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Dilatia

Time Dilation Physics

\[\Delta t = \gamma\,\Delta t_0\]
$21.99 USD
$21.99 USD
할인 품절
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Whose clock is right? Both. Dilatia shows special relativity’s time dilation: a clock moving relative to you ticks slower by the Lorentz factor γ, so Δt = γΔt0. The effect is symmetric between moving observers, and it is measured daily in fast muons and GPS satellites. Pixel-art 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 moving clock runs slow by the Lorentz factor γ compared with clocks at rest. The effect is tiny at everyday speeds but grows without limit as the speed approaches that of light.

Dilatia carries a clock, and so do you. Each of you is sure the other's is slow. Both are right.

In 1905 Einstein built special relativity on two rules: the laws of physics are the same for every observer moving at constant velocity, and every such observer measures the same speed of light. Together they force moving clocks to tick slowly. If a clock moves past you at speed v, the interval between its ticks, as you measure it, is stretched by the Lorentz factor γ.

The effect is symmetric. From Dilatia's point of view you are the one moving, and your clock runs slow. There is no contradiction because the two of you also disagree about which distant events happen at the same time. YOUR CLOCK, NOT MINE. is the right attitude.

It is measured, not just predicted. Muons made by cosmic rays high in the atmosphere live about 2.2 microseconds at rest, too short to reach the ground at nearly light speed, yet many do, because their clocks run slow in our frame. Bruno Rossi and David Hall measured it in 1941; David Frisch and James Smith repeated the comparison with a precise count in 1963. GPS satellites must correct for it too, alongside a larger, opposite effect of gravity on their clocks.

Dilatia is not late. She is just on her own time.

Equations

\[\Delta t = \gamma\,\Delta t_0\]
\[\gamma = \frac{1}{\sqrt{1 - v^{2}/c^{2}}}\]
SymbolMeaningUnit
\(\Delta t\) time between two ticks of a moving clock, as measured by you \(\mathrm{s}\)
\(\Delta t_0\) proper time: the same interval measured by the clock itself \(\mathrm{s}\)
\(\gamma\) Lorentz factor \(\mathrm{1}\)
\(v\) relative speed of the clock \(\mathrm{m/s}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)

Sources

  1. Einstein (1905) Zur Elektrodynamik bewegter Körper, Ann. Phys. 322, 891
  2. HyperPhysics — Time Dilation
  3. Feynman Lectures on Physics Vol. I Ch. 15: The Special Theory of Relativity
  4. Rossi & Hall (1941) Variation of the Rate of Decay of Mesotrons with Momentum, Phys. Rev. 59, 223
  5. Frisch & Smith (1963) Measurement of the Relativistic Time Dilation Using μ-Mesons, Am. J. Phys. 31, 342
  6. Ashby (2003) Relativity in the Global Positioning System, Living Rev. Relativ. 6, 1

Source Einstein, A. (1905). Zur Elektrodynamik bewegter Körper. Annalen der Physik 322, 891–921.doi.org/10.1002/andp.19053221004

Field notes

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