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Four-vector description of the photon-in-a-box problem
Authors: J. Güémez; M. Fiolhais
Ref.: Eur. J. Phys. 40, 025601 (2019)
Abstract: The emission/absorption of a photon and the launch/capture of a massive particle in special relativity Einstein-like boxes are studied, using the fourvector formalism. The study demands the introduction of the centre-of-inertia concept, the relativistic equivalent of the classical centre-of-mass of a system. Then, using Einstein’s principle of the inertia of the energy and the conservation of energy and momentum, we show explicitly, in both cases, that the centre-of-inertia velocity does not change during the processes that take place inside the boxes. We argue that the centre-of-inertia is a useful concept in special relativity as counterpart of the centre-of-mass, and we suggest that it should be explored in the classroom to stress the similarities and the differences between the classical and the relativistic descriptions of mechanical systems.
