# Question about Einsten's Train and lightning experiment

1. Apr 7, 2012

### icexelloss

It might seem to be a stupid question..But I really want to figure it out so I posted it here.

Again, the problem should be familiar to anyone here. Two lightning bolts strike at both end s of a moving train simultaneously (according to the stationary observer).

My question is: In the inertial frame of the train, the lightening strikes at each end of the train will each travel at c to the middle of the train, thus the observer sees a simultaneous lightening strike just like the platform observer. Why this is wrong?

2. Apr 7, 2012

### Austin0

Yes both strikes will travel at c and take the same time to reach the middle train observer according to his clocks and ruler, but will not reach him at the same time because in his frame they did not start at the same time. According to observers at the front and back of the train, the time of the strikes were not the same , The front strike occurring before the strike in the rear.
This of course agrees with the observation of the ground observer who sees the front strike reach the middle of the train first because the observer there is moving toward the light.
Exactly the same applies in reverse if you set the condition that the train observer sees the strikes simultaneously. Then the ground observers clocks would necessarily determine that the strikes were not simultaneous

3. Apr 8, 2012

### Staff: Mentor

Not a stupid question at all...

If the two lightning bolts strike the two ends of the train at the same time in the train's frame of reference then they will indeed meet in the middle of the train. The purpose of the thought experiment is to show that they don't meet in the middle of the train, and therefore that they are not simultaneous in the train's frame of reference.

To see this, imagine that at the point where the two beams of light meet, there's a small explosion when they meet. The explosion is powerful enough to scorch both the train and the platform. The two observers don't necessarily agree about when the explosion took place (maybe they don't have clocks so they don't even know themselves!) but they must agree about where it happened - the scorch marks on the train and the platform tell them.

The platform observer says the two lightning strikes were simultaneous if there is a scorch mark on the platform exactly halfway between the points where the lightning bolts hit. The train observer says that the two strikes were simultaneous if there is a scorch mark exactly at the middle of the train. But because the train was moving, those two points weren't lined up at the moment of the explosion, so there's no way that they both can be marked. If there's a mark at the midpoint of the platform then the mark on the train is somewhere behind the midpoint of the train, and if there's a mark at the middle of the train then the mark on the platform is somewhere ahead of the midpoint on the platform. Either way, the flashes were simultaneous to one observer but not the other.

4. Apr 8, 2012

### icexelloss

Thanks guys. These explanations are indeed satisfying.