Does This Ontological Commitment Make Me Look Fat?

3:am magazine (yes, that’s what it’s called) has a very good interview with Craig Callender, philosopher of physics at UC San Diego and a charter member of the small club of people who think professionally about the nature of time. The whole thing is worth reading, so naturally I am going to be completely unfair and nitpick about the one tiny part that mentions my name. The interviewer asks:

But there is nothing in the second law of thermodynamics to explain why the universe starts with low entropy. Now maybe its just a brute fact that there’s nothing to explain. But some physicists believe they need to explain it. So Sean Carroll develops an idea of a multiverse to explain the low entropy. You make this a parade case of the kind of ontological speculation that is too expensive. Having to posit such a huge untestable ontological commitment to explain something like low entropy at the big bang you just don’t think is worth it.

There is an interesting issue here, namely that Craig likes to make the case that the low entropy of the early universe might not need explaining — maybe it’s just a brute fact about the universe we have to learn to accept. I do try to always list this possibility as one that is very much on the table, but as a working scientist I think it’s extremely unlikely, and certainly it would be bad practice to act as if it were true. The low entropy of the early universe might be a clue to really important features of how Nature works, and to simply ignore it as “not requiring explanation” would be a terrible mistake, even if we ultimately decide that that’s the best answer we have.

But what I want to harp on is the idea of “ontological speculation that is just too expensive.” This is not, I think, a matter of taste — it’s just wrong.

Which is not to say it’s not a common viewpoint. When it comes to the cosmological multiverse, and also the many-worlds interpretation of quantum mechanics, many people who are ordinarily quite careful fall into a certain kind of lazy thinking. The hidden idea seems to be (although they probably wouldn’t put it this way) that we carry around theories of the universe in a wheelbarrow, and that every different object in the theory takes up space in the wheelbarrow and adds to its weight, and when you pile all those universes or branches of the wave function into the wheelbarrow it gets really heavy, and therefore it’s a bad theory.

That’s not actually how it works.

I’m the first to admit that there are all sorts of very good objections to the cosmological multiverse (fewer for the many-worlds interpretation, but there are still some there, too). It’s hard to test, it’s based on very speculative physics, it has a number of internal-consistency issues like the measure problem, and we generally don’t know how it would work. I consider these “work in progress” types of issues, but if you take them more seriously I certainly understand. But “wow, that sure is a lot of universes you’re carrying around” is not one of the good objections.

When we’re adding up our ontological commitments (i.e., the various beliefs about reality we are willing to hypothesize or even accept), the right way to keep track is not to simply add up the number of objects or universes or whatevers. It’s to add up the number of separate ideas, or concepts, or equations. There are an infinite number of integers, and there are only a finite number of integers between zero and a googol; that doesn’t make the former set somehow ontologically heavier. If you want to get fancy, you could try to calculate the Kolmogorov complexity of the description of your theory. A theory that can be summed up in fewer words wins, no matter how many elements are in the mathematical structures that enter the theory. Any model that involves the real numbers — like, every one we take seriously as a theory of physics — has an uncountable number of elements involved, but that doesn’t (and shouldn’t) bother us.

By these standards, the ontological commitments of the multiverse or the many-worlds interpretation are actually quite thin. This is most clear with the many-worlds interpretation of quantum mechanics, which says that the world is described by a state in a Hilbert space evolving according to the Schrodinger equation and that’s it. It’s simpler than versions of QM that add a completely separate evolution law to account for “collapse” of the wave function. That doesn’t mean it’s right or wrong; but it doesn’t lose points because there are a lot of universes. We don’t count universes, we count elements of the theory, and this one has a quantum state and a Hamiltonian. A tiny number! (The most egregious version of this mistake has to belong to Richard Swinburne, an Oxford theologian and leading figure in natural theology, who makes fun of the many-worlds interpretation but is happy to accept a completely separate, unobservable, ill-defined metaphysical category into his ontology.)

