The discussion centers on the shape of spacetime as it relates to the Big Bang, with participants debating whether the universe resembles a toroidal shape, a sphere, or other geometric forms. The consensus leans towards the universe being flat, with no definitive outer edge or shape due to the nature of cosmic expansion. Key concepts include the open and closed universe models, where an open universe is hyperbolic (k<1) and a closed universe collapses back to a singularity (k>1). The conversation emphasizes that the Big Bang occurred everywhere simultaneously, challenging traditional notions of a singular point of origin.
PREREQUISITESAstronomers, cosmologists, physics students, and anyone interested in understanding the fundamental nature of the universe and its geometric properties.
bapowell said:although not globally isotropic
Maybe, but the universe could still exhibit toroidal topology, and it satisfies your three criteria.denism said:as you say, and in addition this form of organization would require some justification because it does not comply with the minimal-sufficiency principle. To my knowledge n-spheres are the highest entropy shapes
bapowell said:Maybe, but the universe could still exhibit toroidal topology, and it satisfies your three criteria.
There is no data supporting any global geometry/topology -- period. But, data does indicate a local universe consistent with flatness, which is evidence consistent with toroidal topology.denism said:OK, I forgot a fourth criterion: minimal sufficiency. In absence of possible verification, no weird proposal of universe shape can be formally rejected, raising the risk of degeneration of this subject. Hence, in an attempt to maintain some rigor in this field, a principle of minimal sufficiency should be observed by rejecting imaginative but supererogatory hypotheses.
I am not aware of data supporting torus
bapowell said:There is no data supporting any global geometry/topology -- period. But, data does indicate a local universe consistent with flatness, which is evidence consistent with toroidal topology.
Could you articulate your minimal sufficiency principle?
EDIT: I'm not advocating for a toroidal universe, just pointing out that it's a perfectly viable possibility.
It has positive and negative principle curvatures, but the Gaussian curvature is zero.denism said:Are you sure that the torus does not cumulate positive and negative curvatures?
They are not -- they are positively curved everywhere.n-spheres are locally flat as well
Right, but none of your criteria are strictly required by observations. We have no data supporting the size (finite vs. infinite) of the universe, whether it is globally compact or bounded, or whether it is globally homogeneous. What we know from observations of the observable universe is that it is approximately homogeneous and close to flat locally. Empirically, all three manifolds of constant curvature -- Euclidean (including toroidal and other flat geometries), spherical, and hyperbolic spaces -- are equally in the running.it is simply making the effort to not introduce hypotheses that are not strictly riquired by new observations.
My feeling is that this curvature is more mathematical than concrete, but it is just a feelingbapowell said:It has positive and negative principle curvatures, but the Gaussian curvature is zero.
bapowell said:They are not -- they are positively curved everywhere.
bapowell said:Right, but none of your criteria are strictly required by observations. We have no data supporting the size (finite vs. infinite) of the universe, whether it is globally compact or bounded, or whether it is globally homogeneous. What we know from observations of the observable universe is that it is approximately homogeneous and close to flat locally. Empirically, all three manifolds of constant curvature -- Euclidean (including toroidal and other flat geometries), spherical, and hyperbolic spaces -- are equally in the running.
denism said:I believed that night would not have been black in an infinite universe? (necessarily forever..)
phinds said:No, that was dealt with conclusively quite some time ago as not being the case. I don't have a reference offhand but I assure you it is true. It has to do with the expansion of the universe. For one thing, it is irrelevant whether the universe is infinite since the only light that reaches us is from the OBSERVABLE universe.
In addition to phinds' response, I'll add that the finite age of the universe also resolves this paradox.denism said:I believed that night would not have been black in an infinite universe? (necessarily forever..)
bapowell said:In addition to phinds' response, I'll add that the finite age of the universe also resolves this paradox.
denism said:something infinite has necessarily always been infinite. The finite age proves that the euclidean 3D space cannot be retained
denism said:OK thanks. The observable universe is the part for which the redshifted wavelengths remain in the visible range?
By finite age, I mean finite time since the big bang. Obviously, if the big bang occurred 13 billion years ago, then there are still CMB photons, as well as starlight, that have simply not had time to reach us yet. This is why the finite age resolves the paradox. It has nothing to do with the size of the spatial geometry.denism said:something infinite has necessarily always been infinite. The finite age proves that the euclidean 3D space cannot be retained
bapowell said:By finite age, I mean finite time since the big bang. Obviously, if the big bang occurred 13 billion years ago, then there are still CMB photons, as well as starlight, that have simply not had time to reach us yet. This is why the finite age resolves the paradox. It has nothing to do with the size of the spatial geometry.
phinds said:Technically, that is exactly correct. In practise, "visible" requires extraordinarily strong telescopes for a long period (see the Hubble Deep Field).
denism said:I asked this question because I read an other interpretation (with which I have some concerns) that the unobservable universe located behind the horizon, corresponds to galaxies for which the recession velocities exceed light speed. Is it erroneous according to you?
phinds said:Not only is it NOT erroneous, it is an understatement in that galaxies IN the observable universe are "now" ("now" gets a bit tricky) are already receding from us FTL. In fact, those at the edge of the OU are receding at about 3c
denism said:I definitely cannot understand this point. My intuitive expectation was that the expansion rate cannot exceed c because it it was the case, everything would disconnect at once, even between the sun and Earth and between your eyes and your screen..
Did you read the problem of the ants on a rubber rope <http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope>[/QUOTE]
The first thing you need to do when studying either cosmology or quantum mechanics it TOTALLY get rid of the concept that your intuition is worth squat. It is not. It's something we all have to get used to.
What you are not understanding is that nothing is traveling FTL in the same reference frame. The universe is expanding. The recession rate has nothing to do with c.
denism said:I definitely cannot understand this point. My intuitive expectation was that the expansion rate cannot exceed c because it it was the case, everything would disconnect at once, even between the sun and Earth and between your eyes and your screen..
Did you read the problem of the ants on a rubber rope <http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope>[/QUOTE]
The expansion is a rate, meaning that the recession velocity increases over distance. The further away something is the faster it recedes. So a galaxy can receded from us at 0.01c that is relatively nearby while another that is very very far away can recede at 2c or 3c or whatever. Note that this also includes light emitted from those galaxies. A galaxy receding from us at 2c that emits light away from us would NOT catch up to the light. In the galaxies frame of reference it is stationary and the light moves at 1c away from it.