TL;DR
This paper revisits Bohr's analysis of Einstein's photon box thought experiment, clarifying issues by reformulating the weighing process and discussing the role of gravitational time dilation and alternative solutions.
Contribution
It provides a new formulation of Bohr's analysis, explicitly incorporating gravitational time dilation effects and exploring alternative resolutions to the thought experiment's paradox.
Findings
Reformulation clarifies the role of time measurement in the photon box experiment.
Gravitational time dilation explains discrepancies in measurements.
Proposes alternative solutions without relying on general relativity.
Abstract
We present a reformulation of Bohr's analysis of Einstein's thought experiment with the photon box, which hopefully settles some unclear issues. The box is weighed by two position measurements, the first immediately before the emission of the photon and the second after a quarter period of oscillation of the box, or alternatively after a half period. These times are precisely defined with respect to the moving clock installed in the box, but vary statistically when measured with a stationary clock outside the box, due to gravitational time dilation in accordance with Bohr's original idea. Moreover, we will discuss two other proposals to solve the apparent inconsistency without invoking the theory of general relativity.
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