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Equation 82 · Part 5 · No Particle Without a Cosigner

Symbol g

Ddet(a, a+δa)  ≈  [max⁡u>0u g(u)]⋅∣δa∣a.D_{\rm det}(a,\, a+\delta a) \;\approx\; \left[\max_{u>0} u\,g(u)\right] \cdot \frac{|\delta a|}{a}.
gg

What this part means

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

Its job in the formula

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

The passage around this formula

Every accelerated detector’s normalized spectrum is the same universal curve g , only rescaled by a/c . For two accelerations separated by a small increment, a and a+δ\delta a , standard calculus for a scale family gives, to leading order in δ\delta a , Ddet(a, a+δa)  ≈  [max⁡u>0u g(u)]⋅∣δa∣aD_{\rm det}(a,\, a+\delta a) \;\approx\; \left[\max_{u>0} u\,g(u)\right] \cdot \frac{|\delta a|}{a}. This is the same trick used to derive Wien’s displacement law: because u\,g(u) rises from zero, passes…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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