# Relativity of simultaneity, understood, now not so sure.

1. Dec 13, 2015

### DAC

Hello PF. I have no problem with the embankment observer. He sees the flashes as simultaneous being equidistant.
Likewise the train observer who sees the flashes as separate given he is closer to one flash.
What I don't follow is what is the significance of this?
Thanks.

2. Dec 13, 2015

### Ibix

The embankment observer sees the flashes simultaneously because, according to him, the two flashes were simultaneous and were emitted equidistantly from him. But the train observer sees the front flash first because she is moving towards the source of the flash.

That's how the embankment observer explains things. But the question is, how does the person on the train understand what's happened? She can say she's at rest. And the light pulses came from the same distance away. So why do they not arrive at the same time?

If Newton had been right then it would be easy to understand. If both light pulses were travelling at the same speed in the ground frame then they can't be the same speed in the train frame. Just like doing 60mph down the road - cars coming the other way approach at 120 while the car behind stays the same distance from you, even though they're both doing 60mph seen from the ground. So she would say the pulses travelled at different speeds.

But Einstein argued that the speed of light is constant in all frames. So the only way the train observer can receive the two light pulses at different times is if thry were emitted at different times. That means that "simultaneous" is not something two observers necessarily agree upon.

You can also derive the Lorentz transforms from this argument, although you'll need somemore detail.

Does that help?

3. Dec 13, 2015

### DAC

Thanks Ibix.
If the train is at rest and at rest relative to the light, I would have thought she sees the flashes simultaneously.

4. Dec 13, 2015

### Mister T

If the train's at rest relative to the tracks, she will. But if she considers herself to be at rest, and the tracks are moving relative to her, she won't.

And you can't be at rest relative to light. Light is always moving relative to you. Being at rest relative to something means the same thing as being in the same state of uniform motion as that something.

5. Dec 13, 2015

### Staff: Mentor

He is closer to one flash in the embankment frame. In the train frame he is equidistant from the flashes. In that frame therefore the flashes could not have occurred simultaneously.

6. Dec 14, 2015

### Ibix

I'm not sure what you mean by "at rest relative to the light". If you mean at rest with respect to the light sources then she'll only see the flashes simultaneously if they were emitted simultaneously. It's perfectly possible to set up a problem where the sources emit simultaneously in the train frame, but you specified the flashes as simultaneous in the embankment frame. They can't be simultaneous in both while the speed of light is invariant.

A related point is that there's nothing special about the frame in which the light sources are at rest. They emit light moving at speed c for any observer. This wouldn't be the case if you replaced the lights with guns, for example.

Which brings me on to the final point. If, by "at rest with respect to the light", you mean that the train observer is in a frame where the light is approaching her at the same speed from in front and from behind, then this is true of any frame in relativity. The flashes can't be simultaneous in all frames.

7. Dec 14, 2015

### Janus

Staff Emeritus
It does not matter whether the sources of the flashes are at rest with respect to the train or the embankment ( or neither), just that they originate simultaneously according to the embankment frame. The fact that they originate simultaneously in the embankment frame means they cannot originate simultaneously in the train frame.

8. Dec 18, 2015

### DAC

Agreed,
I still don't see the significance of the relativity of simultaneity. If the embankment observer is equidistant from two simultaneous flashes he sees them as simultaneous. The train observer, who is not equidistant sees them as separate events. Why doesn't the train observer, knowing he is moving re. the origin of the light, take that into account, and calculate that the flashes must have originated simultaneously although he sees them as separate? Is simultaneity about what observers see, or what originally occurred?
Thank you.

9. Dec 18, 2015

### Ibix

The train observer is equidistant from the flashes. The flashes occur at the front and rear of the train, and the observer is in the middle. How is that not equidistant?

He can't take into account the motion of the light source because it's irrelevant. The light comes out at c regardless. Imagine running the experiment with a pair of flashlamps mounted on the train and a pair on the embankment. The "front" train lamp and the "front" embankment lamp are momentarily co-located. They both trigger; the light travels from both at the same speed and arrives at the observer at the same time.

