I love reading io9, it’s such a fun mixture of science fiction, entertainment, and pure science. So I was happy to respond when their writer George Dvorsky emailed to ask an innocent-sounding question: “Why is the scale of the universe so freakishly large?”
You can find the fruits of George’s labors at this io9 post. But my own answer went on at sufficient length that I might as well put it up here as well. Of course, as with any “Why?” question, we need to keep in mind that the answer might simply be “Because that’s the way it is.”
Whenever we seem surprised or confused about some aspect of the universe, it’s because we have some pre-existing expectation for what it “should” be like, or what a “natural” universe might be. But the universe doesn’t have a purpose, and there’s nothing more natural than Nature itself — so what we’re really trying to do is figure out what our expectations should be.
The universe is big on human scales, but that doesn’t mean very much. It’s not surprising that humans are small compared to the universe, but big compared to atoms. That feature does have an obvious anthropic explanation — complex structures can only form on in-between scales, not at the very largest or very smallest sizes. Given that living organisms are going to be complex, it’s no surprise that we find ourselves at an in-between size compared to the universe and compared to elementary particles.
What is arguably more interesting is that the universe is so big compared to particle-physics scales. The Planck length, from quantum gravity, is 10^{-33} centimeters, and the size of an atom is roughly 10^{-8} centimeters. The difference between these two numbers is already puzzling — that’s related to the “hierarchy problem” of particle physics. (The size of atoms is fixed by the length scale set by electroweak interactions, while the Planck length is set by Newton’s constant; the two distances are extremely different, and we’re not sure why.) But the scale of the universe is roughly 10^29 centimeters across, which is enormous by any scale of microphysics. It’s perfectly reasonable to ask why.
Part of the answer is that “typical” configurations of stuff, given the laws of physics as we know them, tend to be very close to empty space. (“Typical” means “high entropy” in this context.) That’s a feature of general relativity, which says that space is dynamical, and can expand and contract. So you give me any particular configuration of matter in space, and I can find a lot more configurations where the same collection of matter is spread out over a much larger volume of space. So if we were to “pick a random collection of stuff” obeying the laws of physics, it would be mostly empty space. Which our universe is, kind of.
Two big problems with that. First, even empty space has a natural length scale, which is set by the cosmological constant (energy of the vacuum). In 1998 we discovered that the cosmological constant is not quite zero, although it’s very small. The length scale that it sets (roughly, the distance over which the curvature of space due to the cosmological constant becomes appreciable) is indeed the size of the universe today — about 10^26 centimeters. (Note that the cosmological constant itself is inversely proportional to this length scale — so the question “Why is the cosmological-constant length scale so large?” is the same as “Why is the cosmological constant so small?”)
This raises two big questions. The first is the “coincidence problem”: the universe is expanding, but the length scale associated with the cosmological constant is a constant, so why are they approximately equal today? The second is simply the “cosmological constant problem”: why is the cosmological constant scale so enormously larger than the Planck scale, or event than the atomic scale? It’s safe to say that right now there are no widely-accepted answers to either of these questions.
So roughly: the answer to “Why is the universe so big?” is “Because the cosmological constant is so small.” And the answer to “Why is the cosmological constant so small?” is “Nobody knows.”
But there’s yet another wrinkle. Typical configurations of stuff tend to look like empty space. But our universe, while relatively empty, isn’t *that* empty. It has over a hundred billion galaxies, with a hundred billion stars each, and over 10^50 atoms per star. Worse, there are maybe 10^88 particles (mostly photons and neutrinos) within the observable universe. That’s a lot of particles! A much more natural state of the universe would be enormously emptier than that. Indeed, as space expands the density of particles dilutes away — we’re headed toward a much more natural state, which will be much emptier than the universe we see today.
So, given what we know about physics, the real question is “Why are there so many particles in the observable universe?” That’s one angle on the question “Why is the entropy of the observable universe so small?” And of course the density of particles was much higher, and the entropy much lower, at early times. These questions are also ones to which we have no good answers at the moment.
If we posit a Creator (and I’m not) then the universe exists as it does to not simply humble, but abuse, denigrate, and humiliate the minds it was so expertly commissioned to birth. This is malevolence on an unfathomable scale, expressed through immeasurable waste stretched out between distances and times that cannot be understood. It is cruel, but not hateful, depraved, but not vengeful. This is considered pain, carefully presented in careless proportions to blister and disgrace anyone—or anything—that might momentarily dare to ever privately contemplate it is in control.
John, do you think Conway was malevolent to self-aware structures which could possibly evolve in Conway’s Life?
John,
Get a life…my gosh. Pain? Cruel?
Do you believe in the multiverse? Wouldn’t you say that it’s even more cruel?
Axl,
It’s an exercise in the absurd. I’m not saying there is intent, but for those who imagine there is, that this thing was shaped, then that intent is clearly malevolent.
