Finite Hilbert-Space Dimension for Bounce Scattering Implied by the Entropy Ceiling
Year: 2026
Type: article
Abstract: This paper examines whether scattering through a bounce can be described by a finite-dimensional unitary map, and how large that dimension is bounded to be. The calculation is performed in a frame with a finite maximum density, the neutron-branch value rho_A = 9.718e+57 kg per cubic metre, with the electron branch at 2.874e+51 kg per cubic metre for comparison. Headline results include a bounce temperature of 3.278e+22 K, a Landauer cost at that temperature of 3.137e-01 J per bit against 2.871e-21 J per bit at 300 K, a Bekenstein allowance of 1.049e+94 bits for the stated centimetre reference region, and a Margolus-Levitin rate of 2.209e+103 per second for the same region. The dimension is finite but vast, with a base-ten logarithm of order 1e94 for the reference patch, so finiteness gives structure without giving tractability. All numbers are computed from the stated assumptions in the accompanying script; the study is simulated and computed, not measured.
Author: Aldred, William Alexander
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225797064
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