Roger,
I need to clarify something before hand to avoid confusion in what I intend to discuss below.
You have in your discussion with Pentcho repeatedly made the mistake of referring to Lorentz contraction (LC) L' = L/gamma' as "Lorentz transformation". No this is worng. Lorentz transformation (LT) is x' = gamma (x- ut).
Note: the gamma of LT = 1/(1- u2/c2)1/2 where u is the velocity of the reference frame (in SRT) whereas gamma' of LC = 1/(1- v2/c2)1/2 where v is the velocity of the particle (relative to the moving frame of velocity u).
Having clarified that misstatement, here is what I wish to discuss:
You wrote: "It would be exciting if someone devises an experiment that proved relativity wrong. ............ But I am not sure it would have anything to do with my essay. We still learned lessons from relativity, even if the theory has to be modified someday".
Why it has been found difficult to prove SRT wrong is because those trying to prove "Einstein" wrong always pick up the wrong postulate - (1) the constancy of the velocity of light.
At the risk of provoking the wrath of Pentcho, we have to admit that the postulate (1) is right. (Amended as, velocity of light is constant in all directions in a given medium as determined by the refractive index of that medium).
It is the other two postulates that are wrong. (2) Principle of Relativity and (3) Lorentz transformation (LT) [ x' = gamma (x- ut)].
In Kryakos' excellent essay http://fqxi.org/community/forum/topic/1341 he has discussed the damage done to physics by young Einstein with his positivist philosophy (but when he realized this, it was too late).
Influenced by the arch-positivist Poincare, (see my essay) Einstein wantonly dumped Galileo's principle of relativity (which is based on the COMMON MOTION with the unique Local reference frame) and adopted equivalence of all IFR as the second postulate. And he declared that the contradiction between postulates (1) and (2) gets (miraculously) reconciled by adapting LT as the postulate (3).
Now to come to the point:
In Newtonian mechanics (NM) which applies for 'slow' motions, displacement of a particle moving at velocity v is given by x = vt. Here space and time are absolute.
For particles moving at near light velocities (in particle accelerator experiments) the displacement is given by x' = gamma (x- ut). SRT claims that time and space are relative.
So there is a schism in physics (in regard to equation for displacement and also the nature of time and space) which is going unaddressed, by merely making an arbitrary division that "SRT is for fast motion" and "NM is for slow motions". But the question is never raised "What is the theory that applies to the vast middle ground in between fast and slow motions?"
If you consider particles moving at progressively lesser and lesser velocities (0.9c, 0.8c, 0.7c etc) there is a progressive degeneration of the results conforming to the LT equation. After 0.5c the degeneration becomes much greater. For experiments done of earth, for a velocity of v = 30 k/s the LT equation fully breaks down.
This schism in physics has happened because of the blind adaptation of the LT without discerning its physical basis and deriving it from dynamic principles.
It will be obvious that the schism would disappear if there is an one equation which is applicable to all velocities (slow, medium, fast).
In my essay: http://fqxi.org/community/forum/topic/1549
I not only explain where Einstein went wrong but also following Einstein's idea of expanding the thermodynamic approach to whole of physics I also have developed the general equation of motion
x' = gamma vt(1- u/c) --------------(1)
Note: This equation (1) tends to LT -----(2) at near light velocities where v/c tends to 1; and to x = vt -----(3) when v/c tends to zero.
We do not need any new experiments to verify the validity of this equation. Experiments have already been done. If we take the results of all the particle accelerator experiments done in the last hundred years and make a computer analysis, it will show that the results conform to the above equation (1).
Your point of view that what is perceived to be 'mathematical reality' is not 'physical reality' would seem to be confirmed by the fact that LT has an inbuilt error which looms large when the velocities decline.
I would like you to read my paper and give your comments. (For clarity of diagrams I have also attached essay in MS Word format
Best regards,
VirajAttachment #1: 4_A_TREATISE_ON_FOUNDATIONAL_PROBLEMS_OF_PHYSICS2.doc
