant p.61, 1880.
126. Dorsey, N.E., op. cit., p. 36.
127. Young, J., and G. Forbes, Experimental Determination of the Velocity of White and of Coloured Light, Philosophical Transactions, 173, Part 1, pp.231-289, 1883. Relevant page 286.
128. Newcomb, S., see reference 116, p.119.
129. Cornu, A., see reference 119, p. 229.
130 Perrotin, J., and Prim, Annales de l'0bservatoire Nice, Vol.11, Al-A98, 1908.
131. Perrotin, J., Sur la vitesse de la lumiere, Comptes Rendus, 131, 731-734, 1900.
132. Perrotin, J., Vitesse de la lumiere: parallaxe solaire, Comptes Rendus, 135, 881-884, 1902.
134. Foucault, J.L., Determination experimentale de la vitesse de la lqmiere: parallaxe du Soleil, Comptes Rendus, 55, 501-503, 792-796, 1862. Also, Foucault, J.L., Recueil des travaux scientifiques de Leon Foucault, Paris, pp.173-226, 517-518, 546-548, 1878.
135. Todd, D.P., see reference 125.
136. Michelson, A.A., Experimental Determination of the Velocity of Light, Proceedings of the American Association for the Advancement of Science, 27, 71-77, 1878. Also, Michelson, A.A., On a method of measuring the Velocity of Light, American Journal of Science, 15, series 3, 394-395, 1878.
137. Michelson, A.A., Experimental Determination of the Velocity Of Light, Astronomical Papers for the American Ephemeris and Nautical Almanac, Vol.1, Part 3, pp. 109-145, 1880. Relevant pages, 115-116.
138. de Bray, M.E.J.Gheury, The Velocity of Light, Nature, 120, 602-604, Oct. 22, 1927.
139. Michelson, A.A., Experimental Determination of the Velocity of Light, Proceedings of the American Association for the Advancement of Science, 28, 124-160, 1879. See also reference 137.
140. Michelson, A.A., Supplementary Measures of the Velocities Of White And Coloured Light in Air, Water, And Carbon Disulphide, Astronomical Papers for the American Ephemeris and Nautical Almanac, Vol.2, Part 4, pp.231-258, Relevant page 244, 1891.
141. Newcomb, S., see reference 116.
142. Michelson, A.A., Experimental Determination of the Velocity of Light, American Journal of Science, 18, series 3, 390-393, 1879.
143. Michelson, A.A., see reference 139.
144. Newcomb, S., see reference 116.
145. Michelson, A.A., see reference 140.
146. Michelson, A.A., Preliminary Experiments On The Velocity Of Light, Astrophysical Journal, 60, 256-261, 1924. See also reference 124.
147. Michelson, A.A., Measurement Of The Velocity Of Light Between Mount Wilson And Mount San Antonio, Astrophysical Journal, 65, 1-22, 1927. See p.2.
148. Birge, R.T., see reference 120.
149. Froome and Essen, reference 36, p.49.
150. Michelson, A.A., see reference 147.
151. Birge, R.T., see reference 120, P.94.
152. Michelson, A.A., Studies in Optics, p.136-137, Chicago University Press, 1927.
153. Anonymous, Encyclopaedia Britannica, Edition 14, Vol.239, pp.34-38, 1929.
154. Michelson, A.A., F.G.Pease, and F. Pearson, Measurement Of The Velocity Of Light In A Partial Vacuum, Astrophysical Journal, 82, 26-61, 1935.
155. Dorsey, N.E., op. cit., p.75.
156. Birge, R.T., reference 120, p.93.
157. Ibid, pp.96-97.
158. Karolus, A.,and O. Mittelstaedt, Die Bestimmung der Lichtgeschwindigkeit unter Verwendung des elektrooptischen Kerr-Effektes, Physikalische Zeitschrift, 29, 698-702, 1928.
159. Mittelstaedt, O., die Bestimmung der Lichtgeschwindigkeit unter Verwendung des elektrooptischen Kerreffektes, Annalen der Physiks, 2, series 5, 285-312, 1929. See also Mittelstaedt, reference 52.
160. de Bray, M.E.J.Gheury, The Velocity of Light, Isis, 25, 437-448, 1936.
161. Anderson, W.C., A Measurement of the Velocity of Light, Review of Scientific Instruments, 8, 239-247, July 1937.
162. Anderson, W.C., Final Measurements of the Velocity of Light, Journal of the Optical Society of America, 31, 187-197, Mar. 1941.
163. Huttel, A., Ein Methode zur Bestimmung der Lichtgeschwindigkeit unter Anwendung des Kerreffektes und einer Photozelle als phasenabhangigen Gleichrichter, Annalen der Physik, series 5, Vol.37, 365-402, 1940.
164. Dorsey, N.E., op. cit., pp.83-84.
165. Birge, R.T., reference 120, p.97.
166. Essen, L., and A.C. Gordon-Smith, The velocity of propogation of electro-magnetic waves derived from the resonant frequencies of a cylindrical cavity resonator, Proceedings of the Royal Society (London), A194, 348-361, 1948.
167. Aslakson, C.I., Velocity of Electromagnetic Waves, Nature, 164, 711-712, Oct. 22, 1949. Also, Aslakson, C.I., Can The Velocity of Propogation Of Radio Waves Be Measured By Shoran?, Transactions of the American Geophysical Union, 30, 475-487, Aug. 1949.
168. Bergstrand, L.E., Velocity Of light And Measurement Of Distances By High Frequency Light Signalling, Nature, 163, 338, Feb. 26, 1949. Also, Bergstrand, L.E., A preliminary determination of the velocity of light, Arkiv For Matematik Astronomi Och Fysik, A36, No.20, 1-11, 1949.
169. Essen, L., The velocity of propogation of electromagnetic waves derived from the resonant frequencies of a cylindrical cavity resonator, Proceedings of the Royal Society (London), A204, 260-277, 1950. Also, Essen, L., Velocity Of Light And Of Radio Waves, Nature, 165, 582-583, Apr. 15,1950. Also, Essen, L., Proposed New Value For The Velocity Of Light, Nature, 167, 258-259, Feb. 17, 1951.
170. Bol, K., A Determination of the Speed of Light by the Resonant Cavity Method, Physical Review, 80, 298, Oct. 15, 1950.
171. Bergstrand, L.E., Velocity of Light, Nature, 165, 405, Mar. 11, 1950. Also, Bergstrand, L.E., A determination of the velocity of light, Arkiv For Fysik, 2, 119-150, 1950.
172. Bergstrand, L.E., A check determination of the velocity of light, Arkiv For Fysik, 3, 479-490, 1951.
173. Aslakson, C.I., A New Measurement Of The Velocity Of Radio Waves, Nature, 168, 505-506, Sept. 22, 1951. Also, Aslakson, C.I., Some Aspects Of Electronic Surveying, Proceedings of the American Society of Civil Engineers, 77, Separate No. 52, pp.1-17, 1951. Also, Aslakson, C.I., New Determinations Of The Velocity Of Radio Waves, Transactions of the American Geophysical Union, 32, 813-821, Dec. 1951.
174. Froome, K.D., Determination of the velocity of short electromagnetic waves by interferometry, Proceedings of the Royal Society (London), A213, 123-141, 1952. Also, Froome, K.D., A New Determination of the Velocity of Electromagnetic Radiation by Microwave Interferometry, Nature, 169, 107-108, Jan. 19, 1952.
175. Bergstrand, L.E., Modern Determination Of The Velocity Of Light, Annales Francaises de Chronometrie, 11, 97-107, 1957.
176. Froome, K.D., Investigation of a new form of micro-wave interferometer for determining the velocity of electromagnetic waves, Proceedings of the Royal Society (London), A223, 195-215, 1954. Also, Froome, K.D., The refractive Indices of Water Vapour, Air, Oxygen, Nitrogen and Argon at 72 kMc/s, Proceedings of the Physical Society (London), B68, 833-835, 1955.
177. Florman, E.F., A Measurement of the Velocity of Propogation of Very-High-Frequency Radio Waves at the Surface of the Earth, Journal of Research of the National Bureau of Standards, 54, 335-345, 1955.
178. Scholdstrom, P., Determination of Light Velocity on the Oland Base Line 1955, Issued by AGA Ltd., Stockholm, 1955.
179. Plyler, E.K., L.R. Blaine, and W.S. Connor, Velocity of Light from the Molecular Constants of Carbon Monoxide, Journal of the Optical Society of America, 45, 102-106, Feb. 1955.
