In a rotating reference frame, while observing the proper motion of stars due to your spin, would you perceive time dilation when closely observing those stars?
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$\begingroup$ Are you asking if apparent high speed of stars in a rotating frame of reference has similar effects on the observed rate of processes in those stars, like a fast motion in an inertial frame would have? $\endgroup$– Ján LalinskýCommented Sep 16, 2023 at 1:22
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1$\begingroup$ Yes, that's what I was asking . $\endgroup$– A Curious MindCommented Sep 16, 2023 at 4:08
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$\begingroup$ How would that work - you start spinning around, distant stars will slow down in time in your frame at a different rate depending on the observation angle, but not in a frame of somebody next to you who isn't spinning? This does not seem logically possible. Rotation of the observer gives the stars only apparently different speeds, there is no real difference that could cause different rate of processes. $\endgroup$– Ján LalinskýCommented Sep 16, 2023 at 13:13
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$\begingroup$ Your comment is a bit confusing I hope you could clarify more, what doesn't seem logically possible? As far as I know any act of spin makes all stars and planets seem to move around the sky , isn't that motion or proper motion enough to cause time dilation ? Imagine if we replaced the stars with light clocks for pure thought experiment, thank you . Please clarify $\endgroup$– A Curious MindCommented Sep 16, 2023 at 13:45
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$\begingroup$ It is only apparent motion in a non-inertial frame, special relativity results like time dilation do not directly apply. That motion is superluminal for sufficiently distant objects, thus SR cannot logically work in such frames. $\endgroup$– Ján LalinskýCommented Sep 16, 2023 at 13:50
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3 Answers
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No. Note that in a rotating frame the speed of light is not constant, and varies with the distance from the axis of rotation. Any way you slice it, the distant stars are moving much slower than light.
answered Sep 15, 2023 at 21:27
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$\begingroup$ Why? And how's the speed of light not constant in a rotating frame to be exact . $\endgroup$ Commented Sep 16, 2023 at 4:08
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$\begingroup$ Are you telling that in a rotating frame ? When a rotating frame rotates from east to west, and you sent a beam of light from west . It would take shorter time and be blueshifted since you are moving towards the light and from east it takes longer time since ton are moving away from the light ? Isn't that a optical illusion? What if we replaced the stars with massive light clocks? I mean the speed of light Is constant but sometimes takes a longer or shorter path, $\endgroup$ Commented Sep 16, 2023 at 4:15
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$\begingroup$ The speed of light is only constant in an inertial frame. Similarly, light travels in a straight line in inertial frames, but generally in a curved line in a non-inertial frame. For example, the light from a distant star follows a crazy spiral that wraps around the Earth once every day in a frame rotating with the Earth. Since the path the light takes is much longer than the straight line path, but the time taken is the same, the speed of light must be greater. In some sense this is just a coordinate artifact, the result of choosing "bad" (non-inertial) coordinates. $\endgroup$ Commented Sep 16, 2023 at 16:32
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$\begingroup$ As measured in a rotating frame the speed of light really is different in the direction of rotation and opposite it. This is called the Sagnac effect, and again, it's an artifact of using non-inertial coordinates. In an inertial frame the speed of light is always c. $\endgroup$ Commented Sep 16, 2023 at 16:38
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$\begingroup$ It's just the light taking a shorter or longer path because you seem to move towards or away from it , however the question is does that cause time dilation in any way? $\endgroup$ Commented Sep 16, 2023 at 17:12
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Let me take another case to use as an example of how using a rotating coordinate system is accommodated.
Let there be a wheel shaped space station. Let that space station be rotating at an angular velocity $\omega$ such that an accelerometer located at a distance $r$ to the axis of rotation is registering 1 unit of centripetal acceleration. As we know, in that scenario the G-load will be proportional to the distance to the center of rotation. That is: an accelerometer located at $\frac{1}{2}r$ will register half the G-load, and an accelerometer at $2r$ will register twice the G-load, and so on.
