Breaking radio silence here to report on some of the actual work I’ve been able to complete: a new paper with Heywood Tam.
Unitary Evolution and Cosmological Fine-Tuning
Authors: Sean M. Carroll, Heywood Tam
(Submitted on 8 Jul 2010)Abstract: Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville’s theorem implies that no dynamical process can evolve a large number of initial states into a small number of final states. We use the invariant measure on solutions to Einstein’s equation to quantify the problems of cosmological fine-tuning. The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat. The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real. When perturbations are taken into account, inflation only occurs in a negligibly small fraction of cosmological histories, less than 10-6.6×10^7. We argue that while inflation does not affect the number of initial conditions that evolve into a late universe like our own, it nevertheless provides an appealing target for true theories of initial conditions, by allowing for small patches of space with sub-Planckian curvature to grow into reasonable universes.
In English: our universe looks very unusual. You might think we have nothing to compare it to, but that’s not quite right; given the particles that make up the universe (or the quantum degrees of freedom, to be technical about it), we can compare their actual configuration to all the possible configurations they could have been in. The answer is, our observed universe is highly non-generic, and in the past it was even more non-generic, or “finely tuned.” One way of describing this state of affairs is to say that the early universe had a very low entropy. We don’t know why; that’s an important puzzle, worth writing books about.
Part of the motivation of this paper was to put some quantitative meat on some ideas I discussed in my book. The basic argument is an old one, going back to Roger Penrose in the late 1970’s. The advent of inflation in the early 1980’s seemed to change things — it showed how to get a universe just like ours starting from a tiny region of space dominated by “false vacuum energy.” But a more careful analysis shows that inflation doesn’t really change the underlying problem — sure, you can get our universe if you start in the right state, but that state is even more finely-tuned than the conventional Big Bang beginning.
We revisit this question, bringing to bear some mathematical heavy machinery developed in the 1980’s by Gary Gibbons, Stephen Hawking, and John Stewart. Previous discussions have invoked general ideas of entropy or reversibility, but we were able to do a relatively down-to-earth calculation using conventional cosmological models. And we tried our best to explicitly list all of the caveats of the argument, which is important in a context like this where we don’t know all the rules.
We find that inflation is very unlikely, in the sense that a negligibly small fraction of possible universes experience a period of inflation. On the other hand, our universe is unlikely, by exactly the same criterion. So the observable universe didn’t “just happen”; it is either picked out by some general principle, perhaps something to do with the wave function of the universe, or it’s generated dynamically by some process within a larger multiverse. And inflation might end up playing a crucial role in the story. We don’t know yet, but it’s important to lay out the options to help us find our way.
As a graduate student studying inflationary cosmology, I am very interesting in knowing when this paper may hit the arxiv. Any ideas?
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Hmmm…it seems like your paper can also conclude that perhaps God fine-tuned the universe to be what it is so that we can exist. Good work. Well, you can also explain the findings by appealing to a “multiverse”. However, both the multiverse and God are unobservable. So let’s just choose God. 🙂
I choose the multiverse. It’s far less cranky and vindictive.
Does something like the ergodic hypothesis apply? Even if the conditions that lead to a false vacuum and inflation are very rare, the ergodic hypothesis says that eventually they will happen by chance (for suitable definitions of “eventually” when it’s not clear exactly what we mean by time).
And, yeah, that we’re in this unlikely universe means I’m implicitly relying on something like a weak anthropic argument– but weak anthropic arguments ultimately are just selection effects.
Haven’t you heard? The proton is smaller than we thought. All bets are off. 😉
Physical systems are not reversible.
The universe is inhomogeneous (unbounded discrete fractal).
All physical events are causal.
Arguments based on “multiverses”, “anthropic reasoning” and an acuasal “beginning” of nature are bad natural philosophy, foisted upon us poor souls by deluded Platonist glass-bead game players.
