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Equation 50 · Part 7 · No Particle Without a Cosigner

subscript

F˙a(Ω)  ∝  Ωe2πcΩ/a−1,Ω>0,\dot{\mathcal F}_a(\Omega) \;\propto\; \frac{\Omega}{e^{2\pi c \Omega / a} - 1}, \qquad \Omega > 0,
subscript

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

The first check any new object owes the literature is that it reproduce the literature’s own answer in the case the literature has already solved. For a worldline held at constant proper acceleration a forever, coupled linearly to a massless scalar field in the ordinary vacuum, with the switching left on for all time, the Wightman function depends only on the proper-time separation and the standard Fourier transform is exact and textbook: the excitation-branch rate per unit proper time takes the Bose-Einstein form F˙a(Ω)  ∝  Ωe2πcΩ/a−1,Ω>0\dot{\mathcal F}_a(\Omega) \;\propto\; \frac{\Omega}{e^{2\pi c \Omega / a} - 1}, \qquad \Omega > 0. with the proportionality constant fixed by the detector’s coupling strength and dimension — irrelevant here, since it cancels the instant the spectrum is…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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