180. Wadley, T.L., The Tellurometer System Of Distance Measurement, Empire Survey Review, 14, 1957-1958. No.105, pp.100-111, July 1957. No.106, pp.146-160, Oct. 1957. No.107, pp.227-230, Jan. 1958.
181. Rank, D.H., H.E. Bennett and J.M. Bennett, Improved Value of the Velocity of Light Derived from a Band Spectrum Method, Physical Review, 100, 993, Nov. 15, 1955. Also, Rank, D.H., J.M. Bennett and H.E. Bennett, Measurement of Interferometric Secondary Wavelength Standards in the Near Infrared, Journal of the Optical Society of America, 46, 477-484, 1956.
182. Edge, R.C.A., New Determinations of the Velocity of Light, Nature, 177, 618-619, Mar. 31, 1956.
183. Froome, K.D., A new determination of the free-space velocity of electro-magnetic waves, Proceedings of the Royal Society (London), A247, 109-122, 1958.
184. Kolibayev, V.A., Determination Of The Velocity Of Light From Measurements With (Pulsed) Light Rangefinders On Control Bases, Geodesy and Aerophotography, No.3, p.228-230, translated for the American Geophysical Union, 1965.
185. Froome and Essen, see reference 36.
186. Taylor, B.N., W.H. Parker, D.N. Langenberg, Determination of e/h Using Macroscopic Quantum Phase Coherence in Superconductors: Implications for Quantum Electrodynamics and the Fundamental Physical Constants, Reviews of Modern Physics, 41 (3), 375-496, Jul. 1969.
187. DuMond, J.W.M., and E.R. Cohen, Least Squares Adjustment of the Atomic Constants, 1952, Reviews of Modern Physics, 25 (3), 691-708, Jul. 1953.
188. Froome and Essen, reference 36, p.73.
189. Ibid, p.122
190. Karolus, A., Fifth International Conference on Geodetic Measurement, 1965, Deutsche Geodetische Kommission, Munich, p.1, 1966.
191. Simkin, G.S., I.V. Lukin, S.V. Sikora and V.E. Strelenskii, Ismeritel'naya Tekhnika, 8, 92, 1967. Translation: New Measurements Of The Electromagnetic Wave Propagation Speed (Speed Of Light), Measures of Technology, 1967, 1018-1019.
192. Grosse, H., Geodimeter-2A-Messungen in Basisvergrosserungsnetzen, Nachrichten Karten-und-Vermessungwesen, Ser. I, 35, 93-106, 1967.
193. Bay, Z., G.G. Luther, J.A. White, Measurement of an Optical Frequency and the Speed of Light, Physical Review Letters, 29, 189-192, July 17, 1972.
194. Mulligan, J.F., Some Recent Determinations of the Velocity of Light III, American Journal of Physics, 44 (10), 960-969, Oct. 1976.
195. Evenson, K.M., et al., Speed of light from Direct Frequency and Wavelength Measurements of the Methane-Stabilised Laser, Physical Review Letters, 29, 1346-1349, Nov. 6, 1972. Also, Evenson, K.M., et al., Accurate frequencies of molecular transitions used in laser stabilization: Applied Physics Letters, 22, 192-195, Feb. 15, 1973.
196. Blaney, T.G., et al., Measurement of the speed of light, Nature, 251, 46, Sept.6, 1974.
197. Woods, P.T., K.C. Shotton, and W.R.C. Rowley, Frequency determination of visible laser light by interferometric comparison with upconverted CO2 laser radiation, Applied Optics, 17 (7), 1048-1054, Apr. 1, 1978.
198. Baird, K.M., D.S. Smith, and B.G. Whitford, Confirmation Of The Currently Accepted Value For The Speed Of Light, Optics Communications, 31 (3), 367-368, Dec. 1979.
199. Wilkie, T., Time to Remeasure the Metre, New Scientist, 100, No. 1381, 258-263, Oct. 27. Relevant page 260, 1983.
200. Froome and Essen, reference 36, p.127.
201. Mulligan, J.F., reference 194, pp. 967-968.
202. Kohlrausch, R., and W. Weber, Elektrodyn. Maasb., Bd III. p.221, Leipzig, 1857. Also, Kohlrausch, R., Poggendorf's Annalen, Vol. XCIX, p. 10, 1856, and Poggendorf's Annalen, Vol. CLVII, p.641, 1876.
203. Maxwell, J.C., On a method of making a direct comparison of electrostatic with electromagnetic force, Philosophical Transactions, 1868. Also British Association Report, 1869.
204. King, W.F., Description of the Sir W. Thomson's experiments for the determination of c, the number of electrostatic units in the electro-magnetic unit, British Association Report, p. 434, 1869.
205. McKichan, Determination of the number of electrostatic units in the electromagnetic unit, Philosophical Magazine, Vol. XLVII, p. 218. 1874.
206. Rowland, Hall, and Fletcher, On the ratio of the electrostatic to the electromagnetic unit of Electricity, Philosophical Magazine, 5th. series, Vol. XXVIII, p. 304, 1889.
207. Ayrton and Perry, Determination of the ratio of the electromagnetic to the electrostatic unit of electric quantity, Philosophical Magazine, 5th series, Vol.VII, p. 277, 1879.
208. Hockin, Note on the capacity of a certain condenser and on the value of c, British Association Report, p. 285, 1879.
209. Shida, R., On the number of electrostatic units in the electromagnetic unit, Philosophical Magazine, Vol. X, p. 431, 1880.
210. Stoletov, Sur une methode pour determiner le rapport des unites electromagnetiques et electrostatiques, Journal de Physique, p. 468, 1881.
211.Exner, Bestimmung des Verhaltnisses... Sitz. Ber. Wien, Vol. LXXXVI, 1882, and also Exner's Repertorium, Vol. XIX, p. 99.
212.Details from Froome and Essen, reference 36, p. 11.
213. Klemencic, I., Untersuchungen etc., Sitz. Ber. Wien, Vol. LXXXIX, 1884. Also, Sitz. Ber. Wien, Vol. XCIII, p. 470, 1886.
214. Colley, Ueber einige neue Methoden zur Beobachtung electrischer Schwingungen und einige Anwendungen derselben, Wiedemann's Annalen, Vol. XXVIII, p. 1, 1886.
215. Himstedt, Ueber eine Bestimmung der Grosse c, Wiedemann's Annalen, Vol. XXIX, p. 560, 1887. Also, Ueber eine neue Bestimmung der Grosse c, Wiedemann's Annalen, Vol. XXXIII, p. 1, 1888. Again, Ueber die Bestimmung der Capacitat eines Schutzringcondensators in absolutem electromagnet-ischem Masse, Wiedemann's Annalen, Vol. XXXV, p. 126, 1888.
216.Thomson, Ayrton and Perry, Electrometric determination of c, Electrical Review, Vol. XXIII, p. 337, 1888-1889
217. Rosa, Determination of c, the ratio of the electromagnetic to the electrostatic unit, Philosophical Magazine, Vol. XXVIII, p. 315, 1889.
218. Thomson, J.J., and G.F.C. Searle, A determination of the ratio of the electromagnetic unit of electricity to the electrostatic unit, Philosophical Transactions, p.583, 1890.
219. Pellat, Determination du rapport entre l'unite electromagnetique et l'unite electrostatique d'electricite, Journal de Physique, Vol. X, p. 389, 1891.
220. Abraham, H., Sur une nouvelle determination du rapport c entre les unites electromagnetiques et electrostatiques, Annales de Chimie et de Physique, Vol. XXVII, p. 433, 1892.
221. Hurmuzescu, Nouvelle determination du rapport c entre les unites electrostatiques et electromagnetiques, Annales de Chimie et de Physique, Vol. X, p. 433, 1897.
222. Perot and Fabry, Electrometre absolu pour petites differences de potentiel, Annales de Chimie et de Physique, Vol. XIII, p. 404, 1898.
223. Webster, A.G., An experimental determination of the period of electrical oscillation, Physical Review, Vol. VI, p.297, 1898.
224. Lodge and Glazebrook, Discharge of an air condenser, with a determination of c, Stokes Commemoration, p. 136, Cambridge 1899. Also, Transactions of the Cambridge Philosophical Society, Vol. XVIII.
