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Published equation contexts

Δϕclock=−ΔEℏ Δτ\Delta\phi_{\rm clock}=-\frac{\Delta E}{\hbar}\,\Delta\tau

Why this formula appears here

The proper-time loop LP\mathcal L_{\rm P} is where mass stops being a fixed label and becomes something an object can carry a little more or less of depending on what it is doing internally. A composite system with an internal excitation of energy Δ\Delta E above its ground configuration carries additional rest mass Δ\Delta E/c2c^2 , by ordinary mass–energy equivalence — no redefinition of either the relativistic or the everyday meaning of mass, simply the standard bookkeeping in which a system’s total rest energy Mc2c^2 includes whatever internal energy HintH_{\rm int} it holds: M=M0M_0+HintH_{\rm int}/c2c^2 . If the same object is sent along two paths that differ in proper time by Δ\Deltaτ\tau , and its…

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Δϕclock\Delta\phi_{\rm clock}

Symbol Δphi_rm clock

Δphiri_rm clock is part of the quantity the equation computes from the expression on the right.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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Δϕclock=−ΔEℏ Δτ.\Delta\phi_{\rm clock}=-\frac{\Delta E}{\hbar}\,\Delta\tau.

Equation 104 · Evolutionary Physics

The Clock That Comes Back Wrong by Exactly Its Mass

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The proper-time loop LP\mathcal L_{\rm P} is where mass stops being a fixed label and becomes something an object can carry a little more or less of depending on what it is doing internally. A composite system with an internal excitation of energy Δ\Delta E above its ground configuration carries additional rest mass Δ\Delta E/c2c^2 , by ordinary mass–energy equivalence — no redefinition of either the relativistic or the everyday meaning of mass, simply the standard bookkeeping in which a system’s total rest energy Mc2c^2 includes whatever internal energy HintH_{\rm int} it holds: M=M0M_0+HintH_{\rm int}/c2c^2 . If the same object is sent along two paths that differ in proper time by Δ\Deltaτ\tau , and its…

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