# Relativity of simultaneity: the source of the headache

1. Jul 11, 2010

### calebhoilday

Iv been trying to get my head around the special theory of relativity and i think i may have found the particular part of the theory i do not understand; that being relativity of simultaneity.

I was on a train recently, sitting about half way in the carriage, and i noticed two led clocks at either end. I related these two clocks to the two lightning strikes of Einstein's thought experiment, concerning relativity of simultaneity. I considered if exactly half way in the carriage and that the train was at rest than, the passing of the minutes would be considered to be simultaneous, but if the train where moving, this would not be the case. The clock closer to the driver, when the train has velocity would appear to change its digits before the other clock.

This then caused a headache, as i realised this conclusion was inconsistent with the theory. If i was on a train that traveled at 1/2C and the carriage i am in is 3 light seconds long (according to an outside observer), being half way the clock closest to the driver, would be one light second behind a clock in my position and the clock at the other end, would be 3 seconds behind a clock in my position. As i am able to tell that these two clocks are equidistant from my position, I could determine an absolute velocity. This outcome defies the assumption that one can not determine absolute speed and that each inertial frame of reference has equal right in considering itself at rest.

Where have I gone wrong with my understanding relativity of simultaneity?

2. Jul 12, 2010

### zhermes

From inside the train, neither the front nor back clock is moving relative to you (the center). They both therefore tick at the same time, 3seconds after your clock ticks (if they were synchronized initially).

From an outside observer, the front clock ticks a shorter time ahead of the center of the train than the rear clock is behind the center of the train.

3. Jul 12, 2010

### calebhoilday

What occurs if lightning strikes two lightning rods at either end of the carriage, simultaneously to an outside observer?

Synchronisation is a rather particular thing, with how it is done something that needs to be defined.

One can absolutely say, that if i had clocks at either end of a moving train, with me in the middle of them and i used a remote control to turn them on and set them, that they are in fact synchronised. But to have these clocks set and synchronised, at the same position i am in relative to the train, then moved an equal distance in either direction, i find it hard to comprehend how these would be synchronised, considering the train has a velocity.

4. Jul 12, 2010

### djy

Assume the train is moving left to right. In the frame of the train, lightning strikes the right end first, and it meets light rays from the other lightning strike on the left side of the train.

The train and platform observer agree on where in the train the light rays meet. The platform observer thinks the lightning strikes are simultaneous, but since the train is moving right, the rays meet on the left side of the train.

Both methods of synchronization you mention would work in the frame of the train regardless of how fast the train is moving. Indeed, the principle of relativity itself tells us that any experiment performed and observed within the train has the same result regardless of the train's speed.

5. Jul 13, 2010

### calebhoilday

mmm... Iv been thinking about it more and its still not making sense to me. If I consider that light is independent of its emitter (is this right ?), then regardless of if the lightning rods are fixed to the track or to the carriage then the result essentially would be the same.

6. Jul 13, 2010

### djy

The result is the same except for one important difference. In the train's frame, the right end meets its lightning rod (fixed to the track) before the left end meets its rod.

This is a consequence of Lorentz contraction.

In the platform's frame, the train is Lorentz contracted and it's exactly as long as the distance between the rods.

In the train's frame, the distance between the rods is instead Lorentz contracted, so the train doesn't fit between them and each end reaches its rod at different times.

Hopefully you can see the subtlety of how Lorentz contraction and the relativity of simultaneity are related.

7. Jul 13, 2010

### FawkesCa

this maybe a bit strange, but follow me.

when lightning strikes a rob and travels down wires that are at either ends of a train that u sit in the middle of, the train elongates ON BOTHE ENDS EQUALLY due to the speed of light. when the emitters inside the carriage go off, as has been said,light travels at the same speed to the observer. hence, both will appear at the same time inside the carriage, but differently to an outside observer.

if im wrong, say im an construction worker starting out in physics. if this explains it, say i work at Cambridge with 3 PhDs and 2 masters in theoretical physics.