Mass and Energy
Setterfield: I appreciate the problem that you have with your "homework"! Forgive me for being so hard on you! However, if nothing else, it might have given you some appreciation as to how your students fell about the matter! Since particle momentum [p = mc] where [m] is particle mass and [c] is light-speed, and as [mc2] is a constant so that [m] is proportional to [1/(c2)], then it follows that [p] is indeed proportional to [1/c]. In other words, your conclusion that [pc] is conserved is correct.
However, you have not followed through so well on the DeBroglie wavelengths [W] of matter. The relationship is indeed [W = h/(mc) = h/p]. Now it has just been shown above that [p = mc] is proportional to [1/c]. Furthermore, Planck's constant [h] is also proportional to [1/c] so that hc is an absolute constant throughout the cosmos. This is something that has been observationally verified. Therefore with both [h] and [p] being proportional to [1/c], it follows that [h/p = W] will be a constant. Your additional comment about light waves and other waves being affected as a consequence is also out of order. You might recall that experiments done while light was measured as dropping revealed that wavelengths were NOT affected by the process, which is why the frequency must vary with c, and not wavelengths.
In your concluding section that was in parentheses, you suggest there was a huge missing mass problem as every neutrino or atomic particle was so much less massive back in the early days of our Cosmos. This turns out not to be the case, however, as the gravitational constant [G] is changing in such a way that [Gm = constant]. This also means that gravitational acceleration [g] and hence weight will be unaffected by the process. Note too that in all orbit equations the second mass (that of the orbiting body) appears on both sides of the equation and so cancels out leaving only the [Gm] term.
Therefore, planetary orbits will not be affected by variable light speed. Then there was a final cluster of questions relating to momenta of light waves, the Poynting vector, the solar constant and energy impinging on earth from the sun etc. First, as you pointed out the momentum [p] of a light wave is equal to [J/c] where [J] is the intensity. (Note that I have changed your [I] to [J] to avoid confusion of similar letters.) For light in transit where [c] is dropping, this means that the momentum of a photon at reception will be greater than that at emission. But as that effect is happening for every other light wave of given intensity [J], including those in our laboratories, nothing out of the ordinary will be noticed.
This leads on to the second matter relating to the Poynting vector. The Poynting vector [S] is equal to the energy density [U] of the electromagnetic wave multiplied by [c]. Thus we write [S = Uc]. However, the value of [U] is determined by the magnetic permeability and electric permittivity of free space. Now since both the permeability and permittivity of free space are proportional to [1/c], it can be shown that [U] is also proportional to [1/c]. Therefore, for light in transit, [Uc = constant = S]. I would ask you to note here that the most recent work has confirmed that BOTH the permittivity AND the permeability of space must be changing, unlike the approach in the 1987 Report which had only the permeability varying. Finally, there is the matter of the output of energy by the sun and stars, and radioactive sources. The Redshift paper undergoing review at the moment points out that when c was higher, the emitted radiation energy densities were lower as shown by the behaviour of [U] above. In addition, the radiation was comprised of photons whose energy was also intrinsically lower (that is redshifted compared with today's laboratory standard). When these effects are taken into account, radiation from radioactive sources, and the output of energy from the sun and stars is more prolific now than it was then. The mathematical details are in Behavior of the Zero Point Energy and Atomic Constants, in appendix 2. You will find other answers in General Relativity and the Zero Point Energy and Quantized Redshift and the Zero Point Energy.
