# Two lightnings that happen at the same time, a train and a passanger

1. Oct 6, 2011

### Nikitin

allright, I'm finishing up my final Gymnasium physics course and the weirdest chapters (QM and Einstein) are at the end.

So here is a book-example I don't understand:

Lightning strikes at point A and B at the same time (if an outside observer is watching). Between A and B is a train moving at a constant speed in the direction AB. An observer M is sitting right in the middle of the train, ie right in the middle of A and B.

The observer measures that he light coming from B reaches him before the light from A.

OK this is weird. I thought that that speed of light is always c to whoever the observer is. So since the light from A and B is approaching the dude at the same speed, shouldn't the light from A & B reach him at the same time?

If the observer sees the light from B first, this would mean that the observer's relative speed to the light from B is > C.

2. Oct 6, 2011

### Staff: Mentor

Note: Everyone (even the outside observer) agrees that light reaches M at different times.
Only if the light starts out at the same time, which is the point. According to the train observers, the lightning strikes were not at the same time. Simultaneity is frame dependent.

3. Oct 6, 2011

### Nikitin

What? Really? I am so confused, why? Is this just some excuse used to claim that c is always constant?

4. Oct 6, 2011

### Nikitin

also can you help me with some math? how do I turn t02(1 - c2/v2) to the lorentz factor? I don't know how to convert (1 - c2/v2)-1 into (1 - v2/c2)

5. Oct 6, 2011

### Staff: Mentor

The lightning strikes at the same time according to the outside observer on the tracks. But if we assume that light travels at the same speed in every frame, train observers are forced to concluded that the lightning struck B before it struck A.

6. Oct 6, 2011

### Nikitin

so this is just an excuse to say that c is always constant?

well we know how that cern thing went...

7. Oct 6, 2011

### Staff: Mentor

No, it's a consequence of c being invariant. (And overwhelmingly supported experimentally.)
I assume you're joking.

8. Oct 6, 2011

### Nikitin

OK, can you help me with post #4?

thanks for ur patience btw, I really appreciate the help

9. Oct 6, 2011

### Staff: Mentor

Where is this coming from?

In any case:

(1 - c2/v2) = - (c2/v2)(1 - v2/c2)

10. Oct 6, 2011

### Nikitin

well the book says

2) t2 = c2t02/(c2-v2)

==> 3) t = t0/sqrt(1 - v2/c2)

I don't get how they went from 2 to 3

11. Oct 6, 2011

### Staff: Mentor

t2 = c2t02/(c2-v2)

t2 = t02/(1-v2/c2)

Got it? (Divide top and bottom of the fraction by c2.)

12. Oct 6, 2011

### Nikitin

Oh oops thanks lol

13. Oct 6, 2011

### Nikitin

I got another problem, pls help: Inside a spaceship passing earth at 0.6c, time goes slower inside the ship from the POV of earth. But, from the spaceship's POV the earth is moving backwards at 0.6c so the earth is the one whose time is slowing down?

The book claims this isn't a contradiction.. but how?

14. Oct 6, 2011

### Erland

I've said it before and I say it again: I don't like this example. I only get confused when I think of it. But there is a simpler example which demonstrates the relativity of simultaneity. I quote myself from another post:

"... imagine a light being turned on in the middle of the train. The light reaches the front and the back of the train simultaneously, according to an observer on the train. But according to an observer on the embankment, the light will reach the back of the train before it reaches the front of the train, because according to such an observer, the light that reaches the back of the train will have travelled a shorter distance than the light that reaches the front of the train, since train is moving, according to this observer."

15. Oct 6, 2011

### Erland

I think it is easier to see this if we think of a train instead of a spaceship. Again, I refer to another post of my own, where I try to explain this:

16. Oct 6, 2011

### Nikitin

So if the earth gets accelerated so much that it catches up to the spaceship and moves parallel to it at the speed 0.6c, Earthlings who launch themselves in rockets and visit the spaceship find out that the spaceship guys are old?

That.. can't be possible?

17. Oct 7, 2011

### Erland

As far as I undertand it, it will be as you write (provided that the rockets you mention have much smaller velocities than 0.6 c) because Earth is the body which accelerates in this case.

And well, I guess it wouldn't be possible to accelerate the Earth to the speed 0.6 c.

18. Oct 7, 2011

### 2clockdude

But how can simultaneity be frame dependent when events themselves are frame independent? In other words, since events occur independently of any coordinates or frame, i.e., since events occur in only one way, simultaneity cannot be frame dependent.

