uwot wrote:You are quite right to say that referencing special relativity is misleading, it is after all premised on a Euclidean worldview, which Einstein himself consigned to the dustbin with general relativity. It is an idealised, Platonic almost, treatment of premises that do not obtain in the real world.
I merely think of SR as part of the story, not the general case. Einstein wanted to publish his work and handn't yet worked out all the math for the general case. Regular acceleration was there, but gravity made it more complex.
But what I am trying to do is give the non-physicist an overview of what actually happens, and I think the thing that people most associate with special relativity is time dilation. If you take special relativity literally, then the different observers can watching each others atomic clocks ticking, agree that they have ticked the same number of times and when they compare them, agree that they tell different times. No one has successfully explained that anomaly by adhering to special relativity.
Well that's because nobody can compare times under SR. I have two clocks that were synchronized, and they move relative to each other. Each clock runs slower in the frame of the other. Which is actually slower? SR gives no answer since it gives no way to compare the two clocks. SR has the ambiguity of simultaneity which means it is impossible to determine the current time 'over there' where the other clock is.
Most attempts, in my view, involve sleight of hand manoeuvres in which the observers are somehow distracted by an acceleration.
The point I am making, I suppose, is that atomic clocks do not count time, they count vibrations (to put it crudely) of caesium atoms, and the reason the clocks were different in Hafele-Keating, is not that they magically compensated for the same number of ticks, as a literal interpretation of SR would compel you to believe, but rather that they simply counted a different number of ticks.
Physics does not say this. It says clocks measure actual time, that is, temporal distance between two events, and what happens in the H-K experiment is not sleight of hand. Time is just another dimension and the clock is another form of tape measure, and like the tape, it gives accurate results only if pulled straight between the two points being measured.
If you're going to post a different interpretation in your blog (that clocks do not accurately measure time), then don't title this an explanation of relativity. Without the clocks, how does one distinguish (measure) 'actual' time? If you can't measure it, perhaps what you thing of as time doesn't really exist.
Einstein's clock cannot be the slow one since in his frame, stickwoman's clock is the slower one, except you don't give her a clock, which was my protest. If one of the clocks is
actually slower than the other, then this symmetry would not exist. In physics, moving clocks don't run slower, they just measure a shorter temporal distance.
But then, as you point out, H-K was not an exercise in SR, it also measured gravitational dilation and it wasn't conducted in the idealised conditions that exist nowhere in the universe.
That experiment didn't need idealized conditions unless it wanted results accurate to a few more digits. It was a successful demonstration of clocks measuring from point A to B via different paths, and the most straight path (on the westbound aircraft) measured the longest time as predicted. The experiment illustrated GR, not SR, because SR does not cover acceleration, and there is no way to compare clocks without acceleration.
If you think not in terms 3D space that perdures, but rather 4D spacetime with
arbitrary assignment of the four axes (X, Y, Z, and time), then relativity is actually quite simple, and the twins un-paradox is actually easy to visualize. For visualization purposes, most concepts can be reduced to only two dimensions, one spatial and the other temporal. But two orthogonal axes can still be arbitrarily oriented, which is what SR is describing. I've never found a better way of illustrating the twins aging that that. Any two points in spacetime are separated in one of three ways: By pure space, in which case there is exactly one distance between them and no temporal distance, by pure time, in which case there is exactly one temporal distance between the two and no spatial displacement, or right on the boundary in which case both measurements are meaningless, but their vectors are not.