Setterfield: It appears as if I did not make a key point as plain as I would have liked in my previous response. Let me reiterate what it was that I said. "...the gravitational constant [G] is changing in such a way that [Gm = constant]. This means that the gravitational acceleration [g] and hence weight will be unaffected by the process. Note too that in all orbit equations the secondary mass (that of the orbiting body) appears on both sides of the equation and so cancels out leaving only the [Gm] term. Therefore planetary orbits will not be affected by the cDK process. ..." This is not only the case for planetary orbits, but stellar orbits as well. Therefore you have correctly deduced that [Gm] is in fact a constant. A full treatment of this is given in General Relativity and the Zero Point Energy as well as in Behavior of the Zero Point Energy and Atomic Constants, in appendix 2 rather than the 1987 Report, although the [G] data set appears there. Note that as [Gm] occurs in our equations as a single entity, no variation in [G] and [m] separately can be found by gravitational dependent methods. The other matters that Ron raised were all on the basis of a constant [G]. Since this is not the scenario being presented, those problems essentially disappear with [Gm = constant]. (May 14, 1999)
Setterfield: The issue of lightspeed and Einstein's equation
is one which is coming to the forefront of consideration by physicists
as a result of some evidence that lightspeed was much faster in
the early days of the cosmos. In fact, no less than 50 scientific
papers dealing with the topic have been accepted for publication
by scientific journals in 2002 alone. In most cases, there has
merely been tinkering around the edges of the problem. The work
that I have been engaged in has a slightly different answer to
the problem. In a changing c scenario, the energy, E is held constant
in E = mc2 which means that atomic masses, m, vary
as 1/c2. There is experimental evidence for this increase
in atomic mass with time. However, there is a second string attached.
Experimental evidence also indicates that the way masses behave
on an atomic scale is different to the way mass behaves macroscopically.
In fact the evidence suggests that while atomic masses are proportional
to 1/c2, mass as measured on a macroscopic scale is
total energy related and so is constant at all times. Thus Einstein's
equation only applies to the atomic environment, where all the
reactions occur to which it has been applied. As for your second
question, it is correct that we have atomic clocks that can be
calibrated with very small divisions, like nanoseconds or billionths
of a second. You suggest that we should then be able to determine
any change in lightspeed fairly easily. Unfortunately the atomic
clock defeats us here, because the atomic clock ticks at a rate
proportional to lightspeed. Thus, in the atomic realm, lightspeed
is effectively constant. Therefore atomic clocks cannot be used
to detect any change in lightspeed. So while the atomic clocks
allow us to measure extremely small divisions of time, their run-rate
is variable. In that sense, they are like a cheap nasty watch
from a supermarket that does not keep good time, even though they
have been calibrated with very small divisions of time. This matter
also has experimental evidence supporting it. In 1984, Dr. Tom
Van Flandern, of the US Naval Observatory in Washington noted
after examining the run-rate of atomic clocks compared with the
orbital clock (the time it takes the earth to go round the sun
or the moon arouind the earth) that the atomic clock was slowing
compared with the orbital standard. This is in line with the effect
of the slowing speed of light on atomic clocks. Finally, the changes
occurring in lightspeed can be monitored by other indirect means
which give us a feel for how it is behaving.
Setterfield: You ask a very interesting question, which impinges on the nature of mass and energy. I refer you to an article in New Scientist by Marcus Chown on 3 Feb. 2001, pp.22-25 which may assist you. So also will the link: http://www.calphysics.org/questions.html where some relevant matters are discussed in the questions and answers segment, particularly page 5.
Allow me to introduce you to some modern thinking on a section of this matter. It is generally agreed among physicists that matter is made up of massless point particles. The problem for physics has been to account for where the thing we call mass is coming from. There have been a number of attempts to resolve this matter - one recent one being the Higgs boson which is meant to "stick' to particles and impart mass to it - with the particle's mass depending on the amount of 'stickiness'.
Another approach has been from the properties of the vacuum, and this is giving consistent results. On this view, the massless particles (point charges such as quarks and electrons) making up matter are 'jiggled' about the the electromagnetic waves that make up the zero-point energy (ZPE)of the quantum vacuum. As these waves impinge on the particle, it jitters about at speeds very close to, or equal to, the velocity of light, c.
This 'jitter motion', or "Zitterbewegung" as it is named, imparts a kinetic energy to the particle. Since kinetic energy is given by (1/2)mv2, and since the velocity v at which the particle moves is equal to the speed of light, c, then the energy E from this process is given by mc2. (In a strict analysis using the ZPE the factor of 1/2 disappears.) It is for this reason that c enters the discussion, as it is the velocity at which the particle is moving back and forth. We then attach the concept of mass to the conversion constant, m, between the energy of the particle and the speed at which it moves.