The relativity of simultaneity (and effects like length contraction and time dilation) are all what is left after you subtract out the travel time of light. So it is "what originally occurred". The reason we place the observer at the center of the train is just that it's easy to see that the pulses arrive simultaneously at one observer and not the other. You could do the experiment with observers located three quarters of the way along the train, but the scenario isn't quite so clear then.

10. Dec 18, 2015

### DAC

How can the train observer who is moving towards one flash and away from the other be equidistant from both?
It isn't the motion of the light source, it's the motion of the observer.
How can an observer who is not equidistant know what originally occurred. e.g.Let the flash furthest from the train observer take place first. It could then be observed simultaneously with the front flash even though originally it wasn't.
Thanks.

11. Dec 19, 2015

### A.T.

Because the speed of light is independent of the light source movement.

12. Dec 19, 2015

### Ibix

We need to be really careful with terminology here, and I was a bit sloppy myself. What do we mean by flashes? The emission events, or the travelling pulses of light?

The train observer is in the middle of the train. The emissions occur at the front and rear of the train. By definition, then, the train observer is equidistant from the emission events, whenever they happen. If you dispute this, you end up saying that the front half of the train is shorter than the back half (or vice versa) in at least one frame.

In the embankment frame, the scenario is set up so that the emission events occur simultaneously with each other and the moment that the two observers are co-located. So the embankment observer is equidistant from the emission events. If you dispute this, you are saying that one half of the train is longer than the other half in the embankment frame.

Once the emission has happened and the light is propagating, then according to the embankment observer the train observer is moving towards the light from the front source. But, according to the train observer the embankment observer is moving towards the light from the back source. So you can argue that the emissions are simultaneous and the train observer sees them as non-simultaneous because he's moving forwards, or that the emissions are non-simultaneous and the embankment observer sees them as simultaneous because he's moving towards the later one.

You do seem to be using the description in the embankment frame as the "correct" description, and saying that the train observer ought to adjust his perceptions to match the embankment observer. But the point of the principle of relativity is that he does not have to do that. Neither description is better than the other, so you use the one that is convenient. For the train observer it is convenient to consider himself at rest, so he can pour a cup of tea without worrying about how to hit a cup travelling at 0.9c. But in this view the flashes cannot be simultaneous.

You can easily measure how far away from you the light was emitted - triangulation or an intensity measure will do fine. And you can certainly set up different scenarios where the flashes are simultaneous for the train observer and non-simultaneous for the embankment observer. They'd be different scenarios, however.

13. Dec 19, 2015

### Mister T

Suppose it's you in the train car and you rig things up so that the two flashes are emitted at the same time. First, you have to decide how to be sure of that. One way is that if you see the two flashes arrive simultaneously, and you've carefully measured to make sure the distance to each light bulb is the same, then you conclude that they must have been emitted simultaneously. Can you now conclude that the train is at rest? If you instead see one flash arrive before the other, and again confirm that you are midway, do you then conclude that the train is in motion? If that works, it's a way to distinguish between a state of rest and a state of uniform motion. Such a thing, if it were to happen, would be an exception to the Principle of Relativity. No such exception has ever been found, and there are a huge number of experimental results that would have come out differently if there were exceptions, so you have to conclude instead that if the flashes didn't arrive simultaneously they weren't emitted simultaneously.

How can it be that you conclude they weren't emitted simultaneously when that other observer, also midway between the bulbs when the flashes were emitted, sees them arrive simultaneously?

You could even imagine a different version of this thought experiment. Have the bulbs flash repeatedly at some frequency, say 10 flashes per second. You could confirm that when you move toward one bulb the frequency is greater than 10, and when you move away, smaller. Yet if you mount these bulbs at the ends of your train car, and move the train car so that both you and the train car are in motion together, you see 10 flashes per second. The only time you see something different from 10 flashes per second is when you move relative to the bulbs, if you move together with them you see 10.

Since these are just thought experiments you can draw only logical conclusions from them. And you are forced to conclude that if the Principle of Relativity is valid simultaneity is relative. Real experiments confirm the premise, leading us to accept the conclusion; not just on logical grounds, but also on empirical grounds.

Last edited: Dec 19, 2015