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As a thought experiment, I was trying to find a way to constantly dilate time while keeping an object effectively in place. I quickly decided that moving forwards and backwards wouldn't work—the speed would be zero at the turning points.

My next idea was to use circular motion—an object could move at a great speed in circles while staying in the same location.

Would time still dilate for such an object?

EDIT: One of my problems with this concept is that a rotating radius would have different speeds along its length, possibly therefore leading to different degrees of time dilation along its length.

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marked as duplicate by safesphere, user191954, Kyle Kanos, John Rennie special-relativity Oct 15 '18 at 10:35

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Welcome to physics.SE! Cool question.

Yes, this works. In fact, there was a classic test of special relativity done using exactly this technique, Bailey at al., Nucl. Phys. B150(1979) 1. They accelerated muons in a circular accelerator to $\gamma\approx30$, and found their half-lives to be lengthened by exactly that factor. For a more detailed description of the experiment, see example 6 in section 23.2 of this textbook, which I'm the author of.

One of my problems with this concept is that a rotating radius would have different speeds along its length, possibly therefore leading to different degrees of time dilation along its length.

I see. I guess you were imagining spinning a macroscopic object about its center of mass...? That's (a) impractical to do, and (b) much more difficult to interpret, as you've correctly figured out. The particle physics experiment evades this issue by using subatomic particles, which have a definite value of $r$.

I quickly decided that moving forwards and backwards wouldn't work—the speed would be zero at the turning points.

There have actually been tabletop experiments done in this style, with atomic clocks. The effect can still be calculated even though $\gamma$ is varying. The velocities are $\ll c$, but the atomic clocks are extremely precise, so you get a measurable effect. For a brief description, see example 5 immediately above the one I previously mentioned. The reference is Chou et al., Science 329 (2010) 1630.

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  • $\begingroup$ Another classic experiment put atomic clocks on fast jets and flew them around the world. One went east, adding the jet speed to earth's rotational speed. The other went west, subtracting the jet speed from earth's speed. Afterward the clocks disagreed by the (small) predicted amount. $\endgroup$ – mmesser314 Oct 14 '18 at 22:42
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    $\begingroup$ @mmesser314: Yes, I think you're describing the Hafele-Keating experiment. It's a little more conceptually complicated, because there was gravitational time dilation that was comparable to the kinematic time dilation. $\endgroup$ – Ben Crowell Oct 14 '18 at 23:58

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