Is being lonely unnatural for slim particles? A statistical argument

pileofuniversesBeing lonely is unnatural, at least if you are a slim Higgs particle (with mass on the order of the type recently discovered)–according to an intriguing statistical argument given by particle physicist Matt Strassler (sketched below). Strassler sets out “to explain the scientific argument as to why it is so unnatural to have a Higgs particle that is “lonely” — with no other associated particles (beyond the ones we already know) of roughly similar mass.

This in turn is why so many particle physicists have long expected the LHC to discover more than just a single Higgs particle and nothing else… more than just the Standard Model’s one and only missing piece… and why it will be a profound discovery with far-reaching implications if, during the next five years or so, the LHC experts sweep the floor clean and find nothing more in the LHC’s data than the Higgs particle that was found in 2012. (Strassler)

What’s the natural/unnatural intuition here? In his “First Stab at Explaining ‘Naturalness’,” Strassler notes “the word ‘natural’ has multiple meanings.

The one that scientists are using in this context isn’t “having to do with nature” but rather “typical” or “as expected” or “generic”, as in, “naturally the baby started screaming when she bumped her head”, or “naturally it costs more to live near the city center”, or “I hadn’t worn those glasses in months, so naturally they were dusty.”  And unnatural is when the baby doesn’t scream, when the city center is cheap, and when the glasses are pristine. Usually, when something unnatural happens, there’s a good reason……

If you chose a universe at random from among our set of Standard Model-like worlds, the chance that it would look vaguely like our universe would be spectacularly smaller than the chance that you would put a vase down carelessly at the edge of the table and find it balanced, just by accident.

Why would it make sense to consider our universe selected at random, as if each one is equally probable?  What’s the relative frequency of possible people who would have done and said everything I did at every moment of my life?  Yet no one thinks this is unnatural. Nevertheless, it really, really bothers particle physicists that our class of universes is so incredibly rare, or would be, if we were in the habit of randomly drawing universes out of a bag, like blackberries (to allude to C.S. Peirce). Anyway, here’s his statistical argument:

I want you to imagine a theory much like the Standard Model (plus gravity). Let’s say it even has all the same particles and forces as the Standard Model. The only difference is that the strengths of the forces, and the strengths with which the Higgs field interacts with other particles and with itself (which in the end determines how much mass those particles have) are a little bit different, say by 1%, or 5%, or maybe even up to 50%. In fact, let’s imagine ALL such theories… all Standard Model-like theories in which the strengths with which all the fields and particles interact with each other are changed by up to 50%. What will the worlds described by these slightly different equations (shown in a nice big pile in Figure 2) be like?

Among those imaginary worlds, we will find three general classes, with the following properties.

  1. In one class, the Higgs field’s average value will be zero; in other words, the Higgs field is OFF. In these worlds, the Higgs particle will have a mass as much as ten thousand trillion (10,000,000,000,000,000) times larger than it does in our world. All the other known elementary particles will be massless …..
  2. In a second class, the Higgs field is FULL ON.  The Higgs field’s average value, and the Higgs particle’s mass, and the mass of all known particles, will be as much as ten thousand trillion (10,000,000,000,000,000) times larger than they are in our universe. In such a world, there will again be nothing like the atoms or the large objects we’re used to. For instance, nothing large like a star or planet can form without collapsing and forming a black hole.
  3. In a third class, the Higgs field is JUST BARELY ON.  It’s average value is roughly as small as in our world — maybe a few times larger or smaller, but comparable.  The masses of the known particles, while somewhat different from what they are in our world, at least won’t be wildly different. And none of the types of particles that have mass in our own world will be massless. In some of those worlds there can even be atoms and planets and other types of structure. In others, there may be exotic things we’re not used to. But at least a few basic features of such worlds will be recognizable to us.

Now: what fraction of these worlds are in class 3? Among all the Standard Model-like theories that we’re considering, what fraction will resemble ours at least a little bit?

