Equation 32 · The Clock That Comes Back Wrong by Exactly Its Mass

What does this equation mean?

Y=-i\mathbf v\cdot\mathbf K/\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 v × mathbf K/hbar

Result or conditionY

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.

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Y

Symbol Y

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

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i

Symbol i

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

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v

Symbol v

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

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K

Symbol K

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

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=

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

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multiplication

Multiply the quantities on either side.

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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

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