Einstein's Train: Does Speed Exceed c?

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Discussion Overview

The discussion revolves around the thought experiment known as "Einstein's Train," specifically addressing whether the speed of the rear of the train appears to exceed the speed of light (c) from the perspective of an observer on the platform. The conversation explores concepts related to special relativity, including time dilation, length contraction, and the relativistic addition of velocities.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a scenario where the rear of the train seems to approach the front lightning's light at a speed greater than c, questioning the validity of this observation.
  • Another participant asserts that while it may appear that the rear of the train is approaching the light at greater than c, no observer measures speeds exceeding c relative to themselves, citing the principles of time dilation and length contraction.
  • A third participant agrees with the initial observation of the closing speed being greater than c but reiterates that no measurements of speeds greater than c occur relative to any observer.
  • A later reply introduces a different perspective, suggesting that it is the front of the train that approaches the lightning strike faster, while the rear of the train "escapes" from the rear strike.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the scenario, particularly regarding the apparent speeds involved. While some agree that the closing speed can seem greater than c, there is no consensus on the specifics of the observations made by the platform observer.

Contextual Notes

The discussion involves assumptions about the observer's frame of reference and the implications of relativistic effects, which are not fully resolved in the conversation.

Chris Frisella
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Youtube vid of an Einstein's Train example:

From the perspective of the man on platform, the rear of the train seems to be approaching the front lightning's light at greater than c (train's speed + c). Is this correct? I thought there was a rule against that...
 
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That's fine. What is forbidden is that you ever measure speeds greater than c relative to you.

Time dilation, length contraction, and the relativity of simultaneity conspire so that the guy at the back of the train measures the light coming towards him at c (you might want to Google for the relativistic velocity addition formula).

Nothing is moving faster than c relative to you. Nothing is moving faster than c relative to the guy on the train. No rules broken.
 
Chris Frisella said:
From the perspective of the man on platform, the rear of the train seems to be approaching the front lightning's light at greater than c (train's speed + c). Is this correct?
Yes, perfectly correct. The "closing speed" of the light and the rear of the train is greater that c.

Chris Frisella said:
I thought there was a rule against that...
No. Note that no one measures anything to be moving faster than light with respect to themselves.
 
Well, alright then. Thank you both
 
Chris Frisella said:
Well, alright then. Thank you both
I think not the rear of the train but front of the train approaches faster to the front strike and rear of the train "escapes" from the rear strike.
 

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