The answer? A ridiculously, absurdly tiny fraction of them (Figure 3). If you chose a universe at random from among our set of Standard Model-like worlds, the chance that it would look vaguely like our universe would be spectacularly smaller than the chance that you would put a vase down carelessly at the edge of the table and find it balanced, just by accident.

In other words, if the Standard Model (plus gravity) describes everything that exists in our world, then among all possible worlds, we live in an extraordinarily unusual one — one that is as unnatural as a vase balanced to within an atom’s breadth of falling off or settling back on to the table. Classes 1 and 2 of universes are natural — generic — typical; most Standard Model-like theories are in those classes. Class 3, of which our universe is an example is a part, includes the possible worlds that are extremely non-generic, non-typical, unnatural. That we should live in such an unusual universe — especially since we live, quite naturally, on a rather ordinary planet orbiting a rather ordinary star in a rather ordinary galaxy — is unexpected, shocking, bizarre.  And it is deserving, just like the balanced vase, of an explanation.  One certainly has to suspect there might be a subtle mechanism, something about the universe that we don’t yet know, that permits our universe to naturally be one that can live on the edge.

Does it make sense to envision these possible worlds as somehow equally likely? I don’t see it.  How do they know that if an entity of whatever sort found herself on one of the ‘natural’ and common worlds that she wouldn’t manage to describe her physics so that her world was highly unlikely and highly unnatural? Maybe it seems unnatural because, after all, we’re here reporting on it so there’s a kind of “selection effect”.

An imaginary note to the Higgs particle:

Dear Higgs Particle: Not long ago, physicists were happy as clams to have discovered you  –you were on the cover of so many magazines, and the focus of so many articles. How much they celebrated your discovery…at first. Sadly, it now appears you are not up to snuff, you’re not all they wanted by a long shot, and I’m reading that some physicists are quite disappointed in you! You’re kind of a freak of nature; you may have been born this way, but the physicists were expecting you to be different, to be, well bigger, or if as tiny as you are, to at least be part of a group of particles, to have friends, you know, like a social network, else to have more mass, much, much, much more … They’re saying you must be lonely, and that– little particle–is quite unnatural.

Now, I’m a complete outsider when it comes to particle physics, and my ruminations will likely be deemed naïve to the physicists, but it seems to me that the familiar intuitions about naturalness are ones that occur within an empirical universe within which we (humans) have a large number of warranted expectations. When it comes to intuitions about the entire universe, what basis can there possibly be for presuming to know how you’re “expected” to behave, were you to fulfill their intuitions about naturalness? There’s a universe, and it is what it is. Doesn’t it seem a bit absurd to apply the intuitions applicable within the empirical world to the world itself? 

 It’s one thing to say there must be a good explanation, “a subtle mechanism” or whatever, but I’m afraid that if particle physicists don’t find the particle they’re after, they will stick us with some horrible multiverse of bubble universes. 

So, if you’ve got a support network out there, tell them to come out in the next decade or so, before they’ve decided they’ve “swept the floor clean”. The physicists are veering into philosophical territory, true, but their intuitions are the ones that will determine what kind of physics we should have, and I’m not at all happy with some of the non-standard alternatives on offer. Good luck, Mayo

Where does the multiverse hypothesis come in? In an article in Quanta by Natalie Wolchover

Physicists reason that if the universe is unnatural, with extremely unlikely fundamental constants that make life possible, then an enormous number of universes must exist for our improbable case to have been realized. Otherwise, why should we be so lucky? Unnaturalness would give a huge lift to the multiverse hypothesis, which holds that our universe is one bubble in an infinite and inaccessible foam. According to a popular but polarizing framework called string theory, the number of possible types of universes that can bubble up in a multiverse is around 10500. In a few of them, chance cancellations would produce the strange constants we observe.[my emphasis].

Does our universe regain naturalness under the multiverse hypothesis? No. It is still unnatural (if I’m understanding this right). Yet the physicists take comfort in the fact that under the multiverse hypothesis, “of the possible universes capable of supporting life — the only ones that can be observed and contemplated in the first place — ours is among the least fine-tuned.”

