A in a train is passing B in a train, both moving in opposite directions. A sends a light to the floor and back up and B does the same. The thought experiment says that for A, B's light travels farther than it does for B, in a V shape, and for B, A's light ditto. So each's clock runs slower.

My question is why doesn't each have to consider the horizontal distance his own light has to travel - why does he have to consider the other's horizontal distance, but not his own.

My gut says I'm getting something wrong here because it's too simple - I've googled as many keywords as I can and find nothing. This is like an itch I can't scratch. Anyone have a simple, layman's answer?

did you mean to post this in SMP?

No. I have a religious motivation - and I don't like that place.

Each person's own light doesn't travel horizontally in their own frame. The horizontal distance is 0.

Search 'special relativity' in youtube, it'll turn up a lot.

But the cars are transparent and the light does travel horizontally against the background. I don't understand why you can ignore that and claim the measurements are real. Why can't A, when observing B, just measure the vertical distance?

Then maybe you should pray for the answer.

Let's make B stationary on the train platform. As A speeds by in the train he shines his flashlight first onto the floor at his feet and then lifts it to shine directly above his head. For him there is no horizontal movement. B sees A shine the light onto the floor but by the time A lifts the flashlight to shine it directly above his head the train has moved on and B will see the light shining on the ceiling off to A's side hence the V shape for him but not for A.

As a layman, my understanding is that the point of special relativity is that there is no preferred frame of reference. In your example, if you focus on just one of the parties, then you can choose from a series. Is the frame of reference the moving train, so we look at the light path down to the floor and up? Or is it from outside the train, so we add the motion of the train? Or is it from the point of view of the Sun - so we have to take into account the rotation and orbit of the Earth? Or from the centre of the Milky Way? Or our galaxy neighbourhood? Or somewhere else?

Special relativity says it doesn't matter - a very counter-intuitive result. The speed of light is the same for two observers, even when they are moving relative to each other - though this is not true for the speed of other things, such as a train or a ball, that are moving much slower than the speed of light. This is "accomplished" through factors such as time dilation.

So the example of the train is an attempt to contrast the result with a ball or some such compared to light. Again, it is counterintuitive, but it is well supported by experiment. When you ask why doesn't someone have to consider the horizontal difference in their own light beam, you are asking in essence, why doesn't the person on train A look at things from a frame of reference outside of the train? They certainly could, but that would be a different frame of reference.

The problem is there is supposed to be a real difference - A's clock will be slower than B's, B's slower than A's. But if A measures his beam with the background he will get the same time as B - so how could the clock, which isn't looking anywhere, actually register a different time?

The 4 atomic clock on airplane experiment claims different times were actually registered for the clocks on the planes - but why wouldn't the earth clocks be slower than the plane clocks as well? I know there is a gravity issue there as well, but the stuff I read said there was also a velocity factor.

I don't pray about itches - or questions that science is supposed to answer.

It might help to understand if you get rid of the trains, get rid of the tracks, the earth, everything. Just two people floating past each other at a constant speed in space.

From each persons point of view they will be stationary and will only only see the motion of the other person.

It is somewhat hard to understand you without a picture, but I think the answer is that the horizontal distance is 0 for their own light beam. So they are considering the horizontal distance, it just happens to be 0.

You're getting confused by the "background." If you're riding on train A, then it's the background that's moving, and not the train. You're introducing a third viewer ("background") who sees *BOTH* lights going in a V shape.

But if you're on train A, then the A light simply goes up and down.

I think NR is asking why IF you introduce a third observer outside the trains, do the clocks still measure "different" times even though the time dilation for both clocks is the same from the perspective of the third observer. i.e., why is there a "real" difference in times if you can define a third reference frame such that there is no difference in times from that frame. I started to write up a reply but it's a subtle point and actually quite tricky. I'm not sure I can come up with an intuitive layman's answer that would be satisfying. The best way to understand it is to work through the math.

One thing to think about is you have to take into consideration the length of time it takes for the signal to travel from one observer to the other (or other two observers); the signal in this case being the information from the clock(s). This fixes some apparent paradoxes. It's been quite awhile since I've done any SR problems though so I'm not quite sure this is the correct fix here. If I have more time later I may work through it.