Equation 37 · The Clock That Comes Back Wrong by Exactly Its Mass
What does this equation mean?
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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol e^X
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol e^Y
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol e^-X
X is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol e^-Y
Y is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
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What the article says around this equation
Because [X,Y] is itself proportional to the identity, it commutes with both X and Y , so every higher term in the Baker–Campbell–Hausdorff expansion of vanishes identically, at all orders, with no small-loop approximation required:
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