MarkE

Then the graph wasn't what I asked for. I asked whether anyone could draw the shape of the universe on a piece of paper (or explain that drawing in words, which would also suffice). If you can draw the Solar System, and the Milky Way, or the Local Group, it must be possible to make a drawing of the entire universe. If however nobody can do this, then I have a hard time taking the theoretical/mathematical descriptions of that shape too seriously. For all we know these models don't describe the real world, even though they make logical sense. As Richard Feynman once said: “Make every question you ask in research a question about nature. Otherwise you can waste your life in working out the minutiae of theories that most likely will never have anything to do with nature.” Lee Smolin adds to this: "Even worse, we get caught up in petty competitions and academic turf battles between the adherents of different models". I'm not saying that I have a clear indication of what the shape of the universe must be, I just think that, if nobody is able to draw it on a piece of paper, there's no leading, widely accepted shape that's more plausible than any other shape. Therefore it could be spherical, like a globular cluster (which would make the most sense to me). What about you, what shape makes the most sense to you?

First of all, thanks for providing a visualization! It really helps a discussion about the shape of the universe, instead of approaching the subject exclusively by using words and mathematics alone, because the universe must have an overall shape, which must be visualizable. I have a few question regarding the above image: 1. What exactly explains this linear direction of the Big Bang? 2. What does the dark region surrounding the lines represent? 3. Does this imply that a space traveller, at some point after travelling in any arbitrary direction, would observe a non isotropic/homogeneous universe? 4. Would any other observer, anywhere in the universe, from their own perspective, also be located at the blue line?
 Does everybody here disagree with this depiction? @swansont ? @studiot? @Bufofrog The rest? Would you prefer a universe that looks more spherical instead, somewhat like a globular cluster? If so, why (not)?

Could anyone here actually draw ✏️ the universe on a piece of paper? it must be possible, because we can also draw the Solar System, or the Local Group, so why not larger scales? So, is there anyone here who is able to make a rough sketch of how the entire universe would look like? In discussions on the shape of the universe I always read arguments such as: “a three dimensional manifold that is bounded by a three dimensional sphere, that is in turn contained by the four dimensional spacetime manifold”, or something close to the “surface of a balloon”-analogy (which I think is a very bad example, because there can be only a surface if there’s also an inside, which the universe supposedly doesn’t have), but nobody ever tries to actually make that description visible. Is there anyone here who can make this visible? Or just explain in words your drawing, that’s also fine. If this turns out to be impossible, it’s hard for me to take those kind of theoretical arguments very seriously. I hope I’m not the only one.

I think it does: the further away you travel from the Milky Way into deep space (theoretically speaking of course), the further you travel into the past, and therefore the closer you’d approach the Big Bang itself, i.e. the ‘initial singularity’, when there was no space or time, nothing at all, and thus you’re predicting a non-physical boundary, a furthest atom away from us, if you will, instead of space continuing forever. Your stance implies a finite universe, and that all the atoms could be counted, because there is a non-infinite amount of atoms present. Or maybe I’ve interpreted what you meant the wrong way? Well, at least I don’t see a way in which your stance, especially with regard to different observers being closer or further away from the source of the CMBR, could be compatible with the Milky Way being present in an curved, hypersphere-like infinite universe, which continues on forever, and where no observer is closer to any beginning or end, because in that case we would all be equally close to everything, even to the CMBR. If I’m wrong in making this inference, could you please explain to me how you visualize the universe for yourself? Maybe you could draw it on a piece of paper, and then tell me what you drew? In your drawing, what lies beyond the furthest atom away from us? (And again, if there is no furthest atom, then you should have answered “yes” at least once).

What does that imply for the shape of the universe? Could it be closed? Could it be finite? "What is the 3-manifold of comoving space, i.e. of a comoving spatial section of the universe, informally called the "shape" of the universe? Neither the curvature nor the topology is presently known, though the curvature is known to be "close" to zero on observable scales. The cosmic inflation hypothesis suggests that the shape of the universe may be unmeasurable, but, since 2003, Jean-Pierre Luminet, et al., and other groups have suggested that the shape of the universe may be the Poincaré dodecahedral space. Is the shape unmeasurable; the Poincaré space; or another 3-manifold?" https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics "As for geometry, space may be flat and obey the laws of Euclidean geometry, or it may be curved. The curvature may be negative, in which case parallel light beams diverge and the universe is open; or it may be positive, in which case the beams ultimately converge like lines of longitude on a globe and the universe is closed". https://physicsworld.com/a/quintessence/

I have two yes/no questions:
 Would an observer, from any random galaxy in the entire universe…
 1. measure the exact same temperature of the CMBR? 2. observe the same quasars that we observe, and qualify them as quasars as well? 1. yes/no 2. yes/no