225. Rosa, E.B., and N.E. Dorsey, Bulletin of the U.S. Bureau of Standards, 3, p. 433, 1907.
226. Froome and Essen, reference 36, p. 10 and statement p. 48 c.f. Abraham's data, reference 43, shows a uniform correction as stated.
227. Blondlot, R., Comptes Rendus, Vol. XCIII, p.628, 1891. Also, Journal de Physique, series 2, Vol. X, p. 549, December 1891.
228. Blondlot, R., Comptes Rendus. Vol. CXVII, p. 543. Also, Annales de Chimie et de Physique, series 7, Vol. VII, April 1896.
229. Trowbridge and Duane, Philosophical Magazine, series 5, Vol. XL, p.211, 1895.
230. Saunders, C.A., Physical Review, Vol. IV, p.81, 1897.
231. MacLean, Philospohical Magazine, series 5. Vol. XLVIII, p.117, 1899.
232. Mercier, J., Ann. Phys. Series 9, Vol. 19, p. 248, 1923, Vol. 20, p.5, 1923. Also, J. Phys. Radium, (6), Vol.5, p.168, 1924.
233. Millikan, R.A., On The Elementary Electrical Charge And The Avogadro Constant, Physical Review, 2, 109-143, 1913.
234. Millikan, R.A., A new Determination of e, N, and Related Constants, Philosophical Magazine, 34 (6), 1-30, July 1917.
235. Millikan, R.A., Electrons (+ and -), Protons, Photons, Neutrons, and Cosmic Rays, p.121, 242, University of Chicago, 1934.
236. Wadlund, A.P.R., Absolute X-Ray Wave-Length Measurements, Physical Review, 32, 841-849, Dec. 1928.
237. Backlin, E., Absolute Wellenlangenbestimmungen der Rontgenstrahlen, Uppsala Dissertation, 1928.
238. Birge, R.T., Probable Values of the Physical Constants, Reviews of Modern Physics, 1, 1-73, 1929.
239. Bearden, J.A., Absolute Wavelengths of the Copper and Chromium K-Series, Physical Review, 37, 1210-1229, May 15, 1931.
240. Soderman, Absolute Value of the X-Unit, Nature, 135, 67, Jan. 12, 1935.
241. Backlin, E., Absolute Wellenlangenbestimmung der Al Ka Linie nach der Plangittermethode, Zeitschrift fur Physik, 93, 450-463, Feb. 7, 1935.
242. Bearden, J.A., The Scale of X-Ray Wavelengths, Physical Review, 47, 883-884, June 1, 1935.
243. DuMond, J.W.M., and V.L. Bollman, Tests of the Validity of X-Ray Crystal Methods of Determining e, Physical Review, 50, 524-537, Sept. 15, 1936.
244. Birge, R.T., Interrelationships of e, h/e and e/m, Nature, 137, 187, Feb. 1, 1936.
245. DuMond, J.W.M., and V.L. Bollman, A Determination of h/e f1rom the Short Wave-Length Limit of the Continuous X-ray Spectrum. Physical Review, 51. 400-429, Mar. 15, 1937.
246. Backlin, E. and H. Flemberg, The Oil Drop Method and the Electronic Charge, Nature, 137, 655-656, Apr. 18, 1936.
247. Ishida, Y., I. Fukushima and T. Suetsuga, On the Redetermination of the Elementary Charge by the Oil Drop Method, Institute of Physical and Chemical Research, Tokyo, Scientific Papers, 32, 57-77, June 10, 1937.
248. Dunnington, F.G., The Atomic Constants, Reviews of Modern Physics, 11 (2), 65-83, Apr. 1939.
249. Bollman, V.L., and J.W.M. DuMond, Further Tests of the Validity of X-Ray Crystal Methods of Determining e, Physical Review, 54, 1005-1010, Dec. 15, 1938.
250. Birge, R.T., The Values of e, e/m, h/e and a, Physical Review, 58, 658-659. Oct.1, 1940.
251. Miller, P.H., and J.W.M. DuMond, Tests for the Validity of the X-Ray Crystal Method for Determining N and e with Aluminium, Silver and Quartz, Physical Review, 57, 198-206, Feb.1, 1940.
252. DuMond, J.W.M., A Complete Isometric Consistency Chart for the Natural Constants e, m and h, Physical Review, 58, 457-466, Sept. 1, 1940.
253. Hopper, V.D., and T.H. Laby, The electronic charge, Proceedings of the Royal Society (London), A178 (974), 243-272, July 31, 1941.
254. Birge, R.T., A New Table of Values of the General Physical Constants, Reviews of Modern Physics, 13 (4), 233-239, Oct. 1941.
255. Birge, R.T., The 1944 Values of Certain Atomic Constants with Particular Reference to the Electronic Charge, American Journal of Physics, 13 (2), 63-73, Apr. 1945.
256. DuMond, J.W.M., and E.R. Cohen, Our Knowledge of the Atomic Constants F, N, m and h in 1947, and of Other Constants Derivable Therefrom, Reviews of Modern Physics, 20 (1), 82-108, Jan. 1948.
257. DuMond, J.W.M., and E.R. Cohen, Erratum: Our Knowledge of the Atomic Constants F, N, m and h in 1947 and Other Constants Derivable Therefrom, Reviews of Modern Physics, 21 (4). 651-652, Oct. 1949.
258. Bearden, J.A., and H.M. Watts, A Re-Evaluation of the Fundamental Atomic Constants, Physical Review, 81, 73-81, Jan. 1, 1951.
259. DuMond, J.W.M., and E.R. Cohen, Least Squares Adjustment of the Atomic Constants, 1952, Reviews of Modern Physics, 25 (3), 691-708, Jul. 1953.
260. Cohen, E.R., et al., Analysis of Variance of the 1952 Data on the Atomic Constants and a New Adjustment, 1955, Reviews of Modern Physics, 27 (4), 363-380, Oct. 1955.
261. Cohen, E.R., and J.W.M. DuMond, Present Status of our Knowledge of the Numerical Values of the Fundamental Constants, p.152-186, Proceedings of the Second International Conference on Nuclidic Masses, Vienna, Austria, July 15-19, 1963, W.H. Johnson, Jr., editor, Springer-Verlag, Wien, 1964.
262. Cohen, E.R., and J.W.M. DuMond, Our Knowledge of the Fundamental Constants of Physics and Chemistry in 1965, Reviews of Modern Physics, 37 (4), 537-594, Oct. 1965.
263. Taylor, B.N., W.H. Parker, D.N. Langenberg, Determination of e/h Using Macroscopic Quantum Phase Coherence in Superconductors: Implications for Quantum Electrodynamics and the Fundamental Physical Constants, Reviews of Modern Physics, 41 (3), 375-496, Jul. 1969.
264. Cohen, E.R., and B.N. Taylor, The 1973 Least-Squares Adjustment of the Fundamental Constants, Journal of Physical and Chemical Reference Data, 2 (4), 663-718, 1973.
265. Martin, S.L., and A.K. Connor, Basic Physics, Vol. 1-3, p.893, Whitcombe Tombs, Melbourne, 8th edition, 2nd printing. No date given - about 1955 to 1960. Initial report before refinement appeared in Thomson, J.J., Cathode Rays, Philoaophical Magazine, 44, 293-316, 1897.
266. Paschen, F., Bohrs Heliumlinien, Annalen der Physik, 50, series 4, 901-940, 1916.
267. Babcock, H.D., A Determination Of e/m From Measurements Of The Zeeman Effect, Astrophysical Journal, 58, 149-163, 1923.
268. Wolf, F., Eine Prazisionsmessung von e/m0 nach der Methode von H. Busch, Annalen der Physik, 83, series 4, 849-883, 1927.
269. Houston, W.V., A Spectroscopic Determination Of e/m, Physical Review, 30, 608-613, Nov. 1927.
270. Babcock, H.D., Revision Of The Value Of e/m Derived From Measurements Of The Zeeman Effect, Astrophysical Journal, 69, 43-48, 1929.
271. Perry, C.T., and E.L. Chaffee, A Determination Of e/m For An Electron By Direct Measurement Of The Velocity Of Cathode Rays, Physical Review, 36, 904-918, Sept. 1, 1930.
272. Campbell, J.S., and W.V. Houston, A Revision of Values of e/m from the Zeeman Effect, Physical Review, 38, 581, Aug. 1, 1931.
