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Equation 21 · Part 2 · How Fast Can a Horizon Learn Which Path You Took?

Symbol T_chi

ΓTχ\Gamma T_\chi
TχT_\chi

What this part means

TcT_chi 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

TcT_chi 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: ΓTχ\Gamma T_\chi. 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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