← Mathematical compendium

Published equation contexts

ΓTdec\Gamma T_{\rm dec}

Why this formula appears here

Both are deterministic transformations of the assumed overlap law. Neither is a new field-theory result. Numerically inverting the two binary-entropy equations gives: ΓTdec\Gamma T_{\rm dec}. The table is an analytic computation performed for this proposal, not a simulation or an observation. It says that a common phrase such as “one decoherence time” is underspecified. At the 0.9-bit threshold, a Holevo ceiling appears at almost exactly one inverse rate, while the specified decision task needs about 1.49 inverse rates. At the 0.999-bit threshold the two clocks read about 3.29 and 4.13. The disagreement is finite and predictable.

Read the full article-specific guide →

Read the representative guide

Γ\Gamma

Symbol Gamma

Gamma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →
TdecT_{\rm dec}

Symbol T_rm dec

TrT_rm dec is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

ΓTdec\Gamma T_{\rm dec}

Equation 22 · Evolutionary Physics

How Fast Can a Horizon Learn Which Path You Took?

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Both are deterministic transformations of the assumed overlap law. Neither is a new field-theory result. Numerically inverting the two binary-entropy equations gives: ΓTdec\Gamma T_{\rm dec}. The table is an analytic computation performed for this proposal, not a simulation or an observation. It says that a common phrase such as “one decoherence time” is underspecified. At the 0.9-bit threshold, a Holevo ceiling appears at almost exactly one inverse rate, while the specified decision task needs about 1.49 inverse rates. At the 0.999-bit threshold the two clocks read about 3.29 and 4.13. The disagreement is finite and predictable.

Equation guide → · Article →