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Suppose a telescope can see a clock inside a ship traveling near the speed of light, in a circular (constant radius) fashion.

The telescope is at a certain distance perpendicular to the circle of the plane that describes the trajectory of the spacecraft. Right in the center of said circle.

That implies that the telescope remains to constant distance from the spacecraft. In other words, it is not traveling (it is not approaching or moving away).

If the clock in the telescope were to synchronize with the one on the ship, should the clocks remain synchronized?

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Dale
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joseluisbz
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You seem to be asking whether time dilation is an optical effect due to light having to "catch up" with a moving object. The answer is definitely no. Time dilation depends only on the (relative) speeds of the objects, not on the direction in which they are moving. In your setup the clock going around the circle is moving relative to the telescope, even though it isn't getting any nearer or further. So it will be observed to tick more slowly.

Something very similar to what you proposed happens every day in circular particle accelerators. Particles traveling in a circle at nearly the speed of light are found to have much longer lifetimes than particles at rest. That is, their "internal clocks" are observed to be ticking slowly relative to laboratory clocks.

Eric Smith
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First, a spaceship cannot travel at the speed of light. But you don't need to to see this effect. The clocks do not remain synchronized for any non-$0$ speed of the spaceship. Faster speeds mean a bigger mismatch.

This experiment has been done with high precision clocks on supersonic jets. One went east around the world, the other west. This means one jet traveled faster than the other because it was going with the rotation of the earth. When they got back, the clocks disagreed by a few nanoseconds.

mmesser314
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  • That is why I said Suppose, I am aware that it is not possible to travel at the speed of light. What I meant, is that circular and perpendicular flight could imply zero relative velocity (not moving) with respect to the telescope's point of view. Then from the telescope it would be seen that the ship's clock is slow (I don't know if it is fast). – joseluisbz Jun 09 '22 at 16:38
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    I can't find the planes Hafele and Keating used, but they have been described as "commercial", and there is a photo of a Navy propellor driven plane, so "supersonic" is probably inaccurate. And the difference was from -50 ns to 273 ns, depending on direction of travel. – JEB Jun 09 '22 at 17:14
  • @joseluisbz One cannot answer a relativistic question with impossible scenario. Consider this question: Suppose I travel backwards in time. What is the speed of the car (as measured by me) moving past me? How would you answer? – User123 Jun 09 '22 at 20:05