Equation 22 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol N_perp

N_\perp[\Gamma] = \frac{2}{\pi\hbar}\int_\Gamma\left[\langle H(\tau)\rangle - E_0(\tau)\right]d\tau.

N_\perp

What this part means

$N_p$ erp is part of the quantity the equation computes from the expression on the right.

Its job in the formula

$N_p$ erp is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol N_perpArticle meaning

The passage around this formula

…non-negative functional of a timelike worldline in a fixed background spacetime together with a stated local energy convention; because the integrand is an energy and d $\tau$ is a time, the integral has action units and $N_\perp$ is dimensionless. It is invariant under reparametrizing $\Gamma$ ’s own curve parameter, since only proper time 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…

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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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Sources cited in the article section

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