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TU(a(τ))T_U(a(\tau))

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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(τ\tau) varies with proper time, expanding in powers of a˙\dot a , 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 TU(a(τ)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…

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τ\tau

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TU(a(τ))T_U(a(\tau))

Equation 58 · Evolutionary Physics

No Particle Without a Cosigner

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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(τ\tau) varies with proper time, expanding in powers of a˙\dot a , 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 TU(a(τ)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…

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