A Still Better Analogy To Explain Naturalness
    By Tommaso Dorigo | October 15th 2012 08:06 AM | 4 comments | Print | E-mail | Track Comments
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    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    I have discussed analogies here in the recent past, producing the writeup of a recent talk at a conference on the popularization of physics. I also singled out for an independent post a nice analogy to explain the problem of Naturalness (the "unnaturally low" mass of the Higgs boson and the resulting implications for new physics). Today a reader of this blog (signed "Ohwilleke") offered, in the comments thread of the writeup article, a much improved version of my "improvement". See below:

    "Suppose that sum of the profits and losses of ten companies turn out to average out to be $10. If you only know this fact, and that a priori profits and losses in any given year appear to be more or less equally likely in the highly competitive market where these companies operate, what kinds of gross revenues do you expect the average company to have? Knowing only these facts, you might expect for a string of lemonade stands in a busy residential neighborhood. But you would be shocked if you learned that the companies had gross revenues that averaged tens of billions of dollars a year each, for the average profit to net out to $10 simply as a random average, even if profits and losses were equally likely. You would suspect that someone had carefully combed through tens of thousands of corporate reports to come up with a combination that was so equally balanced on purpose."

    "Physicists, similarly, suspect based upon the unnaturalness of the near perfect balancing of the loop corrections in the absence of some unknown non-random principle that causes them to nearly balance out, when compared to the scale of the components, that the loop corrections probably actually balance due to some hidden structure that we haven't yet discovered."


    Or I would suspect that these companies try real hard to get zero profits. Probably have something to do with taxation

    Very nice!

    Hi Tommaso,

    Deep down, I've always had a problem with naturalness as a complete guide to Nature. It works very well when thinking about effective field theories and theories which have an enhanced symmetry in certain limits (e.g., taking fermion masses to zero). But, I think it is a bit much to promote it to near law status.

    The problem is, we don't know the measure and the example you gave demonstrates the problem precisely. In that example you ask, how probable is it that the sum of 10 random variables, which can take on both positive and negative values, would be substantially smaller than the realizations of the random variables themselves? The problems is, how many times did you run the experiment and under what conditions do you get to see the sum? If the experiment was run a sufficiently large number of times, I can guarantee (almost surely) that I will see a sum within an arbitrarily small bound around zero. And if my detector can only register small sums, this is all I will see.

    In the case of the Standard Model, we don't know the measure under which we should be thinking about the problem. To put a fine point on it, we don't know the measure of the initial conditions that would lead to two super-renormalizable operators (the cosmological constant, and the Higgs mass) ending up in the low energy theory of Nature. For the Higgs, maybe there is a symmetry enhancement that we get in certain limits that explains its small mass - supersymmetry certainly does the trick. But Nature does it's own thing and it is possible that we simply have missed something. Our planet orbits at just the right distance from our star to allow life. (And it's also bizarre how our moon is almost the same angular size as the sun!) This observation does not require special dynamics - the measure in this case is set by the huge number of possible solar systems. It may be that our Standard Model is technically unnatural because any large changes in the values of its super-renormalizable operators render a Universe without the possibility of creatures to ponder the beauty of a technically natural low energy theory. Just imagine what the Periodic Table would look like in a Universe with Planck scale electroweak physics. Just imagine what happens to structure formation if the cosmological constant was much different.

    Hi IS,

    you raise important points, and indeed I know your views are shared by many. Anthropic reasoning leads us to shrug shoulders on some coincidences we observe, or at least to put them in a broader perspective. As you probably know I am not too excited by the prospects of new physics at the TeV scale, and keep a sceptical attitude.

    Anyway I keep a didactical attitude here, and do not broadcast this naturalness problem as the big deal some make of it; however, since it is an important ingredient in today's Physics speculations, I think we need to explain exactly what this is to readers who can't integrate quantum loops.