Welcome to this week’s installment of the From Eternity to Here book club. Today we have a look at Chapter Thirteen, “The Life of the Universe.”
Excerpt:
If our comoving patch defines an approximately closed system, the next step is to think about its space of states. General relativity tells us that space itself, the stage on which particles and matter move and interact, evolves over time. Because of this, the definition of the space of states becomes more subtle than it would have been in if spacetime were absolute. Most physicists would agree that information is conserved as the universe evolves, but the way that works is quite unclear in a cosmological context. The essential problem is that more and more things can fit into the universe as it expands, so—naively, anyway—it looks as if the space of states is getting bigger. That would be in flagrant contradiction to the usual rules of reversible, information-conserving physics, where the space of states is fixed once and for all.
Of course we’ve already looked a bit at the life of the universe, way back in Chapter Three. The difference is that we’re now focusing on how entropy evolves, given our hard-acquired understanding of what entropy is and how it works for black holes. This is where we review Roger Penrose’s well-known-yet-still-widely-ignored argument that the low entropy of the early universe is something that needs to be explained.
In a sense, this is pretty straightforward stuff, following directly from what we’ve already done in the book. But it’s also somewhat controversial among professional cosmologists. The reason why can be found in the slightly technical digression that begins on page 292, “Conservation of information in an expanding universe.”
The point is that physicists often think of “the space of states in a region of spacetime” as being equal to “the space of states we can describe by quantum field theory.” They know that’s not right, because gravity doesn’t fit into that description, but these are the states they know how to deal with. This collection of states isn’t fixed; it grows with time as the universe expands. You will therefore sometimes hear cosmologists talk about the high entropy of the early universe, under the misguided assumption that there were fewer states that could “fit” into the universe at that time. (Equivalently, that gravity can be ignored.) This approach has, in my opinion anyway, done great damage to how cosmologists think about fine-tuning problems. One of the major motivations for writing the book was to explain these issues, not only to the general reader but also to my scientist friends.
At the end of the chapter I deviate from Penrose’s argument a bit. He believes that a high-entropy state of the universe would be one that was highly inhomogeneous, full of black holes and white holes and what have you. I think that’s right if you are thinking about a very dense configuration of matter. But matter doesn’t have to be dense — the expansion of the universe can dilute it away. So I argue that the truly highest-entropy configuration is one where space is essentially empty, with nothing but vacuum energy. This is also very far from being widely accepted, and certainly relies on a bit of hand-waving. But again, I think the failure to appreciate this point has distorted how cosmologists think about the problems presented by the early universe. So hopefully they read this far in the book!
Another fantastic chapter which really helped my understanding of entropy and gravity.
For a long time I had thought that part of the attraction of inflation was that it allowed you to posit a suddenly-large universe with all the mass still packed into a relatively small space, thus giving you a low-entropy point (from which the universe could start rolling downhill). But apparently this is still a fringe idea…?
I agree with Clifford that you have clarified the conceptual inversion of the relationship of high entropy and inhomogeneity. (The Penrose argument.)
But of all the concepts in this chapter; general relativity, quantum field theory, black holes, etc.; the most bizarre is that of eternity. We can say some things will never happen because they are too improbable, but then eternity turns that on its head and says such things must happen.
Brian– I don’t think you need inflation to do that; it’s easy to posit a low-entropy beginning from which our universe could have started, just within the conventional hot Big Bang model. The supposed improvement was to make this seem “easy” or “natural.” I’m saying that this impression is a false one, as it’s actually really hard to squeeze the entire universe into the proto-inflationary patch.
What is meant by “information is conserved?” What information is being measured?
Hi Mark,
“Information is conserved” means that if you know the entire state of the system (namely positions and velocities) then you can find the state of the system at any earlier or later time.
The caveat for GR is that we have a lot of freedom for how we label points in spacetime, so to know the “position” it is not enough to just give coordinates but we also have to have some idea of what the coordinates mean. So in addition to the normal coordinates for position and derivatives for velocity, we must also impose some constraints to be able to interpret the coordinates known as gauge-fixing conditions.
In so far as I know, it is a semantic issue whether you consider “positions” to mean the coordinates + gauge fixing to interpret them, or if you think of the positions as the coordinates. In the former case the information is simply the state of the system (x, v) for all the degrees of freedom, while in the latter case the information is (x,v) for the state of the system and the appropriate gauge fixing conditions.
Sean: Since the boundary of the observable universe can be seen as an event horizon, and it continuously gets further out as time since the big bang increases, what impact does that have on entropy and the conservation of information?
What I mean is, every year, even if space itself weren’t expanding, the radius of the observable universe would be expanding by one light year, as light that hadn’t had time to reach us before is now reaching us.
KiwiDamien is completely right about how I’m using “information.” As readers of the book should have figured out by now!
John– no real impact at all. The fact that the universe is homogeneous on large scales means that you can pick any comoving “tube” of spacetime, stretching from the Big Bang into the future, and treat it as an approximately closed system.
If the underlying space is expanding, then the information is not conserved.
I want to add that the correct semantical question is whether information about the big bang is preserved. This is an entirely different question than that of conservation of information. If we want to get even more specific, what we are asking is whether quantum information about the big bang is preserved. That answer is yes, because of all the standard quantum weirdness. Classical information is assuredly not conserved, as it is equivalent to entropy, and in an expanding universe that entropy has no upper bound. We have then the issue of information being created in the vacuum, and that information must be quantum in nature before it is observed as vacuum. Thus we start seeing the foundations of quantum gravity arriving in the tug and pull between quantum information associated with single entangling event (the big bang) and the action of new information being produced at a constant rate.
It should also be pointed out that it is in the preservation of quantum information about an entangling event in a nonconservative environment that we begin to see a qualitative link to inertia, eg the resistance to change in state.
.
I got to thinking about the single-black-hole case in a non-expanding universe. Sean, your argument here was that the black hole eventually evaporates, and the radiation of evaporation has higher entropy than the black hole it came from.
Knowing absolutely nothing about the Hawking equations, I’m having to reason this out without the math, but it seems to me that any virtual particle that finds itself outside the event horizon does so with a particular energy, some of which is carried as velocity. Isn’t it the case then that all radiation that succeeds in not being re-gobbled by the hole has to have a velocity whose magnitude is not only greater than the escape velocity of the event horizon, but has a positive normal direction component, with respect to the event horizon, as well? (Anything with a negative normal component is going to hit the event horizon again, right?)
In the case of One Big Hole, this seems to generate radiation that is anisotropic. Isn’t that a big no-no? And, more importantly, doesn’t that significantly narrow the state space, and therefore reduce the entropy?
I think I agree with all of your preliminary statements, but I don’t understand your conclusions. Hawking radiation is (on average) emitted radially away from the black hole, so it’s isotropic. And it doesn’t narrow the state space at all, since the states are in the black hole.
If I were to more to a point in the otherwise-empty universe that was very far away from the black hole and try to detect radiation in various orientations, I’d discover that it was mostly (mod some amount of transverse scattering and/or decay) coming from one direction. Doesn’t that make the radiation anisotropic?
I think I didn’t use the right terminology when I referred to narrowing the state space. What I really meant to ask was: If the radiation is anisotropic, doesn’t that exclude a huge number of microstates that could apply to the macrostate, and doesn’t that in turn reduce the entropy?