Theories of the Aether Articles relating to the Emergence of | |
---|---|
The Physical and Mathematical | |
Web Publication by Mountain Man Graphics, Australia - Southern Winter 1999 | |
Einstein's Four 1905 Light Postulates |
---|
Once that is recognised, physicists will begin to try to find the causes of the physical deformations imposed by the equations; which themselves contradict the theory now accepted as correct. They will eventually discover that these physical deformations are caused by the physical effects of local motion through a resistively-compressed material medium and that, contrary to any of the [contemporary accepted] theories of physics [today], "ponderable matter", such as atoms and molecules and we ourselves, are made of this one basic material, which completely fills every space in our Universe.
- du Gabriel, 1999
Light Postulate No. 1 |
---|
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,
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 No 2 |
---|
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' t_{A} from A towards B, let it at the 'B time' t_{B} be reflected at B in the direction of A, and arrive again at A at the 'A time' t_{A'} . In accordance with definition the two clocks synchronize if t_{B} - t_{A} = t_{A'} - t_{B}.
"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:-
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.
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,
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. 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 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 t_{A} ('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 t_{B}, and reach A again at the time t_{A'}.
Taking into consideration the principle of the constancy of
the velocity of light [in empty space] we find that:
t_{B}
- t_{A} = rAB/(c-v) and t_{A'} - t_{B} = 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."
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 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 t'_{A} = 0, t'_{B} = 1.5625, t'_{A'} = 3.125, 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 - v^{2}/c^{2}) = 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 c' = 2/3.125 = .64 = q^{2}c 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 No 3 |
---|
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.
(It may be noted that if we adhere to Minkowski's thesis, this mathematically-imposed rate change does not fit the q = sqrt(1-v^{2}/c^{2}) 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 now have 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'/c^{2} seconds, where v is the absolute velocity of the moving system and (as demonstrated in "The Theory of Reality"^{5} and elsewhere, but not here) 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'/c^{2} = -.6 seconds, whereupon both LP2 and LP3 are satisfied.)
If moving systems internally contract by q = (1 - v^{2}/c^{2}) 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 t = t' = t" = 0. Let an event A occur at the coinciding origins at t_{A} = t'_{A} = t"_{A} = 0. Let event B occur at x = 1, t_{B }= 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 at t'_{B} = -.75; t"_{B} = -1. Therefore, 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 No 4 |
---|
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 Relativity-ignored physical reasons), and after the observers adjusted the settings of their clocks by esynching them to fit LP2, LP4 then holds good.
Unknown by the relativists but mathematically proved above and elsewhere, their own equations covertly rest on and impose the real and physical deformations and local-time offsets that the Theory of Relativity overtly denies. Since that theory therefore doesn't fit the relativistic equations, it follows that every experiment that verified the validity of those equations has thereby proved the Minkowski theory untenable.
Footnoted Bibliography |
---|
2. "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.
3. "Space and Time" by Minkowski, 1908; Dover Books, page 82.
4. "The Relativity Program".
5. "The Theory of Reality" by du Gabriel; copyright 1990.