← Back to article

Equation 51 · A Horizon Is a Toll Booth, Not a Loophole

What does this equation mean?

Δt=Δτ/f\Delta t = \Delta\tau/\sqrt f

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationsΔτ/sqrt f
Result or conditionΔ t
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

Δt\Delta t

Symbol Δ t

Δ t is part of the quantity the equation computes from the expression on the right.

Understand this part →

Δτ\Delta\tau

Symbol Δτ

Δτ is an input to the expression that computes the quantity on the left.

Understand this part →

ff

Symbol f

f is an input to the expression that computes the quantity on the left.

Understand this part →

=

=

The expressions on both sides represent the same quantity under the stated assumptions.

Understand this part →

See an illustrated explanation →
√

√

Take a square root.

Understand this part →

change

change

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Understand this part →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

​ E 0 ′ ​ (the amount of energy it would cost a distant experimenter, at infinity, to deliver that same physical resource down to radius r ), and integrate over the corresponding coordinate interval Δ\Delta t = Δ\Deltaτ\tau/f\sqrt f :

Read the equation in its article →

For background, read the article’s source list.

Return to A Horizon Is a Toll Booth, Not a Loophole

See this formula across 1 published context →

Browse the mathematical compendium →