Re: Does Special Relativity contain contradictions?
Posted: October 3rd, 2018, 11:01 am
Some quick comments on the General Relativity discussion, starting here:
Yes. In a small enough volume, in which the gravitational field can be regarded as uniform, the frame is inertial. Hence astronauts in the ISS experience what feels (approximately) like weightlessness even though the force of gravity acting on them is almost the same as it is on us.Halc wrote:Things don't accelerate in such a field, so of course this can be regarded as an inertial frame, since it is one, no?
I would have thought a uniform concentric distribtion of matter (are we talking about a hollow spherical shell of matter?) would result in no net gravitational force inside it. This is the gravitational analogue of the Faraday Cage and Gauss's law.This being within a concentric distribution of matter is exactly such a uniform gravitational field, and clocks within one are gravitationally dilated compared to a stationary clock well outside that field. Neither can locally detect which is which, but if you compare the two (a non-local test), they'll read different values and then each will know which it is.
I'm sure you may be right about the poor wording. I was just doing a quick search as I'm not sure about this stuff myself. At University, as I recall, we had one lecture course on Special Relativity but General Relativity was only briefly covered. I presume the details of General Relativity are considered to be beyond the scope of a BSc Physics course. So anything I've learned about GR is only from popular science books and the internet. Not from proper textbooks.This seems poorly worded if not wrong. I see a lot of commentary on the web taking apart the wording of exactly the part you've quoted here. I think it would be more correct if it talked about being in the gravitational field of exactly one point gravitational source, in which case there would be no exception. Me standing on a planet with the ground exerting a force keeping me stationary in Earth's gravitational field is the same as being in an accelerating ship with the deck exerting the same force keeping me stationary in the ship's accelerated reference frame. That's what the GR rule is, but I thought it was about local forces and physics, not time dilation.
I'm not sure!Am I wrong about that?
Interesting experiment! I guess the SR time dilation effects due to the linear speed could be calculated and factored out.If I put a clock in a centrifuge and whir it up to 1000G, will it dilate the same as being on a star with that sort of gravity? I mean more than it would dilate just from the linear speed of being in that centrifuge? I tried to keep that to a minimum in my example, but there would be no ignoring SR dilation in a centrifuge that violent.
Is that right? Has the increase in gravitational time dilation due to the relative positions of Sun and Moon been experimentally measured? I have read that the difference in gravitational time dilation due to a difference in height above the Earth of as little as 1 foot has been experimentally verified. So it wouldn't be surprising.The wiki talks about an exception within (not necessarily at the center like it says) a concentric distribution of matter, where you also cannot locally detect the difference, but any non-point gravitational source would be an exception. Add more points in different places, and the dilation goes up, but the acceleration might go up or down, depending on the distribution of the points. Gravitationally, clocks run slowest on Earth when the moon is full and we're sandwiched between it and the sun, but our acceleration there is the least since the pull is in opposite directions.