Circular Train Spoilers
I'm posting spoilers for my "circular train" problem. Don't
look if you don't want to see. I am absolutely certain of the
solution below. I've drawn the pictures; I've done the math;
everything works out.

The problem: A circular train 1000 meters in circumference sits
on a circular track (obviously also 1000 meters in circumference).
At some point it starts to move. I (who am stationary with respect
to the track) see the moving train as Lorentz contracted to, say,
500 meters. How does a 500 meter train stay on a 1000 meter track?

The solution: I certainly see the train as Lorentz contracted.
But I still see it as exactly 1000 meters long. Here's how that
can happen:

I say the train starts moving "all at once". But Jeeter, a passenger
on the moving train cannot agree. As far as he's concerned, the
front of his 10 meter passenger car started moving before the
rear----and in the process, the car got stretched out to 20 meters.

(If Jeeter looks across the circle at the cars that are going in the
opposite direction, he says that the rears of those cars started
moving before the fronts, so those cars got crunched. That's how
the whole train still sits on the track.)

Now: Jeeter says his car is 20 meters long. Due to the Lorentz
contraction, I see it as much shorter: exactly 10 meters long.
Which is exactly how long it looked before it started moving.

The Lorentz contractions exactly cancels the stretching due
to Jeeter's perception that different parts of the car started
moving at different times.

My mistake: I kept thinking that the train should look shorter
to me now than it looked to me before it started moving. But
that's not what the Lorentz contraction says. It says that the
train should look shorter to me than it looks to Jeeter.
And that can happen because Jeeter is feeling all stretched out.

The Underlying Fallacy: I assumed it made sense to say
that the train starts moving "all at once". But if one observer
says that, another can't. This, of course, is exactly the
fallacy that underlies all the SR "paradoxes".

The Context: I was thinking about the electric and magnetic
fields near a loop of wire carrying a current and couldn't figure
out why (in the frame of the wire) there is no electric field---
after all, the stream of electrons is Lorentz contracted, so they
should be denser than the protons, no? The train is the electrons
and the track is the wire.