Steve3007 wrote: ↑
October 9th, 2018, 11:19 am
Ok so, as I understand you, you're trying to set up an experiment which compares 450km/sec linear speed with 450km/sec speed in a circle, with therefore large acceleration towards the centre of the circle; the centre of the centrifuge.
Yes, except 450m/sec, not km per sec. I said it wrong the first time. Bob at the equator is moving at that speed, and is also going in a circle, but it takes a day to do a lap, so much lower acceleration. We should run the experiment for at least a day if we were to do this for real, so Bob's net velocity at the end is zero just like that of Alice.
I don't know for sure either, but I suspect the clocks wouldn't stay in sync, and here's my reasoning:
The Alice/Bob experiment shows that two clocks at either end of an accelerating box will get out of sync with each other.
Bob is not in the box here, and the environment is very different where Alice is. Each knows which is which. I'm putting at least 1000 g's on poor Alice.
The Bob-clock is dilated compared to the Alice-clock. So this would be true of two clocks positioned at different points on the radial axis of the centrifuge.
Right, but we're not doing that. Only Alice, at the exact point where she has the same linear speed as Bob, and the same gravitational potential as well
. <-- Pun mildly intended. There is no third clock somewhere else on the centrifuge.
They'd effectively be at either end of a box that's accelerating towards the centre of the centrifuge. In terms of the equivalence principle I think they'd be in the equivalent of a gravitational field whose force vectors point radially outwards and whose magnitude is proportional to v2/r. So I think there would be time dilation between different clocks at different values of 'r' in the centrifuge.
Big time, yes. But we're not doing that. Just Alice in there.
And there would therefore be time dilation between any of those clocks and a clock that is not rotating.
I think it would be the same at exactly one point in the box: the one that moves at 450m/sec. Clearly it runs faster at the center (not moving at all), and slower further out (more V and more acceleration), so somewhere in between they must balance. If acceleration is not a factor, it balances at whatever RPM gives us 450m/sec. If acceleration matters, it balances at a smaller radius than that.
If we want 1000g, we need to pick an r that is about 22m I think, 290000x smaller than the r of Bob who is accelerating at about 1/290th of a g.
Your GR equation is useless since r is identical in both instances. It is computing gravitational dilation of something stationary, not of something moving. The SR equation you use in your program only computes a relative dilation for a clocks separated by h, and we have no h here. The appropriate SR equation is the simple Lorentz factor for 450m/sec in both cases. Acceleration (g) does not play into that equation.
Incidentally, straight after that you said this:
The article you quoted misstates the principle of equivalence: "Einstein’s principle of equivalence tells us that whatever is true for acceleration is true for a gravitational field."
That is just wrong, so I question the rest of the article. The principle says there is no local test to determine which situation you're in.
For the reasons I've been discussing recently, I don't agree with you here. It's not wrong as such. It just doesn't make it clear that acceleration is in every measurable way equivalent to a uniform
I still stand by my assessment of that. Every locally measurable way, yes, but not every measurable way. My Uranus/Earth thing bears that out. Both locally detect a similar g, but the one with the slightly higher g has considerably less actual dilation. There is no local test for actual dilation or for r (the r is what differs between Earth and Uranus). David would be ecstatic if there was such a test, since it would prove that his is the only correct view.