273. Dunnington, F.G., Determination of e/m for an Electron by a New Deflection Method, Physical Review, 42, 734-736, Dec. 1, 1932.
274. Kirchner, F., Zur Bestimmung der spezifischen Ladung des Elektrons aus Geschwindigkeitsmessungen, Annalen der Physik, 12, series 5, 503-508, 1932.
275. Kinsler, L.E., and W.V. Houston, Zeeman Effect in Helium, Physical Review, 46, 533-534, Sept. 15, 1934.
276. Shane, C.D., and F.H. Spedding, A Spectroscopic Determination of e/m, Physical Review, 47, 33-37, Jan. 1, 1935.
277. Houston, W.V., A New Method of Analysis of the Structure of Ha and Da, Physical Review, 51, 446-449, 1937.
278. Dunnigton, F.G., A Determination of e/m for an Electron by a New Deflection Method II, Physical Review, 52, 475-501, Sept. 1, 1937.
279. Williams, R. C., Determination of e/m from the Ha - Da Interval, Physical Review, 54, 568-572, Oct. 15, 1938.
280.Shaw, A.E., A New Precision method for the Determination of e/m for Electrons, Physical Review, 54, 193-209, Aug. 1, 1938.
281. Bearden, J.A., A Determination of e/m from the Refraction of X-Rays in a Diamond Prism, Physical Review, 54, 698-704, Nov. 1, 1938.
282. Chu, D.Y., The Fine Structure of the Line l 4686 of Ionised Helium, Physical Review, 55, 175-180, Jan.15, 1939.
283. Robinson, C.F., The Fine Structure of Hydrogen Isotopes, Physical Review, 55, 423, Feb. 15, 1939.
284. Goedicke, E., Eine Neubestimmung der spezifischen Ladung des Elektrons nach der Methode von H. Busch, Annalen der Physik, series 5, Vol.36, 47-63, 1939.
285. Drinkwater, J.W., O. Richardson, and W.E. Williams, Determinations of the Rydberg constants, e / m, and the fine structures of Ha and Da by means of a reflexion echelon, Proceedings of the Royal Society, A174, 164-188, 1940.
286. Gardner, J.H., Measurement of the Magnetic Moment of the Proton in Bohr Magnetons, Physical Review, 83, 996-1004, Sept. 1, 1951.
287. Birge, R.T., The Values of R and of e/m, from the Spectra of H, D and He+, Physical Review, 60, 766-785, Dec. 1, 1941.
288. Duane, W., H.H. Palmer and C-S. Yeh, A Remeasurement Of The Radiation Constant, h, By Means Of X-Rays, Journal of the Optical Society of America, 5, 376-387, July 1921.
289. Lawrence, E.O., The Ionization Of Atoms By Electron Impact, Physical Review, 28, 947-961, Nov. 1926.
290. Lukirsky, P., and S. Prilezaev, Uber den normalen Photoeffekt, Zeitschrift fur Physik, 49, 236-258, June 14, 1928.
291. Feder, H., Beitrag zur h-Bestimmung, Annalen der Physik, 1. series 5. 497-512, 1929.
292. Olpin, A.R., Method of enhancing the Sensitiveness of Alkali Metal Photoelectric Cells, Physical Review, 36, 251-295, July 15, 1930.
293. Van Atta, L.C., Excitation Probabilities For Electrons In Helium, Neon, And Argon, Physical Review, 38, 876-887, Sept. 1, 1931.
294. Kirkpatrick, P., and P.A. Ross, Confirmation of Crystal Wave-Length Measurements and Determination of h/e, Physical Review, 45, 454-460, Apr. 1, 1934.
295. Whiddington, R., and E.G. Woodroofe, Energy Losses of Electrons in Helium, Neon, and Argon, Philosophical Magazine, 20, 1109-1120, 1935.
296. Schaitberger, G., Ein Beitrag zur h-Bestimmung, Annalen der Physik, 24, series 5, 84-98, 1935.
297. Wensel, H.T., International Temperature Scale And Some Related Physical Constants, National Bureau of Standards, Journal of Research 22, 375-395, April 1939.
298. Ohlin, P., The Smallest 'Quantum' Of Energy, Science, 98, Supp. 10, Dec. 3, 1943.
299. Schwarz, and J.A. Bearden, Bulletin of the American Physical Society, May 1-3, 1941.
300. Panofsky, W.K.H., A.F.S.Green, and J.W.M. DuMond, A Precision Determination of h/e by Means of the Short Wave-Length Limit of the Continuous X-ray Spectrum at 20 kv, Physical Review, 62, 214-228, Sept. 1 and 15, 1942.
301. Bearden, J.A., F.T. Johnson, and H.M. Watts, A New Evaluation of h/e by X-Rays, Physical Review, 81, 70-72, Jan. 1, 1951.
302. Felt, G.L., J.N. Harris, and J.W.M. DuMond, A Precision Measurement At 24500 Volts Of The Conversion Constant, Physical Review, 92, 1160-1175, Dec. 1, 1953.
303. See DuMond, J.W.M., reference 252, p. 465.
304. Rydberg, J.R., On the Structure of the Line-Spectra of the Chemical Elements, Philosophical Magazine, 29, 331-337, 1890.
305. Crowther, J.A., Ions, Electrons and Ionising Radiations, p.272, 274, Longmans, New York, 1936.
306. Birge, R.T., The Balmer Series Of Hydrogen, And The Quantum Theory Of Line Spectra, Physical Review, 17, 589-607, 1921.
307. Cohen, E.R., The Rydberg Constant and the Atomic Mass of the Electron, Physical Review, 88, 353-360, Oct. 15, 1952.
308. Csillag, L., Investigation On The Fine Structure Of Six Lines Of The Balmer-Series Of Deuterium, Physics Letters, 20, 645-646, Apr. 1, 1966.
309. Hansch, T.W., et al., Precision Measurement of the Rydberg Constant by Saturation Spectroscopy of the Balmer a Line in Hydrogen and Deuterium, Physical Review Letters, 32, 1336-1340, June 17, 1974.
310. Weber, E.W., and J.E.M. Goldsmith, Double-Quantum Saturation Spectroscopy In Hydrogen, Physical Review Letters, 41, 940-944, Oct. 2, 1978.
311. Petley, B.W., K. Morris, and R.E. Shawyer, A saturated absorption spectroscopy measurement of the Rydberg constant, Journal of Physics B: Atomic and Molecular Physics, 13, 3099-3108, 1980.
312. Amin, S.R., C.D. Caldwell, and W. Lichten, Crossed-Beam Spectroscopy of Hydrogen: A New Value for the Rydberg Constant, Physical Review Letters, 47, 1234-1238, Nov.2, 1981.
313. Hansch, T.W., Spectroscopy, Quantum Electrodynamics, and Elementary Particles, Precision Measurement and Fundamental Constants II, p. 111-115, B.N. Taylor and W.D. Phillips, editors, Natl. Bur. Stand. (U.S.), Spec. Publ. 617, 1984.
314. Thomas, H.A., R.L. Driscoll, and J.A. Hipple, Measurement of the Proton Moment in Absolute units, Physical Review, 78, 787-790, June 15, 1950.
315. Wilhelmy, W., Eine Neubestimmung des gyromagnetischen Verhaltnisses des Protons, Annalen der Physik, 19, series 6, 329-343, 1957.
316. Driscoll, R.L., and P.L. Bender, Proton Gyromagnetic Ratio, Physical Review Letters, 1, 413-414, Dec.1, 1958.
317. Yanovskii, B.M., N.V. Studentsov and T.N. Tikhomirova, Ismeritel'naya Tekhnika 2, 39, 1959, (Translation: Measurement Of The Gyromagnetic Ratio Of A Proton In A Weak Magnetic Field, Measures of Technology, 1959, 126-128).
318. Capptuller, H., Bestimmung des gyromagnetischen Verhaltnisses des Protons, Zeitschrift fur Instrumentenkunde, 69, 191-198, July 1961.
319. Vigoreaux, P., A determination of the gyromagnetic ratio of the proton, Proceedings of the Royal Society (London), A270, 72-89, 1962.
320. Yagola, G.K., V.I. Zingerman, and V.N. Sepetyi, Ismeritel'naya Tekhnika, 5, 24-29, 1962. (Translation: Determination Of The Gyromagnetic Ratio Of Protons, Measures of Technology, 1962, 387-0393).
