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Equation 10 · Part 1 · No Particle Without a Cosigner

Symbol F_x

Fx(Ω)=∫dτ dτ′ χ(τ)χ(τ′) e−iΩ(τ−τ′) W[x(τ),x(τ′)],\mathcal F_x(\Omega) = \int d\tau\, d\tau'\, \chi(\tau)\chi(\tau')\, e^{-i\Omega(\tau-\tau')}\, W\big[x(\tau), x(\tau')\big],
FxF_x

What this part means

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

Its job in the formula

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

The passage around this formula

…frequency. Third, the field state enters only through W , and changing the field state — the ordinary vacuum, a thermal state, the Boulware, Hartle-Hawking, or Unruh state of a black-hole exterior — changes Fx\mathcal F_x even for a fixed trajectory. Keeping these three inputs — proper time, proper-frame gap, and field state — cleanly separated is what prevents an ordinary coordinate-time effect, like gravitational redshift between two static observers at different heights, from being mistaken for a genuine…

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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

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