God forbid we should be so lucky to live in a universe that is “fine-tuned”![i]

What do you think?lhc

[i] Strassler claims this is a purely statistical argument, not one having to do with origins of the universe.

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20 thoughts on “Is being lonely unnatural for slim particles? A statistical argument

  1. I can’t understand why the physicists are so convinced that our physical constants are random. Randomness implies a distribution of some kind. How can we make any estimate of a distribution when we have only one example to work with? This is the infamous situation of n = 1.

    We already know it is difficult to find other planets with life. How difficult is it going to be to find other universes so we can check their constants?

    I am trying to imagine how to look for other universes… no ideas are coming. It is like looking for God. Where do you look? Oh, I know, in my own heart.

    Well I certainly don’t want to take away the physicists’ religion. That would be too cruel.

    • Corey

      dratman: I don’t know that many physicists are “so convinced” that physical constants are random, but I suspect many physicists are willing to entertain the possibility because many elegant models, e.g., eternal inflation, lead to multiverses with that feature.

      Technically, any data set one encounters is n = 1. Statisticians get by on theory premised on assumptions of varying reasonability — rather like physicists, in fact.

    • Dratman: oh they don’t think we can find these other universes, they are part of an “inaccessible foam”, like imaginary beer bubbles I guess.

      • I do understand that all those universes are supposed to be forever inaccessible. But in that case, you see, they are no different from religious entities. We could never have more than circumstantial evidence for their existence.

        In fact it has often been argued that our situation would be very unnatural if there were no God. Ergo, there is one.

        Likewise, ergo, there is new physics out there somewhere. Otherwise we would be left with an unnatural status quo.

        On another point, possibly related, do frequentists and Bayesians disagree in any practical realm, or are their differences purely about ontology?

        • The disagreements are very rarely put in ontological terms, except I suppose people who debate whether probabilities are “out there”. But as far as inference is concerned, the main thing I care about, the differences have mainly to do with the role of probability in inference, and whether error probabilities of procedures matter once data are available.
          I don’t have a clue as to whether the probabilities imagined from metaphorical random sampling of universes would qualify as subjective probabilities. Or are they subjective assessments of real (but hypothetical) relative frequencies of universes (I think subjectivists often switch back and forth between the two, and it’s hard to pin them down.) anyway, it is a little curious that Corey seems to endorse these, as they appear to fall into the category of “mind projections”.

  2. Corey

    Reading the comments of Strassler’s post, the argument seems to have two parts. First, physical theories are generally of the form of dynamical equations, and dynamical equations tend to couple their outputs such that they have similar orders of magnitude. To the extent that higher level physical theories involve parameters whose values are the ouput of lower level physical theories, it is natural that those parameters would be in roughly the same range.

    Second, in parameterizations that currently appear natural to physicists, the dispersion (measured by, say, variance or entropy relative to Lebesgue measure) of *any* distribution that gives a non-tiny probability to outcomes of a type like our universe is, in technical terms, teensy weensy. So the challenge is to come up with a more physically elegant parameterization which gives these types of universe a larger chunk of parameter space, or equivalently, explain what physical constraint is forcing our universe to have features consistent with only a tiny part of parameter space. (In particular, it would be nice if the explanation were easier to verify than the weak anthropic principle, i.e., the claim that only this tiny chunk of parameter space is consistent with the existence of observers.)

    These both seem reasonable to me.

    • Corey: Thanks for the explanation, I read this too. I can see wanting to get a more complete explanation of the “evidence”, but the probabilistic argument strikes me as absurd. And are we really so sure about the capabilities of the LHC to detect these much sought particles to conclude they’re not there if they don’t detect them in the data they have? I thought in fact that they couldn’t discern particles with high mass. Look, I know very little about these theories, but there does seem to be a strong fanciful side to particle physics that may give too much emphasis to the wonderful worlds they want to envision. I’m sure this would be greeted with ridicule on Strassler’s blog.

