A Temperature Priced by Acceleration: The Unruh and Hawking Toll, Priced
Year: 2026
Type: preprint
Abstract: An accelerated observer in empty space finds the vacuum warm. That is the Unruh effect (1976), and its gravitational twin is the Hawking temperature of a black hole (1974–75): two of the deepest results in modern theory, each a temperature *derived* — not fitted, not postulated — from quantum field theory on a spacetime with a horizon. I credit both derivations at full strength: inside their premises they are theorems, the detector analysis is permanent, and the flat-space/horizon analogy Unruh drew is one of the great clarifying moves of the century. Nothing in this paper falsifies a digit of either result. What I price is the toll's exchange rate and its one declared premise. On declared inputs only, my bench returns the Unruh coefficient hbar/(2 pi c k_B) = 4.055014e-21 K per (m/s^2): at Earth gravity the vacuum warms by 3.976610e-20 K; one kelvin costs an acceleration of 2.466083e+20 m/s^2 (2.514705e+19 g); room temperature costs 7.398249e+22 m/s^2. The Hawking side returns its coefficient 1.226901e+23 K kg: a solar-mass hole sits at 6.170074e-08 K, a 1e12 kg hole at 1.226901e+11 K with a fixed-background evaporation time of 2.665437e+12 yr, and the hole whose temperature equals the microwave background's stated 2.725 K masses 4.502388e+22 kg. Every one of those numbers is derived — inside a premise the bench prints on its own face and this paper prints at full size: a horizon exists for the observer whose temperature this is. The horizon is the premise; the temperature is the toll it charges; and the premise itself is derived nowhere in either paper — counted by my bench as: temperatures derived inside the horizon premise = all of them; the horizon premise itself derived = 0. Grade for this census entry, printed at full size: REASON FOUND / STILL TURNING — a pricing of a derivation's premise and exchange rate, explicitly not a kill and not a falsification. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.
Author: Aldred, William Alexander
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225411557