THE PHYSICAL AND MATHEMATICAL MEANINGS OF
EINSTEIN'S FOUR 1905 LIGHT POSTULATES.
There are four Light Postulates in Einstein's paper. Each has a different meaning than the others. Together, they impose an entirely different basic physical theory than that set forth by the Theory of Relativity. They require that moving systems physically deform in the ways Lorentz described in 1904. This will be mathematically demonstrated herein; thereby proving that Minkowski's thesis, that the deformations are exclusively due to geometrical reasons, is mathematically and physically false.
In his opening remarks Einstein said, "the phenomena of electrodynamics as well as mechanics possess no properties corresponding to the idea of absolute rest". Nowhere in his paper, however, did he deny the idea of absolute motion. Indeed, absolute velocity is the heart of his first light postulate, given on page 38 of Dover Books' copy of his 1905 paper.1
Light Postulate 1 (LP1, below):
"Light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."
In a different 1905 article Einstein said that light is made of particles called "photons," each containing its own "quantum of energy," each and all moving at a velocity c through empty space. LP1 includes that underlying assumption and sets Newton's "empty space" as the referent for the thereby absolute velocity of light. In order to measure such an absolute velocity one would have to attach the origin of a velocity-vector to a permanently identifiable point of empty space itself, which is impossible. That's why, as Newton pointed out, we cannot measure absolute velocities. To here, however, this first Light Postulate doesn't require any method of measurement. It merely assumes that light physically moves through empty space at an absolute velocity, c.
Having recognized that LP1 appears to be "irreconcilable" with Poincare's Principle of Relativity, which Einstein phrased as "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good" and then raised "to the status of a Postulate", Einstein said,
"These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies. The introduction of a 'luminiferous ether' will prove to be superfluous inasmuch as the view here to be developed will not require 'an absolutely stationary space' provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place."
Maxwell's theory was based on a particulate medium called "the luminiferous ether". Each particle of this hypothetical ether was thought to be attached to a point of Newton's stationary space. Any displacement of such a particle was thought to cause a restoring force to arise in the direction of the initial spatial point. LP1 contradicts Maxwell's entire physical theory, leaving empty space itself as the referent for the absolute velocity of light.
Setting empty space rather than Maxwell's ether as referent, however, has no affect on the mathematics since both the ether and Newtonian space were taken as equally stationary. Whether as a wave system or as particles, a ray of light would still pass differently moving observers at variable relative velocities, thus as measured by any inertially moving classical cartesian co-ordinate system. ("Cartesian" co-ordinate systems are those in which unit-rods are and remain the same size in all directions and whose clocks have identical rates and settings as all others.)
Accordingly, Maxwell's equations would not hold good as plotted by differently moving cartesian co-ordinate systems. That, of course, is why LP1 appears to contradict Poincare's Principle of Relativity. The rest of Einstein's paper was devoted to showing how inertially moving systems can measure the variable relative velocity of light as equal to c; thus can hold Maxwell's equations intact in each and all of them, thereby justifying the Principle of Relativity.
Light Postulate 2 (LP2, below):
We are to use light signals to set the "time" per successive clock of any given system. LP2 is given on page 39 in the form of a definition of "synchronism":
"If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighborhood of B. But it is not possible without further assumption [namely, that the two clocks are synchronized with each other] to compare, in respect of time, an event at A with an event at B. We have so far defined only an 'A time' and a 'B time'. We have not defined a common 'time' for A and B, for the latter cannot be defined at all unless we establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A.
"Let a ray of light start at the 'A time' tA from A towards B, let it at the 'B time' tB be reflected at B in the direction of A, and arrive again at A at the 'A time' tA' . In accordance with definition the two clocks synchronize if tB - tA = tA' - tB.
"We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:- 1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B. 2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other."
Whereas LP1 concerns the absolute velocity of light in empty space, LP2 has now implicitly introduced a co-ordinate system with units of length and time, and imposed the use of light signals to calibrate its successive clocks. It is therefore an entirely different Postulate.
