# I Confusion with relativity of simultaneity

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1. Apr 26, 2017

### Grisha

I know variations of these have probably been asked numerous times before, but I'm having trouble with this specific scenario.

Imagine the classic Train Paradox, except instead of lighting strikes we have an observer at the centre of the train shooting laser pulses towards the rear (Event E1) and front of the train (Event E2). Train is moving from left to right at a relativistic velocity V.

For an observer on the station, the light pulse travelling towards the rear has to travel a much lesser distance since the train is moving towards it. Let this distance be 0.5-VT.

Obviously, station observer, who has a moving reference frame, sees the E1 first.

Let us place another man at the back of the train, since he is at rest with the train, light has to travel 0.5 (exactly half the length of the train) to reach him.

But according to the station observer for whom light has to travel only 0.5-VT, the light reaches the man before it actually reaches him, in his own reference frame. How is the moving observer able to see an event before it even happened in the rest frame?

2. Apr 26, 2017

### Vitro

Why do you think the time intervals measured by the train and ground observers between emission and receptions events have to be the same? They do not. The speed of light is the same for both, the distances are different so the times are different. Yet, that does not imply your conclusion.

3. Apr 26, 2017

### Vitro

Give this second man a clock that stops exactly when the light hits it. That's when the second man sees the light. The ground observer will also agree with the reading of that clock when the light hits it.

4. Apr 26, 2017

### Vitro

No observer can see an event before it happens, but different observers can assign different time coordinates to that event in their respective coordinate system. This is not the same as saying that the event happens earlier/later for some observers than others, or that some observers can see in the future of others.

5. Apr 26, 2017

### PeroK

The problem is all the assumptions implicit in this about the absoluteness of simultaneity!

Also, events don't happen in a particular reference frame. Events happen. Each reference frame assigns a time and place to the event.

To help with this I would suggest the following starting point. There are two clocks on the train (front and back). They are in darkness. Two beams of light are emitted from the centre of the train: these strike the clocks and briefly illuminate them.

All observers will agree on the clock readings that were illuminated.

Let's say, for the sake of argument, that the clocks showed the same reading when they were illuminated.

In the train's reference frame, as the clocks are the same distance from the light source and all are at rest relative to each other, the clocks are synchronised. They have the same reading at the same time (in this frame).

In the platform reference frame the rear clock is illuminated first and the front clock is illuminated later (but has the same reading as the rear clock). In this frame, therefore, the clocks are not synchronised. They have the same reading at different times (in this frame).

Thus: simultaneity is relative.

6. Apr 26, 2017

### Grisha

Yes, that's because the ground observer is closer to the clock at the back, so you're saying he will observe it illuminated first by virtue of his position?

7. Apr 26, 2017

### Grisha

I see, the observer on the station is "closer" to the event

8. Apr 26, 2017

### PeroK

No. The speed of light has nothing to do with it. For any measurements in any physics you have to take the travel time of signals into account as part of the measurement. The actual experimental process of measurement of a fast moving train would be complicated by this.

The solution I prefer is to have not single observers, but observers everywhere that is important in your reference frames. These "local" observers can make local measurements without any significant light travel time from an event to them. Before an experiment, the obsevers can all agree their positions and synchonise their clocks. Then, after the experiment, they can all get together and compare results.

In this case, the nearest observer to the rear of the train when the rear clock was illuminated would record the time it showed and the time on his clock. The nearest observer to the front of the train when the light struck would do the same.

This takes all the irrelevant travel time of light from an event to an observer out of the equation.

9. Apr 26, 2017

### Grisha

the train observer will see the station observer move rapidly (but not faster than c)towards the back of the train, and can conclude that he observes the event first, but not before it *happened* (not perceive) in his frame

10. Apr 26, 2017

### PeroK

All observers observe all events after they happen. The amount of time afterwards is directly related to how far they are from the event. This is as true in classical physics as it is in relativity.

Special Relativity has nothing to do with the delay in a signal from an event reaching an observer.

11. Apr 26, 2017

### PeroK

It's also worth noting that SR deals with the time and place of events in different reference frames. This is different from what an isolated obsever may actually "see", "perceive" or "observe". In fact, although a lot of material on SR talks about "observers", it is in fact critical to understand SR as the relationship between reference frames moving with respect to each other.

As I suggested above, I recommend thinking about a reference frame as a whole row of local observers, a short distance apart, at rest relative to each other, with their clocks all pre-synchronised, and ready to record any event that happens close to them.

12. Apr 26, 2017

### Grisha

Can you recommend any good sources for a clearer understanding? preferably youtube videos

13. Apr 26, 2017

### PeroK

To learn it properly, I think you have to study it seriously. I would recommend Special Relativity by Helliwell. The maths shouldn't be a problem, but it does take a concentrated effort to nail SR.

14. Apr 26, 2017

### Staff: Mentor

If it were that easy, people wouldn't write textbooks. Taylor and Wheeler's "Spacetime Physics" is a good starting point for an I-level thread.

15. Apr 26, 2017

### Mister T

Let $t$ be the reading on the stationary clock and $t'$ on the moving clock. Moreover, let's synchronize the clocks so that $t=t'=0$ when the flash of light is emitted at the center of the train. The flash of light reaches the back of the train at times, let's say, $t=1.0$ and $t'=1.1$. So your question really is how can these values not be the same, since they are the times of the same event.

And the answer is that there's no reason to expect them to be the same. The only way they could be the same is if light travels at different speeds in each frame, and the established fact is that it doesn't!

16. Apr 26, 2017

### PeroK

There's also a free text here, written by someone who used to contribute on here, but I haven't seen him around much:

http://www.lightandmatter.com/sr/

17. Apr 28, 2017

### pervect

Staff Emeritus
You could try the paper by Scherr, et al. "The challenge of changing deeply held student beliefs about the relativity of simultaneity" <<link>> on this specific topic. How much it will help, I can't say - if you read it, I'd be interested in your feedback.

It's foucussed more towards teachers than students, but it still might be useful.

18. May 7, 2017

### Grisha

Thanks All, I have started reading "Introduction to Spacetime Physics" by Taylor-Wheeler. Its very nice and engaging. I realize I had some conceptual misunderstandings which are cleared now, I'm about 4 chapters in