14
$\begingroup$

Could I, for example, create a ‘special-relativity refrigerator’: I place a fresh apple in a centrifuge, spin it up such that the tangential speed of the apple is 0.99c, then enjoy a fresh apple at my convenience?

Might we create time capsules like this?

Edit: I am asking hypothetically: a more realistic time capsule choice might be a planet near a black hole.

Hypothetically would a watch placed in a centrifuge spun as described with the apple tick slower than one held in my hand? Assuming the materials are whatever they need to be to not be eviscerated.

Improve this question
$\endgroup$
7
  • 1
    $\begingroup$ Sounds like a way of juicing apples rather than preserving them. No materials are anywhere near strong enough to do as you suggest. If you mean hypothetically, then please say so, but how do you overcome the "artificial gravity" that you've created that way? $\endgroup$
    – Jiminy Cricket.
    Commented Mar 18, 2023 at 23:56
  • $\begingroup$ According to SR, the radius of you apple is unchanged, but the circumfrence is Lorentz contracts by a factor of $7\gt 2\pi$.... $\endgroup$
    – JEB
    Commented Mar 19, 2023 at 0:00
  • 1
    $\begingroup$ Enormous energy requirements to spin-up and spin-down. Possibly more energy than making an apple with your Star Trek matter creator thingy. Definitely more than just driving to the shops and back. $\endgroup$
    – StephenG - Help Ukraine
    Commented Mar 19, 2023 at 0:19
  • 2
    $\begingroup$ Since fridges are rigid bodies, you may enjoy the Ehrenfest paradox of discs. It does not change the clock slowing, yet it shows practical subtleties. $\endgroup$
    – M.S.
    Commented Mar 19, 2023 at 13:21
  • 1
    $\begingroup$ Does this answer your question? Can a ultracentrifuge be used to test general relativity? $\endgroup$
    – John Rennie
    Commented Mar 20, 2023 at 17:17

2 Answers 2

Reset to default
33
$\begingroup$

This has been tested, but with muons rather than apples. Muons spoil much faster than apples ($2.2\mathrm{\ \mu s}$ half life), but they don’t get squished by the enormous accelerations ($10^{18}\mathrm{\ g}$) required to stay in their highly relativistic ($\gamma = 29$) circular motion. It was found that their half life was extended relative to muons at rest in the lab, exactly as predicted by special relativity.

Bailey, J., Borer, K., Combley, F. et al. Measurements of relativistic time dilatation for positive and negative muons in a circular orbit. Nature 268, 301–305 (1977). https://doi.org/10.1038/268301a0

Improve this answer
$\endgroup$
12
$\begingroup$

The premise of the question doesn't really involve rotating reference frames. The circular motion of the clock or apple can be straightforwardly analyzed in an inertial lab frame. The clock moving at $0.99c$ would tick 1/7 as fast, in the lab frame. The apple would last 7 times as long. This is true regardless of whether the motion is in a straight line or a circle. The circular motion only means that the inner and outer edges of the clock/apple would age at different rates.

Improve this answer
$\endgroup$
3
  • 3
    $\begingroup$ And of course the apple's kinetic energy is 6 times its rest mass energy. For a 200 g apple, that's almost 30 billion kilowatt-hours of KE. :) $\endgroup$
    – PM 2Ring
    Commented Mar 19, 2023 at 4:13
  • $\begingroup$ @sten Ehrenfest's paradox isn't really a problem with rotating reference frames - it's a problem with rigid bodies, and that rigid bodies have problems in SR shouldn't be a surprise when you consider that a displacement of one end of a rigid body must instantaneously be transmitted to the other end, faster than light. Rotating reference frames work just fine, the only trickiness is one also present in Newtonian mechanics - they're non-inertial $\endgroup$
    – Tristan
    Commented Mar 20, 2023 at 14:41
  • $\begingroup$ @Tristan fair point, I reworded the opening $\endgroup$
    – Sten
    Commented Mar 20, 2023 at 17:13

Not the answer you're looking for? Browse other questions tagged or ask your own question.