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I agree with all your points except: > QM strongly suggests that it isn't an argument over which is certainly out of scope here (however it did answer my ques

I agree with all your points except: > QM strongly suggests that it isn't an argument over which is certainly out of scope here (however it did answer my question); and > The Big Bang is not a single point. It's a spacelike line which I think is wrong for the standard cosmology. See Davis & Lineweaver 2004 <https://ui.adsabs.harvard.edu/abs/2004PASA...21...97D/abstract https://ui.adsabs.harvard.edu/abs/2004PASA...21...97D/abstra...> notably fig. 1 and the expalanatory text scattered within. Why would (cosmological) t=0 be a line rather than a point, a 3-volume, or some even weirder non-Lorentzian structure? I can't think of why it would be a line other than (reaching here) nonvanishing vorticity (in either the sense of the Raychaudhuri equation or because of ~axisymmetry with spin), and those aren't features of the standard cosmology. Obviously I've seen Penrose diagrams with the BB drawn out to look like a horizontal line, but have never taken that to be anything other than for legibility or print-reproducibility reasons, similar to the dimensional reduction of the diagram itself. I would be grateful for a reference with explanatory text if you think this is wrong. Absent published authority, I think you could also take this up with Pössel (Max-Planck-Inst. Astro. Haus der Astronomie) who by sheer coincidence ran a related twitter thread <https://twitter.com/mpoessel/status/1551119783315251200 https://twitter.com/mpoessel/status/1551119783315251200> in which he writes (among other things): " ... 23/ ... Let's forget about the hot Big Bang phase, pretend that 24/ all the galaxies taking part in cosmic expansion are point particles corresponding to galaxies we see in the observable universe today were at one and the same location. 25/". @johncarlosbaez has been all over that thread on Twitter too, and would probably engage with your it's-not-a-point-it's-a-line point. I am pretty certain that Pössel means we ignore the "hot Big Bang phase" to mean not just the first few minutes (up to the synthesis of helium) (which is a fairly common time frame for "hot Big Bang") but up to early structure formation, and that he'd clarify if asked. I agree that in the standard cosmology there are an infinite number of causally disconnected points one "instant" after the Big Bang, but don't see how that can't follow from the standard BB singularity. Of course a BC universe is not standard cosmology, so alternative final shapes don't raise my eyebrows at all, unless you wish to argue that in General Relativity, no BC universe can even in principle have a point wherein all other points are in its past light cone. All that said, I'm not sure why you're objecting to slicing as having a dependency on choice of coordinates. I did write that \Sigma is not physical. I will now write that it is very convenient to calculate in some set of coordinates, and that it is possible not to fall into holes (pardon the pun) while doing so. Finally, I'd like to turn on its head your second sentence. Relativity allows some physical distributions of stress-energy to pick out a meaningful set of coordinates. (as has been known in cosmology for many years. cf. <https://arxiv.org/abs/1211.6338 https://arxiv.org/abs/1211.6338> §2 notably p 4)

