Does special relativity hold for rotating reference frames?

Question

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.

Answer 1

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

Answer 2

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.