Timeline for Ambiguity in applying Newton's shell theorem in an infinite homogeneous universe
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2019 at 15:26 | comment | added | A.V.S. | In GR there is a language to distinguish between coordinate system artifacts, statements about specific reference frames, statements true for a specific observer and observer independent statements. Historically, before the language of GR evolved, there had been works making statements roughly equivalent to arbitrarily accelerated spaceship. | |
| Jul 16, 2019 at 13:53 | comment | added | pela | Hmm… if I understand you correctly, in GR the problem isn't really a problem — even considering only flat universes — since I can't make the spaceship accelerate by Birkhoff's theorem in the first place. There isn't a solution, like there is in the Newtonian case, that will apparently make the spaceship move? | |
| Jul 16, 2019 at 12:59 | comment | added | A.V.S. | Yes, solution (FRW metric) has the same basic properties, but there are new options: closed and open cosmologies, and the Friedmann equations now has additional terms (with $k$ and $p$) and the cosmological constant is more “natural”, it is the interpretation in terms of shell theorem that needed to be changed: GR is a nonlinear and local theory, generally it is not possible to write a solution as an integral of sources over some domain. The closest one has to shell theorem is Birkhoff's theorem which is for vacuum spacetimes only. | |
| Jul 16, 2019 at 8:33 | comment | added | pela | I think I've been a bit vague on defining whether the problem is Newtonian or GR. But isn't this solution equally valid in GR? | |
| Jul 15, 2019 at 18:39 | comment | added | A.V.S. | @pela: re: part of the shells outside the obs. uni. In Newtonian world the speed of signals propagation is infinite, so observable universe is all there is. If signal propagation at a finite speed is important, you need to use GR, with it much more intricate causal structures. In general relativity, the homogeneous and isotropic universe is a solution of Einstein equations called FRW metric. | |
| Jul 15, 2019 at 16:18 | comment | added | pela | Thanks again! I think your last comment is what I failed to see. I've now discussed the problem with three cosmologists, and see the basically my thought experiment just creates a Hubble flow, either expanding or collapsing. And if I try to make my universe static by introducing some Λ-ish term, that will affect the motion of both dust particles and spaceship. I'm still a bit in doubt, though, about the fact that the shell aren't centered on the spaceship's observable universe, and that there may be an effect from not being able to feel gravity from the part of the shells outside the obs. uni. | |
| Jul 15, 2019 at 15:58 | vote | accept | pela | ||
| Jul 11, 2019 at 20:40 | comment | added | A.V.S. | @Chris: State of rest (or of uniform motion) is not absolute even in Newtonian theory if you do not have a dedicated set of objects which would serve as a reference for inertial motion. See my extended answer. | |
| Jul 11, 2019 at 20:33 | history | edited | A.V.S. | CC BY-SA 4.0 |
Extended the argument, added discussion of Newtonian cosmologies, and other answers.
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| Jul 11, 2019 at 16:13 | comment | added | Chris♦ | This doesn't make sense. You seem to be implying that, based on an arbitrary choice of what you consider $x$, the whole universe will collapse towards that point. | |
| Jul 11, 2019 at 7:29 | comment | added | A.V.S. | @jawheele: But my point is that the physics (Newtonian gravity) is distinct from artifacts of particular formalization (potential with a good falloff). OP's physical intuition is correct, it just need better framework to be expressed. But I also see your point and will extend my answer later today. | |
| Jul 11, 2019 at 7:17 | comment | added | pela | @jawheele I think I'm okay with "multiple accelerations", because in A.V.S.'s model, everything collapses together, meaning that any particle (including the spaceship) approaches any other point at an accelerating speed. | |
| Jul 11, 2019 at 7:15 | comment | added | pela | Thanks for the reference, A.V.S.. I'm still a bit confused though: We agree that in Newtonian dynamics, space doesn't collapse, right? Only matter within space. And that would mean that Newton's universe cannot be infinite, since that would require traversing an infinite distance in a finite time. So basically the solution in a Newtonian universe is that you can't keep adding symmetric shells, because at some point you'll reach the edge of the universe? | |
| Jul 11, 2019 at 7:12 | comment | added | jawheele | This feels a bit disingenuous. It feels like you're saying "everything's hunky-dory with basic Newtonian gravity with these inputs", which I emphatically disagree with, but I think a more honest answer expressing your point is the statement "there exists a generalization of basic Newtonian gravity that handles your inputs in such a way that these apparent contradictions make sense". You haven't addressed why the contradictory basic Newtonian gravity interpretation of OP's observations (e.g., the spaceship has multiple accelerations) arises. | |
| Jul 11, 2019 at 6:38 | comment | added | A.V.S. | @pela: Newtonian gravity in some aspects is much closer to GR than most people realize. You can also have a static Newtonian universe if you add cosmological constant term and it would be precise limit of Einstein static universe in GR and it also would not be stable. On a more technical level a geometric formulation of Newtonian gravity better equipped to deal with situations like infinite matter distributions is a Newton-Cartan theory, see this paper arxiv.org/abs/gr-qc/9604054 for a sample of cosmologies. | |
| Jul 11, 2019 at 6:00 | comment | added | pela | Thanks for your answer, A.V.S.! I'm tempted to think that this is the solution, but I'll have to think a bit more about it. So, basically a static, dust-filled, Newtonian universe is impossible, in contrast to what Newton thought. But how about a GR universe with an exact amount of dark energy to counteract matter? Maybe that's unrealistic because it's unstable… | |
| Jul 10, 2019 at 14:49 | history | answered | A.V.S. | CC BY-SA 4.0 |