Unruh effecteffect
In 1976, William Unruh showed that an observer with constant acceleration in a vacuum will detect thermal radiation of particles. This striking result arises from quantum field theory in curved spacetime: different observers can disagree on the particle content of the same state. The effect is closely related to Hawking radiation from black holes; indeed, an observer hovering above a black hole horizon experiences acceleration and sees Unruh radiation. The temperature formula is simple: it is proportional to acceleration. At an acceleration of 10^20 m/s², the temperature would be about 0.4 Kelvin — still very cold.
How it works
Although the effect is too weak to measure in a car or rocket, it becomes important in strong gravitational fields, such as near black holes, where the equivalence principle (acceleration is equivalent to gravity) comes into play. This helps explain why black holes are not completely black.
💡 If you're afraid of freezing in the vacuum of space, just accelerate to incredible speeds — the vacuum itself will warm you up! (Though, first, you'll be squashed.)
k_B T = \frac{\hbar a}{2\pi c} \quad \text{or} \quad T = \frac{\hbar a}{2\pi c k_B}
T — observed vacuum temperature for the accelerated observer; a — proper acceleration of the observer (m/s²); ħ — reduced Planck constant (ħ ≈ 1.0546×10⁻³⁴ J·s); c — speed of light in vacuum (c ≈ 3×10⁸ m/s); k_B — Boltzmann constant (k_B ≈ 1.38×10⁻²³ J/K). For a = 10^20 m/s², T ≈ 0.4 K.