• Pixel-art sticker of Zerpa, personifying Zero-Point Energy, with the caption “Never Fully At Rest.”

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Zerpa

Zero-Point Energy Physics

\[E_n = \hbar\omega\left(n+\tfrac{1}{2}\right)\]
Regular price $4.99 USD
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Meet Zerpa, a quantum harmonic oscillator who is never fully at rest: her levels are E = ħω(n + ½), so even the lowest level still holds ħω/2 and she can never have zero energy. Even at absolute zero she keeps a residual jiggle. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

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

Meet Zerpa, a quantum oscillator who can never be perfectly still, even at absolute zero.

A mass on a spring in classical physics can have any energy, including zero. In quantum mechanics a harmonic oscillator can only have energies E_n = ħω(n + ½), for n = 0, 1, 2 and so on. The levels are evenly spaced by ħω. And the lowest level, n = 0, is not zero but ħω/2: the zero-point energy.

The reason is the uncertainty principle. To have zero energy, the oscillator would need to sit exactly at the bottom with exactly zero momentum, and quantum mechanics forbids pinning down both. The ground state is the best compromise, a small spread in position and momentum.

Zero-point motion is real and measurable. It is why liquid helium does not freeze at normal pressure even near absolute zero, and it shifts the vibrational energies of molecules, which shows up in their spectra.

Zero-point energy is sometimes misrepresented as a source of free power. It is the lowest possible energy, so no energy can be extracted from it.

Equations

\[E_n = \hbar\omega\left(n+\tfrac{1}{2}\right)\]
Symbols
SymbolMeaningUnit
\(E_n\) energy of level n \(\mathrm{J}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(\omega\) angular frequency of the oscillator \(\mathrm{rad/s}\)
\(n\) quantum number (0, 1, 2, …) —