Equation 28 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol H

\langle H(\tau)\rangle

H

What this part means

H 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

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

Full expressionSymbol HArticle meaning

The passage around this formula

…enters, and invariant under any passive coordinate change of the ambient spacetime, since both d $\tau$ and a comoving-frame energy are scalars. It is not invariant under boosting the local tetrad used to evaluate $\langle$ H( $\tau$ ) $\rangle$ — a different local observer at the same event assigns a different local energy — which is why the convention must be pinned to the processor’s own rest frame and stated explicitly, not left implicit the way it usually is in flat-space quantum speed limit work.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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