The cosmological multiverse, while on much shakier empirical ground than the many-worlds interpretation, follows the same pattern. The multiverse is not a theory, it’s a prediction. You don’t start with the idea “hey, let’s add an infinite number of extra universes!” You start with our ideas of general relativity, and quantum mechanics, and certain plausible field content, and the multiverse comes out, like it or not. You can even get a “landscape of different vacua” out of very little theoretical input; Johnson, Randall and I showed that transitions between states with different numbers of macroscopic spatial dimensions are automatic in a theory with just gravity, vacuum energy, and an electromagnetic field, while Arkani-Hamed et al. showed that the good old real-world four-dimensional Standard Model coupled to gravity supports a landscape of different vacua that depends on the masses of the neutrinos. The point is that these very complicated cosmologies arise from very simple theories, and it’s the theories we should be judging, not their solutions.

The idea of a multiverse is extremely speculative and very far from established — you are welcome to disagree, or even better to ignore it entirely. But please disagree for the right reasons!

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45 Responses to Does This Ontological Commitment Make Me Look Fat?

  1. Hal S says:

    I think this debate is somewhat silly. It effectively boils down to a question of whether one believes that quantum mechanics and gravitation can be unified. If one takes the position that they can be unified, then one currently must resort to a “stringy” view of the universe, and one must identify mechanisms by which the cosmological constant takes a small value (which in some sense is basically a question similar to whether model parameters, such as mass etc, are correlated in totality or are independent). The alternative is that gravity and quantum mechanics are independent, such as discussed in this paper:

    http://www.cs.okstate.edu/~subhashk/quantijtp.pdf

    I for one subscribe to unification, and do not believe the cosmological constant is a wholly independent parameter. Justification for this point of view is that we actually do have theories that are robust enough to unify gravity and quantum mechanics. So while there is a certain amount of independence as symmetries are broken and parameters take on observed values, there is still ultimately some sort of functional dependence that restricts those values (e.g. some correlation function). The evidence is simply overwhelming that our universe is fundamentally quantum, and that “waviness” is absolutely fundamental as well.

    So my advice? Stop trying to make classical analogies to things that are clearly not classical. Accept that classicality is a low energy phenomena, or rather an emergent phenomena stemming from existence in a sufficiently mixed state.

  2. John R Ramsden says:

    Excluding multiverse and many worlds notions by treating the universe as a concept instead of an instance of a broader concept isn’t the only error those guys may be committing. They also defy observation, or reasonable extrapolation of the obvious fact that practically everything in nature occurs in vast profusion, despite this in many cases not being at all obvious or plausible to earlier observers. So why should universes be any different?

    As for the low initial entropy conundrum, it is equally obvious to a multiverse believer such as myself that it must somehow emerge from the maximal entropy of an earlier universe generation. The only way I can see to resolve this paradoxical (even apparently nonsensical) conclusion is that once a universe reaches a maximal entropy, it rescales as if “searching out” asymmetries and the latter start a new generation.

    On that assumption, a multiverse scenario could be experimentally verified if there were any way to distinguish a Big Bang inflation which diluted existing asymmetries (the conventional view) versus the complementary picture, sketched above, in which any above a certain scale had been ironed out. The latter need not contradict the idea of a minimal scale; this could still exist at any given scale, and indeed might need to for the necessary apparent “clean break” between universe generations to be possible.

  3. Hal S says:

    Just as an illustration of correct thinking. Consider the Mott problem. This is a nice quantum analogy one can use as to why one would think that all the masses of fundamental particles might be correlated at some level (rather than randomly distributed). In this example Mott and Heisenberg were able to show that the variability was in the ultimate determination of which path was being taken, not that the points detected would be random. As an analogy it is useful, since one would expect that the rest masses of fundamental particles should follow some sort of function in some configuration space, and not be randomly determined.

