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Eloc dτ=E∞ dtE_{\rm loc}\,d\tau=E_\infty\,dt

Why this formula appears here

Collect the ledger. N⊥N_\perp[Γ\Gamma] , the cumulative orthogonalization count, is an exact and dimensionless consequence of the Levitin-Toffoli bound integrated over proper time, valid without approximation in the quasi-static driving regime and bounded above by the sharper Deffner-Lutz result outside it — that piece is DERIVED. The identity ElocE_{\rm loc}\,dτ\tau=E∞E_\infty\,dt is an exact consequence of the definition of Killing energy in a static spacetime, proven here for the specific case of N⊥N_\perp[Γ\Gamma] rather than asserted by analogy — also DERIVED. That no energy-convention bookkeeping can extract a net gain from this identity is a direct corollary, not an assumption.

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ElocE_{\rm loc}

Symbol E_rm loc

ErE_rm loc is part of the quantity the equation computes from the expression on the right.

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Published contexts (1)

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Eloc dτ=E∞ dtE_{\rm loc}\,d\tau=E_\infty\,dt

Equation 106 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Collect the ledger. N⊥N_\perp[Γ\Gamma] , the cumulative orthogonalization count, is an exact and dimensionless consequence of the Levitin-Toffoli bound integrated over proper time, valid without approximation in the quasi-static driving regime and bounded above by the sharper Deffner-Lutz result outside it — that piece is DERIVED. The identity ElocE_{\rm loc}\,dτ\tau=E∞E_\infty\,dt is an exact consequence of the definition of Killing energy in a static spacetime, proven here for the specific case of N⊥N_\perp[Γ\Gamma] rather than asserted by analogy — also DERIVED. That no energy-convention bookkeeping can extract a net gain from this identity is a direct corollary, not an assumption.

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