Time dilation of a rotating disk

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Discussion Overview

The discussion revolves around the concept of time dilation as it relates to a rotating disk and the experiences of multiple observers positioned at different points relative to the disk. Participants explore the implications of acceleration and the relativity of simultaneity in understanding time differences between observers in motion.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants express confusion about the relative time differences perceived by observers in motion, particularly between a high-speed observer and a stationary observer.
  • One participant proposes an experiment involving four observers (A, B, C, D) on a rotating disk and suggests a hierarchy of time experienced, but acknowledges uncertainty about the correctness of their reasoning.
  • Another participant emphasizes that the scenario involves accelerating observers, which complicates the symmetry of time dilation and leads to absolute differential aging.
  • A different perspective suggests that understanding the rotating disk scenario requires familiarity with the relativity of simultaneity, which is crucial for resolving apparent paradoxes in special relativity.
  • One participant introduces a hypothetical scenario involving a hexagon instead of a circle, discussing how acceleration at the corners could affect the perception of time between observers, while noting that the results may vary based on the radius and velocity of the disk.
  • Another participant reiterates the hexagon analogy, suggesting that larger shapes would lead to longer intervals where both observers perceive each other's clocks as running slower.
  • Some participants clarify that there is no absolute reference frame, and both observers are stationary relative to their own frames, which adds complexity to the discussion.

Areas of Agreement / Disagreement

Participants express a range of views on the implications of acceleration and the relativity of simultaneity, indicating that multiple competing perspectives remain without a clear consensus on the correct interpretation of time dilation in this context.

Contextual Notes

The discussion highlights the limitations of applying straightforward time dilation concepts to scenarios involving acceleration and rotating frames, as well as the dependence on definitions of motion and reference frames.

  • #31
John Morrell said:
Would I be right in saying that in the original question, none of the observers are actually moving in any of the other observers' frames of reference except the guy not standing on the disc? They are all accelerating at different amounts, but if you take any of their instantaneous frames of reference none of the other people on the disc are moving at all. They have always been the same distance away in the same direction.
I'd say, no. Or else a satellite in geosynchronous orbit isn't moving relative Earth's FOR, which I'm pretty sure isn't the case.
 
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  • #32
Chris Miller said:
Or else a satellite in geosynchronous orbit isn't moving relative Earth's FOR, which I'm pretty sure isn't the case.

What do you consider to be "Earth's FOR"? If a satellite in geosynchronous orbit is directly above you, standing on the equator of the rotating Earth, and you remain still, motionless on the rotating Earth, the satellite remains directly above you: it doesn't move at all relative to you. Doesn't that count as not moving in "Earth's FOR"?
 
  • #33
Chris Miller said:
I'd say, no. Or else a satellite in geosynchronous orbit isn't moving relative Earth's FOR, which I'm pretty sure isn't the case.
What do you mean by "earth's FOR"? The non-rotating frame where only the Earth’s centre is at rest? Or the rotating frame where the entire Earth and geostationary satellites are at rest?
 
  • #34
Yeah, the thing about FOR's is that they are essentially coordinate systems. You relate distances, times, velocities, etc in relation to an arbitrarily chosen point or observer. In the frame of reference of a person on earth, the satellite never changes position. The same position vector points from you to the satellite at any time. Likewise, all the people on the disk do not move in relation to each other.
 
  • #35
I guess I see Earth's FOR as including a vast region of space at which it is at the center and not moving relative to, whereas the satellite, which is far from the center, is.
 
  • #36
Chris Miller said:
I guess I see Earth's FOR as including a vast region of space at which it is at the center and not moving relative to

Is this frame rotating or not? You can pick either answer: both are valid. But you have to be clear about which you are using. And then you have to realize that answers to other questions can depend on which you pick. If you pick the non-rotating frame (which is often called an "Earth-Centered Inertial" frame in the literature), then yes, the satellite is moving relative to this frame. But if you pick the rotating frame (which is often called "Earth-Centered Earth-Fixed"), the satellite is not moving. So whether the satellite is moving depends on which one you pick: there is no unique answer to the question.
 
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