Thanks everybody for your responses! Nobody today of course knows what dark energy is, and understands what causes it and why, so I don’t think we can be sure that there’s no link between a BH and dark energy (which, as pointed out earlier, may represent the BB, from all sides around the universe, and therefore shares the singularity nature, because the BB is also referred to as a singularity (the so-called ‘initial singularity’). So what lies beyond the universe may have (attractive) properties. We also don’t know what lies beyond the observable universe, if anything, so we can’t be sure that the universe is a closed space, and that it is infinite, and because we don’t know this for sure, it might as well be finite, which may imply that the galaxies are not moving away from each other simply because spacetime itself expands, and that the galaxies don’t truly move because they’re just along for the ride, rather, it could also that they are truly moving, because they're attracted to this 'edge' of the universe, which functions as a kind of inside out BH attracting all galaxies from all sides, and therefore the attraction is expected to be stronger further away. When I say ‘edge’ or ‘boundary’, I don’t mean something physical as a circumference around the universe. It’s not made of matter, which, to me, only strengthens the similarity between dark energy and a BH because a BH is also can't possibly be made of ordinary, Standard Model, matter. I never understood an ‘infinite universe’ anyway, how do you visualize such a universe? How would you draw that on paper? But I don’t want to do philosophy. I'm not going to choose to 'believe' one explanation over the other, so I’m not choosing sides here, but so far, I have no reason to refute this unorthodox explanation. So, all in all, I remain skeptic in rejecting any correspondence between the nature of BHs and dark energy. It’s a complicated topic, and nobody today grasps the full picture. But thanks a lot for all your replies, I’m going to take everything into consideration, and read some more books regarding this subject!

Not my words: ”It demonstrates that the Fibonacci numbers grow at an exponential rate equal to the golden ratio φ.” (Source)

1, 2, 3, 4, 5 = linear 1, 2, 4, 8, 16 = exponential 1, 2, 3, 5, 8, 13, 21 = exponential (since the Fibonacci numbers also grow at an exponential rate equal to the golden ratio φ) But the cosmological constant is not exactly constant. It has a (tiny) positive value. So that means that φ today is not φ tomorrow. And since attraction near the singularity of BH is stronger (because it goes into infinity), the gravitational “φ” is increasing its value as well. So how is the exponentiality of the gravitational attraction of matter approaching a BH different from the exponentiality of galaxies getting pulled closer to the Big Bang? I am not a mathematician, but I really don’t see the difference, they’re both examples of exponential attraction.

Galaxies are not merely moving away from us, but at an accelerating pace, exponentially. Similarly, the gravitational field of a black hole attracts matter exponentially. I’m wondering whether the reason for this exponentiallity might be the same, only inside out.

In time they will, won't they? Leading to the 'heat death' of the universe? Alright, I think I get it now: so the inverse-square law remained the same, with or without dark energy, it did not influence the body-body relationship, right? In that case I've misinterpreted the article, but thanks for pointing it out. OK so the article doesn't support or refute the question I had. That mean I still have the question. So I'm wondering what you think about it. Let me repeat what I said: Well, can the be a connection of some sort? Or should in that case the redshift have to follow the inverse-square law for any connection to exist between A) the gravitational attraction associated with black hole singularities on the one hand, and B) the gravitational attraction associated with the Big Bang's 'initial singularity' on the other hand (which is exerting a gravitational pull on all galaxies, and so galaxies closer to the Big Bang (which are further away from us) experience stronger attraction, and thus a higher redshift)?

No deviations, so it follows the inverse-square law, then? (Because if you say 'no', shouldn't there be deviations?)

Newton's inverse-square laws states that a massive body, which is closer to another massive body, experience more inward attraction. So when it approaches a massive body, it will accelerate, which is similar to the redshift that all the galaxies in the universe experience, only not inward, but outward. So maybe the universe is an inside out black hole of some sort? It kind of makes sense, because when I say 'outward' I mean at the Big Bang, which is known to have arisen from an 'initial singularity'.

“Dark energy is an unknown driving force behind the acceleration of the universe, and we’re measuring the inverse-square law below the dark-energy length scale to look for a possible new gravitational phenomenon. Kapner and his colleagues use a sensitive device called a torsion balance to test the inverse-square law, attempting to shed some light on dark energy. And the results regarding the dark-energy length scale? “There are no deviations from the inverse-square law,” Kapner insists. “We see it behaves just as Newton predicted.” The test, he says, establishes that there is nothing new at the dark-energy length scale". (Source: https://phys.org/news/2007-01-dark-energy-inverse-square-law.html) Does this mean that dark energy obeys the inverse-square law? And does this in turn imply that, to understand what dark energy is, we can include what we know about the gravity near black holes (i.e. singularities)?

So when you're improving yourself, when you're getting ahead in life, do you consider that the same natural process compared to when you're putting any effort in it? There's a difference, right? I'm trying to find out what the difference is between a human being and innate matter. By pointing out the similarities between the two, as you're doing, instead of the differences, even thought you're 100% right with every word you say, isn't very helpful in finding out how to distinguish us from non-living matter.