PROTON RADIUS
High precision empirical measurement = 0.84 fermi
QED-based estimates + 0.877 to 0.9 fermi
Discrete Scale Relativity = 0.814 fermi
GOOOOAAAALLL! Notify the octopus!
SCORE: DSR 1/QED 0
I believe you’re misinformed. Your statements about the universe are in disagreement with the Cosmological Principle. And Special Relativity clearly indicates that there be causally separated events.
I suppose you may disagree with these theories, but there is a great deal of experimental evidence to support them.
I don’t know what you’re talking about either, but my theory involves something I call the Plywood Principle.
P.S. I am not a crank.
I don’t have the reference handy now, but can dig it up if necessary. Back in the 1990s, John D. Barrow wrote a paper in the Physical Review D (certainly a respectable journal) in which he concluded “there is no horizon problem for inflation to solve” (perhaps not an exact quote, but if not, then rather close). I remember reading the paper, and briefly discussing it with Barrow at the Texas Symposium in Munich in 1994, but haven’t seen it cited much.
Barrow is not a crackpot (though he did accept some Templeton money), PhysRevD is a respectable journal and this is an important problem in cosmology. Thus, I would expect the paper to be highly cited, unless another paper has refuted it. Since the first apparently hasn’t happened, have I missed the second?
In any case, I’d be interested in Sean’s (and any other informed) opinion.
I remember having a lot of discussions with George Ellis way back in the 90s about this issue. I strongly agree that what inflation does is merely to push the fine-tuning problems back to an earlier epoch where they are effectively under the carpet (or beyond the horizon, if you prefer a different metaphor). In fact we were planning to write a sort of spoof of Galileo’s “Dialogue concerning the Two Chief World Systems” featuring characters with names like “Inflatio” and “Anthropicus” …. but never got around to it.
PS. To anyone of a Bayesian persuasion statements about probability are statements about the extent to which a logical proposition or theory is credible given the observations. Sean is saying that the observed Universe is improbable given our theory of inflation. The question whether our observed Universe renders inflationary theory improbable is not the same, and is indeed much more interesting…
In your book with George, I think you make this point rather clearly with respect to the flatness problem. Can the horizon problem be solved in the same way? I can see the solution to the first (and am surprised that many even still consider it a problem) but not the second (at least not from the arguments in your book with George).
You definitely need to write the spoof!
Here’s your funding: http://www.passco.com/tuit.htm
While looking for the Barrow reference, I came upon this gem, worth quoting the abstract in full:
http://adsabs.harvard.edu/abs/2010AmJPh..78..728B
We consider the optimal positioning of an even number of identical crew members in a coxless racing boat so as to avoid the presence of a sideways wiggle as the boat is propelled forward through the water. We show that the traditional (alternate port and starboard) positioning always possesses an oscillating nonzero transverse moment and associated wiggling motion and that the problem of finding the zero-moment positions is related to a special case of the subset sum problem. We find the one (known) zero-moment rig for a racing Four and show that there are four possible such rigs for a racing Eight, of which only two are known. We show that only balanced boats with crew numbers that are divisible by four can have the zero-moment property and give the 29 zero-moment solutions for racing Twelves, which have zero transverse moments. Some aspects of unbalanced boats in which the numbers of port and starboard oars are unequal are also discussed.
I knew that moving to Cambridge would bring John over to the dark side. 🙂
I also ran across
http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?db_key=PRE&bibcode=1993QJRAS..34..117B&letter=.&classic=YES&defaultprint=YES&whole_paper=YES&page=117&epage=117&send=Send+PDF&filetype=.pdf
reminding me why I miss the QJRAS. This and similar articles by Longair, Rees, George Ellis, Harrison etc were (and are) some of my favourite reading.
“The question whether our observed Universe renders inflationary theory improbable is not the same, and is indeed much more interesting…”
The probability of the model given the data vs. the probability of the data given the model: the distinction can be quite important. This example illustrates the point: My data is that a person is pregnant, my model (or theory) is that this person is female. The probability of the data, given the model (and no other information) is about 3%. The probability of the model, given the data, is 100%.
