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Equation 34 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol X

[X,Y][X,Y]
XX

What this part means

X is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

X is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

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 eXe^XeYe^Ye−Xe^{-X}e−Ye^{-Y} vanishes identically, at all orders, with no small-loop approximation required:

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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