The standard thermodynamic interpretation of black holes assigns temperature, entropy, and thermal radiation to the event horizon. All three concepts presuppose the ability to measure energy. We argue that this prerequisite fails at the horizon: proper time for stationary observers vanishes exactly at any Killing horizon—a coordinate-invariant consequence of classical general relativity—and energy measurement requires nonzero temporal duration. Energy is therefore not "infinitely uncertain" at the horizon but operationally unmeasurable, rendering temperature and entropy inapplicable rather than merely divergent. The redshift cancellation that yields a finite Hawking temperature is algebraically correct but operationally empty: it computes what a measurement at the horizon would yield if such a measurement could be performed, but no measurement apparatus can operate where proper time does not elapse. We further demonstrate that the computational apparatus underlying all derivations of the Hawking effect—mode decomposition, vacuum state selection, Bogoliubov transformation—is frame-dependent and singular at the horizon. The information paradox is not resolved by these findings but rather shown to be not established: its premises require thermodynamic concepts that are inapplicable at the horizon. The resulting picture—maximal indeterminacy for external observers, well-defined physics for infalling observers—is a form of complementarity that follows from the algebraic structure of quantum field theory at null surfaces rather than being postulated. These conclusions apply to all Killing horizons, including cosmological and Rindler horizons.
Alexander Yiannopoulos (Thu,) studied this question.