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Equation 103 · Part 2 · The Bit Comes Back Before the Bearing

Symbol t

FQ(t)  ≈  f1 tβ,tG(δ)  ≈  βf1 δ2.F_Q(t) \;\approx\; f_1\,\frac{t}{\beta}, \qquad t_G(\delta) \;\approx\; \frac{\beta}{f_1\,\delta^2}.
tt

What this part means

t 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

t 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

…f1f_1 , the achievable variance scales as 1/(N f1f_1) , in contrast to the quadratically better Heisenberg scaling available only when probes are used coherently together [ 13 ] . Modeling the collected radiation up to time t as contributing Nγ(t)N_\gamma(t) ∼\sim t/β\beta roughly independent quanta gives, as a stated phenomenological ansatz rather than a first-principles evaporation calculation, FQ(t)  ≈  f1 tβ,tG(δ)  ≈  βf1 δ2F_Q(t) \;\approx\; f_1\,\frac{t}{\beta}, \qquad t_G(\delta) \;\approx\; \frac{\beta}{f_1\,\delta^2}. This model has an explicit conservation ceiling built in: it cannot be extended past the compass’s own total…

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