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Equation 55 · Part 4 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol c^2

⟨H⟩ b⋅v/(ℏc2)\langle H\rangle\,\mathbf b\cdot\mathbf v/(\hbar c^2)
c2c^2

What this part means

The square of c: multiply c by itself.

Its job in the formula

c2c^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

The passage around this formula

…with a spectrum, different on every energy eigenstate. Repeating the loop calculation of the previous section on a state with sharp energy ⟨\langle H⟩\rangle gives a phase ⟨\langle H⟩\rangle\,b\mathbf b⋅\cdotv\mathbf v/(ℏ\hbar c2c^2) that varies from state to state. A central extension, by definition, must give the same phase to every vector in the representation; a state-dependent phase is not a central extension, it is an ordinary consequence of ordinary dynamics, and it can be removed by working with true,…

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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.

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Sources cited in the surrounding passage

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