Dear Sergey,
The question I asked you is that has there been even a single experiment which has confirmed, that when x' = gamma(x -ut) the corresponding time is
t' = gamma(1- ux/c2)t?
And your answer: See the Ives-Stilwell experiment . This concerns time dilation equation (1) (below).
YOU ARE MAKING THE SAME GRAVE ERROR THAT GEORGE ELLIS DID JUST TWO DAYS BACK. YOU ARE CONFUSING BETWEEN THE SO-CALLED TIME DILATION EQUATION (1) AND LORENTZ TIME TRANSFORMATION EQUATION (2)
t' = t/(1 - v2/c2)1/2 --------------------(1)
t' = gamma(1- ux/c2)t ----------(2)
Just like you referring me to Ives-Stilwell Experiment by confusing equation (1) for equation (2), George Ellis also made the same error by referring to another group of experiments. He wrote: "all those collider experiments at places like SLAC and CERN verify it millions of times over each time they do a run".
My reply was: In those "millions of times" of verifications, what was verified was
a) that displacement is given by x' = gamma(x -ut) where U IS THE VELOCITY OF ORBIT OF THE EARTH and gamma determined by u. Hence the gamma-factor (for all experiments conducted on earth) is a constant. Gamma = 1.000000005.
b) And in the experiments to verify the decay time of a muon at CERN it confirmed the 'time dilation equation' t' = t/(1 - v2/c2)1/2. In this v is the velocity of the particle in the gamma-factor. In this equation gamma is a variable. In the CERN experiment gamma v = 0.99c and gamma = 7.088, and when moving in a cosmic ray (as in Feynman example below, v = 0.9c and gamma = 2,294.
To quote from Feynman: . For example, before we have any idea at all about what makes the meson disintegrate, we can still predict that when it is moving at nine-tenths of the speed of light the apparent time that it lasts is (2.2x10-6)/ sq rt [ 1- (9/10) squared] sec; and that our prediction works ..." (Vol I Ch 15 - 7).
FOR SRT TO BE CORRECT ON ITS FUNDAMENTAL CONTENTION OF THE LORENTZ TRANSFORMATIONS, (see Einstein's statement below) WHEN THE MUON DECAYS AFTER MOVING THROUGH A DISPLACEMENT GIVEN BY x' = gamma(x -ut) THE CORRESPONDING TIME HAS TO BE GIVEN BY (2)
t' = gamma(1- ux/c2)t. -------(2)
But this time is given by (1).
When I framed the question that way:
George Ellis HONESTLY CONCEDED. "YES I AGREE THAT THAT SPECIFIC EQUATION (2) PER SE HAS NOT BEEN VERIFIED BUT TIME DILATION (i.e equation 1) HAS, WHICH IS ITS CORE ELEMENT".
So Sergey, here is the fundamental contention of SRT in Einstein's own words: :.. "The insight which is fundamental for special theory of relativity is this: The assumptions 1)[constancy of the velocity of light] and 2) [principle of relativity] are compatible if relations of a new type ('Lorentz transformation') are postulated for the conversion of co-ordinates and the time."(Autobiography, p. 55).
I WILL ASK THE SAME QUESTION AGAIN FROM YOU AS WELL. CAN YOU GIVE EVEN ONE EXPERIMENT THAT HAS CONFIRMED THE EQUATION
t' = gamma(1- ux/c2)t?
Best regards,
Viraj