Timeline for Euclidean geometry in non-inertial frame
Current License: CC BY-SA 3.0
14 events
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| Mar 2, 2021 at 9:12 | comment | added | Shashaank | But wouldn’t the whole metric, including 𝑔_tt be still of flat space time, Minkowski space time? Wouldn’t the Reimann tensor vanish just like it does for the metric written in an accelerating coordinates ( hyperbolic motion) in flat space time ? The whole space time would still be flat, Minkowskian,right? Just changing coordinates can’t change the flat Minkowskian space time to a curved one? | |
| Apr 13, 2017 at 12:39 | history | edited | CommunityBot |
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| Aug 21, 2015 at 7:22 | comment | added | Selene Routley | @seeking_infinity Have you read the "Ehrenfest Paradox" wiki page BTW, for an alternative explantion of the "problem" with variable angular speed? It is simply that even the relaxed notion of Born Rigidity cannot be upheld during these periods, but it can be applied to a uniformly rotating disk. | |
| Aug 21, 2015 at 7:15 | comment | added | Selene Routley | @seeking_infinity Correct, and real materials are always in a state of strain when rotating uniformly. In Newtonian physics, you can idealize by setting the elastic constants to infinity, which means that the stress from acceleration begets no strain. You cannot idealize in this way in SR/ GR because that implies infinite speed of sound. What I mean by rigid motion at steady state from a central observer is that, if a pattern is imprinted on the disc, the central observer sees that pattern rotating rigidly.But this pattern is a distorted version of what's on the disk before it begins spinning. | |
| Aug 21, 2015 at 7:08 | comment | added | seeking_infinity | @Timaeus I dont agree that the problem is only when angular speed is increasing. Even a uniformly rotating disc is an accelerating motion. | |
| Aug 20, 2015 at 15:39 | comment | added | Timaeus | And real disks strain even in Newtonian mechanics they star in differentially so that each element is pulled harder by the parts of smaller radius than it is pulled by the parts of larger radius that is physically necessary for a Newtonian disk to rotate at constant velocity in Newtonian mechanics. | |
| Aug 20, 2015 at 15:37 | comment | added | Timaeus | I read the question as very very general. The phrase "make this disk rotate at velocity of the order of c" leaves open many ways to get it up to speed. I could shoot lasers at it from above and below to that each part gets an outwards acceleration of exactly what I want when I want it, or through balls, same thing. I can get it up to speed in any way I want. If the disk has bonds instead of being a disk of dust then there is a question about what happens if or when I stop making it do whatever I want. But I could keep making it go at a steady speed if I want. | |
| Aug 20, 2015 at 15:08 | comment | added | Selene Routley | @Timaeus Perhaps I'm not being clear enough: the problem is when the disk's angular speed is increasing: not when it is steadily rotating: yes the motions of the points on the disk from a central observer will seem to rigidly rotate at steady state. Another way to say this is that the speed of sound in a material cannot be infinite - this is what conveys the motion to everything as it spins up to speed. | |
| Aug 20, 2015 at 14:54 | comment | added | Timaeus | But things can move in a way that seems Newtonian rigid to one observer, it just won't seem rigid to other observers. And that is 100% the issue going on in this example. If you are moving as a Newtonian rigid object to a central observer you won't be Newtonian rigid according to other observers. You make it sound like it isn't possible to exert forces on a disk to make it rigidly move according to some observer. As long as the edge goes at sunlight speed it is possible. Making it sound like you can't do that makes it seem magical. | |
| Aug 20, 2015 at 14:49 | comment | added | Selene Routley | @Timaeus I think I'm saying the same thing from a different angle: rather than saying that rigidity (property of a body) isn't a meaningful relativistic invariant, I'm saying that motion by Euclidean isometry is incompatible with STR, unless everything is at steady state. | |
| Aug 20, 2015 at 14:37 | comment | added | Timaeus | Newtonian rigidity isn't impossible because of how bodies interact. Newtonian rigidity is not a relativistic invariant. So it doesn't make sense as a property of any system. | |
| Aug 20, 2015 at 11:45 | history | edited | Selene Routley | CC BY-SA 3.0 |
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| Aug 20, 2015 at 11:35 | history | edited | Selene Routley | CC BY-SA 3.0 |
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| Aug 20, 2015 at 11:27 | history | answered | Selene Routley | CC BY-SA 3.0 |