    http://en.wikipedia.org/wiki/Mott_problem

  4. Lino D'Ischia says:

    This entire discussion strikes me as the epitome of what is happening in science: the descent into the nonsensical. Science, in most respects, is concerned with what we understand as ’cause and effect,’ with the set of possible ’causes’ delimited to those that we know. What is so troublesome about the invocation of ‘multiverses’ is its entire unknowability–we’re talking about entirely different universes (!), unknown regions completely cut-off, by definition, from that of our own! Why don’t we just say that giant green fairy monsters brought about the initial low entropy of our universe. Of course, this is complete nonsense. But, if you reply that we can discount this possibility because we have no way of proving these monsters exist, I simply have to answer that we do have proof of their existence: low initial entropy. Circularity in reasoning has now entered the scene. How do we ever usher it out? To me, this should be a great cause of concern for all thinking scientists.

  5. Juzer says:

    Sean, re: # 19, would the multiplying numbers of epicycles to keep up with more and more accurate measurements in the Ptolemaic theory of planetary motion count as a disqualifier?

  6. ComeOn says:

    Agree with Lino (comment 29), except why do you think this is happening all over science? Can you point to any research in Biology or Chemistry where this problem of “unknowability” is present, permitting a descent into the nonsensical? You cannot. In fact, it is only in some esoteric branches of physics where this happens, such as string theory and many-universes cosmology. The bread and butter of particle physics is concerned with what we can observe in colliders, so this issue does not arise.

  7. Hi Sean,

    If the Universe had begun in a high entropy state we’d still have worlds with beaches with dark patches of sands, although they’d be VERY rare.

    In this case would you invoke Jesus/God/Church to explain why we are the only such improbable planet?

    No, of course you wouldn’t. The universe probably started in a low entropy state cos that’s the way things start, really, I mean it would be a lot of effort to create a high entropy starting state..

  8. Sean Carroll says:

    Juzer– it depends. If you were just adding completely independent epicycles, specified by new parameters each time, then yes, it would make things more complicated. But if you had some pattern that connected all the epicycles (a geometric series or something like that), it could still be quite simple. It’s all about how much information is required to specify the theory.

  9. Archie Pelago says:

    Callendar *isn’t* really saying that the arrow of time doesn’t need explaining. His main point is contained in the following:

    “suppose we judge the constraint on initial conditions to be lawlike. (I think that there are some powerful arguments for this.) Then all the universes that don’t begin in a low entropy state are, strictly speaking, unphysical and have zero probability. The initial state is then hardly monstrously unlikely (hence demanding explanation), but rather has probability one!”

    which is very sensible indeed. Though I would very much like to hear what his powerful arguments are.

  10. Meh says:

    #29 and #31 : It wasn’t until the mid 20th century when we discovered that our galaxy was not the entire universe. In 60 years, we went from thinking that our galaxy was the entire universe to KNOWING that there are as many galaxies in the universe as there are stars in our galaxy, if not far more.

    Sean is saying that he won’t rule out the possibility that it may be something that we will never know (because IMO, that’s what bright minds do; they keep all possibilities open), but that we probably will find out.

    The field of medicine is pretty pathetic compared to what it could be; given that most doctors will throw pills at every problem you have. “no, my runner’s knee doesn’t hurt anymore now that I’m high as a kite”. We have no solid grasp of “nutritional science”; have you ever tried to get your full day’s worth of potassium? It’s impossible. Physics is different from other sciences because we admit what we don’t know. Physics goes beyond the knowledge of biology or chemistry. My passion for physics started in my high school chemistry class when I asked my teacher to explain why covalent bonds behave the way they do; he had no answer.

    Biology is further explained by Chemistry. Chemistry is further explained by Physics. How can you complain about the honesty of physicists when you are forced to turn to them for the knowledge that is beyond your field of study?

    Physics is further explained by discovery.

  11. James Goetz says:

    First, Craig appears off when he says that low entropy at the Big Bang needs no explanation. But perhaps the brute fact is that physics might never have that explanation, which is far different than saying initial low entropy needs no explanation.

    “There are an infinite number of integers, and there are only a finite number of integers between zero and a googol; that doesn’t make the former set somehow ontologically heavier.”