For an absolutely stationary system this method would indeed allow all clocks to be "synchronous" (have identical settings at a given instant). For systems moving at v in the empty space in which light moves at c, however, clocks set by this method would not be synchronous. I therefore now establish by definition that any two clocks of a moving system are "esynched" if, as plotted by them,
Esynching uses Einstein's conceptual method to calibrate the settings of successive clocks of an inertially moving coordinate system so they will measure the variable one-way relative velocity of light as equal in both directions on any given line. Since the one-way times per oppositely moving ray are not the same on the axis of a system's motion as plotted by synchronous clocks, this requires that the "time" of successive clocks B must be adjusted (i.e. hand changed) so that they are. Because the esynched clocks of a moving system therefore do not have identical settings as each other (other than in directions exactly perpendicular to a system's direction of motion), such esynched moving systems are no longer cartesian.
Note: Since clocks and coordinate systems are inventions of Man, and since we are free to elect how we choose to treat them, this is not an objection to Einstein's method. Rather, it's a refinement of his semantics. As Poincare', who invented this method of setting clocks to fit Equation 1, said in a 1904 symposium, "The watches adjusted in that manner do not mark, therefore, the true time, they mark what one may call the local time, so that one of them is late compared to the other." Knowing that clocks so adjusted would not be "synchronous," Einstein merely redefined the word.
In another paper2, Einstein said,
“But if one deals with a phenomenon that necessitates the simultaneous consideration of objects situated at places of different gravitational potential [different places anywhere, would do], then we must employ the time t in the terms where the time appears explicitly (i.e., not only in the definition of physical quantities); since otherwise the simultaneity of the events would not be expressed by the identity of the values of their time.
"Since in the definition of the time t’ one does not employ an arbitrarily chosen instant, but rather a clock situated at an arbitrarily chosen place, the laws of nature, when one uses the time t', cannot vary therefore with the time, but may well vary with the place. "It was clear to Einstein that clocks set to accord with his definition of "synchronization" do not simultaneously have identical settings, thus that "the simultaneity of the events would not be expressed by the identity of the values of their ‘time’”. The sad thing is that most of his followers think that because Einstein defined the successively offset esynched clocks as "synchronous", they really are synchronous. That is one of the many ways in which defective semantics blocked theoretical physicists from understanding the physical meanings of their own equations.On page 42 of the Dover Books' article, Einstein considered the results of letting a moving rod use his clock-setting method to check the synchrony of its clocks:-
"We imagine further that at the two ends A and B of the rod clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the 'time of the stationary system' at the places where they happen to be. These clocks are therefore 'synchronous in the stationary system.'
"We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established above for the synchronization of two clocks. Let a ray depart from A at the time tA ('time' here denotes 'time of the stationary system' and also 'position of the hands of the moving clock situated at the place under discussion'), let it be reflected at B at the time tB, and reach A again at the time tA'. Taking into consideration the principle of the constancy of the velocity of light [in empty space] we find that:
tB - tA = rAB/(c-v) and tA' - tB = rAB/(c+v)
where rAB denotes the length of the moving rod - measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous while observers in the stationary system would declare the clocks to be synchronous."
If, in fact, the speed of light really were a constant relative to moving systems, the observers on the moving rod would find that their synchronous clocks are synchronous. Instead, Einstein's mathematics (though not Einstein overtly) had now assumed (Light Postulate 2.5?) that the relative speed of light physically passing an inertially moving system is a variable in different directions, thus is not a constant.
In accord with Einstein's denial of the notion of absolute rest, we will now consider a co-ordinate system K attached to a material body that we assume moves in empty space at 1 mile per hour. Let clock A be placed at the origin and clock B at x = 1, one unit away on the X-axis of motion, where "one unit" is taken as the distance light travels in vacuo in one second. Using light signals to esynch its clocks, they will be so close to synchronous that any discrepancies will be infinitesimally small and can be ignored.
Let a unit-rod of K, with its own clocks set identically to those of K, now be given a velocity of .6c in empty space in the same direction as K. We will call it co-ordinate system K' (x', y', z' and t'). Since Minkowski asserted later that a moving system preserves "in each case a constant spatial extent"3, let us assume (as Relativity claims) that the length of this unit-rod, thus the distance between clocks A and B of K', remains physically unchanged. (As demonstrated in TRP 4 and elsewhere, but not here: If rod K' remains undeformed in its direction of motion, almost-synchronous system K will measure it as undeformed rather than Lorentz-contracted. A moving rod will be measured as locally Lorentz-contracted if and only if it is Lorentz contracted, even though the actual amount is unknown.)
