The reflection of photons from mirrors reveals that Einstein’s special theory of relativity does not withstand the rigour of mathematics. Consequently, new theories are needed to explain the physical phenomena. I highlight a contradiction in Einstein’s 1905 papers [1,2], best described in the thought experiment set out below.
Steve, in the stationary reference frame, observes the two-photon decay of a particle of mass . The Planck relation determines the frequencies of the photons that he observes, i.e. , where is the Planck constant, is the particle’s loss of mass that is converted to photonic energy, and is the speed of light. Let the direction of the photons oppose each other and be parallel to the -axis of Steve’s reference frame. The total energy before and after the two-photon decay remains constant at
Monica is in a moving reference frame with constant velocity parallel to Steve’s -axis. According to § 7 of , first equation page 912, she observes the frequencies of the two photons as and The sum of the energy of the two photons is Thus in the moving reference system, as asserted in , the total energy before and after the two-photon decay also remains constant at
Monica now uses two ideal mirrors to reflect the photons towards their source. She does not observe a change in energy and the mirrors remain stationary for her. In the moving system, the photon frequencies before and after the reflection are unchanged. The energy remains
On the other hand, again by use of § 7 of , Steve observes the frequencies of the returned photons as and Thus, in the stationary system, the energy after reflection calculates to
The principle of relativity, as asserted in axiom 1 § 2 of  (page 895), implies that the system state, before and after an interaction, changes the same for both Steve and Monica. However, the result and contradicts that affirmation. That being the case, the propositions put forward by Einstein are now falsified.
The many physical observations cannot be doubted, however every explanation that is based on Einstein’s postulates is no longer defendable; new explanations are needed that withstand mathematical rigour and corroboration by experience . . . that is all there is to it.
References: A. Einstein, “Zur Elektrodynamic bewegter Körper“, Annalen der Physik, vol. 322, pp. 891-921, 1905. (English translation)  A. Einstein, “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?“, Annalen der Physik, vol 323, pp. 639-541, 1905. (English translation)
P.S. In (3) and (4) only the energy was addressed, the same contradiction holds true for momentum. After the photon reflection the following change in momentum still needs to be accounted for:
and again we note the discrepancies in (4.a) when compared to (3.a)
PPS: Additionally, (1) and (4) violates the law of energy conservation, thus challenging the explanation given for the Doppler effect for electro-magnetic radiation.
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