Originally Posted by

**DrRocket**
If you are trying to sound like a snotty little kid you are succeeding admirably. Not only did I read your entire post, I apparently understood what you actually said, and failed to say, better than did you.

I am not trying to be snotty, but I get intemperate when I feel as if someone hasn't read a post of mine carefully. Doubly so if I feel it happens twice. If you did indeed see that I had put "for an observer on the tracks" in my post, then I apologize. But I also fail to see how there's any ambiguity as to which inertial frame I'm measuring simultaneity from (which is presumably why your post contained an explanation on how simultaneity is dependent on inertial frame).

As I stated, you statement ot setting up the problem by

*ignoring length contraction* and having the trains cross at the same time from the perspective of an observer on the tracks is not well defined. When you invoke simplified Newtonian mechanics in the form of SUVAT equation, you have then defined the problem. But then too the answer is quite clear. The trains will cross at the same time from the perspective of an observer in reference frame of the rails -- because you set up the problem to have just that precise outcome.

So you're saying that even with relativistic speeds, SUVAT can accurately describe which train wins for an observer on the tracks? That the phenomena of length contraction doesn't modify any of the SUVAT results? If so, I don't see how that's possible.

If the trains are traveling such that the fronts cross the finish line simultaneously in the frame of the observer on the tracks then the geometric center of the faster train will cross first, since it is shorter and traveling faster. Ditto for the caboose.

That would imply that length contraction doesn't change the expected position of a point forward most on the fast moving train, right? Which would make that forward most point the "origin" for the contraction, right? (Meaning that before and after the Lorentz transformation, it's position will remain unchanged).

But now take the case of a point aft most on the train, near the caboose. It will appear, to an observer on the tracks, to have traveled a greater distance than the nose of the train when the nose of the train crosses the finish line, right? (Otherwise there wouldn't be any length contraction at all). Which means the SUVAT equations can't hold for any points aft of the very nose of the train. You need to factor in the length contraction to get an accurate result (which clearly the regular SUVAT equations do not do).

So now put a second train with its nose right on the tail of the first's caboose. And have it, unconnected, accelerate at the same speed as the train ahead of it such that at any infinitely small instant the two are in the same inertial frame. Its nose will have appeared to have contracted towards the nose of the first train (if not, then the two trains will disconnect, which I believe you said wasn't the case). But you should be able to evaluate that second train in isolation to the first, in which case it'd be an identical case to the first train just with a slightly larger distance. Which would mean its nose wouldn't contract towards the nose of the first train, but be perfectly predictable using the SUVAT equations.

Which means the path of a point connected to the first train can't be calculated using SUVAT, but the path of that exact same point, from a second train, can be calculated using SUVAT, which leads to a contradiction, which should not be possible. This isn't a complicated paradox, so someone has already posed it and someone else has already solved it, or length contraction wouldn't be an accepted scientific theory. Which means somewhere I made an invalid assumption in my train (pun intended) of logic, and I don't understand what that is. Please tell me where, I honestly don't see it. (Note, in any cases of ambiguity for frame of reference, assume the tracks).

I can draw some pictures if this last little bit was confusing.

If you wan to "google" something try googling special relativity and go read about the Lorentz transformation. Or better yet, go read Rindler's book on special relativity. You might just learn something.

I understand the math involved, that's not the issue. And I understand the time dilation and added mass effects. It's just the exact nature of the length contraction which has me curious. A few days ago I would tell you I understood it, but the more I think about it, the more I realize I couldn't program it in to a simulation because its exact mapping is still a bit of a mystery.

Or here's an even simpler example: take a singularity and accelerate it to .9c relative to yourself. Are there any differences in its position at some given time from what SUVAT would tell us? What if it's a long rod traveling along its long axis? What if its two singularities the same distance from each other as the long rod is long, but entirely unconnected?

While reading Rindler's book might be a fine way of my learning the answer, so to is asking pointed questions to learned people. This method also (hopefully) takes less time.