321. Yanovskii, B.M., and N.V. Studentsov, Ismeritel'naya Tekhnika, 6, 28-31, June 1962, (Translation: Determining The Gyromagnetic Ratio Of A Proton By The Gamma Method Of Free Nuclear Induction, Measures of Technology, 1962, 482-486).
322. Driscoll, R.L., and P.T. Olsen, report to Comite Consultatif d'Electricite, Comite International des Poids et Mesures, 12th Session, Oct. 1968.
323. Yagola, G.K., V.I. Zingerman, and V.N. Sepetyi, Ismeritel'naya Tekhnika, 7, 44, 1966. (Translation: Determination Of The Precise Value Of The Proton Gyromagnetic Ratio In Strong Magnetic Fields, Measures of Technology, 1967, 914-917).
324. Hara, K., H. Nakamura, T. Sakai and N. Koizumi, Report to the Comite Consultatif d'Electricite, Comite International des Poids et Mesures, 11th Session, 1968.
325. Studentsov, N.V., T.N. Malyarevskaya, and V.Ya. Shifrin, Ismeritel'naya Tekhnika, 11, 29, 1968. (Translation: Measurement Of The Proton Gyromagnetic Ratio In A Weak Magnetic Field, Measures of Technology, 1968, 1483-1485).
326. Olsen, P.T., and R.L. Driscoll, Atomic Masses and Fundamental Constants 4, p.471, J.H. Sanders and A.H. Wapstra, editors, Plenum Publishing Corp., New York, 1972.
327. Olsen, P.T., and E.R. Williams, Atomic Masses and Fundamental Constants 5, p.538, J.H.Sanders and A.H. Wapstra, editors, Plenum Publishing Corp., New York, 1976.
328. Wang, Z., The Development of Precision Measurement and Fundamental Constants in China, Precision Measurements and Fundamental Constants II, p.505-508, B.N. Taylor and W.D. Phillips, Eds., National Bureau of Standards (U.S.) Special Publication 617, 1984.
329. Vigoreaux, P., and N. Dupuy, National Physical Laboratories, Report DES44, 1978.
330. Kibble, B.P., and G.J. Hunt, A Measurement of the Gyromagnetic Ratio of the Proton in a Strong Magnetic Field, Metrologia, 15, 5, 1979.
331. Williams, E.R., and P.T. Olsen, New Measurement of the Proton Gyromagnetic Ratio and a Derived Value of the Fine-Structure Constant Accurate to a Part in 107, Physical Review Letters, 42, 1575-1579, June 11, 1979.
332. Chiao, W., R. Liu, and P. Shen, The Absolute Measurement of the Ampere by Means of NMR, IEEE Transactions on Instrumentation and Measurement, IM-29, 238-242, 1980.
333. Schlesok, W., Progress in the Realization of Electrical Units at the Board for Standardization, Metrology, and Goods Testing (ASMW), IEEE Transactions on Instrumentation and Measurement, IM-29, 248-250, 1980.
334. Tarbeyev, Y.V., The Work Done at the Mendeleyev Research Institute of Metrology (VNIIM) to Improve the Values of the Fundamental Constants, Precision Measurements and Fundamental Constants II, p.483-488, B.N. Taylor and W.D. Phillips, editors, National Bureau of Standards (US) Special Publication 617, 1984.
335. Taylor et. al. reference 263, pp. 407-415.
336. Williams, E.R., P.T. Olsen, and W.D. Phillips, The Proton Gyromagnetic Ratio in H2O - A problem in Dimensional Metrology, Precision Measurement and Fundamental Constants II, p.497-503, B.N. Taylor and W.D. Phillips editors, National Bureau of Standards (U.S.) Special Publication 617, 1984.
337. Rutherford, E., Radioactivity, p. 326, Cambridge University Press, 1904.
338. Soddy, F., Radioactivity: An etementry treatise from the standpoint of the disintegration theory, p. 147, 'The Electron' Printing and Publishing Co., London, 1904.
339. Rutherford, E., Radioactive Substances and their Radiations, pp.24-25, Cambridge University Press, 1913
340.Curie, M., et. al., The Radioactive Constants as of 1930, Reviews of Modern Physics, 3, 427-445, 1931.
341. Rutherford, E., J. Chadwick and C.D. Ellis, Radiations from Radioactive Substances, pp.24-27, Cambridge University Press, 1930.
342. Crowther, J.A., see reference 305, pp.328-329.
343. Seaborg, G.T., Table of Isotopes, Reviews of Modern Physics, 16, 1-32, Jan. 1944.
344. Glasstone, S., Sourcebook on Atomic Energy, pp.125-127, 1st Edition, Macmillan, London, 1950
345. Strominger, D., J.M. Hollander, and G.T. Seaborg, Table of Isotopes, Reviews of Modern Physics, 30, 585, 1958.
346. U.S. Navy, Basic Nuclear Physics, p.104, United States Bureau of Naval Personnel, Washington D.C., 1958.
347. Korsunsky, M., The Atomic Nucleus, p. 52-54, 220, Foreign Language Publishing House, Moscow, 1958.
348. Gregory, J.N., The World of Radio Isotopes, 12-17, 26, Angus and Robertson in association with the Australian Atomic Energy Commission, Sydney, 1966.
349. Goldman, D., Chart of Nuclides, 8th edition, Revised March 1965, quoted by Wehr, M.R., J.A. Richards and T.W. Adair III, in Physics of the Atom, Appendix 5 and 6 pp.499-505, 3rd edition, Addison Welsey, Reading, Mass., U.S.A., 1978.
350. Lederer, C. and V. Shirley, Table of Isotopes, 7th edition, Wiley, New York, 1978.
351. Friedlander, G., et al. Nuclear and Radiochemistry, 3rd Edition, Wiley, New York, 1981.
352. Cavendish, H., Philosophical Transactions, 83, p.388, 1798. Also W.A. Heiskanen and F.A. Vening Meinesz, 'The Earth and Its Gravity Field', p.155, McGraw-Hill, New York, 1958.
353. de Boer, H., Experiments Relating to the Newtonian Gravitational Constant, Precision Measurement and Fundamental Constants II, p.565, B.N. Taylor and W.D. Phillips (editors), National Bureau of Standards (U.S.) Special Publication 617, 1984.
354. Cohen, E.R., and J.W.M. DuMond op. cit. (see Reference 33), p.16.
355. Cook, A.H., Experimental Determination of the Constant of Gravitation, Precision Measurement and Fundamental Constants, p.475, D.N. Langenberg and B.N. Taylor (editors), National Bureau of Standards (U.S.) Special Publication 343, August 1971.
356. Heiskanen, W.A. and F.A. Vening Meinesz, op. cit., p.155.
357. Cohen, E.R., and B.N. Taylor, op. cit., (see Reference 58), p.699.
358. Stacey, F.D., and G.J. Tuck, Non-Newtonian Gravity: Geophysical Evidence, Precision Measurement and Fundamental Constants II, p.597-600, B.N. Taylor and W.D. Phillips (editors), National Bureau of Standards (U.S.) Special Publication 617, 1984.
359. Luther, G.G., and W.R. Towler, Redetermination of the Newtonian Gravitational Constant 'G', Precision Measurement and Fundamental Constants II, p.573-576, B.N. Taylor and W.D. Phillips (editors), National Bureau Of Standards (U.S.) Special Publication 617, 1984.
360. de Bray, M.E.J. Gheury, Astronomiche Nachrichten, 230 (5520), pp.449-454, (1927). Bull. Soc. Astron. France (l'Astronomie), 40. p.113 (1926), and 41, pp.380-382, 504-509, (1927). Ciel et Terre, 47, pp.110-124, (1931). Nature, 127, pp.522, 739-740, 892, (1931), and 133, pp.464, 948-949, (1934), and 144, pp.285, 945, (1939). Isis, 25, pp.437-448, (1936). Editorial and other notes on this topic: Ciel et Terre, 43, pp.189, 222, (1927). Nature, 120, p.594, (1927), 129, p.573, (1932), 138, p.681, (1936).
Anderson, W.C., Jour. Opt. Soc. Am., 31, pp.187-197, (1941).
Birge, R.T., Nature, 134, pp.771-772, (1934).
Edmondson, F.K., Nature, 133, p.759-760, (1934).
Gramatzki, H.J., Zeits. f. Astrophysik, 8, pp.87-95, (1934).
Kennedy, R.J., Nature, 130, p.277, (1932).