In summarising this, the team of physicists at CIPA have this to say. "The kinetic energy associated with the ZPE-driven Zitterbewegung is what provides the energy for the E = mc2 relation. The real stuff is the energy, E, and ... it is only our (obstinate) habit of believing that matter must possess mass that leads to our insisting that there must exist a right hand side to this equation, namely mc2. In reality (perhaps) there is no mass, just the energy, E, that the quantum vacuum gives in the form of Zitterbewegung ... In a sense this does away for the need for a veritably magical transmutation of energy into matter or matter into energy. In this view, we never get energy by destroying matter. We get energy by liberating some or all of the kinetic energy that the quantum vacuum puts into the Zitterbewegung of what are really massless quarks and electrons."
I trust that this helps. (13 March, 2003)
Setterfield: This concerns relativity and how this affects the debate on changing c values. Back in the early part of the 20th century when both lightspeed changes and relativity were being discussed, the validity of relativity was considered important. It was for that reason that some did not accept the idea of c variation. Nevertheless, several items appeared in the scientific literature that seemed to overcome the objections that had been raised. Some of those articles are cited in the 1987 Report on The Atomic Constants, Light and Time available on our website. More recently, it has been shown by several different articles that the action of the Zero Point Energy will account for all the predictions of General Relativity without the necessity of relativistic concepts. See for example my paper on “General Relativity and the Zero Point Energy” which can be accessed from our website. In this case, since the effects of relativity can be accounted for by the ZPE, which at the same time is giving rise to the variation in lightspeed, there is no contradiction between the two proposals.
Setterfield: The radiometric dates for the two main types of
stars are involved. This shows that radioactive decay was there
at the beginning, and consequently so was nuclear burning. This
is backed up by observations at the frontiers of the cosmos and
the associated redshift. The two are cross-linked. The rate of
burning was higher when lightspeed was higher, but so also was
the opacity or opaqueness of the star. This trapped the light
in and the various types of star can be accounted for by this
process. The outcome is that the output of light from any given
star is independent on light-speed. The high value for lightspeed
during Creation Week gave the stars the physical characteristics
we see today by this light "injection" process. This
has been explained more fully in A
Brief Stellar History.
Setterfield: A question has been asked about the behaviour of the energy E of emitted photons of wavelength W and frequency f during their transit across space. The key formulae involved are E = hf = hc/W. The following discussion concentrates on the behaviour of individual terms in these equations.
If c does indeed vary, inevitably
some atomic constants must change, but which? Our theories should
be governed by the observational evidence. This evidence has been
supplied by 20th century physics and astronomy. One key observation
that directs the discussion was noted by R. T. Birge in Nature 134:771, 1934. At that time c was measured as declining, but there
were no changes noted in the wavelengths of light in apparatus
that should detect it. Birge commented: "If the value of
c is actually changing with time, but the value of [wavelength]
in terms of the standard metre shows no corresponding change,
then it necessarily follows that the value of every atomic frequency
must be changing." This follows since light speed, c, equals
frequency, f, multiplied by wavelength W. That is to say c = fW. If wavelengths W are unchanged in this process, then frequencies
f must be proportional to c.
Setterfield: The first thing is that the energy of emitted photons as they travel through the universe stays steady; that does not change. Their speed slows down due to the change from potential to kinetic energy of the fabric of space itself. When this happens, more virtual particles are in existence at any given time and this is exactly the same as asking a runner to jump more hurdles in a given distance. The light maintains its energy, but its slowing is due to the fact that any virtual particle in its way will absorb and then re-emit it. All this takes time. Very little time, granted, but time nevertheless. This is why light is slowing. It is not a matter of lost energy.
I would suggest you read Helen’s laymen's summary .
Setterfield: Thank you for your note. You ask about the formula describing the relationship between c and radioactive decay. This is described in detail in Atomic Constants, Light and Time, starting about where I linked.
You then stated you have a problem understanding Einstein’s equation, maintaining energy constant with changing c. You ask how mass (m) can change. Mass in this equation refers only to atomic mass, not step-on-the-scale mass. Atomic mass is measured differently and its increase can be seen in the chart here, with the references underneath.
Atomic masses are dependant upon the strength of the Zero Point Energy. According to most physicists, matter is made up of charged point particles (such as electrons and quarks) that are without mass as you and I think of mass. Many physicists try to impart mass to these charged point particles by using the Higgs boson, while others point out that the same effect can be achieved by the impacting electromagnetic waves of the Zero Point Energy (the ZPE). If we consider this second alternative, which is easier to visualize, these waves jiggle the point particles at relativistic speeds -- that is speeds at, or very close to, the speed of light, c. This ‘jiggling’ motion imparts an energy to the particles which appears as mass, in accord with Einstein’s relation.
