Time Dilation & Contraction: Conflicting Clocks

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Discussion Overview

The discussion revolves around the concepts of time dilation and length contraction as experienced by observers in different frames of reference, particularly focusing on a scenario involving two clocks on a moving ship and an observer at a station. Participants explore the implications of special relativity on the perception of time and distance between these clocks.

Discussion Character

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

Main Points Raised

  • One participant describes a scenario where a ship carries two clocks, one aligned with its motion and the other orthogonal, suggesting a contradiction in how time dilation and length contraction affect them.
  • Another participant prompts for clarification on what constitutes the contradiction, hinting at the relativity of simultaneity where observers in relative motion perceive each other's clocks as ticking slower.
  • A participant clarifies that the observer remains at the station, which influences their perception of the clocks on the ship.
  • One participant explains that the orthogonal clock does not experience length contraction, while the station observer sees the light traveling a longer zigzag path to the moving clock, resulting in a perceived slower ticking rate.
  • Another participant elaborates on the asymmetry in the ticking of the aligned clock, detailing the calculations for the time taken for light to travel between the mirrors from the station's perspective.
  • It is noted that the aligned clock appears to have different travel times for light going forward and backward, while the orthogonal clock has equal travel times, leading to different perceived ticking rates.
  • A participant asserts that an observer on the ship would see both ship clocks ticking identically and perceive the station observer's clock as slow, with the station itself appearing contracted.

Areas of Agreement / Disagreement

Participants express differing views on the implications of time dilation and length contraction, with no consensus reached on the interpretation of the observed phenomena. The discussion remains unresolved regarding the nature of the perceived contradictions.

Contextual Notes

Participants reference specific calculations and scenarios that depend on the definitions of time dilation and length contraction, as well as the assumptions about the observers' frames of reference. Some mathematical steps and assumptions remain unresolved.

intervoxel
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The ship leaves the station carrying two mirror clocks. One aligned with the motion. The other, orthogonal to the first. One suffers length contraction but the other does not. I suppose time dilation acts on both. So we have a contradiction here. What is happenning in fact?
 
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(a)What do you think the observer on the ship sees regarding her local clocks?

(b) Now try to write down [explain] excatly what you think is a 'contradication' and post it here.

(c) Hint: What is the 'contradiction here: Observers in relative motion each see the other's clock as ticking slower than their own.
 
I forgot to say that the observer remains at the station.
 
The one aligned orthogonal suffers no length contraction. But, from the station observer, light is following a zigzag path between the mirrors. Thus, the station observer sees the train clock 'tick' slower because of the longer light path. The longer light path is sqrt(L^2 + (vt)^2), L being distance between mirrors. This must equal distance light travels, so we have ct = sqrt(L^2 + (vt)^2) . Solving for t, we get tick of train clock as seen from station: (L/c)/sqrt(1-(v/c)^2).

Now, for horizontal clock, we have contracted length L' = L sqrt(1-(v/c)^2). Here the train clicks are asymmetric, seen from the station; the station observer sees the train observer treat the sum of the asymmetric clicks as two even clicks. For the station observer, for the click with light moving the same direction as the train, t0 = L'/(c-v); for the other click, t1 = L'/(c+v). If you work this out, you see that t0+t1 = 2(L/c)/sqrt(1-(v/c)^2), consistent with the clock rate for the orthogonal clock.
 
The one aligned with the direction of motion (light goes forward and backward between the mirrors) will appear to the station observer that the light going forward will take longer to travel the distance, shorter time to travel the backwards distance. This distance is the same for both directions and contracted.

The other one will have equal travel times, both clocks will "tick" the same rate (meaning a round trip light bounce will be the same time for both), and both tick slower than the observer's clock at the station.

An observer on the ship will see both ship clocks act and tick identically, and will see the station observer's clock to be slow, and the station contracted.
 
Last edited:
Thank you all. Things are clear now.
 

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