• Pixel-art sticker of Muonet, personifying Time Dilation, with the caption “Fast Clocks Run Slow.”

IndexRelativity & CosmosSticker

Muonet

Time Dilation Physics

\[\Delta t = \gamma\,\Delta t_0\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Muonet, a muon born 15 km up whose clock runs slow. At rest he lasts about 2.2 microseconds, barely 660 m of travel. At 0.995c relativity stretches that about ten times, so he covers roughly 6.6 km and reaches the ground. 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 Muonet, a particle born high in the sky who carries a clock that runs slow.

Cosmic rays smash into air molecules about 15 km up and make muons, heavy cousins of the electron. A muon at rest decays in about 2.2 microseconds on average. Even at nearly the speed of light, that is only enough time to travel about 660 m.

Yet huge numbers of muons reach the ground. Special relativity explains it: a moving clock runs slow by the factor γ, so Δt = γΔt₀. At 0.995c, γ ≈ 10. From the ground, the muon lives about 22 μs and can cover about 6.6 km.

The faster the muon moves, the bigger γ gets and the farther it travels before decaying. From the muon's own point of view, its clock is normal and the atmosphere is squashed shorter instead.

Muon detectors on mountains and at sea level were used in the 1940s and 1960s to measure this effect directly.

Equations

\[\Delta t = \gamma\,\Delta t_0\]
Symbols
SymbolMeaningUnit
\(\Delta t\) time measured by an observer who sees the clock moving \(\mathrm{s}\)
\(\gamma\) Lorentz factor \(\mathrm{dimensionless}\)
\(\Delta t_0\) proper time measured in the clock's own frame \(\mathrm{s}\)