In any case, once the acceleration stops (simultaneously in both locomotives because our clocks remain synchronized.) I see the train as shrinking for a while, whilst the rear engineer sees it as stretching.

This is a red herring. You and the rear engineer are in the same frame; you therefore have to agree about the length of the train. I agree that there can be optical illusions going on, but those optical illusions have absolutely nothing to do with the problem; they are just a distraction. Your exposition would be much clearer without them (and without the confederates along the track, etc.)

Using this information, you establish that the front locomotive stops accelerating before the rear one (even though, according to your earlier measurements, they started to accelerate at the same time.)

Sure—IF the accelerations stop at the same time as measured on the moving train—but not at all if they stop at the same time as measured from the ground. Do you understand that you’ve added a new assumption here?

Your objection to the kinked world lines is a red herring; we can round out those corners and still tell essentially the same story. IF the two ends of the train perform their accelerations along the same time paths, as measured from the ground, then passengers on the train must see the train stretch. IF they perform their accelerations in some other way, then, as I’ve told you multiple times, the outcome can be anything at all depending on the choices that are made. Your example illustrates exactly that.

KINEMATICS OF AN ACCELERATING TRAIN

A train consisting of all locomotives (so that all parts can accelerate simultaneously) sits stationary on a track and is measured by all to be L units long. For simplicity, assume just two locomotives. I sit in the front locomotive and synchronize with the engineer in the rear locomotive, say by means of light signals, an acceleration at a fixed rate for a short but finite interval. You, standing by the front of the train, have confederates at known distances along the track, including one at the rear of the train, who signal you with light flashes about observed events.

At a precise time, I send a light signal to the rear engineer to begin the acceleration. Knowing the speed of light and the length of the train, I begin the acceleration of the front locomotive at precisely the time that the rear engineer receives the light signal.

At the instant the front locomotive starts to move, you on the platform note the time. Your confederate at the rear of the train is instructed to send you a light signal the instant he sees the rear of the train start to move. Knowing the length of the train and the speed of light, you calculate (from the time you received the light signal from your confederate) that the rear of the train and the front of the train started moving simultaneously. (This is the last time you will see such simultaneity for the train.)

[On board the train, at the start of the acceleration, my engineer and I will SEE a strange optical illusion. It appears to me that the train is stretching (because at the instant I accelerate the front locomotive, the light signals from the accelerating rear locomotive haven’t reached me yet). It is an optical illusion because the engineer in the rear locomotive sees the train as shrinking. We can both measure the proper length of our train by means of timing a reflected light signal running the length of the train and conclude that the proper length remains L.]

In any case, once the acceleration stops (simultaneously in both locomotives because our clocks remain synchronized.) I see the train as shrinking for a while, whilst the rear engineer sees it as stretching. Once the light signals at the time acceleration stops have reached both me and the other engineer, we now both SEE, as well as MEASURE, our moving train at length L.

Out on the platform, something strange is happening. You have asked your confederates along the track to send you a light signal if an end of the train stops accelerating just as it passes them. Using this information, you establish that the front locomotive stops accelerating before the rear one (even though, according to your earlier measurements, they started to accelerate at the same time.) You now measure the train as shrinking as the rear engine continues accelerating while the front engine has assumes a state of constant motion. The train will continue to shrink until you measure all parts to stop accelerating and move uniformly. At this point, you will measure the length of the train with the help of your confederates, and it will be less than L by exactly the amount given by the Lorentz contraction. On board the train, I and my engineer will continue to measure the length of the train as L.

THE IMPOSSIBLE KINKED WORLD LINES OF YOUR DIAGRAM DO NOT PICK THIS UP. THE STARTING AND STOPPING OF AN INFINITE ACCELERATION OCCUR AT THE SAME TIME. WITH CARE, A PROPER MINKOWSKI DIAGRAM CAN BE DRAWN CONSISTENT WITH THIS GEDANKEN EXPERIMENT OF A FEASIBLE ACCELERATION.

You persist in thinking that I’ve *assumed* the train stretches. Instead, the assumption of simultaneous acceleration all along the train car forces me to *conclude* that the train stretches. The stretching is a *surprise*, not an arbitrary assumption.

This is the surprise: Assuming simulatneouos acceleration forces you to conclude that the train car stretches.

Of course that’s not at all a surprise once you understand it. But I’ve discovered that many people (including myself) are surprised by it at first. When we get to the point of understanding it, we’re not surprised anymore, and we’ve learned something. If you insist on dismissing it as unconditionally unsurprising (particularly after being one of the most vocal deniers for days on end), then you’re missing the entire point.

PS—The pole-in-the-barn paradox is also completely unsurprising once you understand it. But it’s still a neat example.

Be it resolved that if a stick, measured as one meter long by a stationary observer, is put into motion in such a way that it remains one meter long to said stationary observer, then it must be the case that the stick has been somehow physically stretched so that its proper length is more than one foot. This has to be true, because the stick must be Lorentz contracted to the observer.

Be it also resolved that this is not Einstein’s rigid meter stick– it is a silly putty meter stick.