# Two light sources in train

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1. May 13, 2015

### johann1301

I am standing in the middle of a train. There are two lightsources attached to the train. One in the front, and one in the back. Both aimed at me, both with the same distance from my position in the train. No matter how fast the train is moving, i will always stay equally distanced to them. The lights are connected with equally long cables to a switch i am holding. Assuming that the lights are identical. The train is always moving at a constant velocity in a inertial referance frame.

If i flip the switch, will i see the to lights flash at the same time, regardless of my velocity?

2. May 13, 2015

### ghwellsjr

Yes, as long as the train has been at a constant velocity for a sufficient length of time for any transients to die down.

3. May 13, 2015

### pervect

Staff Emeritus
Yes - this is a variant of Einstein's "train experiment". See for instance http://www.bartleby.com/173/9.html, or any of the large number of PF posts on "the relativity of simultaneity". According to you, with equal length cables, the lights will flash at the same time. They will not, in general, flash at the same time in other frames of references, though. If you had multiple trains moving at different rates, each train would have it's own notion of "simultaneity" based on equal-length cables. The cables actually complicate the thought experiment, Einstein's definition of simultaneity is very similar to "equal length cables", but he actually used signals propagating through a vacuum rather than signals propagating through a cable to define simultaneous events.

What makes the cable results equal to the vacuum results is the principle of relativity, the theoretical assumption that the laws of physics that determine how signals propagate down a cable appear the same in all reference frames.

4. May 13, 2015

### johann1301

For instance accelerated frames of references?

5. May 13, 2015

### ghwellsjr

I disagree. It's Einstein's second postulate not his first postulate that establishes that the propagation of signals through cables are the same in all reference frames. In fact, that is part of the definition of a reference frame in Special Relativity.

Without that second postulate (or its equivalent), the round trip time for both paths will be equal in all inertial cases but you cannot conclude that the one way propagation times are equal in all inertial cases.

6. May 13, 2015

### Ibix

Yes. Also, other frames in motion at constant speed with respect to you.

7. May 13, 2015

### ghwellsjr

All bets are off with accelerated frames because there is no standard definition for them and there is no standard method to establish simultaneity. Pervect's comment is true even for inertial reference frames.

8. May 13, 2015

### johann1301

So i will not see the two lights flash at the same time, regardless of my velocity?

Im totally confused now. First yes, then no?

9. May 13, 2015

### Staff: Mentor

You will unambiguously, no wiggle room, no dispute at all, see both flashes at the same time if the train does not change its speed between the moment when you press the switch and when the flashes of light reach your eyes.

10. May 13, 2015

### johann1301

Thats what i thought.

Will I also see both flashes at the same time regardless of the inertial velocity? (i.e the velocity before i flip the switch)

11. May 13, 2015

### Ibix

You can always consider yourself at rest, as long as you don't accelerate. So you will always see the flashes at the same time and be able to deduce that they were emitted at the same time.

All other observers will agree that you see the flashes at the same time, but will not agree with your deduction about the simultaneity of the emissions. For them, one of the pulses has to chase you while you move towards the other one. For the reception to be simultaneous, the emission must have been non-simultaneous.

12. May 13, 2015

### Staff: Mentor

Yes. One thinking about this problem is that as far as you are concerned the train is at rest while everything outside the train (platform, rails, people watching from outside the train) are moving backwards at some constant speed. It doesn't matter what they're doing, your lights and wires and electrical flashes will all behave the same way.

BTW, the equivalent fo this experiment has been done many times, by taking advantage of the fact that the surface of the earth is moving in different directions and speeds at different times of day and different times of year, because the earth is both rotating on its axis and moving around the sun.

[Edit: I should add, to be perfectly clear, that you "see" the flashes when they hit your eyes. That's not the exact same time that the flashes left the lights at thend of the train]

Last edited: May 13, 2015
13. May 13, 2015

### ghwellsjr

I already gave you the answer to this question in my first post.

Keep in mind that the issue of "did the lights flash at the same time?" and "did you see the lights flash at the same time?" or two entirely different kinds. You were asking about the second issue for which the answer is yes for inertial motion. You don't need to establish a frame of reference for that to be true--it is true experimentally every time it has been tried. The first issue is a matter of establishing the definition of simultaneity for distant events for which the one-way propagation of signals needs to be stipulated because it cannot be measured or determined by experiment.

14. May 13, 2015

### ghwellsjr

That is not a "deduction", it's a stipulation or a definition or a postulate. It's part of the establishment of an inertial frame of reference according to Einstein's Special Relativity. It's not something that we can deduce from experiment.

15. May 13, 2015

### Ibix

I'm not sure I completely agree with you there. Certainly I'm using the assumption of the isotropy of light speed. However, I then deduce the simultaneity or not of the flashes from the arrival time of the flashes and that assumption (or any other convention I choose to use).