Let there be a set of atomic clocks, located at various distances to the center of rotation. All those clocks go around at the same angular velocity, but the clocks located further away from the center are travelling a longer distance than the clocks closer to the center. Therefore: for the clocks located further from the center a smaller amount of time will elapse than for the clocks closer to the center of rotoation.
The mathematics of GR allows the following: if you use a rotating coordinate system then in terms of that representation there is a corresponding centrifugal gravitational potential. In terms of that gravitational potential: for clocks located a lower levels of that gravitational potential a smaller amount of proper time will elapse.
Therefore:
If the only information you have access to is:
-the onboard measurements of G-load
-amount of proper time elapsing at various points inside the space station
then both representations predict identical measurement readings.
Another way of saying that is: when confined to onboard measurements only: using a non-rotating coordinate system or a rotating coordinate system is observationally identical.
Among the goals of formulating GR was the point that I discussed above: to have a mathematical framework in place that includes the property that both a non-rotating and a rotating coordinate system can be used: both representation will describe identical observations.
(When using a rotating coordinate system it is necessary to specify the amount of rotation relative to the non-rotating coordinate system.)
The essential point is: when your measurements are confined to onboard measurements then as a matter of principle there is no difference to percieve. Both representations, non-rotating coordinate system or rotating coordinates system: identical perception.
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Yeah, in a rotating reference frame, observers would perceive time dilation effects when closely observing objects, including stars. This phenomenon is known as the "Sagnac effect" and is a consequence of both special and general relativity.
The Sagnac effect occurs when an observer rotates with respect to distant objects. It leads to a difference in the round-trip travel times of light rays following opposite directions around the rotation. As a result, clocks located at different positions in the rotating frame will run at slightly different rates. This effect has been experimentally observed in various systems, including interferometers and rotating platforms.
In the context of your question, if you were in a rotating reference frame (e.g., a spinning spaceship), and you were closely observing stars, you would perceive time dilation effects. Clocks closer to the axis of rotation would run slightly faster than those farther from the axis due to the Sagnac effect. This is a manifestation of the broader principle that relative motion, acceleration, or gravitational fields can lead to time dilation according to the theory of relativity.
It's SUPER important to note that the Sagnac effect is generally a small and subtle effect, especially at the relatively slow speeds of rotation typically encountered in everyday situations. However, it becomes more significant at very high speeds, such as those close to the speed of light, or in highly precise experimental setups like interferometers used for tests of relativity.
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$\begingroup$ The statements about the Sagnac effect in this answer are for the most part incorrect. That is too bad; the Sagnac effect is of crucial importance; presenting it correctly is essential. The Sagnac effect is unrelated to time dilation effect. The Sagnac effect has the following unique property: both in terms of pre-relativistic mechanics and relativistic mechanics the prediction of the effect is the same. That is: (quoting Kevin Brown's discussion) a pure Sagnac apparatus does not discriminate between relativistic and pre-relativistic theories. $\endgroup$– CleonisCommented Sep 17, 2023 at 8:20
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$\begingroup$ There is an ambiguity in the expression 'to be in a rotating frame of reference'. Unfortunately, many authors use that expression in a sloppy way, causing babylonian confusion. In order to ensure self-consistency: the expression 'frame of reference' refers to attribution, not to whether the observer is physically rotating. Let's say a panorama has been painted onto the inner wall of a large cylinder, you are in the center, and the cilinder is made to revolve around you. You see the panorama. Then your frame of reference is a rotating frame, while you are not physically rotating yourself. $\endgroup$– CleonisCommented Sep 17, 2023 at 8:58
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$\begingroup$ Further about 'frame of reference'. Of course in most cases the reason to use a rotating coordinate system (in calculation) is that the system to be modeled is physically rotating. For instance, when a car is speeding around a banked corner there is the option of treating the velocity as angular velocity. But the car enters the corner coming from a straight and exits to a straight; the transitions are smooth. For self-consistency: in calculation the option of using a rotating coordinate system is always available, independent of physical state. $\endgroup$– CleonisCommented Sep 17, 2023 at 9:52