Relativity Reexamined

Let us repeat the "Gedanken - Experiment" by Albert Einstein: to synchronize two clocks. At that time, Einstein did not fully recognize the following: "When reflected photons push back the reflecting object (recoil effect) and change its velocity" (: Léon Brillouïn in Relativity Reexamined, Academic Press 1970). Therefore, "The usual statement of the relativity principle requires that frames of reference be extremely heavy ... The old-fashioned principle of relativity is a dream; it represents only a limiting case, but may not, for instance, be used without much care when it comes to moving ... particles ... of very small masses ".
Instead of radar pulses which are delta functions, as employed by Einstein, we use more realistic pulses sinc(2πt / τ) , where sinc(x) = sin(x) / x . These pulses are modulated with the signal exp(iωt) of an atomic clock, while synchronizing the clocks of laboratory O and laboratory O' :

After recoil, the wavelength of the carrier wave has become: 2πc / ω + 2 h / m₀c , by the Compton effect. But, in order to be modulated, the condition ω' >> 2π / τ or τ / 2 >> π / ω' must be fulfilled. Thus τ / 2 >> π / ω + h / m₀c² >> h / m₀c² .
Conclusion: the spread of the radar-pulses in time must be much greater than the Compton time = h / m₀c² , in order to be able to synchronize clock O with clock O' of a reference frame with rest mass m₀. It is impossible to sychronize clocks within intervals smaller than the Compton time.

In addition to the above, the following thought-experiment can be performed, which affects the space-like part of the Lorentz transformations:

Conclusion: the spread of the radar-pulses in space must be much greater than the Compton (wave)length = h / m₀c , in order to be able to compare lengths in O with those in O' of a reference frame with rest mass m₀. It is impossible to compare lengths within intervals smaller than the Compton (wave)length.