# Relativity: light in train with person in it

• accountkiller
accountkiller
Throughout our relativity section in class, we've had two problems with light and a train, and I'm confused as to why they are two different answers.

The first is that Mavis is on a train moving close to the speed of light, and lightning bolts hit the left (back) and right (front) part of the train. Mavis thinks the right one struck first since she is moving toward that part, since the train is moving with her in it, so the wave front of that one reached her before the other one.

Now, another problem says that two lights shoot in from the middle of the train (distance of train divided by 2), one goes straight left, hitting left wall and one goes straight right, hitting right wall. Again, the train is going close to the speed of light. However, the answer for this one is that in Mavis's perspective, she sees the light reaching both walls at the same time, because she is in rest frame, because to her, the cart isn't moving.

Well, to her, the cart isn't moving in the first problem either, right? So how come she has different perspectives in the two scenarios?

I'd appreciate an explanation, thank you!

(It's not a homework problem but just me asking a question about a concept, so I hope this is the right category.)

The key problem here is that what is 'simultaneous' to one observer is not 'simultaneous' to another one.
In the second situation, Mavis is in the frame in which the two events of light hitting each side of the train are simultaneous, while in the first situation, she is not.

To make it a little more technical and, hopefully, more clear:
if you define the two events as
A = flash hits the front of the train,
B = flash hits the back of the train
then the two situations are basically described as:
1) "A and B happen simultaneously in some rest frame (i.e. the station) and Mavis is moving with respect to that frame (in the special relativistic sense, i.e. with constant velocity)"
and
2) "A and B happen simultaneously in the rest frame of Mavis."

Throughout our relativity section in class, we've had two problems with light and a train, and I'm confused as to why they are two different answers.

The first is that Mavis is on a train moving close to the speed of light, and lightning bolts hit the left (back) and right (front) part of the train. Mavis thinks the right one struck first since she is moving toward that part, since the train is moving with her in it, so the wave front of that one reached her before the other one.

Now, another problem says that two lights shoot in from the middle of the train (distance of train divided by 2), one goes straight left, hitting left wall and one goes straight right, hitting right wall. Again, the train is going close to the speed of light. However, the answer for this one is that in Mavis's perspective, she sees the light reaching both walls at the same time, because she is in rest frame, because to her, the cart isn't moving.

Well, to her, the cart isn't moving in the first problem either, right? So how come she has different perspectives in the two scenarios?
Because in the second scenario both beams depart from the center at the same moment (and this happens at a single point in space and time so there are no simultaneity issues, all frames should agree both beams departed from the center at the same moment), while in the first scenario both beams reach her at the center at different moments, so if she assumes the train was at rest and that both beams moved at c the only way she can account for this difference is to assume the lightning struck both ends at different times. Note that in the first scenario, we assumed that the lightning struck both ends simultaneously in the frame of the observer on the track who sees the train moving, and that's why we get the conclusion that both beams reach the center at different moments; you could instead consider a different physical scenario where both ends were struck simultaneously in Mavis' frame, and in this case both beams would reach Mavis at the center at the same moment (but in this case, the track observer would have to conclude that the two strikes happened non-simultaneously)

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The first problem is asserting that when Mavis is moving toward the source of light (which is when the light is moving to the left), it takes less time than when she is moving away from the source of light (which is when the light is moving to the right), assuming that the same distance is involved in both cases, correct?

So let's apply that idea to the second problem. The light going to the left will take less time to hit the rear wall than it takes for the light going to the right to hit the front wall, correct? But Mavis can't see that yet. She has to wait for the two wave fronts to reflect back to her so that she can then see them, correct? So now the light reflecting off the rear wall (moving to the right) will take more time to come back to her than it takes for the light reflecting off the front wall (moving to the left) to come back to her, correct? And guess what? Since the distances in both round trip light trips are the same, and they each experience both a longer time trip and a shorter time trip (but in a different order), the totals for both round trips are the same. That is why Mavis sees them as reaching the walls at the same time, correct?

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## 1. What is the theory of relativity?

The theory of relativity is a fundamental principle in physics that explains the relationship between space and time. It was developed by Albert Einstein in the early 20th century and includes two main theories: special relativity and general relativity. Special relativity deals with objects moving at a constant speed, while general relativity includes the effects of gravity.

## 2. How does relativity apply to light in a train with a person in it?

In this scenario, the person in the train is moving at the same speed as the train, which is also the reference frame. According to the theory of special relativity, the speed of light is constant in all reference frames, so the person inside the train will observe light traveling at the same speed as someone outside the train. This is because the train and the person inside are both moving at the same velocity.

## 3. Can light travel faster or slower in a moving train?

No, the speed of light is constant and does not change in different reference frames. This is one of the key principles of the theory of relativity.

## 4. How does time dilation play a role in this scenario?

According to the theory of special relativity, time is relative and can appear to pass at different rates for observers in different reference frames. In this scenario, the person inside the moving train will experience time passing slower compared to someone outside the train, due to their relative speed. This phenomenon is known as time dilation.

## 5. What are some practical applications of the theory of relativity?

The theory of relativity has many practical applications, including GPS technology, which relies on precise time measurements to determine location. It also plays a crucial role in modern physics and has led to advancements in areas such as nuclear energy and particle accelerators.

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