Unruh Effect 3D: Rindler Trajectory & Vacuum Detection

Observer's Proper Acceleration

Acceleration a —

Detector mode frequency ω —

Live Readouts

Proper accel. a

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In units of g

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Unruh temperature T

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Occupation n̄(ω)

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Inertial detections

Accelerated detections

How it works

The purple observer follows a genuine hyperbolic Rindler worldline — the exact trajectory of constant proper acceleration in relativity — swept back and forth so it stays in view:

x(τ) = (1/α)(cosh(ατ) − 1)
t(τ) = (1/α)sinh(ατ)          (c = 1, visualization units)

Its worldline asymptotically approaches the light cone — exactly like a real accelerated observer forever chasing but never reaching c. The cyan observer drifts inertially alongside it for contrast. Both readouts feed from the same real Unruh formula as the 2D version: T = ħa/(2πck_B) sets the temperature from your acceleration slider, and n̄(ω) = 1/(e^(ħω/k_BT) − 1) sets how fast the accelerated detector lights up with real detected quanta at mode frequency ω. The inertial detector's rate is pinned at zero — the same vacuum field, unaccelerated, stays empty by definition.

Acceleration a — physical proper acceleration (m/s², log scale) driving both the real Unruh temperature and the visual sharpness of the Rindler bend.
Mode frequency ω — the field mode the accelerated detector is tuned to; lower ω gives higher occupation at fixed temperature.
Vacuum field — toggles the ambient shimmering point-cloud representing the underlying quantum field's vacuum fluctuations (not detected particles — those only appear as bright sparks at a detector).

Real, peer-reviewed QFT result (Fulling 1973, Davies 1975, Unruh 1976), and the flat-spacetime cousin of Hawking radiation via the equivalence principle: a uniformly accelerated frame is locally indistinguishable from sitting near a black hole's horizon.

Accelerated observer (Rindler path) Inertial observer Detected quantum

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