Einstein's equations from CPT, with nothing quantised

Jacobson’s derivation of the Einstein equation from the Clausius relation assumes three things it does notsupply: a temperature at every local Rindler horizon, an entropy proportional to that horizon’s area withthe same coefficient everywhere, and such a horizon at every point in every null direction. We show thattaking CPT to be a symmetry of the universe, and not only of its laws, supplies all three. The entropylaw comes from the entanglement of the state the symmetry forces and not from Bekenstein-Hawking, sonothing is borrowed back from the theory being derived. The metric is a fixed background at every step andno gravitational degree of freedom is quantised. Nineteen properties of general relativity follow against fourinputs, among them the sign of Newton’s constant, four large spacetime dimensions, and Λ as an integrationconstant. Four observations would end the fold, two of them cosmological measurements now being made.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-06
DOI
https://doi.org/10.5281/zenodo.23176873
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

Einstein's equations from CPT, with nothing quantised

B. H. Wiseman
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Einstein's equations from CPT, with nothing quantised

B. H. Wiseman
preprint en

Abstract

Jacobson’s derivation of the Einstein equation from the Clausius relation assumes three things it does notsupply: a temperature at every local Rindler horizon, an entropy proportional to that horizon’s area withthe same coefficient everywhere, and such a horizon at every point in every null direction. We show thattaking CPT to be a symmetry of the universe, and not only of its laws, supplies all three. The entropylaw comes from the entanglement of the state the symmetry forces and not from Bekenstein-Hawking, sonothing is borrowed back from the theory being derived. The metric is a fixed background at every step andno gravitational degree of freedom is quantised. Nineteen properties of general relativity follow against fourinputs, among them the sign of Newton’s constant, four large spacetime dimensions, and Λ as an integrationconstant. Four observations would end the fold, two of them cosmological measurements now being made.

Zenodo (CERN European Organization for Nuclear Research)
AARNet (Australia) (AU)
Relativity and Gravitational Theory
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Einstein's equations from CPT, with nothing quantised — B. H. Wiseman · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS