So when you ask “where is my misinterpretation”, there are multiple answers. One of those answers is: You just made up that stuff about value. Another is: You wrote “assumption” when the correct word was “conclusion”. You do this a lot.

(Incidentally, the conclusion is a special case of the more general conclusion that the ratio of the prices of two goods should be equal to the ratio of their values at the margin. No assumption is made about what that ratio is.)

I see that your reading comprehension problems continue.

OK Steve, so where is my misinterpretation or missing context. It sure seems to me like you are saying that future scones (birds in the bush) should be valued the same as present scones (birds in the hand). On the other hand, your argument also depends on future money be valued much less than present money (100 % daily interest!).

You are right, in fact E did consider an accelerated body, but he didn’t describe it as such. He considered an object with “constnat motion” following a circular path in space (not spacetime–Minkowski hadn’t chimed in yet) describing the object as having a constant “velocity”–I assume he meant speed. In fact, he considered a form of the train paradox–by asking what an observer at the pole would conclude about the a clock on the equator. He concluded, based on SR, that the pole observer would observe the equator clock as running slow relative to the clock at the pole. He hadn’t invented GR yet, so he didn’t address the fact that the clock on the equator is undergoing less gravitational acceleration than a clock at the pole because of centrifugal force, which under GR would cause the clock at the equator to run faster. Like everyone since, E wanted to apply a theory based on interial frames to non-inertial frames.

(Interestingly, in this problem, E did the same thing as the train paradox solvers try to do–consider a polygon, looking only at the sides and ignoring the vertexes, and then lets the polygon deform smoothly into a circle. He adds an assumption to his two principles at this point–”If we assume that the result proved for a polygonal line is also valid for a continuously curved line…” Tricky, tricky. Mathematically, this seems wrong to me. In a circle, every point becomes a vertex, so to speak.)

Nowhere does he do a Steve thought experiment where he says “what happens if we start a stationary earth spinning”.

Just the opinion of a “crank”.

Incidentally, I do want to go way back to your suggestion that this has something to do with the Ehrenfest Paradox; despite the superficial similarity, I think it’s quite different. In this problem, we can really do all the interesting analysis from inertial frames, by assuming a square track with rounded corners (as I did) or an elongated racetrack (as you did). The Ehrenfest Paradox concerns the appearance of the *radius* from the point of view of a train passenger, and for this, I think you really do need to consider non-inertial frames. (Though maybe you see a way to do this that I don’t).

As for this: future consumption should be valued the same as present consumption — I haven’t the foggiest idea what that statement even *means*, and if I ever said any such thing (which I doubt) I bet there was some important context you’ve omitted.

Steve – You are being confusing by posing this problem in terms of instantaneous accelerations, which are needlessly confusing. and especially by posing this problem in terms of a train, which doesn’t normally stretch the way you have it doing. You should replace the front and back of your train by individual spaceships connected by a string the way Bell does. The point, as you say, is that accelerations, gradual or instantaneous, that begin simultaneously in one frame aren’t simultaneous in other frames.

The reason you get different answers from those physicists get is that your assumption of simultaneous acceleration is unnatural to physicists – the railroad cars we see in ordinary life are rigid objects, not stretchy ones. Your answer to the puzzle, though technically correct, depends on some unphysical slight of hand.

Incidentally, you have a tendency to do the same sort of thing in economics – start with an unnatural assumption (e.g. future consumption should be valued the same as present consumption*) and reach some conclusion that you like but that most people find absurd.

I realize that people do try to analyze acceleration in SR, since GR is intractable. I’m sure crack physicists know a lot of tricks to do this with some confidence (additional things that have to be included above and beyond the Lorentz diagram). I don’t know what happens if you accelerate a train at an instant. Either do you. Its never been done.

SR is an axiomatic logical structure. You cannot deduce true conclusions a logical structure if you contradict one of its a crucial axioms. The axioms of SR include inertial frames and rigid rods. You are askingme deduce a conclusion using SR (Lorentz diagram) while contradicting one of SR’s axioms (letting a train change its inertial frame). I’m not saying you can’t deduce true propositions about a train that changes its inertial frame, just that you can’t do it using only the axioms of SR. You need something more.

For example, ninety percent of the people who claim to demonstrate the consistency of the twin paradox within SR, actually invoke GR at the turn around point. They say, time slows at the turn around because according to GR time slows for bodies undergoing acceleration. That is not proving the twin paradox within SR. I don’t think it proves it using GR either, but that is another issue.

You might meditate on this: The whole *point* of SR was to firm up the foundations of electrodynamics, a subject in which particles are SUBJECT TO FORCES and therefore ACCELERATE. You might meditate on the fact that there are electromagnetic forces, and hence acceleration IN EINSTEIN’S PAPER.

If SR forbade us to ever think about acceleration, it would be a really really really stupid theory. Fortunately, it doesn’t and it’s not.

If your position is “acceleration is impossible to think about”, then you’ve graduated from confusion to crankdom. (Another symptom of crankdom is that you *still* haven’t told me what you think is wrong with the diagram I provided—-you’re rejecting the conclusion even though you can’t find a mistake in the argument.)

I am absolutely through with this discussion.