Hi Jim
Apologies, but who’s Conway?
Sean,
“The second is simply the “cosmological constant problem”: why is the cosmological constant scale so enormously larger than the Planck scale, or event than the atomic scale? It’s safe to say that right now there are no widely-accepted answers to either of these questions.”
Just to note — while there are no widely-accepted answers, it’s not that there aren’t any candidate answers. There are QG models in which the smallness of the CC comes out automatically, as a consequence of some generic postulates, i.e. without fine-tuning (btw, as part of etiquette, I’m not going to quote the references — an interested reader can certainly find them on their own). 😉
Okay kiddies, stay on-topic or there will be lots of deleting. Hint: if you’re not talking about length scales or cosmological measures, you might be off-topic.
I wish I could remember who, but someone with a reasonable amount of clout once said that both space and time might not be fundamental ‘things’ in our universe, but merely manifestations of certain quantum-level mechanisms. If that is true, does it still make sense to ask why the universe is so big? One thing I’d quite like to know is why the speed of light is so incredibly slow.
vmarko,
QG models that don’t even reproduce classical GR or even explain how gravity decouples from all the other interactions at the Planck scale don’t count.
John: “Hi Jim. Apologies, but who’s Conway?”
I think Jim is referring to mathematician John Conway who has written about self awareness and free will. Less likely, he is referring to comedian Tim Conway who has written about golf.
Sean: I hope this is on topic.
John,
Actually he’s referring to Jimmy Conway, the character from Goodfellas.
I assume when you mentioned the universe is 10^{27} cm across, you mean “the observable” universe. Why should that enter into the discussion? Shouldn’t we be talking about the size of the entire universe? May that not be infinite?
I thought the universe was (nearly) spatially flat, which would mean an unbounded, infinite universe. Do I have my GR wrong?
John,
Conway also created the game of life: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
Randy Roberts,
Ahhh, I know him now! Thanks.
Sean, can you please provide the source of the anthropic explanation, “complex structures can only form on in-between scales, not at the very largest or very smallest sizes”.
I’d like to read more about it.
‘Big’ suggests a boundary condition. Where is the boundary and what is beyond? If no such boundary condition exists, what is the meaning of size?
Surely the universe is big because of the Anthropic Principle.
If you make the quite reasonable assumption that all configurations of universes that obey our laws of physics exist, via the Mathematical Universe Hypothesis, then lifeforms will arise more often in bigger universes. So we would be quite surprised to find ouselves in a small one.
In fact, no matter how big you guess our universe to be (including beyond the visible universe) it’s much more likely to be way bigger.
It’s such a difficult topic to tackle because it’s difficult to physically prove. Our best bet is of course to continue to probe the smaller scales. The topic of continuous vs discrete spacetime is especially tantalizing because it could go a long way to help resolve some of these questions at one scale; which would have big implications for the other.
In regards to the boundary condition brought up by Paul Pelosi; I think you have to look at the limits imposed by the speed of light. There is a space-like, geometrical boundary condition as a result of the time-like boundary condition. So then I think it becomes a philosophical question of whether or not it matters what is beyond the boundary if you can’t interact with it anyway. If it has no effect on our physics or possibly even out mathematical constructs, then does it really exist at all? An overly utilitarian thinker like myself would say no. I can imagine what’s happening beyond the boundary or even in a parallel universe, in the future, or in the past; but imagining Hitler as Iron Man doesn’t make the idea any more realistic in regards to the physics of this universe. We are, again and assumingly forever, limited by time and entropy.
It is very tempting for me to come up with reasons that are essentially anthropic (as Ray has posted) but also based on a supposition. Let’s say that the evolution of intelligent life is extremely rare, and perhaps unique. (Life itself seems to happen quickly, but we have yet to see any evidence of other intelligences.) We know that it took the best part of five billion years of earth’s history to get to this point. Adding another nine billion for the abundance of planets to grow seems fair. This time-scale can then set the size of the observable universe, which is a small numerical factor greater than the speed of light times the age of the universe.
The number of galaxies and stars can similarly be posited to be large enough for this rare event of intelligent life to have happened in the available time.
As far as I know we do not have any idea what the measure of the landscape of possible universes is. If there were an argument that small universes are favoured, and furthermore, if we do find ourselves alone, then the argument above becomes more convincing. That is, we get a universe of a size large enough reasonably to have produced this rare thing, intelligent observers.
One additional thing to note: When making any argument based on the anthropic principle – if allowed in the first place – then I think it becomes inconsistent to speak of anything beyond the observable universe. This is pretty well a gut feeling on my part, but is probably a whole area of debate in itself.
Wasn’t this problem solved long ago, using the weak-anthropic principle (the dash is crucial), by Dicke, in the context of explaining the Dirac coincidences?
