Einstein's 1911 Approach to Gravitational Redshift: From Nothing to Too Much

In 1911, Einstein revisited his earlier application of the equivalence principle to gravitational phenomena, deriving simple expressions for gravitational redshift, time dilation, and light deflection. In this paper, I critically examine the logical structure of Einstein’s 1911 derivation of the gravitational redshift (and time dilation) and argue that it contains an internal inconsistency that gives rise to an infinite regress paradox. Specifically, the derivation implies that the presence of a finite gravitational redshift necessitates its doubling–and so on ad infinitum–when the result is reintroduced into the same reasoning. I reconstruct Einstein’s argument step by step, highlight the source of the paradox, and discuss its implications for the logical coherence of the heuristic method underlying his early gravitational reasoning. Although general relativity later provided a rigorous mathematical formulation for gravitational redshift and time dilation, I contend that this paradox should not be dismissed as historically irrelevant. Instead, it exposes conceptual tensions at the foundations of Einstein’s heuristic approach and offers insight into the philosophical underpinnings of general relativity.