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

What does this equation mean?

M0c2Δτ/ℏM_0c^2\Delta\tau/\hbar

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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M0M_0

Symbol M_0

M0M_0 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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c2c^2

Symbol c^2

The square of c: multiply c by itself.

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Δτ\Delta\tau

Symbol Δτ

Δτ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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change

change

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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superscript

superscript

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.

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How to interpret it

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What the article says around this equation

The shared M0M_0c2c^2Δ\Deltaτ\tau/ℏ\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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Sources cited in the surrounding passage

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