Kitchener, Nature, 144, p.945, (1939).
Machiels, A., Zeits. f. Astrophysik, 9, pp.329-330, (1935).
Maurer, H., Physik. Zeitschr., 30, p.464, (1929).
Mittelstaedt, O., Physik. Zeitschr., 30, pp.165-167, (1929)
Omer, G.C. Jr., Astrophys. J., 84, pp.477-478, (1936), Nature, 138, P.587, (1936).
Salet, P., Bull. Soc. Astron. France (l'Astronomie), 41, p.206, (1927).
Smith, A.B., Science, 93, p.475, (1941).
Takeuchi, T., Zeits. f. Phys., 69, pp.857-858, (1931). Proc. Phys. Math. Soc. Japan, 13, p.178, (1931).
Vrkljan, V.S., Zeits. f. Phys., 63, pp.688-691, (1930). Nature, 127, p.892, (1931). Nature, 128, pp.269- 270, (1931).
Wilson, O.C., Nature, 130, p.25, (1932).
The proposal of physical constants varying with cosmic time was proposed by Dirac in a form somewhat different to that presented here. However many of the consequences were similar. The comments of Kovalevsky are pertinent.
Dirac, P.A.M., Nature, 139, p.323, (1937). Proc. Roy. Soc. (London), A165, pp.199-208, (1938). Proc. Roy. Soc. (London), A333, pp.403-418, (1973). Proc. Roy. Soc. (London), A338, pp.439-446, (1974). Nature, 254, p.273, (1975).
Kovalevsky, J., Metrologia, 1, No.4, pp.169-180, (1965)
361. French, A.P., 'Principles of Modern Physics', pp.40-41, Wiley, New York, 1959. Also Fowles, G.R., 'Introduction To Modern Optics', pp.216-217, Holt, Rinehart and Winston, New York, 1968.
362. French, op. cit., p.41. Also, Jenkins, F.A., and H.E. White, 'Fundamentals Of Optics', third edition, pp.481-482, McGraw-Hill, New York, 1957.
363. Ditchburn, R.W., 'Light', second edition, pp.36-37. Blackie, 1963.
364. Hoyle, F., 'Frontiers Of Astronomy', p.139, Heinemann Ltd., London, 1956.
365. Swihart, T.L., 'Physics of Stellar Interiors', p.82, Pachart Publishing House, Tucson, Arizona, U.S.A., 1972.
366. French, op. cit., p.75. Also Birge, R.T., Probable Values of the Physical Constants, Reviews of Modern Physics, 1, p.61, 1929.
367. French, op. cit., p.20, 84.
368. Kittel, C., and H. Kroemer, 'Thermal Physics', second edition, p.402, W.H. Freeman and Co., San Francisco, 1980.
369. Jaroff, L., A Star of Another Colour, summarising Nature article in Time, p.72, December 2, 1985.
370. Anonymous, Ancient Chinese suggest Betelgeuse is a young star, New Scientist, p.238, October 22, 1981, quoting Fang Li-zhi in Chinese Astronomy and Astrophysics, Vol. 5, p.1, 1981.
371. Margon, B., The Origin of the Cosmic X-ray Background, Scientific American, Vol. 248, No.1, pp.104-119, January 1983.
372. Narlikar, J., Was There a Big Bang?, New Scientist. Vol 91, pp.19-21, 1981. Also quoted in Science Frontiers, No.17, Fall 1981.
373. Anonymous, Cosmic Background Not So Perfect, New Scientist, Vol.92, p.23, 1981. Also quoted in Science Frontiers, No.18, Nov.-Dec. 1981.
374. Audouze, J., and G. Israel, editors, Cambridge Atlas of Astronomy, p.382, Cambridge University Press, 1985.
375. Landsberg, P.T., and D.A. Evans, 'Mathematical Cosmology', p.93-94, Oxford University Press, 1979.
376. Ibid, p.69.
377. Pearson, T.J., et al., Superluminal expansion of quasar 3C273, Nature, Vol.290, pp.365-368, also p.363, April 2, 1981. Many recent examples.
APPENDIX I: NON-TECHNICAL SUMMARY
Time and its measurement has an important place in our lives. To the scientist, time is one of three basic quantities, the others being mass and distance. These three quantities allow physicists to describe anything in the cosmos. If time is doing something unexpected, our view of the universe may be faulty. We are all familiar with the 'pips' that give the exact time from our radio stations. When we hear them, we usually check our watches in order to make sure they are keeping 'correct' time as dictated by the pips. In so doing, we implicitly assume that those pips are keeping time without variation. In this situation, we have two methods of measuring time. There is the standard given by the pips, and there are our watches. We all know that our watches are less reliable than the standard and that they require periodic correction if that standard is to be maintained by them.
In like fashion, there are two basic clocks by which cosmic time is usually measured. The first we are well familiar with. It goes by the name of DYNAMICAL TIME. The basic unit of dynamical time is the period it takes the earth to go once around the sun. Subdivisions of this period give us hours, minutes, days, seconds and so on. If we say that I a person is 35 years old, we mean that the individual concerned has been on this planet for 35 of its orbits around the sun. This is time we are all accustomed to. A moment's thought makes it apparent that dynamical time is governed by gravitation. The earth's orbital process is the result of the sun's gravitational pull. Dynamical time is thus a gravitational clock.
The second clock is used in a variety of ways, but has one basic feature common to all: the atom and atomic behavior. This ATOMIC CLOCK is used to measure the age of the rocks, the fossils, the moon, the stars and the universe itself. There is an actual timepiece called the caesium clock which ticks away this atomic standard. Until 1967, all our time was regulated by the dynamical clock. Since then, atomic time has been gradually introduced world-wide using the caesium clock.
An atom can be thought of as a miniature solar system. There is the central nucleus made up of protons and neutrons in tight motion about each other similar to a multiple sun system such as the star Castor. Then the electrons move about this central nucleus like planets around a star. The intervals on the atomic clock are defined as the period taken for one revolution of an electron around the nucleus of an ordinary hydrogen atom.
CLOCKS THAT DON'T KEEP TIME
Just as the time kept by our wrist watches seems to drift against the standard kept by the 'pips', so also there seems to be a variation between the two cosmic timepieces. From 1955 until 1981, Dr. Thomas Van Flandern of the U.S. Naval Observatory in Washington measured by an atomic clock the time taken for the moon to complete its orbit around the earth. The moon in its orbit is keeping dynamical time since it is a form of gravitational clock. One method of checking its orbital period is by occultation, that is when the moon passes in front of a distant star.
Looking at the results of these measurements, Van Flandern concluded that the atomic clock was slowing down relative to the dynamical standard. In other words, there were fewer and fewer ticks of the atomic clock in the time it took the moon to orbit the earth once. Van Flandern was not sure which clock was the one that was varying. It is at this point that the report to which this Appendix is attached comes into focus. Not only does it solve the dilemma, it also completely reinforces Van Flandern's conclusion.
THE ATOM AND LIGHT
If atomic time is drifting against the dynamical standard, then other atomic quantities measured in dynamical time should also show the effect. It makes no difference which clock is in fact varying, the observed result will be the same. The quantities to look at will be those that bear units involving time. One of the prime candidates is the speed of light. All light comes from atomic processes, and the speed of light is measured in kilometers per second. Note the time-tag on this physical quantity.
Now the atom will act in a completely consistent way if the usual laws of conservation are valid. In other words, the atom will not be able to detect any change within itself as all of its processes are geared to each other. It is only as we look at atomic processes from outside, in dynamical time, that any change will be noted. We then have to check to see if it is atomic phenomena or gravitational processes that are changing. In either scenario it can be shown that theory will agree with observation only if distances (one of the three basic quantities) remain unaffected.
Seen from outside the atom, dynamically, an atomic second will get longer if the atomic clock is slowing down. This means that there were more atomic seconds in a dynamical interval in the past. Now in one atomic second, light will always travel the same distance. Therefore, more atomic seconds in a dynamical interval means that light will have traveled further. Consequently, if atomic processes were faster in the past, the speed of light would have been faster. This provides a useful cross-check on atomic behavior. The speed of light is usually given the shorthand symbol of 'c'.
