$$a(\tau)$$

Equation 55 · Evolutionary Physics

No Particle Without a Cosigner

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

A second limit worth naming, because it is where the eternal-acceleration answer above starts to strain, is slow time dependence. Barbado and Visser worked out the response of a detector whose acceleration a($\tau$) varies with proper time, expanding in powers of $\dot a$ , $\ddot a$ , and higher proper-time derivatives of the acceleration [ 8 ] . At leading order, wherever the acceleration changes slowly compared to the local orthogonalization timescale it sets for itself, the detector reports the instantaneous Unruh temperature $T_U(a(\tau)$) at each moment, as though briefly and locally eternal. This adiabatic recovery is the second known limit this construction inherits rather than derives: it…

Meanings in this article

• $a$: the acceleration.

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