Question about "odometer" analogy and time dilation

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    Time dilation
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Discussion Overview

The discussion revolves around the analogy of an odometer in relation to time dilation and the implications for two starships moving towards each other in space. Participants explore the concept of measuring time and distance through spacetime, the synchronization of clocks, and the potential to determine relative motion based on clock readings from probes launched from each starship.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that a clock can be viewed as an odometer measuring distance through spacetime, proposing that longer paths result in less experienced time.
  • Another participant counters that longer paths through spacetime actually correspond to more experienced time, challenging the initial analogy.
  • There is a discussion about the symmetry of the paths taken by probes launched from the starships, with some arguing that the paths will be symmetric if the acceleration profiles are identical.
  • Concerns are raised about the interpretation of "horizontal motion" in the context of spacetime and how it relates to the probes' trajectories.
  • One participant questions the meaning of timing in the scenario, asking who measures the time delays involved in launching the probes.
  • Another participant emphasizes that both starships can consider themselves at rest, suggesting that any experiments conducted will not reveal which is actually moving.
  • There is a suggestion to read related material discussing the geometrical analogy between the twin paradox and Euclidean space, highlighting the challenges of determining absolute motion in special relativity.
  • One participant asserts that the odometer analogy does not explain time dilation but rather differential aging.
  • A later reply proposes a hypothetical scenario involving time delays and asks for calculations regarding the readings of the probes when they meet.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the odometer analogy in explaining time dilation and the implications of symmetry in the paths of the probes. There is no consensus on the correctness of the initial claims, and the discussion remains unresolved regarding the interpretation of motion and time measurement.

Contextual Notes

Limitations include assumptions about the synchronization of clocks, the nature of motion through spacetime, and the interpretation of time delays in the context of relativity. The discussion also reflects varying understandings of the implications of the odometer analogy.

  • #31
phinds said:
The odometer analogy does NOT explain time dilation, it explains differential ageing.
This is incorrect. It explains both if applied correctly.
 
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  • #32
FIL said:
I don't think the video was wrong I probably just misunderstood it.
But this is the point. There are several members here who are qualified to determine whether the video was wrong or if you misunderstood. Both happen frequently.
 
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  • #33
Mister T said:
By symmetrical do you mean simultaneous? Recall that simultaneity is relative. Two events that are simultaneous in the rest frame of one of the ships will not be simultaneous in the rest frame of the other ship.

Edit: By this I mean that if the two launches are simultaneous in the rest frame of one of the ships, they will not be simultaneous in the rest frame of the other ship.
Later in the thread I amended the scenario so that the probe launches occur when the two ships measure an agreed upon distance between themselves after they pass.

After seeing the spacetime diagram Ibix provided I understand it doesn't matter, if motion is regarded as relative the proper time each probe accumulates will always be identical. I was supposing some version of absolute motion without entirely realizing it, I thought it was more of a case of "objectively, there is a true velocity each ship carries with respect to the other, but there's no way to detect it" as opposed to it truly being relative.
 
  • #34
Ibix said:
both at 0.4c. Five minutes later they launch probes, represented by the thinner lines moving at 0.95c. They catch up with the opposite spaceship at 12.27 minutes after the first meeting.
Why were these values chosen?
Of course, they are correct,
and a computer wouldn't have any problem with them,
but the arithmetic seems (in my opinion) unnecessarily complicated to make your point.
A return leg of 0.8c would have been better.
(An outgoing leg of 0.6 would also help simplify the arithmetic.
I have a fondness for 3/5, 4/5, 15/17... https://en.wikipedia.org/wiki/Pythagorean_triple .)
 
  • #35
robphy said:
Why were these values chosen?
0.6c and 0.8c made for a very long chase phase (5 mins to launch, then 30 mins to overtake) and I wanted the diagram to be reasonably wide and short so you can see the ticks clearly. 0.4 and 0.95 were pretty arbitrary, I admit.
 

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