Equation 119 · Part 3 · The Clock That Comes Back Wrong by Exactly Its Mass

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mc^2/\hbar

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What this part means

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.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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The passage around this formula

Here is the strongest objection this construction has to survive, and it is not hypothetical — it was argued in print for over a decade. In 2010, Müller, Peters, and Chu proposed that an ordinary light-pulse atom interferometer’s gravimeter phase already constitutes a measurement of the gravitational redshift at the atom’s Compton frequency m $c^2$ / $\hbar$ , reading the standard interferometer as an implicit realization of exactly the proper-time phase this paper formalizes [ 6 ] . Wolf, Blanchet, Bordé, Reynaud, Salomon, and Cohen-Tannoudji objected immediately: the standard three-pulse Mach–Zehnder gravimeter phase, computed by the ordinary classical-action method, is $\phi$ $\approx$ k_{ $\rm$ …

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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

These citations provide research context; check each source for the exact claim it supports.