1. Jun 25, 2013

### cataclysmic

I'm reading "Relativity: The Special and the General Theory" and I'm at the end of Chapter 9 & confused.

If I understand correctly, this is what he has said so far (in my own words):

Say that lightning strikes 2 points (A and B) on a railway embankment. To determine whether the two strokes of lightning struck at the same time, you could place a person half way between A and B, and provide him with mirrors so that he could see points A and B at the same time. If that person saw the two lightning strokes hit at the same time, then they actually did hit at the same time.

But now say there's a train traveling along the embankment going from A and towards B. If a person on the moving train tried use the same method to determine whether the two strokes of lightning hit at the same time (i.e. he looked into his mirrors when he was at the half-way point between A & B), he'd see that they did NOT hit at the same time... because he's traveling towards B and so the light from the lightning at B would hit his eyes sooner than the light from the lightning at A (which he's moving away from).​

I understand all of that, but then Einstein concludes (his words):

"Thus we arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa..."​

That's what I don't understand. Wouldn't it be more accurate to say that events which are simultaneous relative to the embankment ARE ALSO simultaneous relative to the train... BUT a person on the train just can't detect that they're simultaneous because of his motion.... in the same way that if the person on the train were trying to determine the simultaneity of two gunshots (at A and B) with his ears (not his eyes), he'd think that they were not simultaneous because he's moving towards the soundwaves from gunshot B and therefore hears them sooner? So to summarize, the guy in the train perceives a distorted view of reality because of his motion - he thinks two events were not simultaneous when they actually were.

So who is right - me or Einstein? No doubt it's Einstein who is right, so if anyone can help me see what's wrong with my own explanation that would be great... thanks.

2. Jun 25, 2013

### WannabeNewton

Well Einstein is correct because there is no one inertial observer who's notion of simultaneity is more "correct" than that of another. There is no privileged state of inertial motion so the simultaneity in that observer's frame is perfectly valid.

3. Jun 25, 2013

### cataclysmic

Thanks, but I still don't understand.

Say I'm in the middle of a pond, and two people at opposite shores drop identical rocks into the pond. I could try to detect whether the rock hit the water simultaneously by observing when the waves in the water caused by each rock reach me. If the waves reach me at the same time, I can conclude that the rocks hit the water simultaneously.

However if I was traveling towards the person on one shore (person A), I'd detect the waves from that rock (rock A) first, so I'd wrongly conclude that rock A hit the water first. I might detect the waves from rock A a minute before I detect the waves from the other rock - and conclude that rock A was dropped a minute before rock B, when they were actually dropped at the same time.

I expect you'd agree that my motion is giving me a skewed (wrong) view of reality. And if I was in motion and determining when each rock hit by when I heard the sound of the splash (sound waves instead of water waves), I'd also have a wrong view of reality. When I'm stationary in the middle of the pond, my conclusion is more "correct" than when I'm in motion. If I can say that my conclusion from a stationary position is more correct when I'm using water & sound waves to determine whether events are simultaneous, why can't I say for the same reasons that my conclusion from a stationary position is also more correct when I'm using light waves to determine whether events are simultaneous?

4. Jun 25, 2013

### Mentz114

I'm selecting this part of your post because it seems to encapsulate your misunderstanding.

What Einstein is saying in the quote is precisely that there is no 'actual' simultaneity of spatially separated events. It depends on the point of view and state of motion. Thus simultaneity is relative.

5. Jun 25, 2013

### Staff: Mentor

The key difference:
In the water+waves case, you can look at the water and say whether you're moving or not; and because the waves are travelling at a constant speed in the water, the waves will only be moving at that speed relative to you if you are at rest in the water.

In the light case:
There is no water to look at to settle the question of whether you're moving or not; the light is travelling through a vacuum. And the kicker - the light is always moving at speed c relative to you, no matter what your velocity is. In the train experiment the light from both flashes moves past both observers at speed c, despite the fact that it's coming from different directions and the train observer is moving relative to the platform observer.

Thus, there is absolutely no justification for saying that the platform observer is at rest while the train observer is getting a "distorted" view because of his motion; we could just as easily say that the train is at rest while the ground and platform observer are moving backwards, so it's their view which is distorted.
(And before you reject this alternative as outrageous, you might want to consider the situation as seen by an observer watching through a telescope from mars, which is moving at some miles per second relative to both earth and train - from his point of view they're both getting "distorted" views).

