Question on special relativity

Click For Summary
The discussion revolves around the observer's perception of two light rays emitted simultaneously from two sources while the observer moves towards one source. The key issue is the relativity of simultaneity, which states that events perceived as simultaneous in one frame may not be simultaneous in another. From the sources' perspective, the rays meet at the midpoint, but the moving observer perceives them as arriving at different times due to their motion. This discrepancy arises because the speed of light remains constant, but the observer's movement alters their position when the light reaches them. Understanding this concept is crucial for resolving the apparent paradox in the observer's experience of the light rays.
  • #31
understood. thank you! So my mistake was to consider my question as a paradox, while it was simply an empirical demonstration that simultaneity is relative.
 
Last edited:
Physics news on Phys.org
  • #32
Exactly!..
 
  • #33
Again, from the Einstein train example, the staionary observer sees te light flashed at the same time. The one in motion catches the lead flash before the rear flash.

Question is: what is the mathematics behind this?

Assume the train is 150,000 km in lngth which places the train observer 17000 km in the middle. It will take the light from the front flash 0.5 sec to reach the stationary observer. If the train is moving at 0.5 c, how long will it take the front falsh light to reach the moving observer on the train - DO THE MATH! Not just words - DO THE MATH

I have a feeling it is still 0.5 seconds but it shouldn't be
 
  • #34
stevmg said:
Assume the train is 150,000 km in lngth which places the train observer 17000 km in the middle. It will take the light from the front flash 0.5 sec to reach the stationary observer. If the train is moving at 0.5 c, how long will it take the front falsh light to reach the moving observer on the train - DO THE MATH! Not just words - DO THE MATH
How long will it take according to whom? The observer on the train or the observer on the platform? What's the proper length of the train? It the train is 150,000 km long, the middle would be 75,000 km from each end.

Since you use a time of 0.5 seconds, perhaps you meant the train to be 300,000 km long? If so, then the light from each flash would take 0.5 sec to reach the middle of the train according to train observers.

According to the platform observer, it would take less time since the length is shorter and the train moves towards the incoming light. The length of the train would be shorter by a factor of γ = 1.155. So if the proper distance between the middle and ends of the train is L = 0.5 light-seconds, that distance would be L/γ according to the platform observer. To find the time for the front flash to reach the middle of the train, use:
L/γ - vt = ct

Solving for time, you get:
t = L/[γ(c+v)] ≈ 0.29 sec
 

Similar threads

I Understanding Einstein's second postulate of special relativity
  • · Replies 57 ·
2
Replies
57
Views
7K
A Electrodynamics of moving bodies - §2: On the relativity of... (again)
  • · Replies 35 ·
2
Replies
35
Views
4K
I How Does Special Relativity Affect Perceptions of Simultaneity?
  • · Replies 32 ·
2
Replies
32
Views
2K
I The Einstein Clock aka Light Clock
  • · Replies 34 ·
2
Replies
34
Views
2K
I Basic Special Relativity question but the math isn’t working
  • · Replies 17 ·
Replies
17
Views
1K
I Variation of the lightning train thought experiment
  • · Replies 26 ·
Replies
26
Views
3K
I Understanding Relativity of Simultaneity in Resnick, Part II
  • · Replies 20 ·
Replies
20
Views
2K
I Why doesn't relativity of simultaneity lead to a contradiction?
  • · Replies 17 ·
Replies
17
Views
2K
I Proof of Special Relativity w/ Michelson–Morley Experiment
  • · Replies 20 ·
Replies
20
Views
3K
I Symmetry of motion in the special theory of relativity
  • · Replies 37 ·
2
Replies
37
Views
3K