why the Lorentz transformations forbid passing to a reference system with the speed equal to that of light despite there are particles (photons) traveling at this speed? in other words I see the fact that the Lorentz transformations forbid placing oneself in an inertial system that travels at the speed of light (due to the cancellation of the denominator $1-\beta^2$) and that there is a photon that travels at this speed, which is a contradiction. Generally the explanation is that an observer cannot have zero mass. Despite this I see the possibility of having a luminary system coinciding with the existence of a particle traveling at the speed of light, hence the contradiction that I said above. Can anyone explain to me the right point of view that I need to adopt?
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1A photon doesn't have a rest frame because it obeys $\mathrm{d}s^2=0$, so can't measure time or space. – J.G. Feb 24 '22 at 10:21
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I also was surprised of this singularity, and tried to obtain Lorentz transformation from the invariance of the wave equation considering general change of coordinates. I only arrived at the fact that the transformation itself shall obey the wave equation, whose solution is generally a wavepacket travelling at light speed. – QuantumPotatoïd Jul 01 '22 at 10:34