A & B Clocks: Why Velocity Time Dilation is Not a Paradox

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Discussion Overview

The discussion revolves around the concept of time dilation as described by special relativity, specifically addressing why the observation that two moving clocks (A and B) run slow relative to each other is not considered a paradox. The scope includes theoretical explanations and conceptual clarifications regarding reference frames and the nature of time.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that the different observations of time dilation from each clock's reference frame are not paradoxical because the passage of time is relative to the observer.
  • One participant introduces the concept of the relativity of simultaneity, explaining that events perceived as simultaneous in one frame may not be simultaneous in another, which contributes to the understanding of time dilation.
  • Another participant compares the situation to the perception of angular size, arguing that just as angular size depends on the observer, so too does the rate at which clocks tick, emphasizing that clock rates are not intrinsic properties.
  • A participant agrees that it is consistent to have different results in different reference frames and cautions against drawing conclusions about one frame based solely on observations from another non-uniformly moving frame.

Areas of Agreement / Disagreement

Participants generally agree that the observations of time dilation are not paradoxical due to the relativity of time and simultaneity. However, there is an ongoing debate regarding the implications and interpretations of these observations, indicating that multiple views remain on the topic.

Contextual Notes

The discussion does not resolve the complexities surrounding the interpretations of time dilation and simultaneity, leaving open questions about the implications of these concepts in different reference frames.

daudaudaudau
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We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?
 
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daudaudaudau said:
We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

But it is!
 
daudaudaudau said:
We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

Because the passage of time is not absolute. It depends on the observer. There's nothing inconsistent about having different results in different reference frames.
 
daudaudaudau said:
We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?
I'd say it's because of the relativity of simultaneity--two events which happen at the same time-coordinate in one frame may happen at a different time-coordinates in another. If the two clocks read 0 when they departed one another, and are moving apart at 0.866c (so the time dilation factor is 0.5), then in A's rest frame, the event of clock A reading 20 years is simultaneous with the event of clock B reading 10 years; but in B's rest frame these two events are not simultaneous, instead the event of clock B reading 10 years is simultaneous with the event of clock A reading 5 years (and the event of clock A reading 20 years is simultaneous with the event of clock B reading 40 years).
 
daudaudaudau said:
We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

Suppose that you and I look at each other from a distance. You say that my (angular) size is small. I say that your (angular) size is small. Is this a paradox? No, because the angular size of an object is not an intrinsic property of that object. The angular size depends on the observer as well. Einstein's big discovery was the realization of the fact that the clock rate is not an intrinsic property of the clock. The rate depends also on who is watching that clock.
 
sylas said:
There's nothing inconsistent about having different results in different reference frames.

I agree with this statement. You are not allowed to draw any conclusions about the conditions of a particular frame based solely on measurements made from a non uniformly moving frame.
 

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