IndexQuantenMug

The Accelerant

Unruh Effect Physics

\[T = \frac{\hbar a}{2\pi c k_B}\]
$21.99 USD
$21.99 USD
Sale Ausverkauft
Size

Meet The Accelerant. Accelerate through empty space and it looks like a warm bath, but only to you. You'd need 10²⁰ m/s² to feel 0.4 K. Predicted, not yet seen directly. On the mug: T = ħa/(2πck_B). Pixel-art full-wrap black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A uniformly accelerating observer sees the vacuum as a thermal bath at T = ħa/(2πck_B), about 4×10⁻²¹ K per m/s². It has not yet been observed directly.

The Accelerant never stops speeding up, and to it the empty universe feels warm.

In 1976 William Unruh showed that the quantum vacuum depends on who is looking. An observer who moves at constant velocity sees empty space. An observer with constant proper acceleration a sees a thermal bath of particles at temperature T = ħa/(2πck_B), the formula on this mug. A horizon forms behind the accelerating observer, and the bath is tied to it, much as Hawking radiation is tied to a black hole's horizon.

The effect is tiny. T ≈ 4.06×10⁻²¹ K for every 1 m/s² of acceleration. A worked number: at Earth's surface gravity, 9.8 m/s², that is about 4×10⁻²⁰ K. To feel 0.4 K you would need about 10²⁰ m/s².

It is a prediction, not an observation. No experiment has yet seen the Unruh effect directly.

“The faster I gain speed,” says the Accelerant, “the warmer nothing gets. Only for me.”

Equations

\[T = \frac{\hbar a}{2\pi c k_B}\]
\[T \approx 4.06\times10^{-21}\ \text{K}\times\frac{a}{1\ \text{m s}^{-2}}\]
\[a = 10^{20}\ \text{m/s}^{2} \;\Rightarrow\; T \approx 0.4\ \text{K}\]
SymbolMeaningUnit
\(T\) Unruh temperature seen by the accelerating observer \(\mathrm{K}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(a\) proper acceleration of the observer \(\mathrm{m/s²}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)

Sources

  1. Unruh (1976) Notes on black-hole evaporation, Phys. Rev. D 14, 870
  2. Crispino, Higuchi & Matsas (2008) The Unruh effect and its applications, Rev. Mod. Phys. 80, 787
  3. NIST CODATA 2022 — Planck constant

Source Unruh, W. G. (1976). Notes on black-hole evaporation. Physical Review D 14, 870–892.doi.org/10.1103/PhysRevD.14.870

Field notes

Alle anzeigen
1 3
Alle anzeigen