6. Jun 26, 2013

### Naty1

It takes a while for this stuff to sink in...It took an "Einstein' to first figure it out....and he got lots of help from others....Lorentz, Fitzgerald, Maxwell,etc....

Wikipedia has a good discussion on 'simultaneity'....here is a portion ....

It is good to keep in mind that relative velocities of observers are just that....relative....there is no 'absolute' velocity among observers....all have one velocity relative to earth, another relative to my car on a highway, yet another relative to our sun, and they are even different relative to each other depending on which is chosen as the reference.

7. Jun 26, 2013

### Markus Hanke

I suppose it all boils down to the simple fact that events in space-time are separated in both space and time; and the separation in time is constant at 1 second every 300,000km for all observers. Because of this, whether or not two events are perceived as simultaneous will depend on the state of relative motion of observer and events.

8. Jun 26, 2013

### ghwellsjr

Your analogy masks the problem. Instead, consider a river with evenly flowing water. There are three bridges crossing over the river with you on the middle bridge half way between the outer bridges. Two people on the outer bridges drop rocks in the water at the same time. Do you see the waves arrive at your location at the same time?

9. Jun 26, 2013

### Naty1

I posted:
An additional perspective and way to think about relative motion....like on the train versus on the embankment:

In the context of Special Relativity, “at rest” means “not moving relative to a specified inertial frame of reference.” It means that the spatial coordinates are constant while the temporal coordinate varies…inertial observers cannot determine, by experiment, if they are “in motion” or “at rest”…. You are at rest when you’re not moving in your own frame of reference. There is no universal or absolute state of rest. Inertial observers cannot determine, by experiment, if they are “in motion” or “at rest”.

10. Jun 26, 2013

### TheBC

Cataclysmic,
Great you try to sort out how Einstein's thought experiment works. Don't go too fast on this.
The question is:
If the train observer does not SEE the flashes simultaneously, why does this mean they did not HAPPEN simultaneously? (Or is the train observer not SEEING the flashes simultaneously, but they still HAPPENED simultaneously?)

We want to know what happens at the front and the rear of the train when the train passenger is at the embankment observer. Let's call that event X.
Just to refresh your mind: the embankment observer is in the middle of the two flashes, and he will recieve the lightbeams at the same time. Therefore he concludes that -at event X- both flashes happened.
The embankment observer also takes note that both lightbeams do NOT hit the train passenger at the same time (because -according to the embankment observer- the train observer moves away from him, hits first the front beam, and later the rear beam...i.e two different events).

Now the train passenger. He reasons as follows:

<< I consider myself (and the train) immobile! If -I repeat: IF- both flashes also occur simultaneously for me when I meet the embankement observer (event X), then both lightbeams should reach me at the same moment. Why?
3 steps:
1/ I am in the middle of the train, and RELATIVE TO THE TRAIN the speed of both light beams is identical (in special relativity the light speed is not bound to an ether frame. Which makes the -never detected- ether completely superfluous).
2/ I.o.w. If for me, at event X, the two flashes occur, then the light beams will cover -relative to me (and/or the train) equal distances in equal times. Hence, in that case, the beams have to (and will) reach me at the same moment.
3/ But .... the light beams do NOT reach me at the same time(*). Therefore, for me, both flashes did NOT happen simultaneously. >>
For the passenger there is some proper passenger's wristwatch time ticking (a sequence of successive proper wristwatch time indication events) between the two flashes occuring, whereas for the platform observer the two flashes happen at one and the same embankment observer's wristwatch time indication. Actually, for the train passenger at event X no flashes happen at the front or rear of the train! I can give you a Loedel diagram to visualize all this but on this forum people generally prefer just mathematics, which I will not get into here because it too abstract. I.o.w. I leave it to you how to interpret the meaning of 'simultaneity'. Please keep in mind that it seems to me that on this forum anything beyond just mathematics (s.a. the physical meaning or the existence of a spacelike simultaneous event) is considered wishfull thinking, philosophy, ontology, etc...

11. Jun 26, 2013

### Staff: Mentor

FYI, a Loedel diagram is mathematical too, specifically it is geometry.