
charon » 20 Oct 2019, 20:18 wrote:Why on earth (no pun intended) should space be 'flat'? It's a manydimensional affair. 'Flat' is counterintuitive. I don't know why these things are complicated.
Faradave » 20 Oct 2019, 17:54 wrote:A positive spatial curvature model accommodates cosmic expansion (as per balloon analogy) with a limited past and unlimited future.
It also simplifies "dimension" to mean just one kind: radial unidirectional time, with "space" merely a bidirectional derivative (that 3surface enclosing a 4D temporal field).
It also happens to predict a dimensionless constant of nature, observed as speed limit c, with an inherent value of one (and like the fine structure constant, having no real units). This value is precisely finite, constant, universal and invariant as we observe c to be.
BurtJordaan wrote:We have to measure it from within
BurtJordaan wrote:You know the arguments against this [curvedspace, radialtime] and we are not going to debate it again here.
BurtJordaan wrote:Well, the flat and negatively curved Friedmann cosmology also accommodate [cosmic expansion from a limited past and unbounded future, and] a lot more.
BurtJordaan wrote:Your "prediction" [of speed limit c] is nothing more than a pictorial representation of what is generally known as "spacepropertime coordinates" (a.k.a. Epstein coordinates), first publicized in 1981 by Lewis Carroll Epstein as "Relativity Visualized".
 2013Jorrie wrote:A peculiar feature of the Epstein diagram  the lightcone is replaced by a lightsphere that "looks the same" for all inertial observers, but they observe different portions of it. Lewis Carroll Epstein has cautioned against taking this concept too literally  he actually called it "a myth" in his book, albeit a very useful one.
BurtJordaan wrote:the oneway speed of light is simply a matter of choice of coordinate system  flat Minkowski spacetime coordinates.
the global curvature of space, which, as far as we can tell is zero, meaning "flat like a tabletop"
It may pay off if you would Google "spatial curvature" to find out more.
charon » 21 Oct 2019, 04:34 wrote:Burt wrote:
the global curvature of space, which, as far as we can tell is zero, meaning "flat like a tabletop
Which is a bit like talking about the redness of a strawberry which, as far as we can tell is twelve, meaning 'wet like water'.
Faradave » 21 Oct 2019, 03:46 wrote:I'm not trying to antagonize but I thought we had agreed that in the coordinates you presented in cosmic heart the worldline of an observer at rest points radially outward toward the future (i.e. toward future spatial "foliations" or "simultaneities").
…when we say the universe is flat it is not in the same sense that a piece of paper is flat, but rather means that the geometry of the universe is such that parallel lines will never cross, the angles in a triangle will always add up to 180 degrees, and the corners of cubes will always make right angles. We call this kind of geometry (the kind you learned in school) Euclidean geometry.
charon » 21 Oct 2019, 20:49 wrote:Didn't the quantum business upset the Newtonian ideas? Why isn't Euclidean geometry affected too? Or is it?
we almost certainly live in a spatially infinite universe.
charon » 22 Oct 2019, 16:03 wrote:Since when were aesthetic reasons considered good science?!
charon » October 22nd, 2019, 12:05 pm wrote:
If one asks, if it's limited, what is beyond the limitation  seeing as there's no such thing as literally nothing  they waffle.
A_Seagull » 22 Oct 2019, 22:19 wrote:Physics is all about measurement and relating those measurements in a mathematical framework.
BurtJordaan » October 22nd, 2019, 7:55 pm wrote:charon » 22 Oct 2019, 16:03 wrote:Since when were aesthetic reasons considered good science?!
Flat also happens to be the simplest of the 3 possible options, mathematically speaking. So if the uncertainty is spread equally to each side of flat, why won't we choose flat?
'Occam's razor' and all that, you know...
But do they waffle? Or perhaps you misunderstood what they were saying?
Yes, one can waffle whether the universe is flat, or positively or negatively curved. But as noted in my last post, the empirical evidence overwhelming favors a flat (spatially infinite) universe.
If you say they are waffling about what is “beyond” the universe, I seriously doubt that. You may have, again, misunderstood them.
The universe is, all that there is, so nothing is beyond it. This fact can, however, become a terminological dispute, which is of no great moment.
Some people speak, theoretically, of a “multiverse” — more than one universe. And there are several ways in which a multiverse could be true.
However, if one defines “universe” as all that exists, then there is only one universe by definition. In that case the supposed “multiverse” represents subsets of the “universe” — all that there is.
A finite but unbounded universe, with positive curvature, is one that can, in principle (though not in practice) be circumnavigated. “Unbounded” means that there is no edge — no frontier beyond which space somehow “stops.”
However, if the universe is like this (and, as noted, the evidence shows that it isn’t) it does not follow that there is something beyond the universe, or that it is expanding “into” anything.
OTOH, brane theory holds that there is a higherdimensional 4space and that our universe is a 3space brane expanding into that 4space, and that there are other branes that may collide. This could be true, but there is no evidence (that I know of) that it is true, and more important, there is no need for such a 4space, to explain the expansion of a finite but unbounded 3space. But, again, although a finite but unbounded 3space is possible, the evidence shows that the universe is flat — spatially infinite.
BurtJordaan » October 23rd, 2019, 8:32 am wrote:A_Seagull » 22 Oct 2019, 22:19 wrote:Physics is all about measurement and relating those measurements in a mathematical framework.
This exactly what is happening. The mathematical framework that fits the measurements best says that the universe is very likely to be spatially infinite.
A_Seagull » 23 Oct 2019, 03:42 wrote:Mathematical models can be extrapolated beyond the data set for which they are formed, but this does not mean that the extrapolation is valid.
Oh, yes, they waffled! I was there, I'm not making it up. If we could access those discussions now you'd see it.
You're saying 'the universe' may mean several  or at least more than one  universes. Forgive me, I'm not creating this confusion! I mean, you must see the point and not just brush it off. From now on, whenever the term 'universe' is used I'm going to ask which one. Would that be fair?
I know, but that's all nonsense if 'universe' means an infinite, limitless totality. It can't be finite and infinite both. So which one are you talking about?
It can only expand if it has a certain size or quality to begin with. Something can only get bigger when it's smaller first. But if it's infinite and limitless then the idea of expansion doesn't arise because it doesn't apply.
Faradave » 21 Oct 2019, 03:46 wrote:I thought we had agreed that in the coordinates you presented in cosmic heart the worldline of an observer at rest points radially outward toward the future (i.e. toward future spatial "foliations" or "simultaneities").
Jorrie wrote:Nope, outward indicates the scale factor and its vagaries, you should portray time going perpendicular to your radial...
Jorrie wrote:If you insist on viewing it directly into the large end, you will be forced to have a nonlinear timescale, like my 2billionyear rings.
Jorrie wrote:I think you can still do your "Epsteinlike" stuff if portrayed like that.
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