Let a ray now emit from A at t' = 0, along X of K'. Einstein's mathematics requires that it will take 1/(c-v) = 2.5 seconds for a ray to go from A to B and 1/(c+v) = 5/8 seconds to get from B back to A. It will thus take 3.125 seconds for the ray to round-trip the moving unit-rod. Therefore, the moving system would find that:
t'B - t'A = 2.5 and t'A' - t'B = 5/8
which doesn't fit LP2.
Unfortunately, Einstein didn't say what the moving system is now to do about it; which is to change the setting of all clocks B. In the present case, clock B has to be turned back by .9375 seconds; and is thereupon "offset" by that amount compared to clock A of its own system. Given that, then:
whereupon LP2 is satisfied.Let the moving rod now be set perpendicular to its direction of motion and then esynched. Since the one-way relative velocity of light is c' = sqrt(1 - v2/c2) = q = .8 both ways, it will take equal times each way. Since that already fits Equation 1, LP2 doesn't require nor impose any offsets in the perpendicular directions.
To there, however, system K' would have found that the average relative velocity of light on X is
and that on Y and Z it is c' = qc. Therefore esynching, alone, is not enough to let a moving system measure the average relative velocity of light as equal to c. Knowing this, Einstein proceeded accordingly.
Light Postulate 3 (LP3, below) appears on page 40:
"In agreement with experience we further assume the quantity 2AB/(tA' - tA) = c, to be a universal constant -- the velocity of light in empty space."
Whereas LP1 concerns the absolute velocity of light in empty space and LP2 concerns how to esynch successive clocks of a moving system, LP3 imposes the additional requirement that regardless of the velocity of a system through empty space, it must measure the average round-trip relative velocity of light as equal to c, the absolute velocity of light in empty space.
That requires two things:
1. The physical rate at which clocks of a moving system beat must be variable - a function of their absolute velocity. (The one exception, treated in TRP4 and elsewhere but not here, is this: If a physical system shrinks by q2 = 1 - v2/c2 in its direction of absolute motion and by q in the perpendicular directions, no rate change of its clocks would be needed.)
2. Since light passes a moving system at a different average relative speed on the axis of motion than it does in the perpendicular axes, a rate change that accommodates one such speed cannot satisfy the other. For that, unit-rods, thus co-ordinate systems attached to them, must physically deform in a way such that their length in the direction of motion ends up q-shorter than in the perpendicular directions. As demonstrated in TRP, any degree of length deformations that satisfies this relation, with the appropriate clock-rate changes then needed, will suffice to hold the variable relative speed of light a measured constant, c, in a round-trip in any direction.
We will now mathematically explore the first such requirement for system K', thus any inertially moving system whose length in the direction of motion remains physically unchanged. As shown above, it would take 3.125 seconds for a round-trip ray to traverse the moving rod. LP3, however, requires that co-moving system K' must measure this as t'A' = 2 seconds. Accordingly, K' clocks must run slow by
in which dt' is "one second" as beat of by K' clocks, dt is "one second" as beat off by K clocks, and dt'/dt is the ratio of those clock-rates as plotted by the almost stationary system K. Holding the length of the rod physically unchanged thus requires that dt'/dt = .64 = 1 - v2/c2; whereupon
as plotted by the moving system K'.(It may be noted that if we adhere to Minkowski's thesis, this mathematically-imposed Q-rate change does not fit the q = sqrt(1-v2/c2) value required by the Lorentz Transformations. For that, unit lengths—thus the moving rod and all moving system—must themselves contract by q in their direction of motion.)
In accord with LP3 coupled with Einstein's page 49 admission that (due to its different angular velocity), "a balance-clock at the equator must go more slowly ... than a precisely similar clock situated at the poles under otherwise identical conditions", coupled with Minkowski's assertion that a moving rod maintains "a constant spatial extent", we will now assume that clocks of unshrunken K' do run slow by dt'/dt =.64. Letting a ray emit from its clock A at t'A = 0, we then have:
t'B = 2.5 x .64 = 1.6 and t'A' = 3.125 x .64 = 2.
In order for K' to obey Equation 1, the moving system's observers had to manually insert into each successive clock B the artifice that makes all relativistic equations work, i.e. the local-time offsets presented by Lorentz in 1904 and included in all relativistic transformation equations. Accordingly, to obey LP2 clocks B must now be turned back by -vx'/c2 seconds, where v is the absolute velocity of the moving system and (as demonstrated in "The Theory of Reality"5 and elsewhere) x' is always the distance between any two of its clocks as measured by the moving system itself. (The value of absolute v is neither known nor needed for that. Neither is any differently moving co-ordinate system as observer. The local time offsets of clocks B compared to clocks A is built into a moving system by the very act of manually esynching its own clocks.) In the present case, clock B has to be turned back by -vx'/c2 = -.6 seconds, whereupon both LP2 and LP3 are satisfied.
