## Mass and Energy
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.
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.
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)mv In summarising this, the team of physicists at CIPA have
this to say. I trust that this helps.
Setterfield: This concerns relativity
and how this affects the debate on changing c values. Back in the early
part of the 20
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 Metrologia Vol. 1, No. 4, 1965. He stated 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 indeed run at different
rates, and that Planck's constant is also changing. The evidence
concerning clock rates comes from the work of T. C. Van Flandern,
then of the US Naval Observatory in Washington. He had examined
lunar and planetary orbital periods and compared them with atomic
clocks data for the period 1955-1981. Assessing the data in 1984,
he noted the enigma in Precision Measurements and Fundamental
Constants II, NBS Special Publication 617, pp. 625-627. In
that National Bureau of Standards publication, Van Flandern stated "the number of atomic seconds in a dynamical interval is
becoming fewer. Presumably, if the result has any generality to
it, this means that atomic phenomena are slowing down with respect
to dynamical phenomena."To back up this proposition, Planck's constant, h, has been measured as increasing throughout 20th century. In all, there are 45 determinations by 8 methods. When the data were presented to a scientific journal, one reviewer who favoured constant quantities noted, "Instrumental
resolution may in part explain the trend in the figures, but I
admit that such an explanation does not appear to be quantitatively
adequate." Additional data came from experiments by Bahcall
and Salpeter, Baum and Florentin-Nielsen, as well as Solheim et
al. They have each proved that the quantity 'hc' or Planck's
constant multiplied by light-speed is in fact a constant astronomically.
There is only one conclusion that can be drawn that is in accord
with all these data. Since c has been measured as decreasing,
and h has been measured as increasing during the same period,
and hc is in fact constant, then h must vary precisely as 1/c
at all times. This result also agrees with the conclusions reached
by Birge and Kovalevsky.From this observational evidence, it follows in the original equation
E = hf = hc/W, that since f is proportional to c, and h is proportional
to 1/c, then photon energies in transit are unchanged from the
moment of emission. This also follows in the second half of the
equation since hc is invariant, and W is also unchanged according
to observation. Thus, if each photon is considered to be made
up of a wave-train, the number of waves in that wave-train remains
unchanged during transit, as does the wavelength. However, since
the wave-train is travelling more slowly as c drops, the number
of wave-crests passing a given point per unit time is fewer, proportional
to c. Since the frequency of a wave is also defined as the number
of crests passing a given point, this means that frequency is
also proportional to c with no changes in the wave structure of
the photon at all. Furthermore, the photon energy is unchanged
in transit. ( September 14th 2001.)
I would suggest you read Helen’s laymen's summary .
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.
Concerning your two questions: They are both dealing with the concept of mass and energy. You quote Einstein’s equation E=mc 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=mc 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=mc 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/c 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. 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.
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, 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
Here are a couple of explanations: Here are a couple of great YouTube videos about it: Hope that helps. |