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Equation 50 · Part 2 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol b

T(b)G(v)T(−b)G(−v)T(\mathbf b)G(\mathbf v)T(-\mathbf b)G(-\mathbf v)
bb

What this part means

b 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

b 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

…saying explicitly why. Φ\Phi[LG\mathcal L_{\rm G}] does not come from a new term added to any Hamiltonian; it comes from how already-unitary translation and boost operators compose. Each operator in the product T(b\mathbf b)G(v\mathbf v)T(-b\mathbf b)G(-v\mathbf v) conserves probability on its own, and the product of unitaries is unitary regardless of whether the factors commute, so the loop as a whole still conserves probability and leaves every expectation value of energy and momentum exactly where an ordinary,…

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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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