    Second, Sean, if a multiverse hypothesis depends upon the concept of fundamental time, then an infinite number of integers look fat. For example, nobody should doubt the existence of an infinite number of past and future Plank time coordinates independent of phenomena, but nonetheless, an infinite number of Plank times could never have elapsed (regardless if the length of Plank time intervals vary throughout a multiverse). Likewise, since fundamental time requires a past infinite elapse of time, then fundamental time is impossible. The elapse of time emerged.

    Given the above, a multiverse hypothesis with fundamental time is infinitely heavy while a multiverse hypothesis with emergent time might work if it has no other impossible obstacles.

  12. John R Ramsden says:

    @Meh (#35) Well said, and your initial observation illustrates the first point I made in #27.

    Although Lino (#29) may have a point at present, his attitude sounds very much like that of the guy who lamented that the composition of stars must remain forever unknown – only a year or two before the development of spectroscopy. 😉

  13. Meh says:

    Thanks John,
    I was thinking about this last night, and remembered the question that I always come up with when discussing a multiverse: What defines a universe? Is it a collection of dimensions? Would parallel universes just be copies of our own? if that’s the case, then what is the boundary that separates the two universes? Is it just scale? If it’s just the measure of entropy as Lino #29 says, then it really just depends on the parameters of the system we define. The entropy of a black hole, our solar system, and an intergalactic region of space, could philosophically/hypothetically all be different universes if entropy is the defining parameter.

  14. Emil says:

    When I think about the multiverse I remember the problem we have solved in the first year of college physics: why does light travels in a straight line? The solution involved considering the light takes all possible paths between 2 points (it can go all the way to the moon and back before hiting my eye) but only on the straight line the interference would be constructive. Of course I do not expect to measure any change away from the straight path and I think this is equivalent to saying that those other paths do not exist – but that does not prevent the light wave function to be defined for any point in our universe (both in time and in space). So multiverse seems like a nice construction that allows us to explain our observations but it also says that other wolds have no influence on how we experience our world.

  15. Jordan says:

    The original postulation of a single neutrino with spin 1/2 emitted during Beta decay rather than two neutrinos with spin 1/4, three neutrinos with spin 1/6, etc., seems a case where we favored the quantitatively simpler hypothesis.

    For a little discussion, see: http://plato.stanford.edu/entries/simplicity/#QuaPar

  16. Itai Bar-Natan says:

    By the way, I’d like to ask: is the Big Bang really a low entropy state? It has all of the energy uniformly distributed throughout all of space, which seems to me like a good way of maximizing entropy rather than minimizing it. The fact the it evolves into a low-entropy state seems to come from the fact that the expansion of the universe is non-adiabatic; if the universe expanded slowy enough, atoms would have the time to reach Boltmann-like isotope ratios, and density inequalities would have time to balance themselves rather than forming stars and galaxies.

  17. A H says:

    “The cosmological multiverse, while on much shakier empirical ground than the many-worlds interpretation, follows the same pattern.”

    There can be no empirical evidence for the many-worlds interpretation, or any other sound interpretation of quantum mechanics. This sloppy use of philosophical terms really undermines your arguments.

  18. Todd says:

    I absolutely love the wheelbarrow metaphor. Occam’s Razor is great but – what with its near-mystic “cutting both ways” and all – it lacks the concrete attraction of Carroll’s Wheelbarrow.

  19. James Sweet says:

    A related thought experiment — and I apologize that I can’t remember who I am stealing this from, maybe Stephen Hawking, maybe Kip Thorne, hell maybe even Sean, I honestly don’t remember — is this:

    If a spaceship begins travelling away from you at the speed of light, and you know it will travel in that same direction and same speed indefinitely, which is the most parsimonious universe? One in which that spaceship continues to exist, even though you will never even in principle be able to catch up with it or observe it? Or one in which the spaceship ceases to exist?

    I would argue the former, even though it requires more “ontological commitments” by Callender’s definition.

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