← Mathematical compendium

Published equation contexts

f(r)\sqrt{f(r)}

Why this formula appears here

A processor held at fixed altitude near a black hole’s horizon runs slow. Not metaphorically: its proper time τ\tau , the time its own internal clock and its own quantum gates actually tick through, elapses more slowly than the coordinate time t used by a bookkeeper stationed far away, by the ordinary gravitational redshift factor f(r)\sqrt{f(r)} . A distant observer watching that processor through a telescope sees every one of its gates run in slow motion. Turn the statement around, though, and something more interesting appears to fall out. If the processor’s own clock is the one that is running normally — and by the equivalence principle, locally it is — then from the processor’s point of view…

Read the full article-specific guide →

Read the representative guide

ff

Symbol f

f 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 →
rr

Symbol r

r 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.

f(r)\sqrt{f(r)}

Equation 3 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

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

A processor held at fixed altitude near a black hole’s horizon runs slow. Not metaphorically: its proper time τ\tau , the time its own internal clock and its own quantum gates actually tick through, elapses more slowly than the coordinate time t used by a bookkeeper stationed far away, by the ordinary gravitational redshift factor f(r)\sqrt{f(r)} . A distant observer watching that processor through a telescope sees every one of its gates run in slow motion. Turn the statement around, though, and something more interesting appears to fall out. If the processor’s own clock is the one that is running normally — and by the equivalence principle, locally it is — then from the processor’s point of view…

Equation guide → · Article →