How does the relativity of simultaneity work in the classic train example?

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In summary: In everyday language, time is a noun. It is something that we use to order our days. It is measured using clocks. But what is it really? In physics, time is a fundamental quantity. It is the rate at which events happen. It is the same in all reference frames. So, for example, if I shine a light at A and someone at C sees the light, they both agree on the time that the light was shone. This is because the speed of light is the same in both reference frames. Now, let's take a more complicated example. Suppose I am travelling on a train and I am at S. I shine a light at A and someone at C sees the light
  • #1
Jupiter
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I don't get how it works. Using the classic train example...
train with speed v rel. to S -->
[========C'=========>S'
A----------C-----------B----------S
|----L-----|

First of all, why do we use light to measure time? Why don't we use time to measure time, if that makes any sense? For instance, suppose at t=0, t'=0. Suppose A shines a light at t=0. Then doesn't S' measure that A shines the light at t'=0, ignoring this confusing light travel stuff? Same with B. What does it matter where the light goes and when it gets there?

Now if someone is sitting at C in S, and someone shines a light at A the time it takes to reach C is
t=L/c
But if someone is sitting at C' in S', he too will measure c for the speed of light. And according to this observer, the light has to travel the same distance L (half the length of the train), so the time it takes to reach C' according to an observer there is
t=L/c
So both these observers agree with the time at which the light was shone. Same thing with a light from B. So if something is simultaneous in S it should be simultaneous to S'.

Can someone point out my fatal flaw?
 
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  • #2
Why don't we use time to measure time, if that makes any sense?

This is part of the point of learning all of these "paradoxes"; mentally we have some meaning of time that works for everyday situations, and it is difficult to accept that this mental meaning we have isn't the "right" meaning.

We can't use "time" to measure time, we use clocks to measure time. There are lots of ways to build clocks; but for the purposes of these thought experiments, light clocks by far have the simplest internals.
 
  • #3
I still don't get how the light from A will get to C before C' if the speed of light is the same in each reference frame. In classical mechanics, S' would measure
vlight=c-vtrain so the time it would take to reach C' would be
t'=L/(c-vtrain)
Clearly, the larger vtrain, the larger t' and only with vtrain=0 will t'=t. But this is not classical mechanics. The speed of light does not change. Why won't both find
t=L/c=t'?

Hurkyl, what exactly is time?
 

FAQ: How does the relativity of simultaneity work in the classic train example?

What is the concept of relativity of simultaneity?

The relativity of simultaneity is a concept in the theory of relativity that states that the perception of simultaneity is relative to the observer's reference frame. This means that events that are simultaneous for one observer may not be simultaneous for another observer in a different reference frame.

How does the relativity of simultaneity challenge the traditional concept of time?

The relativity of simultaneity challenges the traditional concept of time by showing that the perception of time is not absolute, but rather dependent on the observer's reference frame. This means that time can appear to pass differently for different observers, depending on their relative motion and position.

Can the relativity of simultaneity be observed in everyday life?

Yes, the relativity of simultaneity can be observed in everyday life. For example, if two people are walking towards each other at different speeds, they will perceive the timing of events differently. One person may see an event as happening simultaneously, while the other person may see a slight delay due to their relative motion.

How is the relativity of simultaneity related to the concept of time dilation?

The relativity of simultaneity is related to time dilation in that both concepts demonstrate that the perception of time is relative to the observer's reference frame. Time dilation refers to the slowing down of time for an object in motion, which can also affect the perception of simultaneity.

What is the significance of the relativity of simultaneity in modern physics?

The relativity of simultaneity is a fundamental concept in modern physics, as it is a key aspect of the theory of relativity. It has important implications for our understanding of time, space, and the nature of reality. It also plays a crucial role in many areas of physics, including cosmology, astrophysics, and particle physics.

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