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Suppose you have an object that is rotating rapidly about its central axis. Let's say that the rotation is so fast that tangential velocity of the outermost part of the object is nearly relativistic. For example, it could be a radioactive molecule placed in some advanced optical centrifuge. Would the molecule experience time dilation? i.e. would its half-life change?

Note there is no "inertial" motion, only rotation, in this thought experiment. Note also that this might be different than the case of a neutron star, where gravitational time dilation may be dominant. Here I would just like to consider special relativistic effects

Superbee
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Yes, a purely rotating object experiences time dilation. For further reading, I suggest you look into https://link.springer.com/content/pdf/10.1007/BF02764025.pdf