Equation 105 · Part 6 · The Clock That Comes Back Wrong by Exactly Its Mass

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M_0c^2\Delta\tau/\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

The shared $M_0$ $c^2$ $\Delta$ $\tau$ / $\hbar$ term, common to both arms, is an overall phase and drops out of any interference signal — consistent with the rule that only relative phase between branches is ever observable. What survives is a clock-visible term set entirely by the internal-energy difference, first proposed as an observable interferometric signature of general-relativistic proper time by Zych, Costa, Pikovski, and Brukner [ 10 ] , and later reframed explicitly as a quantum analogue of the twin paradox by Loriani and collaborators [ 11 ] .

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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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