Equation 31 · The Clock That Comes Back Wrong by Exactly Its Mass

What does this equation mean?

X=-i\mathbf b\cdot\mathbf P/\hbar

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 operations-imathbf b × mathbf P/hbar

Result or conditionX

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

X

Symbol X

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

Understand this part →

i

Symbol i

i is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

b

Symbol b

b is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

P

Symbol P

P is one of the signed contributions combined to compute 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 →

multiplication

Multiply the quantities on either side.

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

That triviality is what makes the loop phase exact rather than approximate. Write X=-i $\mathbf b$ $\cdot$ $\mathbf P$ / $\hbar$ and Y=-i $\mathbf v$ $\cdot$ $\mathbf K$ / $\hbar$ . Their commutator is

Read the equation in its article →

For background, read the article’s source list.

Return to The Clock That Comes Back Wrong by Exactly Its Mass

See this formula across 1 published context →

Browse the mathematical compendium →