Resumen
Einstein's early thought experiment of “riding on a beam of light” motivates a basic question in relativity: if every inertial observer measure photon to propagate at , then what can be said about the description of a fermion in a photon-like viewpoint? This paper argues that a passive (non-boosting) Lorentz transformation must be distinguished from an active (boosting) transformation. In an active boost, a particle is physically accelerated, its total energy increases, and the Lorentz factor can diverge as . In a passive transformation, by contrast, the particle is not accelerated; only the observer's description changes. Passive transformation has two invariances: the known rest mass and the total energy invariance. Under this interpretation, the usual divergence obtained by inserting into the massive-particle expression does not apply to the photon-fermion comparison, because that divergence belongs to active acceleration. Instead, the fermion's finite total energy is preserved and may be represented in the photon-like description by the massless form , without implying that the fermion has physically lost its rest mass. The paper also discusses proper-time assignments through the Planck relation , and comments on time dilation, length contraction, and “relativistic mass” in terms of energy content rather than relative speed alone. Possible connections to particle-antiparticle annihilation and horizon crossing near black holes are briefly outlined. Keywords special relativity; Lorentz transformations; active and passive transformations; Minkowski interval; beam of light; black holes, Feynman's path integral