Question on special relativity

Click For Summary
SUMMARY

The discussion centers on the concept of the relativity of simultaneity in special relativity, specifically regarding two light sources and a moving observer. Participants clarify that while light rays emitted from two sources meet at the midpoint from the sources' perspective, the moving observer perceives them as arriving at different times due to their motion towards one source. This discrepancy arises because the observer's frame of reference alters the timing of when the light rays are perceived, illustrating that simultaneity is not absolute but depends on the observer's relative motion.

PREREQUISITES
  • Understanding of special relativity concepts, particularly the relativity of simultaneity.
  • Familiarity with the speed of light as a constant (c) in all inertial frames.
  • Basic knowledge of reference frames in physics.
  • Ability to analyze scenarios involving relative motion and light propagation.
NEXT STEPS
  • Study Einstein's theory of special relativity, focusing on the relativity of simultaneity.
  • Explore the implications of light speed invariance in different inertial frames.
  • Examine thought experiments related to moving observers and light signals, such as the train and lightning example.
  • Learn about Lorentz transformations and how they relate to time dilation and length contraction.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in deepening their understanding of special relativity and its counterintuitive implications regarding time and simultaneity.

  • #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

Undergrad Understanding Einstein's second postulate of special relativity
  • · Replies 57 ·
2
Replies
57
Views
7K
Graduate Electrodynamics of moving bodies - §2: On the relativity of... (again)
  • · Replies 35 ·
2
Replies
35
Views
5K
Undergrad How Does Special Relativity Affect Perceptions of Simultaneity?
  • · Replies 32 ·
2
Replies
32
Views
2K
Undergrad The Einstein Clock aka Light Clock
  • · Replies 34 ·
2
Replies
34
Views
3K
Undergrad Basic Special Relativity question but the math isn’t working
  • · Replies 17 ·
Replies
17
Views
1K
Undergrad Relational event horizons?
  • · Replies 11 ·
Replies
11
Views
702
Undergrad Variation of the lightning train thought experiment
  • · Replies 26 ·
Replies
26
Views
4K
Undergrad Understanding Relativity of Simultaneity in Resnick, Part II
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Why doesn't relativity of simultaneity lead to a contradiction?
  • · Replies 17 ·
Replies
17
Views
2K
High School Am I understanding the concept of proper frame of reference?
  • · Replies 33 ·
2
Replies
33
Views
1K