# B Einstein Train experiment with a consequence?

1. Mar 11, 2016

### Marrrtin

If we take a look at the experiment were two observers A (inside a train) and B on the platform observering the train as it pass by. Person A will stand in the exact middle of the train and send out a light wave. Person A will observe the light to hit the wall at the same time, while person two will see the light hit the back of the train before the front.
So Einstein says that simultainity is relative, and that what is right depends on the reference frame(whether the light hits the back before the front (B) or back and front at the same time (A).

However, what if the front and the back of the train had a censor that need to be hit by the light at the same time or else a gun would fire a shot and kill observer A. Observer A would think he is safe because he observes the light hit the the front and back at the same time, but not observer B who will see the light hit the back of the train first.
So what will happend? If (accordingly to Einstein) both observers are right in what they are observering, will the person be shot or not? :S
I know there is something I have missunderstood somewhere, but I dont now what that is, and I have tried to figure it out for a while now so Im greatfull for some help!

2. Mar 11, 2016

### Staff: Mentor

Basically it is not possible to build such a sensor. All frames will agree if the gun fires, so in one frame the sensor will detect simultaneous hits, but in other frames the device will detect hits that are desynchronized by a specific amount.

It might help to think of a specific sensor design and we can help you understand how it would work.

3. Mar 11, 2016

### Marrrtin

I cant think of any spesific sensor, but I can make the question a little different:
Suppose their is two guys on the train (lets call them A and B). One in the front and one in the back. In the middle of the train there is a light buble. When this is switch on the light will travel in both directions on the train. As soon the light reaches one of the persons he will fire a gun towards the middle of the train. Suppose both A and B will fire in the exact same height and width so that the bullets will hit one another. When the two bullets hit will fall on the train floor at the same place they hit each other. Person A and B on the train will claim that they will see the light at the same time, and therefore fire the gun at the same time, and therefore will the two bullets hit one another and fall to the floor at the exact middle of the train.
However a third person C, outside the train will claim the person A (in the back of the train) see the light first and therfore fire his gun before person B. Then the bullet from person A will travel a farther distance before hitting the bullet from person B, and therefore the two bullets will hit each other closer to the front of the train and land on the floor closer to the front.
If both reference frames (C ouside the train or A/B on the train) are right were will we find the bullets? In the middle of the train or closer to the front? As you can see there is something that I dont understand, I just dont know what it is :/

4. Mar 11, 2016

### Orodruin

Staff Emeritus

5. Mar 11, 2016

### Staff: Mentor

This part is correct.

Here you would need to use the relativistic velocity addition formula. If you work it out, person C will also predict that the bullets will meet in the center.

6. Mar 11, 2016

### Kevin McHugh

Are you related to Schroedinger? Your experimental design sounds a lot like the cat in the box.

7. Mar 11, 2016

### Marrrtin

Okei, thank you very much! However, I have some idea how reletavistic velocity works but I just cant see how that explaines my "problem". Could I get a short explanation please.
Best regards biologist trying to get a simple understanding of relativity and physics

8. Mar 11, 2016

### pixel

Such a sensor could be built in observer A's frame of reference. But it couldn't be built for both A's and B's frames, as simultaneity is relative. When the experiment is done both A and B will agree that no shot was fired. The thing to realize is that while B sees the light hitting the front and back of the train at different times, he can, using the Lorentz transformation, calculate that in A's frame of reference the events were simultaneous so no shot should have been fired.

9. Mar 11, 2016

### Orodruin

Staff Emeritus
There are several parts you need to take into account. The easiest case is when the bullets are massless and travel at the speed of light in all frames. You then do not need to care too much about relativistic velocity addition because you already know the bullet speed. What you do need to take into account is that the train is still moving. Therefore, you must check where the train center is in relation to the bullet meeting point based on this.

10. Mar 11, 2016

### FactChecker

No. C will say that A fired first and that bullet traveled farther. But the middle of the train will also travel forward to the point where the bullets collide.

11. Mar 11, 2016

### Staff: Mentor

You really have to work out the math on this one. The question of where the bullets meet depend on three things, the velocity of the bullets, their starting times, and their separation. The relativity of simultaneity requires that their starting times differ. Length contraction makes the separation shorter than in the train frame. And relativistic velocity addition makes their speeds different from what you expect in the train frame. All of these balance so that they meet in the middle.

12. Mar 12, 2016

### Marrrtin

Great! That helped alot! Thanks for sorting this out for me!! :)

This point was very clearifying! Thanks!