So, while I completely agree that I am basing my deduction on an assumption, it's still a deduction.

16. May 13, 2015

### johann1301

What if the light sources are no longer attached to the train, but attached to the train station. Lets imagine that the train passes the two lights in such a way that they both are triggered to flash when one of the lights is in front of me, and one behind me, both equally distanced from me. Will i then see the light in front of the train first?
I think the question boils down to: Does the velocity of the light sources matter?

17. May 13, 2015

### Ibix

It makes no difference to the arrival times whether the light sources are attached to the train or not. You (on the train) will see Doppler shifted light (so the pulse coming from behind you will be red-shifted while the one from in front will be blue shifted), which the person on the platform will not. In your original setup the platform observer saw Doppler shifted light whereas you did not. That's the only difference.

18. May 13, 2015

### A.T.

http://en.wikipedia.org/wiki/Special_relativity#Postulates
• The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body." (from the preface).[1] That is, light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.

19. May 13, 2015

### ghwellsjr

They are the same assumption. One is not a deduction of the other one.

20. May 13, 2015

### Staff: Mentor

For the question you are asking, no it does not matter.

21. May 14, 2015

### ghwellsjr

Maybe some spacetime diagrams will help. Let's assume the length of the train in its rest frame is 6000 feet and the cables propagate signals at 60% of the speed of light. In my diagrams, I show you as the blue line with dots every microsecond. The ends of the train with the lightsources are shown in black also with dots every microsecond:

At time zero, you flip the switch and send the thick red signals towards the lightsources. At the Coordinate Time of five microseconds, the two signals reach the lightsources which send the light signals back to you as shown by the thin black lines. They both arrive to you at your time of 8 microseconds as indicated by your clock.

This scenario is defined, described and depicted in the train's rest frame.

Now let's transform the coordinates of all the events (dots) in the defining frame to a new frame moving at 30%c. This makes the train move to the left at 30%c:

Now the signal in the cable going to the left is traveling at about twice the speed of the signal in the cable going to the right and they reach their lightsources at different Coordinate Times and even though the light signals have different distances to travel back to you, they both arrive at your clock time of eight microseconds, just as in the rest case.

I want to do one more case at around 75%c:

In this case, the length of the train is contracted to 4000 feet. You can see that at the Coordinate Time of 4 microseconds. The time on your clock is dilated by 50% so that the 8 microseconds that it takes for the light to reach you happens at the Coordinate Time of 12 microseconds.

According to Special Relativity, all of these depictions are equally valid, none is preferred, not even the rest case. They all depict the same measurements that you can observe.

Last edited: May 20, 2015
22. May 19, 2015

### ghwellsjr

As long as you can actually trigger the two light sources to flash when they are equally distanced from you, according to your rest frame, then you will see both flashes at the same time. But this raises the question of how you can get this to happen.

The challenge is that the specification of when and where they flash is according to your rest frame but the light sources are at rest according to the train station's rest frame. There are many ways to implement such a scenario but I'm going to suggest one that I think is the simplest.

Let's imagine two probes at either end of the train that can trigger the two light sources that are some distance apart along the track in front of the train station. One probe is mounted higher than the other so that each probe can only trigger one light source. Then the only issue is how far apart are the two light sources? A naive approach might be to put them as far apart as the Proper Length of the train (the length of the train in its own rest frame). Let's assume the Proper Length of the train is 6000 feet and is traveling to the left in front of the train station at 30%c. Here is a spacetime diagram depicting the rest frame of the two light sources shown as the thick green lines placed 6000 feet apart:

The ends of the train are shown in black. When the probe at the trailing end of the train reaches the light source on the right, it triggers the light flash shown as the thin green line propagating upwards and to the left. When the probe at the leading end of the train reaches the light source on the left, it triggers the light flash shown as the thin green line propagating upwards and to the right. You are shown in blue. The two thin green light flashes do not arrive at you at the same time and if we transform to the train's rest frame, we can see why:

The reason is, of course, that the distance between the light sources is contracted and so they are not triggered at the same time in the train's rest frame but we can easily fix this by moving them further apart as shown here:

Now the question is: How far apart must the light sources be in their own rest frame? And the answer is: Gamma (1.048 at 30%c) times the Proper Length of the train as shown here:

So as long as the train station knows the speed and Proper Length of the approaching train, it can place the light sources the correct distance apart so that you will eventually see both flashes at the same time.

In this scenario, it matters in the sense that the train station must know ahead of time what the velocity of the train will be when it gets to the light sources but as long as this information is established correctly, the same scenario will work at any velocity.

Last edited: May 19, 2015