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Equation 22 · Part 2 · How Fast Can a Horizon Learn Which Path You Took?

Symbol T_rm dec

ΓTdec\Gamma T_{\rm dec}
TdecT_{\rm dec}

What this part means

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.

Its job in the formula

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.

The passage around this formula

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.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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