2) Meaning of the invariance. ------[ Return home ]
The mathematical result obtained (invariance of the wave structure) would be enough to trap a recently converted relativist and who would believe again in Einstein if something was not added here.
The good axample to show what happens is to consider sound-waves in air. With them, we will see what is the difference between a fictitious mathematical property and a physical one.
We know that the sound-wave equation in the rest frame is:
LaplacianF-[1/cc]ddF/dtdt=0, with c the sound-wave velocity.
Now, we are in an open-top car in motion where we hear that a siren at rest changes of frequency relatively to us due to the Doppler effect produced itself by the lack of isotropy of the sound-wave velocity as a result of our motion. We have also problems to light a cigarette due to the wind (proof of our absolute motion).
But, in the moving frame (open-top car), if we use shorter unit-lengths according to the formula L'=L.sqrt(1-bb) with b=v/c and if we decrease the frequency of the time base of the clocks according to F'=F.sqrt(1-bb) and finally, if we use the method of Einstein to synchronize the clocks (in assuming that the sound-wave velocity is isotropically c), as explained here, the Lorentz' transformation will exist between the rest and moving frame, and the wave equation above will be the same in the open top car frame. Such a result leads us to obtain also the mathematical isotropy of the sound-wave velocity in the open-top car frame, but it is not physical result.
The proofs for that are the Doppler effect (siren) and the wind (problems to light a cigarette). And the mathematical result is not physical, because we have used clocks not synchronized to obtain the result.
Finally, an additional proof is that, if we try to consider the open-top car frame (with its clocks not synchronized) as as valid as the rest frame, we are going to obtain logical problems like in relativity (twin paradox and barn&pole).
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