If moving systems internally contract by q=sqrt(1 - v2/c2) in the direction of motion, their esynched clocks would have to run q slow in order to satisfy LP3. The Lorentz transforms would then apply. Let two such Lorentzian systems, K' and K" moving at .6c and .8c respectively, be esynched before their origins coincide with that of K at
Let an event A occur at the coinciding origins at tA = t'A = t"A = 0. Let event B occur at x = 1, tB = 0 as plotted by almost stationary system K. It would be plotted at x' = 1.25 and x" = 1.66. Because of the offsets of the esynched clocks of K' and K" at those places, event B would be plotted att'B = -.75; t"B = -1;
so
tA = t'A = t"A = tB =/= t'B =/= t"B.
System K would thus plot the events as simultaneous but esynched systems K' and K" would find them non-simultaneous. We thus see that if events happen simultaneously as plotted by a given system they cannot be plotted as simultaneous by any differently moving esynched systems. Hence, rather than being an attribute of nature, "the relativity of simultaneity" is a consequence of the way we choose to set our clocks.
Even so, the prior three Light Postulates and what they impose permit any moving system to attach a velocity vector to any one of its own points, and still measure the variable relative velocity of light as a constant, c, in any and all directions. This is what Einstein promised to do and that was how he did it!
Light Postulate 4 (page 41):
"Any ray of light moves in the ‘stationary' [i.e. moving] system of co-ordinates with the determined [i.e. measured] velocity c, whether the ray be emitted by a stationary or by a moving body. Hence
velocity = (light path)/(time interval);
where time interval is to be taken in the sense of the definition given in section 1."
Most textbooks omit (and all relativists ignore) the portions I italicized. That omission makes it seem as though a given ray of light really does move at the same speed relative to all differently moving systems. That, of course, is physically impossible!
Although LP4 is given in the form of a Postulate, it is actually a consequence of the prior three. After lengths of moving system have suitable deformed and the clock-rates have been changed to accord with LP3 (either manually or for long-ignored physical reasons), and after the observers adjusted the settings of their clocks by esynching them to fit LP2, LP4 then holds good.
As mathematically proved above and elsewhere, the relativistic equations rest on and impose the real and physical deformations and local-time offsets that the Theory of Relativity verbally denies. Since that theory therefore doesn't fit its own equations, it follows that every experiment that verified the validity of those equations has thereby proved the Minkowski theory untenable.
It is time for Theoretical Physics to examine the underlying causes of the real and physical deformations upon which the equations are grounded. Once physicists do, they will realize that the relativistic equations describe and rest on the affects of local motions through a compressibly-resistive movable material medium that totally fills the entire Universe; the very same material out of which atoms and molecules are made.
Perhaps that's why God, in His ineluctable wisdom, allowed the Theory of Relativity to survive for almost a century: To prevent the experimentally verified relativistic equations from being interpreted as proof that Lorentz's physical theory is correct. (Since his hypothetically incompressible universally stationary ether could not undergo the distortions comprising the em-wave systems Lorentz considered to be the essence of "ponderable matter"; unless such waves propogate infinitely fast, which his equations rule out, Lorentz's equations themselves disagree with his thesis.)
Rather, as I eventually discovered, at our level of size the world is exactly as it appears to be to the senses of a normal person, and contrary to the opinions of our relativistic physicists, the human mind - as demonstrated in and by The Theory of Reality - is perfectly able to fully understand every structure and every mechanism that exists in our Universe.
Footnoted Bibliography
- "On the Electrodynamics of Moving Bodies" A. Einstein, 1905; in "The Principle of Relativity" by Dover Books, page 37.
- “Jahrbuch der Radioaktivitat und Elektronik", "Uber das Relativitatprinzip und die aus demselben gezogene Folgerungen" by Einstein, 1907; translated by H. M. Schwartz, 1976, American Journal of Physics, June, September and October, 1977. October issue, page 900.
- "Space and Time" by Minkowski, 1908; Dover Books, page 82.
- "The Relativity Program."
- "The Theory of Reality" by du Gabriel; Copyright © 1990.