Now the data indicate that the strength of the Zero Point Energy has increased with time. You will see evidence of this in the measurements of Planck’s constant, h, which is the middle chart on the above page linked. Planck’s constant itself is a direct measure of the strength of the ZPE. The measured increase in h shown by the graph thereby indicates that the strength of the ZPE has increased with time. But several things happen as the strength of the ZPE increases. First, as we have noted, Planck’s constant h increases because the number of waves of all wavelengths of the ZPE increase proportionally. Second, the speed of light, c, drops in inverse proportion to h. This means that the charged point particles are moving more slowly in response to each impact because they, too, move at the speed of light, c, the speed of the impacting electromagnetic waves. Third, the diameter of each point particle increases as the ZPE strength increases. This occurs because, as Boyer commented, “the quantum zero-point force also expands the sphere” [MacGregor, “The Enigmatic Electron,” p. 28, Dordrecht: Kluwer, 1992.]. A stronger ZPE will therefore expand the sphere of the charge that makes up the point-like entity of the electron or quark.
But this is not all. Equations show that the particle’s mass is dependent not only on h and c, but also on the oscillating particle’s damping constant. This can be considered in the same way that there is a damping constant for a ball-bearing that is oscillating on the end of a long vertical spring and immersed in a pot of oil. If that oil was replaced by a more viscous oil, or perhaps honey or treacle, the damping constant of the system would increase. Similarly, an increase in the strength of the ZPE is equivalent to increasing the viscosity of the vacuum. Since the strength of the ZPE and the size of the damping constant are two of the key factors that determine the mass of the point particle, the simultaneous increase in both these factors means that the mass of the atomic particle measured in the atomic environment will also increase.
An alternative way of looking at this is to consider again the ball-bearing and spring system with the oil. The same effect on that system would occur if the viscosity of the oil remained unchanged, but the diameter of the ball-bearing increased, thereby increasing its mass. The damping constant would then increase also, since the rate of oscillation would be slower. From the point of view of the system, then, the slower oscillation and the increase in diameter of the oscillating object implies that the mass of the object has increased since a larger diameter of the same material implies greater mass. From the point of view of the atomic environment, the mass of the point particle has increased because (1) its diameter is greater; (2) it oscillates more slowly and (3) the damping constant has increased.
You may wonder why the mass of particles in an atomic environment differs from mass-on-the-scales. There is some evidence for this. Here is a quote from an article by Raymond Birge, in his article "Probable Values of the Physical Constants" as published in Review of Modern Physics, vol. 1, 1929 p. 48. Is this too old? Don't worry, the same problem was found by Dicke in the American Journal of Physics, vol 28 no. 4, pp 344-347, 1960. There has been more discussion in physics journals about this 'problem' continuing. Here is Birge's account:
Other work indicates that mass measured macroscopically such as those in deflection experiments, depends on the total energy of the system which remains unchanged as the ZPE increases, whereas the mass measured in an atomic environment is dependent upon the strength of the ZPE.
Setterfield: Thank you for your note.
Concerning your two questions: They are both dealing with the concept of mass and energy. You quote Einstein’s equation E=mc2 as the basis for the discussion. And then you give an example of a penny (or coin), its mass and its energy on the basis of that equation. It is at this point that a correction needs to be made.
In 1929, Professor R.T. Birge pointed out that the rest mass of an electron as measured in the atomic environment was considerably different from the rest mass as measured by mass spectrometers in a macroscopic environment. He commented, “The figures thus point to the startling conclusion that the e/m of an electron is less when it is inside an atom than when it is outside. If this conclusion seems unacceptable, then it would appear that there is some general error in the equations of the quantum theory of atomic structure.” (R.T. Birge in Reports in Progress on Physics, vol. 1 No. 1 pp 47-48)
In 1960, the same problem was still evident. Professor R.H. Dicke pointed out in an article in the American Journal of Physics that there is a difference between the inertial mass of atomic nuclei and the mass of the same nuclei measured in an atomic environment using E=mc2. This led Dicke and Brans to formulate a theory of gravity which, for a while, rivaled that of general relativity. His theory was ultimately disproved on the basis of a prediction which was not fulfilled, but the discrepancy which he noted in the data remained.