THE SPEED OF LIGHT OBSERVATIONS
There have been 16 different methods for measuring the speed of light, c. A brief summary of how those methods worked can be found in the main report under the relevant headings. When each method is taken individually, the measured values show a decay in c with time. When all 163 values are taken together, they still reveal a decay in c. However, it is desirable to use only the best data. Accordingly, those values which had been rejected by the experimenters themselves, or their fellow scientists, were set aside, along with those values which had a large margin of error. The 57 best possible data points that were left still show a decay in c with time. The drop is something like 1500 kilometers per second over a period of 300 years. These refined data are listed in 11, and illustrated in the Figures II, III, and IV.
All date in this report are treated uniformly. Firstly, all the readily available data have been tabulated. Those data regarded as unreliable by the experimenters themselves, or their peers, have been noted and the reasons listed. We often use these rejected data, but they are omitted from our refined analysis. Any trend in the data is discovered by a mathematical procedure called a 'least squares linear fit'. This means that a straight line is put through the data in the optimum position having due regard to all the observations. If the line is horizontal, there is no variation with time and the quantity will be considered a true constant. If the line slopes, the data is taken to indicate some systematic trend with time.
A further check is applied to discover how significant these trends are. There is the correlation coefficient, r, which indicates how well the line fits the data points. Values of r range between 0 and 1. If all points lie on the line then r = 1, no matter whether the line is sloping or horizontal. A value for r above 0.8 is often accepted as indicating a good fit to the data. Confidence intervals, expressed as a percentage, are then applied to the data trend and the linear fit. It is customary to acknowledge that the result should be taken seriously if the confidence interval lies in the 90% to 100% range.
Using these procedures indicates that c does decay with time, and that the decay does have a formal statistical significance. This suggests that the speed of light was indeed higher in the past, and that atomic processes were faster as Van Flandern indicated. Light from distant galaxies thus took less time in transit as atomic processes and light speed are inextricably linked. This means that if the atomic clock has registered an age of, say, 10 billion years for the universe, then light will have traveled a distance of 10 billion light years in that atomic period. However, the dynamical clock could have registered a completely different age. No matter what dynamical age is appropriate, this result means that light could have got back from those parts of the universe 10 billion light years away in that appropriate dynamical interval. Note in passing that some claim the evidence suggests an atomic age for the universe of 15 or 20 billion years. In this case, the values in the above examples would be adjusted accordingly.
RELATIVITY AND LIGHT
A changing c scenario bothers some people because of Einstein's use of c in relativity theory. However, it can be shown that relativity is still valid with changing c. Some physicists have proposed an approach that deduces relativity without light entering the argument at all. Others have shown that changes are possible in the physical quantities involved in the equations provided that the effects are mutually canceling. This approach is shown to be valid and one example appears in the next section.
OTHER ATOMIC QUANTITIES
If the trend indicated by Van Flandern's observations and the decaying speed of light is genuine, then other atomic quantities that have a time-tag on them should also show the effect. This is the third leg of the tripod of evidence. The first leg involved observations on an astronomical scale in which Van Flandern recently highlighted the problem. In the second leg, the observations of c on an intermediate scale over the last 300 years also indicated an atomic slow-down. Finally, there is this third leg in which the microcosmic world of the atom itself is explored.
In all, we have considered about 25 different methods by which these various atomic quantities have been measured. Their treatment statistically was the same as for the c data. A united testimony emerges. Those quantities with the time tag 'per second', as c had, all displayed a statistically significant decay with time, like c. Those quantities that had the units of 'seconds', like Planck's constant (h erg-seconds), would be expected to move in the opposite way and increase with time. Again, in each instance a statistically significant increase in the measured value has been recorded.
AN ATOMIC CROSS-CHECK
An interesting cross-check can then be made. There are some atomic quantities that combine both those values that are decreasing, like c, with those that are increasing, like Planck's constant, h. The ratio hc should in fact be absolutely constant as all the time terms cancel out. This is despite the fact that the individual parts making up the quantity have been measured as varying. When hc is measured over the lifetime of the universe, by examining the most distant astronomical objects, the testimony is that it is an absolute constant. The same is found for all those similar quantities containing mutually canceling time-dependent parts. Note that if only one of those mutually canceling parts, like c, was varying, and the other, like h, was not, then hc would not be measured as being constant. We would then suspect that our theoretical approach was in error, that atomic processes may be unchanging with time, and that some other effect was causing c to decay.
Instead of that, those atomic quantities with mutually canceling time-dependent terms show a stability, a constancy, in some cases to over six figures since measurements began. In other cases there is a small random fluctuation about some fixed value. This behavior should be emulated by c and those other time-dependent quantities if they were indeed true constants. This is not observed. The conclusion is that the atom itself is, in fact, registering a slow-down in its processes, and the third leg of the tripod of evidence is in place. There is thus a united testimony from three levels of measurement to the validity of this effect.
Tables 23 and 24 summarize the statistical treatment on all atomic quantities. From Table 24, it becomes apparent that the best data show a completely concordant slow-down in all relevant quantities, including c, over dynamical time. The size of the change for each quantity is virtually the same. In other words atomic processes are indeed acting in unison with c and each other as the slow-down occurs. Furthermore, in each case the slope of the best fit straight line through the data points lessens with time. That is to say the line becomes more and more horizontal. This indicates that the atomic slow-down is best described by a curve of lessening gradient as in figures III and IV rather than the sloping straight line of Figure II. As a consequence, it would seem that the further back in the past we go, the more quickly the atomic clock ticked. It therefore registers a systematically old date when compared with the dynamical standard.
RADIOACTIVE DECAY AND STARS
All forms of dating by the atomic clock are subject to this effect. This includes radiometric dating whether it be the uranium/lead, thorium/lead, lead/lead, rubidium/strontium, potassium/argon, carbon 14 or any other. The rate at which a radioactive element decays from, say, uranium to lead or from potassium to argon, is dependent upon how fast the atomic clock ticks. In Table 19, the decay rates of two-thirds of the main naturally occurring radioactive elements indicate a slowing atomic clock, despite improved measurement techniques which tend to reverse the trend. Since the radioactive elements are absolutely tied to the atomic clock, they, like the speed of light, will register an atomic age for the cosmos of, say, 10 billion years no matter what age is recorded by the dynamical clock.
Despite more rapid radioactive decay in the past, proportional to c, the equations demand that the actual intensity of radiation be proportional to 1/c. For example, if the speed of light was 10 times its present value at some stage in the past, then radioactive decay would have occurred 10 times more quickly. However, although 10 times as much radioactive decay was occurring in a given interval, the intensity of radiation from each decaying atom was only 1/10th of today's value. Accordingly, the total observed intensity would only be the same as today's level. In a word, radioactive decay was far safer and much less of a problem in the past with higher c than it is today.
A similar situation occurs with regard to the dating given by the ages of stars since stars burn their fuel a process related to radioactive decay. Thus stars go through their life cycle more rapidly with higher values for c. Hand in hand with this faster aging process, proportional to c, goes a radiation intensity proportional to 1/c. Therefore, even though the amount of light coming from a star was proportionally greater, this was exactly offset by the fact that its intensity was lower. Consequently, net observed light intensities were unchanged, with solar and planetary temperatures unaffected.
A CHOICE IS NEEDED.
Experimental measurements thus support the conclusion that atomic time is slowing against dynamical time. The question now arises whether it may not in fact be dynamical time that is varying. If this were the case, it would mean that atomic intervals were constant and that dynamical time was speeding up, with shorter and shorter intervals. The earth would thus be going faster and faster around the sun and also spinning faster on its axis. In either case, whether the variation is atomic or dynamical, the result remains unchanged, namely that atomic time registers as systematically old against the dynamical standard which we are all used to.
The difficulty is fairly readily resolved, however. It can be demonstrated that gravitational phenomena are completely independent of any changes in the atom or c. In other words, if the atom is varying, the dynamical clock is not affected. Furthermore, the physical behavior of the gravitational constant, G, would be in contradiction to conservation laws and theory if the atom were not changing. Thirdly, things tend to slow down, wear out, and get older, rather than speed up and go faster with time as a dynamical variation would require. Dynamical variation would seem to break this physical principle which is called the 2nd law of Thermodynamics. In addition, if c decay is taken as causing the atomic changes rather than the other way round, the dynamical clocks are not affected at all. Each scenario conspires to indicate varying atomic processes and constant dynamical ones.
