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.
Hmmm…maybe the ‘why today’ bit is answered by weak anthropological argument? For critters like us to evolve, we need solar systems that contain rocky planets that themselves contain CHON atoms in abundance (along with trace amounts of heaver metals). That sets a lower boundary on when during the universe’s lifecycle we could appear, because it would have to be after first generation stars. That rules out us evolving in a universe with a length scale significantly smaller than the cosmological constant length scale. Likewise, we couldn’t evolve in a very old universe where the stars have essentially gone out, which rules out the scenario of us evolving in a universe with a length scale significantly larger than the cosmological constant length scale.
So, maybe the answer is that we happen to exist at this time when the scales are similar because this is also (coincidentally?) the time at which life like us is most statistically likely to evolve; the universe’s conditions are right. Much younger and the elements and solar systems aren’t in place. Much older and those big sources of heat energy to drive metabolisms ‘uphill’ aren’t available. Leaving a tens or hundreds of billions of years ‘sweet spot’ for life which overlaps with the time period where universe length ~ cosmological constant length scale.
Fascinating! Thank you, Sean. A thought, slantwise, from a dilettante, on scales and structure, at least as far as people-space. It has taken 13.8bn years to get to us. Our planet is perhaps the pearl in the oyster of this region of the galaxy. To make Earth required the deaths of several/many stars in succession to produce the right balance of heavy nuclei capable of forming rocky planets and people. I argue that there may be a handful of systems within the galaxy that host planets capable of supporting complex life of our scale, which has come about from 4bn years of development from simpler lifeforms. Even now, we require the support of bacteria, plants and so on, to keep us, and our planet ‘alive’. And – at cellular/molecular level – we are always dealing with systems that work quantum mechanically. We can join the dots from Planck to planet in size and time. But is life, as we think of it, important in the thermodynamics of the universe or is it an occasional blip?
The observable universe is only so big. And precisely so big. Lots to observe these days, but someday not so much:
http://m.space.com/11380-big-bang-evidence-universe-trillion-years.html
The universe is so damn big, because I said so… Not really, but it is still pretty dang big anyways.
Take look at the length contraction equation. It is the only equation in physics that I know of that determines how large distances would be. Then when you put the speed of light in there for the velocity, it says length or “space itself” becomes really small, zero. Then you put another speed in there that is slower than the speed of light, length becomes much larger.
I think it could really be that simple. Then space would be so big, because we are traveling this slowly relative to the speed of light. If energy came about first in the universe, then the appearance of matter would have created a frame of reference with longer distances. Then the size of the universe could just be an illusion. For all we know it could just be one Planck Length in diameter from the frame of reference of a photon.
The interesting part about this, if you assumed it was true, is that it would mean that the expansion of spacetime wouldn’t be limited by the speed of light. Space could expand however fast it wanted to in order to makes sure every observer measured light to travel the same constant speed… There is no limit to how much acceleration could change the amount of length measured from one instance to another according to relativity theory.
It has become accepted that inflation can happen faster than light. I don’t see how else it could get past relativity, rather if General Relativity was a final theory or not.
Nitin Khanna said: 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.
I think this isn’t really correct. We do have expressive levels of complexity both in small scales and in large scales. So I do not really believe Sean will come up with a credible citation for that. Am I wrong, Sean?
Vmarko,
Yeah, I didn’t think you had a response for me.
Sean, one question:
in the last but second paragraph you say that the reason why the universe is so big is, roughly speaking, that the cosmological constant is so damn small, as its inverse naturally sets the length scale of empty space.
But in the paragraph above you write that there is a “coincidence” problem, i.e. that the universe is roughly as big as the length scale set by the cosmological constant today, but this scale is time-independent !
So the question is: how can the smallness of the cosmological constant be considered the reason for the dimension of the universe, if this is a matter of a momentary coincidence ?
Will the universe keep getting bigger, in terms of the furthest known quasar? http://i.imgur.com/yVQ5cgJ.png
Or will there eventually be a furthest quasar of all time?
@vmarko,
I am also interested in your answer to Dave’s rhetorical question. Is it true that the models you are talking about cannot reproduce classical GR in some limit?
It is obvious that cosmology and physics have no answers as of today,why gravity is so weak and cosmological constant so small.My guess is that life will not be possible if gravity was stronger. So we are back to the anthropic principle! But even that is not very satisfactory. It is hard to believe that universe, where 96% of the stuff has nothing to do with life as we know it, was designed with humans in mind. Also most ridiculous assumption would be that our measly little planet serves any useful purpose in the universe. So as eastern religions professed long time back, it is impossible to understand creation by human logic. Puzzle, puzzle, puzzle again!!
Mirko– That’s a good question, sorry for the ambiguity. The “size of the observable universe” grows with time —until we hit a point where the cosmological constant energy is most of the universe, and then that size settles down to a constant number. That is happening right now, when it could easily have happened much earlier or later; that’s the coincidence problem. The small value of the cosmological constant allows the size of the observable universe to be large, although back in the past the actual value was considerably smaller.
Weinberg’s argument is that if it had happened much sooner, i.e. a larger cosmological constant, then there would have been no time for galaxies to form. If it would happen much later, then the stars would have burned out and there could be no-one to watch it (i.e. weak-anthropic explanation).
Personally, I remain sceptical of “problems” unless one can convince Carlo Rovelli that it is a problem. 🙂
Also, “right now” seems like “blink and you’ll miss it”. Actually, the universe started accelerating a few billion years ago, so it is hardly “right now”. Yes, compared to infinity it’s close to now, but compared to infinity everything is close to now.
Whenever someone talks about the coincidence problem and has a graph using redshift or logarithms, I think about Reagan on television during the Cold War, when he always used the Mercator projection when discussing the Soviet threat.
Can we at least agree on what needs an explanation? If two numbers are vastly different, it is deemed “unnatural”. If they are close, it is deemed a coincidence.
Thanks for the reply. I will try to grasp the problem even more.
Pretty sure the Universe is as large as it is ’cause it’s trying to get away from stray bullets from the U.S.
LOL!
Is http://www.astro.ucla.edu/~wright/DL-vs-z-25Dec06-75.gif
current with respect to https://en.wikipedia.org/wiki/File:CosmoDistanceMeasures_z_to_1e4.png#/media/File:CosmoDistanceMeasures_z_to_1e4.png ?
I.e., is http://i.imgur.com/yVQ5cgJ.png limited to the lookback time distance of the big bang?
Is there an ekpyrotic interpretation of the Big Bang as the accretion emissions of a Big Crunch quasar?
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My big question is why does the speed of light in vacuum has the exact value it does, not a tiny bit more or less? It must have a relation to the CC or Plank scale. Wish someone could calculate c because I believe this value is not fundamental.
That’s not the way science works. If you believe it is not fundamental, then you calculate it.
Can anyone tell me how to compute the number “10^26 cm” for the length scale determined by the cosmological constant? I get something more like 10^29.
“But the universe doesn’t have a purpose, and there’s nothing more natural than Nature itself ”
We don’t know the extant of universe. We also don’t know as to how it was created. So how we can so emphatically that it has no purpose
Space is not only expanding but it is expanding at accelerated rates continuously since its inception. But why total matter and radiations ( energy) is not increasing commensurately? Was total matter plus energy present in universe as on date same as at the time of creation?
Vacuum energy or cosmological constant or dark energy are presumed to be associated with empty space. It implies with the expansion of space ( on the contrary accelerated expansion), more and more vacuum energy is appearing in universe. Even if we assume that density of vaccum energy remains constant or decreasing, but total vacuum energy of universe should increase at accelerated rates. My query is from where this additional vaccum is emerging out?