More recently, Audi and Wapstra, in 1995, noted a continuing discrepancy in the masses of atomic nuclei when measured by inertial means compared with the nuclei of the same elements measured in the atomic environment using E=mc2. This is discussed briefly in Nuclear Physics A, vol 595, pp 413-415, in the major article entitled “The 1995 update to the atomic mass evaluation.”
It is becoming apparent that masses measured macroscopically via inertia are showing different results than when measured atomically. This appears to be a consistent trend over the last 70 years or so. Since, as Dicke points out, “the inertial mass is given by the energy of the system”, it seems that macroscopic, or inertial, means of measurement are measuring a quantity that is related to the total energy of the system. An examination of the relevant equations using the ZPE/lightspeed approach shows that this quantity will remain constant. By contrast, atomic measurements of mass are measuring mass in terms of Einstein’s equation which, in some instances, is called the Q value mass.
It seems, then, that macroscopically, we’re measuring a different quantity as mass than we are atomically. Because macroscopic measurements are measuring the total energy of the system, this would not be the ‘m’ in Einstein’s equation, but would involve more than that. It is actually a measurement of E. And since E stays constant, we would not expect any change here. This means that macroscopically, mass remains unchanged. However, when measured in the atomic environment, the quantity ‘m’ in Einstein’s equation has been shown as varying, and in such a way that the total energy of the system remains constant with a change in light speed. Thus ‘m’ in the atomic environment varies as 1/c2. This can be seen on the graphs – scroll down to the last of the three graphs. The references for these measurements are posted below it.
In other words, the mass of the kilogram bar in Paris or the mass of a coin or the mass of the earth itself will remain unchanged under changing light speed conditions. This matter is going to be the subject of a paper which is currently in progress.
[in response to a discussion going on in an email group, this response was submitted to them and we thought it would clarify some matters here as well]
It is indeed correct to say that Einstein's Special Relativity requires the speed of light to be the same for different observers, regardless of their velocity. However, it is also correct to say that Relativity does not preclude a change in the universal speed of light over time. All that Einsteinian Relativity requires is that there be an upper maximum speed limit in the universe. Just recently, another development occurred in this matter. New Scientist for 1 November, 2008, contained a lead article entitled Shedding Light which discussed the research of Mitchell Feigenbaum from Rockerfeller University, New York. He has developed a version of Relativity which precludes the necessity for the speed of light to enter the discussion at all. All that this version of Relativity requires is that there be an upper maximum velocity in the universe, with no specification as to what that velocity is. It is usually assumed that this is the current speed of light, but nothing in the theory demands that, as the article is at pains to point out.
There is another aspect to this which is related to the vacuum Zero Point Energy (ZPE). A variety of data suggest that the ZPE has varied with time. The data suggest that a basic increase in the strength of the ZPE was due to the initial expansion of the universe. This increase in the ZPE strength brings about decrease in the speed of light. One way of explaining this effect is as follows. The energy inherent in the vacuum, the ZPE, is large and exists in the form of electromagnetic waves of all wavelengths. Just like waves on the ocean, these waves meet, peak and crest. In the ocean, this confluence of waves often forms whitecaps, and a similar phenomenon occurs with the vacuum waves. However, instead of forming foam, these vacuum energy waves form a locally increased concentration of energy which results in the formation of virtual particle pairs. This occurs because energy and mass are interconvertable - something that has been experimentally proven. There is a whole zoo of these virtual particle pairs, such as positive and negative electrons, proton - antiproton pairs, positive and negative pions etc, which momentarily flash into, and then out of, existence. It is estimated that in the volume of a human body there will be some 100 billion billion virtual particle pairs manifested at any instant. It is for this reason that it is sometimes called "The seething vacuum".