raattgift 4y ago
Just to be provocative (in reality I agree with you that light cones are more fundamental objects than any spacelike hypersurface, and that light cone surfaces are physically meaningful at least in the local neighbourhood of p) I'll drop in some Bob Geroch: "[Special Relativity] emerges as just one more physical system. It consists, just like the others, of certain fields subject to a certain system of first-order, quasilinear partial differential equations. The causal cones of special relativity (which reflect the speed of light) have no special significant over the causal cones of any of the many other such systems in physics." <https://arxiv.org/abs/1005.1614 https://arxiv.org/abs/1005.1614> (That democracy of causal cones paper is surprisingly relevant to some of the conversations you are running here tonight, particularly §2. I think you might especially enjoy the last paragraph on p. 6, notably its last two sentences starting "We note that, quite generally, C is a nonempty, open convex cone of tangent vectors...". In the context of our discussion, you might not enjoy the part starting at the bottom of p. 7 to the start of §3 :-).)
pdonis 4y ago
> which I think is wrong for the standard cosmology. I have no idea why you would think that, since the very paper you link to explicitly shows diagrams in which the Big Bang is obviously not a single point but a spacelike line. > Why would (cosmological) t=0 be a line rather than a point, a 3-volume, or some even weirder non-Lorentzian structure? Because that's what you get when you take the appropriate limit. > Obviously I've seen Penrose diagrams with the BB drawn out to look like a horizontal line, but have never taken that to be anything other than for legibility or print-reproducibility reasons, similar to the dimensional reduction of the diagram itself. You are mistaken. The point of a Penrose diagram is to show causal structure; that is how it is constructed, so that light cones on the diagram exactly match light cones in the spacetime it's a diagram of. That means that if it were really true that the entire universe was in the future light cone of the Big Bang, the Big Bang would have to be a point, and the diagram as a whole would be an inverted triangle that was the future light cone of that point. Which obviously is not the case for Penrose diagrams of the universe as a whole. As for "published authority", as I noted above, you gave one yourself: the Davis & Lineweaver paper. It agrees with what I have been saying, not with what you have been saying. > I agree that in the standard cosmology there are an infinite number of causally disconnected points one "instant" after the Big Bang Then you are contradicting yourself, since this is impossible if the Big Bang is a point. It is only possible if the Big Bang is a spacelike line. > but don't see how that can't follow from the standard BB singularity. It does. The issue is not "the standard BB singularity", but your mistaken belief that that singularity is a point. It's not. It's a spacelike line.

raattgift 4y ago

Just to be provocative (in reality I agree with you that light cones are more fundamental objects than any spacelike hypersurface, and that light cone surfaces are physically meaningful at least in the local neighbourhood of p) I'll drop in some Bob Geroch: "[Special Relativity] emerges as just one more physical system. It consists, just like the others, of certain fields subject to a certain system of first-order, quasilinear partial differential equations. The causal cones of special relativity (which reflect the speed of light) have no special significant over the causal cones of any of the many other such systems in physics." <https://arxiv.org/abs/1005.1614 https://arxiv.org/abs/1005.1614> (That democracy of causal cones paper is surprisingly relevant to some of the conversations you are running here tonight, particularly §2. I think you might especially enjoy the last paragraph on p. 6, notably its last two sentences starting "We note that, quite generally, C is a nonempty, open convex cone of tangent vectors...". In the context of our discussion, you might not enjoy the part starting at the bottom of p. 7 to the start of §3 :-).)

pdonis 4y ago

> which I think is wrong for the standard cosmology. I have no idea why you would think that, since the very paper you link to explicitly shows diagrams in which the Big Bang is obviously not a single point but a spacelike line. > Why would (cosmological) t=0 be a line rather than a point, a 3-volume, or some even weirder non-Lorentzian structure? Because that's what you get when you take the appropriate limit. > Obviously I've seen Penrose diagrams with the BB drawn out to look like a horizontal line, but have never taken that to be anything other than for legibility or print-reproducibility reasons, similar to the dimensional reduction of the diagram itself. You are mistaken. The point of a Penrose diagram is to show causal structure; that is how it is constructed, so that light cones on the diagram exactly match light cones in the spacetime it's a diagram of. That means that if it were really true that the entire universe was in the future light cone of the Big Bang, the Big Bang would have to be a point, and the diagram as a whole would be an inverted triangle that was the future light cone of that point. Which obviously is not the case for Penrose diagrams of the universe as a whole. As for "published authority", as I noted above, you gave one yourself: the Davis & Lineweaver paper. It agrees with what I have been saying, not with what you have been saying. > I agree that in the standard cosmology there are an infinite number of causally disconnected points one "instant" after the Big Bang Then you are contradicting yourself, since this is impossible if the Big Bang is a point. It is only possible if the Big Bang is a spacelike line. > but don't see how that can't follow from the standard BB singularity. It does. The issue is not "the standard BB singularity", but your mistaken belief that that singularity is a point. It's not. It's a spacelike line.