Equation 40 · The Clock That Comes Back Wrong by Exactly Its Mass
What does this equation mean?
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.
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
Symbol Phi
dimensionless as a phase must be, and mass is recoverable from it as.
Symbol L_rm G
m G is part of the quantity the equation computes from the expression on the right.
Symbol b
b is one factor in the product that computes the quantity on the left.
Symbol v
v is one factor in the product that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Call []=m\,/ the loop’s phase debt : what the representation charges for a loop the classical group considered free. The loop invariant carries units of , exactly the units of / , so is dimensionless as a phase must be, and mass is recoverable from it as
For background, read the article’s source list.
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