We begin to get to the basic reason for all the observed variations if we consider atomic changes and c decay both as symptoms instead of being the root cause of the trouble. However, the observations require every atom to tick in unison throughout the cosmos and for all light to behave uniformly. This united slowing of atomic clocks and decaying light speed indicates that the properties of free space must be altering, like the magnetic permeability. Relativity points out that these properties are controlled by what is called the cosmological constant, L. Furthermore, for conservation to be valid, L, must be proportional to c2. We can therefore write a L equivalent for c in our equations. Atomic processes and c are consequently under the control of L as a decay in L means a decay in c and slowing atomic clocks. However, L not only governs the properties of space, it also manipulates the behavior of the universe, so the atomic slow-down warns us of cosmic changes.
THE BEHAVIOR OF THE UNIVERSE
We are all familiar with the force that exists in a stretched rubber-band tending to snap it back to its minimum position. The cosmological constant, L, acts in precisely the same way. Perhaps it would be more accurate to consider an expanded balloon which has the same force acting to restore it to its smallest size. That is roughly a picture of the universe. The cosmos expanded to its maximum size extremely rapidly in the process scientists call the 'Big Bang'. Following that event, L has been acting in such a way as to deflate the cosmological balloon. At its maximum extension, the rubber in the balloon is thinnest, and thickest when collapsed. In a like manner, we may consider the fabric of space to become 'thicker' with time under the action of L. Put scientifically, the permeability, or energy density of free space, has increased, and the metric properties of space have changed. This slows both light and the atomic clocks uniformly.
A rubber band, or balloon under the action of such a force will begin to follow a special form of behavior. This behavior is more complete when a weight on the end of a spring is set in motion. It is called simple harmonic motion. The force acting within the spring plays a similar role to L. At the maximum extension of the spring the force is at a maximum, while the spring in its rest position has the minimum force exercised. The magnitude of the force is thus given by the extension. In like manner, L was greatest when the universe was at its maximum size and became less as the cosmos collapsed. There are a set of equations that describe the behavior of L under these circumstances. To give it the full title, the behavior is that of an exponentially damped sinusoid. The curve for L is a typical example of this. Since c is related to L, it is possible to test this approach by fitting a related curve to the c data. The test is passed as a result. The details of equations are given on page 7, and the curve fit to the c data is illustrated in Figure IV.
The concept of a collapsing universe seems to be at variance with popular notions of an expanding cosmos. However, the reason for believing that the universe is expanding actually turns out to be evidence for a decay in the speed of light! By way of explanation, we are all familiar with the wail of a police siren and the manner in which the siren's pitch drops once it has passed us. Light behaves in a similar way to sound. If an object is coming towards us and emitting light, the 'pitch' of that light is higher than normal. If it is receding from us the 'pitch' of the light drops, just like that of the siren. More correctly, we should say that for recession, the wavelength of light is increased, or moves towards the red end of the rainbow spectrum. As we look at the light from distant galaxies, we find that it is shifted towards the red end by progressively greater amounts for increasingly more distant objects. This effect is called the red-shift. It has usually, though not always, been interpreted as indicating that the distant galaxies are moving away from us and that the universe is expanding.
Some controversy has surrounded this interpretation of late, however, and a variety of alternatives explored. The decay in c offers a valid mechanism for the effect. Most are familiar with the wave-like properties of light. The distance from the crest or trough of any wave to the mid-point is called the amplitude. Some wave energy is locked up for light in the wave amplitude. The equations demand that, for a decay in c, the amplitude energy increases. That means the crests must go higher and the troughs get deeper as c decays. This is also the reason that radiation intensities increase. However, for energy to be conserved with light in transit, the wave amplitudes must grow at the expense of the wavelength. Energy is therefore taken from the wavelength which gets longer or redder, since longer wavelengths have less energy. As c decays, a red shift will consequently occur in light from distant objects. The further away those objects are, the more c has decayed and the greater will be the resultant red-shift. Far from indicating an expanding universe, the red-shift gives evidence for slowing c and atomic processes.
QUASARS AND THE MAXIMUM VALUE FOR C
The red-shift may also supply details as to the upper maximum value that c attained. Coming uniformly from every direction in space are the two background radiations, one in the X-ray region of the spectrum, the other in the microwave portion. It is customary to attribute the microwave background to the 'echo of the Big Bang'. However some like Narlikar dispute this contention. He pointed out that the microwave background looked very similar to light from stars, galaxies, or other celestial objects that had simply been red-shifted. It was back in 1983 that Bruce Margon, Professor of Astronomy at the University of Washington, noted that the two backgrounds had a great deal in common and that one behaved very much as the other. The only difference he noted was that the microwave differed from the x-ray by a wavelength factor of ten million. This being the case, we get a value for c virtually at the time of the Big Bang of about 10 million times c now. Since we know that the universe is say 10 to 15 billion years old in atomic time, this value of 10 million times c now allows us to put in an important origin point on the c decay graph. This origin point is thus determined by observation, given the validity of the proposal by Margon. The c data tie in the points down this end of the curve, and the form of the decay is fixed by generally accepted theory. This allows some confidence to be placed in the final result.
It also supplies a possible answer to one of the problems associated with quasars. They are the most distant astronomical objects on the red-shift data and are hyperactive, ultra-luminous centers of galaxies. The source of this intense activity has been somewhat conjectural. However it is safe to say that with a higher value for c in the past, the stars in the centers of all galaxies, (the 'old' or Population II stars) would go through their life cycle much more rapidly. Many stars end their life in a spectacular outburst called a supernova which produces as much light as 100 million normal stars. The end product also results in vast X-ray emission. With a life cycle that was shortened by higher c, there would be many stars going through a supernova process at any one time and X-ray emission would be intense. This would enhance the X-ray producing process of any black holes at galactic centers. The reason for the X-ray background may therefore have been tracked down as well as a possible explanation for the quasar ultra-luminosity.
THE CURRENT STATE OF THE COSMOS
The quasars supplying the microwave background would appear to be virtually at rest after the Big Bang expansion and before the collapse set in. As the collapse started, the red-shift would be partly offset as any motion towards an observer produces the reverse effect (or blue shift). Between the microwave and the X-ray backgrounds would be a relatively small region of space where the red-shift factor dropped from 10 million down to the quasar value of about 2. That region of space represents the area where the action of L built up the contraction speed of the cosmos to its terminal velocity This would make it difficult to find quasars in that region and to date only relatively few objects are known beyond red-shift 3. This rapidly dropping red-shift over a small distance means that few objects are involved. It also means that there is no effective background radiation in the wavelengths from X-rays to microwaves. Apart from the microwave background, then, the observed red-shift is a net result of c decay coupled with universal contraction
The c data curve indicates that cosmological contraction is virtually at a minimum. This is deduced by the fact that the decay pattern has tapered off to a nearly zero rate of change as evidenced by Table 24. Consequently, one is permitted to speculate as to what will happen next. The form of the decay curve for c or L both allow two possibilities. The exponentially damped motion could taper to a zero rate of change quite quickly and stay there. This is suggested by the Table 24 results. Alternatively, it is also possible that once the minimum is reached, the motion could slowly climb back to a slightly higher equilibrium point. This suggests that, perhaps, a slight universal re-expansion may occur, though it will be a small effect over some time. This option is supported by some values of the relevant constants that were published in 1986 and a value for h in 1987. Before it can be definitely decided, all data must show a consistent trend. Future monitoring of the situation is therefore absolutely essential.
When all the best-fit date curves are extrapolated back in atomic time, they each show essentially the same features. This family of curves is illustrated in Figure V. From them, the collapse in the run rate of the atomic clock appears to have started roughly 600 million years ago in atomic time. Up until then the run rate followed a slightly sloping straight line. The rollover to the collapse seems to have been complete about 50 million years ago atomically and the final steep linear collapse set in. These dates correspond to important events in the fossil record. It was about 600 million years ago on the atomic clock that the Cambrian fossils recorded a burst of life geologically. It was also about 50 million years ago, atomically, that the present geological era, the Cenozoic, commenced with its mammal dominance. This report has dealt mainly with physics and astronomy. In the second report, it is hoped to demonstrate that c decay has supplied the mechanism guiding natural selection into some of the changes recorded by these fossils and explore other implications in astronomy, geology and biology.
CLICK HERE TO SEE FIGURE V
This report was converted and formatted in HTML by Derek Miller (firstname.lastname@example.org)
May 10, 1999. March 8, 2003. Greek letters are in Symbol font and may not be correctly rendered by all browsers. Corrections, May 14, 1999, August 19, 1999.