Here’s the Barrow reference: http://adsabs.harvard.edu/abs/1995PhRvD..51.3113B (It’s from 1995, but the Texas Symposium was in 1994; I suppose I had read a preprint originally.) Here’s the quote (from the abstract; see text for details): It is shown that homogeneous cosmologies display no “isotropy problem” for inflation or quantum cosmology to solve.. OK, “isotropy problem” and not “horizon problem”, but that is just a naming issue. (We observe isotropy and simple arguments make it difficult to understand since in the past the horizon scale was smaller than areas of, say, similar CMB temperature on the sky today.)
Instead of updating the Dialogue, what about something based on the second Blackadder series? Let’s see, Peter Coles would be Blackadder, I would be Baldrick, Sean would be Melchett and Virginia Trimble would be Elizabeth. And, of course, Rocky Kolb would be Lord Flashheart. 🙂
So, is this like saying that “the set of universes that are similar to ours” forms a set of small measure, or is it saying that it forms a “non dense” set (in an appropriate topology)?
“I choose the multiverse. It’s far less cranky and vindictive.”
God loves you, Jennifer, the multiverse doesn’t. You’ll see after death, as we all shall see.
brandon — there’s a link right there in the post.
ollie– it’s a set of small measure; that’s where the number quoted in the abstract comes from.
Thanks Sean.
So the observable universe didn’t “just happen”
What does this mean, in the context? That inflation + the anthropic principle isn’t sufficient?
I believe that we need to consider some form of natural selection occurring within the multiverse. I have elsewhere suggested (over at NPR 13.7 blog) that we find ourselves in a large, inflated, complex universe, because their is selective survival advantage to baby universes which favor complex information processing. The idea of cosmic natural selection is not new. Lee Smolin proposed it a number of years ago. He however thinks that black hole production confers selective advantage. I think it is the generation of complex information.
e.
Sean et al,
I find this paper relevant with respect to another recent result, that being the purported new mass of the proton, and fine tuning in general.
Consider the conundrum that we are faced with: namely, particle accelerators have replicated this result for decades and it may be wrong. Thus, how can we trust just one particle accelerator producing the new result? The utility of repeatability in science seems to be thrown out the door.
Now suppose that the actual mass of the proton is off by another n%, but that detecting it requires an even more sensitive experiment. This means we will adjust the standard model to fit the most recent result, but given the precision of the model we might be wrong.
Now suppose that the universe is extremely fine tuned, and further suppose that in order to get to a “theory of everything” you need to be able to measure the precision of x to n digits. At this point there are three forks in the road:
1) the standard model at time t is consistent with all available evidence thus produced and is correct
2) the standard model at time t is consistent with all available evidence and is wrong, but will be corrected in the future when a more sensitive experiment is designed
3) the standard model at time t is consistent with all available evidence and is wrong and no experiment can ever make a precise enough measurement (at least vaguely akin to a chaotic system). You might even be able to prove that you can’t make the measurement.
Is this overgeneralization of “fine tuning”, or do you consider it plausible that we could find ourselves in position 3?
Is ANY part of the multiverse hypothesis scientifically testable?
Perhaps what the little circle of glass-bead game players need is for M. Kaku to step into the center and “read the mind of God” for the group?
Untestable postmodern pseudoscience. Ain’t it unreal, man!
So Sean puts some precision into the ‘fine tuning’ of the universe. Good work.
God and multiverse are the same thing. If God is part of this universe, then it is not God right? If it is outside, and did its ‘creation’, then by definition it is on another ‘universe’ – thus multiverse. Fine tuning automatically imply the existence of ‘something’ outside of this universe before its existence. It also means it is impossible for any intelligence in this universe to know what’s ‘outside’, just that the ‘outside’ exists.
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