Now here is the important point. As a photon of light progresses through the vacuum, it encounters a virtual particle and is absorbed. The particle pair annihilates almost immediately afterwards, whereupon the photon is re-emitted and goes on its way - only to encounter another virtual particle... The process then is repeated. These interactions between the photon and the virtual particles in its path are very fast, but they take a finite amount of time. It is rather like a runner going over hurdles. The more hurdles, the longer it takes the runner to reach the destination. As the strength of the ZPE built up with time, the numbers of virtual particle pairs in a given volume also built up. Thus, an increasing ZPE strength meant more interactions between the photon and virtual particles over a given distance. Thus the speed of light appears to have slowed down over any given distance. Under these conditions, it can be assumed that the speed of the photon between its interactions with virtual particles has always remained the same. It is this speed, which has always remained unchanged on this scenario, that is the upper limit velocity in the universe. In this case, there is then no conflict with the recent developments in the theory of Relativity, which is continuing to undergo re-evaluation.
The second part of the discussion itself comes in two parts. The first relates to Einstein's equation E = mc^2 and the second deals with gravitational phenomena. As far as Einstein's equation is concerned, the experimental data indicate that it is valid at the level of atomic and sub-atomic interactions. It is also at this level that experimental data have shown that the masses of subatomic particles has increased as the strength of the ZPE has increased. In fact the equations show that sub-atomic masses, m, are proportional to the square of the ZPE strength while lightspeed is inversely proportional to ZPE strength. This means that energy is conserved in those reactions where E= mc^2 is applicable. All this is discussed in my paper "Reviewing the Zero Point Energy" published in the Journal of Vectorial Relativity in September 2007, Vol 2:3, pp. 1-28.
It is then sometimes stated that this equation also applies to macroscopic phenomena. This may be an unwarranted extrapolation since all the experiments that we have done have only confirmed that it holds in the sub-atomic or nuclear level. There is another reason. The origin of sub-atomic and nuclear masses on the approach using the Zero Point Energy shows that those masses are entirely due to the battering these particles receive from the impacting waves of the ZPE. This "jiggling" was given the name "zitterbewegung" by Schroedinger. This energy from this 'jiggling' appears as mass at the subatomic level from Einstein's equation. As a result, they are then related phenomena, and Einstein's equation is specifically relevant in this case.
The origin of mass on a macroscopic scale then becomes an entirely separate matter, and this is not the occasion to discuss that as a short-cut is available to us. As far as gravitational phenomena are concerned, the above article shows that the quantity Gm is a constant for all changes involving the ZPE variations. Here, G is the Newtonian gravitational constant which inherently contains units of mass in its denominator. Thus G multiplied by mass m will always be a constant for any system under ZPE changes. This is important because the equations relating to planetary orbital periods and radii all contain Gm as a single entity. The second mass which appears in these equations occurs on both sides of the equation, and so cancels out in the analysis. As a result, it follows that orbit times and radii remain fixed for all changes in the ZPE. The gravitational clock thereby ticks at a constant rate.
Setterfield: Thanks for raising this question. The experimental proof that I had in mind specifically is the behavior of mu mesons or muons. It is well-known that as an object approaches relativistic velocities, its mass increases. This will happen according to SED theory because more impacting waves of the ZPE are being encountered in a given time and so more "jiggling" of the particle occurs, and this results in a greater mass.
Given that fact, we know that cosmic rays enter our atmosphere at speeds quite close to that of light. As they hit the upper atmosphere they form charged radioactive particles called mu mesons or muons which then rain down on us. At rest, a muon has a mass of about 207 times that of an electron. They decay (to form an electron and two neutrinos) with an average life or mean life of about 2.15 x 10-6 seconds. Under normal conditions, most mesons produced by cosmic rays in our upper atmosphere would have decayed long before they reached the ground. However, since the muons produced by the cosmic rays are traveling at speeds close to that of light, their mass will have increased. This means that their mean or average life will have been increased so that some can reach the ground. The experimental arrangement allows their mean life to be measured and it turns out to be 15 to 16 times longer than for those muons traveling at non-relativistic velocities. [For example, see the discussion and experimental arrangement in A.P. French, Principles of Modern Physics, pp.165-167, John Wiley & Sons, New York, 1959. See also Special Relativity: What Time is it?].
Thus the resulting increase in mass of the subatomic particles results in a slowing of the decay rate. In relativity theory, this effect is attributed to "time-dilation" without an actual physical mechanism. However, it can be shown on the SED approach that the slowing of atomic clocks is due to the mass increase with velocity. The math behind this can be viewed in General Relativity and the Zero Point Energy in the preamble to equation (31).
I trust that this helps