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.

Indeed, but I think that Erwin Schrödinger was onto something. He was right by pointing out that there's a difference between living organism and innate matter, with respect to entropy, even though they're both subject to the same laws of physics. But I still don't see what this difference is.

Yes it predicts disorder, because the probability of disorder is higher than that of order. That does not mean that with absolute certainty that it's disorder is what you're going to get. As an analogy, it's like winning the lottery: if you buy a lottery ticket, you're probably not going to win, but there is a small probability that you will. So one would predict that you don't win. I didn't say that there must be 2 laws of physics to explain the difference between order and disorder, which distinguishes living organisms from innate matter, I said this: So what's the difference between the two? That's the 'non-random factor' I was referring to.

But isn't the opposite of 'random' something like 'directed', or even 'intentionally/knowingly'? Doesn't 'total randomness' mean machine-like, robot-like, factory-like, a clockwork-universe? Erwin Schrödinger once said that living organisms possess some kind of 'negative entropy', thereby not violating the 2nd law of thermodynamics or anything, but pointing out that there is a higher probability for disorder than for order, but we humans obviously do work, and make an effort, which makes sure that the low probability outcome becomes reality, because if we wouldn't, the high probability outcome, that which has most chance to develop, would become reality (because it's very easy to have a climate crisis, to not graduate, to become fat, etcetera). That sounds a lot like the opposite of 'randomness'. So we have to take matters into our own hands to make sure that the natural way of things isn't going to happen. That's the difference between innate things, and living things. They're both made of the same atoms, but innate things don't know things, and so they don't have intentions. Living organisms do. When I asked the question what this non-random factor is, you replied with: "the laws of physics and the biochemical laws". So you're not making a distinction between the two, then. But the way I see is that there must be a distinction, because entropy predicts chaos and disorder. On the other hand, life forms, and especially humans, do the exact opposite, by creating order. If the exact same laws of physics can cause both order, or (naturally) disorder, then what's the difference between the two? Aren't there 2 different paths one can take within 1 set of laws of physics? What's the difference between the atoms in innate and living matter? Because living organism are made of the exact same atoms compared to innate matter, but there's obviously a difference between the two. What's the difference, if it's not a different law of physics?

I always believed that evolution was a completely random, undirected process, simply the result of random mutations and chance events. But then I read about the 'Infinite monkey theorem' experiment: “Given fifty-eight possible keys, it would be 58 x 58 x 58 x 58 ... fifteen times over, which is about 283 trillion trillion attempts. But remember we have a million monkeys working, and let's say they type forty-five words a minute, so the fifteen keystrokes that make up the phrase take just four seconds. And they never rest or sleep. How much time, then, according to probability laws, before one of them finally types, “Call me Ishmael”? Answer: about 36 trillion years, or roughly 2,600 times the age of the universe. So a million monkeys typing furiously would never even reproduce one book's single, short opening line. Moral: Forget the monkeys-and-typewriters thing. It's bogus. Can you get the cosmos we see, including the complex biological designs of the brain and the trumpeter swan, through random atom collisions alone? If randomness requires thirty-six trillion years to type a single passage of fifteen letters and spaces, the answer is obvious: not a chance”. (Source: 'Beyond Biocentrism') In another book I've read something similar: “Given fiftey-eight possible keys, the number of attempts would have to be 58 x 58 fifteen times over, which is three trillion trillion, before success could be expected. With a million never-sleeping monkeys working, all faultlessly typing sixty words a minute (so that typing fifteen keystrokes takes just four seconds), one of them would indeed eventually type "Call me Ishmael." But odds are it would take thirty-eight trillion years. Three thousand times the age of the universe. So a million monkeys typing furiously would never even reproduce one book's single short opening sentence. Bottom line: randomness has far less power to achieve results than is popularly imagined.” (Source: 'Zoom') So my question is: do you agree with the author(s)? If you agree with the author: This would imply that complexity can’t be the result of randomness. But if it’s not randomness that could have determined the path of our evolution, which would lead to us, human beings, what’s the non-random factor directing this evolution, then? Or consider of the universe at large, and the 'anthropic principle'. If our Solar System, and its place in a fine-tuned universe, can't be the result of complete randomness, what's this supposed 'non-random factor', then, if it exists at all? If you don't agree with the author: Let's say you refute the claim that the author is making, and you believe that we are the result of random mutations, and complete chance events, this means that you believe that, at some point, the monkeys would eventually type "Call me Ishmael". Because if you don't believe that, that would indicate an inconsistency in your thinking, because then you would agree with the author.