“The first is the “coincidence problem”: the universe is expanding, but the length scale associated with the cosmological constant is a constant, so why are they approximately equal today? The second is simply the “cosmological constant problem”: why is the cosmological constant scale so enormously larger than the Planck scale, or event than the atomic scale? It’s safe to say that right now there are no widely-accepted answers to either of these questions.”
Eugenio Bianchi and Carlo Rovelli know, and have written about it. People should either cite them, or write a paper demonstrating where they are wrong.
Their arXiv paper is the one you should read. A shorter version was published in Nature, along with an opposing viewpoint courtesy of Rocky Kolb (who, not that long ago, was telling us that Omega_matter was 1—draw your own conclusions).
Well, then, nothing anyone says will be useful in the face of confusion. =D
Else I would point out that planets emerge early, and life emergence was rapid, so it is a somewhat illusory problem.
It took some 100’s of million years for both – round of to a few billion years – so with the size of the observable universe it had to be coincidental with the increase to maximum complexity density. (If complexity is defined as particle configurations.)
In other words, in essence it is the same anthropic observation as for the intermediate size of cells.
I thought reheating after inflation and the standard model of particles were responsible for that. I hear the latter is finetuned, but much less than the universe itself.*
* Unless this recent review is correct, and there isn’t much of a cosmological constant finetuning problem: “ρvac ≃ −2 × 10^8 GeV^4 + ρ_B + ρ_EW_vac + ρ_QCD_vac + · · · (516)
If one does not want to estimate µ, one can simply plot ρ_vac as a function of µ as done in Fig. 5. Clearly, regardless of the precise value of µ [set by the size of the universe – the Hubble constant – it seems], we are very far from ρ_vac ~= 10^72 GeV^4 always mentioned in the literature.”
[ http://arxiv.org/pdf/1205.3365v1.pdf ]
@David Rutten:
“both space and time might not be fundamental ‘things’ in our universe, but merely manifestations of certain quantum-level mechanisms.”
My interest is mainly astrobiology, so my knowledge of cosmology is more along the question here (size and age, and enough particles). But as it happens, I stumbled on correlated results that implies gravity (so 3+1 D space and time) can result from entanglement effects. Having entanglement universal makes gravity (energy) classical. Reversely, (super)gravity is the background of superstring theory, which experiences universal entanglement.
@Helbig: “Eugenio Bianchi and Carlo Rovelli know, and have written about it. People should either cite them, or write a paper demonstrating where they are wrong.”
Wrong. That there are no widely-accepted answers is not tied to any specific result.
And if the paper is meritorious it will be recognized. If _they_ tries to demonstrated how it is not wrong is a good start.
[Coincidentally when I scanned it I noted some problems.
– They propagate the false claim that people historically thought Earth was flat. [ https://en.wikipedia.org/wiki/Myth_of_the_flat_Earth ]
– They also state, which Planck several times has tested to ever better precision since 2010, that the universe may not be flat.
Those problems may or may not be relevant to the technical part of the paper, which was too confused to just browse for understanding. But it goes towards the quality.]
@Helbig: “Eugenio Bianchi and Carlo Rovelli know, and have written about it. People should either cite them, or write a paper demonstrating where they are wrong.”
Wrong. That there are no widely-accepted answers is not tied to any specific result.
I think it’s fair to say that there are no widely accepted answers. But why? Because no-one has them? Or because people ignore them?
And if the paper is meritorious it will be recognized.
Unfortunately, it sometimes happens that meritorious papers are not recognized until long after they are written.
If _they_ tries to demonstrated how it is not wrong is a good start. “
You have this backwards. They wrote their paper. Should they write another one saying “we were right”? If the paper is right, people should cite it, and the answers should be widely recognized. If it is not, someone should write a paper saying what is wrong with it.
– They propagate the false claim that people historically thought Earth was flat.”
I’ll grant you this one, but it is not really relevant to their conclusions. Giving them the benefit of the doubt, they do write “humanity” and not “people in the middle ages”. I’m sure that most cavemen thought that the Earth was flat.
– They also state, which Planck several times has tested to ever better precision since 2010, that the universe may not be flat. “
Their paper was written before the Planck results were available. One can’t fault them for that.
“I thought the universe was (nearly) spatially flat, which would mean an unbounded, infinite universe. Do I have my GR wrong?”
As you write, it appears to be nearly flat. There are three caveats. First, it could be nearly flat, but have a positive curvature and, assuming a simple topology, be very big, but finite. Second, the topology might not be simple, so it could be finite even if it were exactly flat. Third, the assumption that we can extrapolate what we observe in the observable universe to all of the universe, namely homogeneity and isotropy on large scales, to the entire universe, might not be right. In that case, what we observe might tell us nothing about whether the universe is finite or not.