I agree that light from events can reach observers in different frames differently, but what the heck has this got to do with the events themselves? I would say that it has everything to do with said observers physically separating during the observation, but nothing to do with how the events themselves actually occurred.

What say you?

19. Oct 7, 2011

### Erland

In SR. time is just a coordinate. The phenomenon is analogous to the following: If we rotate a cartesian coordinate system in the plane, two points which had the same x-coordinate before the rotation will have unequal x-coordinates after the rotation.

20. Oct 7, 2011

### DaveC426913

Two events are separated by spacetime (otherwise there's only one event). How much time they are separated by is dependent on the observer's frame of reference.

21. Oct 7, 2011

### 2clockdude

Your "time" is a coordinate value, but all physical phenomena are
completely independent of coordinates, because Nature quite clearly
doesn't need or use coordinates. Coordinates are merely tools of
description, and artifacts related to the choice of coordinates cannot
affect physical phenomena, only the _description_ of them.

Events can occur physically in only one way, regardless of how some
set of silly observers views the events by using light rays from them
or by using coordinates. Events can be either truly simultaneous or
not, and in Einstein's train example, he assumed that they were truly
or absolutely simultaneous. Why, then, did not both observers see
them as they really were? The only way that observers can actually
see how the events actually occurred is by placing truly synchronous
clocks _at_ the events. This is not done in relativity theory, is it?

22. Oct 7, 2011

### Erland

How do you define "truly simultaneous events" and "truly synchronous clocks"?

It seems that you believe that there exists an "absolute time" which is independent of all observers. It doesn't.

23. Oct 7, 2011

### DaveC426913

The only "truly"* simultaneous events are events that occur coincident in both space and time.

(*is there another kind? falsely simultaneous?)

Now, how one distinguishes two events that are in the same spatial location at the same time is a tricky one.

No, he does not.

There is no such thing as absolute simultaneity in Einstein relativity.

In fact the relativity is short for 'relativity of simultaneity'. That is the central postulate of Einstein, from which all other phenomena are derived.
It cannot be done.

There is no such thing as "really".

You are espousing Newtonian physics, which has been deprecated in favour of Einsteinian physics, as it better describes the universe we observe.

Last edited: Oct 7, 2011
24. Oct 7, 2011

### DrGreg

All true.
Not true, and you haven't given any argument why it should be.
Also not true.

In special relativity, two events can be related in one of three ways:
1. if they have timelike separation, it is possible to travel from one to the other slower than the speed of light; an inertial observer will take the maximum time to travel, other observers will take a shorter time, but the time is never zero
2. if they have null separation, it is possible to travel from one to the other in a straight line at exactly the speed of light;
3. if they have spacelike separation, it is impossible to travel from one to the other; different inertial observers will disagree over whether they took place at the same time or not, or what order they occurred in
All observers (i.e. all coordinate systems) agree over which of the three types of separation applies to a given pair of events, whatever else they may disagree over.

Simultaneity is a coordinate-dependent property: it is simply the equality of two time coordinates. In general relativity, you are free to choose pretty much any coordinate system you like. The coordinates are just a set of 4 labels you apply to each event. In special relativity we deliberately restrict ourselves to using coordinate systems in which the speed of light is always the same value c. One we have adopted that constraint, we cannot also impose a constraint of simultaneity being absolute as those two constraints are not compatible with each over (as the train-lightning thought experiment shows).

25. Oct 7, 2011

### pervect

Staff Emeritus
It's convenient to think of "simultaneity" as being an artifact of perception.

The short way to show this is to use the Einstein definition of simultaneity, which defines simultaneity in a specific frame as being defined by the midpoint method. You place a pair of stationary clocks at two different locations, and you synrhonize them via a signal emitted at the midpoint. The two events where the synchronizing signal reaches each clock are considered to be simultaneous.

That definition is all you need to show that simultaneity is relative in special relativity where the speed of light is always constant.

You can spend / waste a lot of time trying to come up with some "better" definition of simultaneity, the consequence of any "better" method would be to induce a perferred frame. But no experimental result has ever shown any reason to prefer one frame over another.

You could perhaps pick some particular frame by fiat and declare it to be "the one and true perferred frame", but if you actually try to calculate in it, you'll find it inconvenient to say the least.

For instance you could write down a Lagrangian using the generalized coordinates (I've done it, but I've never seen a published paper taking this approach). You'll find that the derived momenta in this formalism are not proportional to velocity, however, in the low velocity limit.

Basically, making Newtonian physics work in the low-velocity limit demands Einstein's clock synchronization procedure, which demands that the notion of simultaneity be frame-dependent.