Undergrad Einstein's Train: Does Speed Exceed c?

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SUMMARY

The discussion centers on Einstein's Train thought experiment, specifically addressing the perception of light speed from different frames of reference. It confirms that while the rear of the train appears to approach the front lightning's light at a speed greater than the speed of light (c), this does not violate the principles of relativity. Key concepts such as time dilation, length contraction, and the relativity of simultaneity are crucial in understanding that no observer measures speeds exceeding c relative to themselves. The relativistic velocity addition formula is essential for grasping these concepts.

PREREQUISITES
  • Understanding of Einstein's theory of relativity
  • Familiarity with the relativistic velocity addition formula
  • Knowledge of time dilation and length contraction
  • Basic grasp of frames of reference in physics
NEXT STEPS
  • Study the relativistic velocity addition formula in detail
  • Explore the implications of time dilation in practical scenarios
  • Investigate length contraction effects in high-speed travel
  • Examine case studies demonstrating the relativity of simultaneity
USEFUL FOR

Physics students, educators, and anyone interested in the principles of relativity and their applications in modern physics.

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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