Equation 37 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol e^X

e^Xe^Ye^{-X}e^{-Y}

e^X

What this part means

$e^X$ 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

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

Full expressionSymbol e^XArticle meaning

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 $e^X$ $e^Y$ $e^{-X}$ $e^{-Y}$ vanishes identically, at all orders, with no small-loop approximation required:

Read this part in the article →

Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

See this notation across published equations →

The article lists its research sources here.