FOREWORD

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
SRI International
August 1987

 

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INDEX

ABSTRACT.

I. INTRODUCTION.

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.
(B). Gravitation.
(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.

VII. CONSEQUENCES.
(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.

REFERENCES

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.
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.

 

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ABSTRACT:-

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 + e^kt(b + dt). This is verified by the c data curve fits.

 

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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.

 

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THE ATOMIC CONSTANTS, LIGHT, AND TIME

I. INTRODUCTION:-

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 + e^kt(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).

 

TABLE A
 
 

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
 
 

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).

 

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TABLE 2 - RESULTS OF BRADLEY'S OBSERVATIONS
 
 

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.

 

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(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:

TABLE B
 
 

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
 
 

Whittaker¹⁰¹, Kulikov¹⁰⁷, suggest K = 20.511: c is then above c(now) for most values.

 

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CLICK HERE TO SEE FIGURE I

TABLE 4 - TOOTH WHEEL EXPERIMENTAL VALUES
 
 

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.
11. Perrotin¹³¹.
12. Perrotin's¹³² mean of the 1900.4 and 1902.4 determinations.
13. Perrotin¹³³.
14. Prim's¹³⁰ analysis of the 1902.4 determination after Perrotin's death.

 

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(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
 
 

* 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.

 

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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
 
 

* 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.

 

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TABLE 8 - RESULTS 1960-1983 - MAINLY LASER
 
 

1. Modulated light. Baseline error corrected 1967 (see Froome and Essen²⁰⁰).
2. Microwave interferometer.
3. Geodimeter.
4-11. Laser methods. Discussion in Mulligan²⁰¹.
6. Result corrected for new definition by Blaney et. al.¹⁹⁶.

 

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TABLE 7 - RESULTS* BY SIX METHODS 1945-1960
 
 

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

 

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* 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.

 

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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.

TABLE C
 
 

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
 
 

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).

 

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TABLE 10 - C VALUES BY WAVES ON WIRES
 
 

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).

 

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(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)