  3. I completely agree with you.
    I have always been baffled why physicists want
    to image a meta-person selecting universes at random
    and then saying ours is unlikely.
    There is no one selecting universes at random.
    And, as you point out, “at random’ is not well defined.
    We could put many probability measures over the set of universes
    that makes ours very likely.

    • Corey

      normaldeviate: “There is no one selecting universes at random.”

      I’m curious as to how you’ve ruled out the possibility that the physics that hold in the *observable* universe are the result of a stochastic process. If your argument is sufficiently compelling, you’ll be in line for a Nobel Prize in Physics!

    • Normaldeviate: That would be brilliant, i.e., showing a distribution that made our universe likely. I take it Strassler and others think it can’t be done with the constraints they assume.
      I just don’t see why they’d find it more plausible or comforting to suppose lots of other universes with different laws and parameters. It sounds like the philosopher’s “possible worlds”, as in modal logic. Some well-respected scientists warned me about particle physics theorizing some time ago, and it surprised me then; but maybe there’s something to their criticism.

  4. Corey: That’s not what I said.
    They claim our universe is unlikely for an imaginary
    being selecting universes at random
    according to a measure that a particular
    physicist finds natural

    • Corey

      normaldeviate: I was going for the most charitable interpretation; taken literally, what you wrote is a strawman. Physicists don’t mention any “meta-person” doing the selection — at least, not when they’re writing for other physicists instead of making analogies for the general public — and the hierarchy problem and the (as yet hypothetical) lonely Higgs problem refer to the physics of the observable universe.

      • I realize they don’t mention a meta-person.
        My point is that they compute a probability
        from the point of view of being “outside” and
        as if one were
        “drawing a universe at random” which
        is meaningless.

      • Corey: But there’s a huge set of theoretical presuppositions that goes way beyond the “observable” (see my comment on “aesthetics” below). And the resulting new physics will be less constrained by actual experiments, at least if what I read is correct (e.g., about string theories/models).
        Should we be comforted by the fact that in talking to one another the physicists don’t feel the need to justify their metaphors? I don’t think so. (Perhaps they should bring in more scientists from outside, with different perspectives, actually.) An interesting argument I’ve heard is that if the universe is unnatural, in the manner they’re worrying about, then people won’t be interested in continuing to do physics. Maybe because it will feel too descriptive, without a sweeping and unified explanation. This might be seen as more of a utilitarian, heuristic argument than one based on the goal of understanding the physical world.

        • Corey

          Mayo: I guess I have a bit more respect for physicists’ aesthetic sense (at least in some composite way — I’m not so sure about any individual physicist’s aesthetic sense). From what I’ve read on the subject, it seems to me that an aesthetically pleasing physical theory corresponds to one which has a small description as, say, a set of equations, or equivalently, a computer program. Given my own feelings on Solomonoff induction, I’m inclined to favor such theories, not in terms of belief so much as in terms of what theories are useful to entertain in order to derive some testable consequence.

  5. I find it amusing that the physicists speak as if the data and hard reality are forcing them to these way-out theories.In Wolchover’s article, we hear that
    “In peril is the notion of “naturalness,” Albert Einstein’s dream that the laws of nature are sublimely beautiful, inevitable and self-contained. Without it, physicists face the harsh prospect that those laws are just an arbitrary, messy outcome of random fluctuations in the fabric of space and time.”

    And yet they think they’re going about it in a manner that excludes aesthetics, emotion, and feelings. She quotes one physicist:

    “But I just don’t think we can analyze it on an emotional basis. It’s a logical possibility that is increasingly favored in the absence of naturalness at the LHC.”

  6. Django

    Corey, et al: Maybe there is more than one “meta-person” , e.g., “meta-people” to choose and create among the various worlds/universes. That would certainly stir the pot – sort of like a Greek pantheon with maybe lesser (demi) and major “persons”.

  7. I happened to notice a comment by Cosma Shalizi on physics vs Bayesian entropy: It doesn’t have to do with this post, but some of the physicist readers might find it intriguing: Shalizi always has wise insights.

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