So there is a correspondence? Could you elaborate some more please, I'm trying to understand what the difference between your statement/calculation and the non-correspondence is (al already pointed out by @swansont). I already thought that it would be unlikely that those two sources that I shared in my initial questions would both, independently, claim the exact same thing, but would both be wrong. @beecee pointed out that they probably meant something else as the way I was interpreting it, and your comment seems to show what this is, so I believe you're on the right track in better explaining what they meant by it. Could you therefore please elaborate a bit more on this?

So there is no correspondence between the Schwarzschild radius of a black hole and the observable universe (as these two sources both are wrongfully implying)?

@beecee So both the author of the book, as well as this calculation, are wrong?

"The mass and radius of the observable universe fit the same relationship defined by the mass and Schwarzschild radius of a black hole". I've read this sentence in the book 'Einstein's Monsters: The Life and Times of Black Holes'. Here's the calculation. What's the significance of this correspondence? Is it expected that there should be relationship between the two, and if so, why?

Thanks everyone for taking the time to respond to my question. In the meantime I asked the same question at some place else, and found my answer. The miscommunication lies within the distinction between Feynman diagrams on the one hand (since these diagrams are not gauge invariant), and the experiments that had been undertaken on the other hand. In the first case, it’s a clear no, but in the second case, experimental evidence (such as the Casimir effect) demonstrate that it’s a yes (which is closest to what @joigus said: yes and no). This distinction was the answer I was looking for, but thanks anyway everybody for your time to write a reply!

Are virtual particle pockets of energy? In other words: are virtual particles force carriers? If not, if they’re in no way a form of energy, and in no way associated with kinetic energy because they’re not actually moving/vibrating at all, but rather just ‘theoretical and mathematical constructs’, as some argue, then why are they called ‘particles’ in the first place? How is that not a misleading term, because, if you’re a particle somewhere in the universe, you’re definitely not ‘nothing’ (which is what ‘a mathematical construct’ basically implies). And if you’re not nothing, that means you therefore must be something, i.e. some sort of kinetic/potential energy, albeit very little. A little bit is still something. Three other things don’t make sense to mee if virtual particles don’t exist, and are to be regarded as mere mathematical constructs: 1. If the mathematics describes something that is not out there in the real world, if for instance those virtual photons that appear in Feynman diagrams don't describe what's taking place in reality, then why do we take the those mathematical descriptions seriously? 2. Why hasn’t some of the quantum fluctuations hypotheses, that describe how the universe came into existence, been refuted immediately? For instance the ‘vacuum genesis’ (or: ‘zero-energy universe hypothesis’) has been proposed by Edward P. Tryon. He suggested that the Universe may be a large-scale quantum-mechanical vacuum fluctuation (since vacuum fluctuations appear as virtual particles, which are always created in particle-antiparticle pairs). I don’t intend in invoke a discussion about the plausibility of this hypothesis, I’m only bringing it up to find out why it hasn’t been refuted immediately because, if virtual particles don’t describe reality, this hypothesis should never have been regarded as a potential candidate in the first place, but only as a mathematical theory, without the reference to the universe we're living in. 3. Virtual particles are also described in the phenomenon of ‘Hawking radiation’, in which a virtual pair that appears very close to the event horizon, one may ‘steal’ energy from the other and escape as a real particle, while the other is drawn back in and disappears, effectively stealing the energy from the black hole. Virtual particles, once again, seems to be not simply a mathematical construct, but actually out there, interacting, located close to black holes (which are also actually out there of course, nobody would deny the existence of black holes). So virtual-ness seems to be able to embody a role between ‘not real’ and ‘real’, which would mean that they are forces of nature that do exist, albeit in some kind of purgatory-like state, limited by Heisenberg's uncertainty principle. So, do virtual particles exist? Please prelude your answer by first a 'yes' or a 'no'.