(Un)Naturalness, Explained

This week I’m in California, at a conference celebrating two famous professors, from whom I learned an enormous amount when I was a graduate student and postdoctoral researcher. More on this later in the week.

Today, I just want to let you know I have completed the core of my naturalness article, which I began writing a couple of weeks ago.

The first part of that article was intended as in introduction to what the concept of naturalness means, and what physicists are implying when they say that “if the universe is really described only by the Standard Model (the equations we use to predict the behavior of the known particles and forces), plus gravity, then the universe is unnatural.” The second part of the article (now an accompanying article) was on the nature of quantum fluctuations of fields — an essential feature of our quantum world — and about how those fluctuations contribute to the energy stored in empty space (the “vacuum energy”). The third part of the article explained how the average value of the Higgs field, and the Higgs particle’s mass, are determined by how the energy of empty space depends on the Higgs field’s value. And now, the fourth part of the article tries to explain the argument that leads to the conclusion that a universe described by the Standard Model’s equations is unnatural. The argument isn’t technical (there are no equations) but the logic is sophisticated; you may find that you have to read it a couple of times and think about it.

Soon I’ll add a section on various possible solutions to the problem of the unnaturalness of the Standard Model (adding something to Standard Model in such a way as to evade the naturalness problem; a complicated “multiverse” structure to the universe, with different laws of particle physics in different places; and arguments that this is all just the wrong way of thinking about the problem and there’s no conundrum at all.)

One issue I addressed in the latest update is a question that many commenters ask: can you quantify how unnatural is the Standard Model? The answer is “yes, roughly”, and how it’s done is in the text. Of course you’re free to disagree with that answer, but you ought to have a good reason, rather than just be grumpy about it.

Another important aspect of what I’ve added, which is relevant to many of the comments I got on the earlier parts of the article, is that naturalness has absolutely nothing to do with infinities, renormalization, cutting off a calculation in an arbitrary way, or any of these other technicalities you may have read about. It is unfortunate that there is widespread misunderstanding of this point… and for this reason, you will often read, in books and articles even by scientists and by the most educated science writers, that infinities are a big player in the story of naturalness. But it is straightforward to see that the naturalness problem has nothing to do with any of this. For one thing, there are theories (here `theory’ = set of equations that describes a possible universe) that are finite, need no infinite renormalization, require no arbitrary cut-off at short distance and high energy, and yet have the same naturalness problem as all of the other theories that, like the Standard Model, have one or more lonely, lightweight Higgs-like fields.

The issue here isn’t that the calculations in the Standard Model of the Higgs field’s and Higgs particle’s properties involve infinities — in fact no infinities may arise at all. It is that the results of the calculation are highly sensitive and involve near-perfect cancellation between apparently unrelated effects. [In the lingo: it’s not quadratic divergences but quadratic sensitivity that is at the heart of the naturalness problem.] It is this apparently bizarre cancellation that lies at the heart of what makes the Standard Model apparently unnatural, and why so many scientists suspect that — even beyond the Standard Model’s failure to explain dark matter and the origin of neutrino masses, or play nice with gravity — it is unlikely to encompass the whole of particle physics at the energies probed by the Large Hadron Collider.

22 responses to “(Un)Naturalness, Explained

  1. But Matt. How can we call imagination a solution for such huge problem?

    • Torbjörn Larsson, OM

      It is very rude to go up to hardworking scientists and call what they are doing fantasies. Especially when they deliver hard results like the Higgs field.

      Ironically that you yourself indulge in fantasies that require a) lying about the science (e.g. “infinite steady state universe”, “case closed”) to open up a gap and then b) inserting magic action in the gap doesn’t seem to bother you.

      The case that has been closed of is precisely magic action, since our current universe was a result of previous inflation.

  2. Can any sort of ad-hoc imagination really called a solution of a really bizarre cancellation ?

  3. It’s like the “not invented here” syndrome going on. There is a testable solution existing but it’s created by “an outsider”, hence no good. Anyway, I’m looking forward to see your solutions in the next post.

  4. You said : If Vmax is around 500 GeV there would be no problem , and we do not know what Vmax is , in addition we know from the LHC that it’s about 500 , then where is the problem , is it imaginary one depending on :If Vmax is so big then we got a problem ?but till now it is not too big then what????

  5. Time dilation is a physical reality (naturalness) and it prevents singularity (infinity). If the “rest mass” is a physical reality, then the Cosmological constant Λ is zero, this reduces to the original field equation of general relativity. So the rest mass is unnatural – we need no bizarre cancellation ?

  6. The plant on the edge of the table is unnatural because such a situation would require time to be infinite slow. By the same token singularities are unnatural. A non-existing singularity cannot explode into a Big Bang. A non-existing cosmological constant cannot be a problem.

  7. Diego R. Strassler

    i’m proud of being a strassler good luck mate

  8. Diego R. Strassler

    oh and i’m 14 by the way good work

  9. Before postulating a random infinite eternal metaverse we must face a conundrum of the highest degree :
    In such kind of existence we must at least propose some thing to generate different laws ,constants , principles and rules for each random part of that extension , but random generation of these in eternal multiverse will render every region path thru G = zero , h= zero , C = zero and every other constant will path in a state of zero ……
    Conclusion :
    ALL regions of the eternal multiverse NOW are cold , dead , lifeless void.

  10. In addition , do you realize that in such a random infinite eternal thing many adjacent regions will be in a state of collapse simultaneously , so what will be existing in the (nothingness) among them ? Is this science ?

  11. What are the generators of random regional boundaries ? What happens if some adjacent regions are exploding simultaneously ?

    Yes kimmo run away fast , facts are near.

  12. Then upon reflecting we find that from all infinite universe types only the one with eternal , unchanging generator of laws ,constants…etc that generates an eternal infinite static steady state universe is the viable one , BUT , …a very huge one ,….. It is mathematically proved that in such a universe no way to avoid entropy increase to the degree of total randomness, UNLESS , again a very big one , directed ,controlled , specified external input is provided…………case closed.

    • If it is so within unnaturalness, … “Various ways have been developed to describe the “semantics” of automation languages conceptually, building on mathematical logic” – then, no way to avoid entropy increase to the degree of total randomness. UNLESS , again a very big one intervene, there will be catastrophe (naturalness) ?

  13. aa.sh you somehow jump to the conclusion that there is only one other answer …. I can think of at least two other choices on the same data. You are living in a simulation and there was a plethora of the ones (historically many believed that) and it would give you the same results as your preferred answer. We should be scientific about such matters.


    From Science to God, challenges science’s assumption that the material world is the primary reality. Rather than trying to account for consciousness in terms of the material world, it proposes that consciousness is as fundamental as space, time, and matter -perhaps even more so.
    The roots of this alternative worldview go back two hundred years to Immanuel Kant, who drew a clear distinction between the things in-itself and our experience of it. We think we see the world out there, but all we ever observe is the image created in the mind.
    In Physics, space and time have been demoted from their absolute status. They are, showed Einstein, relative to an observer’s point of view. In their place we find the absoluteness of light. For a photon traveling at the speed of light, as all photons do, time and space disappear. In some strange way, light seems to lie beyond both space and time – and, since it has no mass, beyond matter too.

    Mathematical logic is an addiction like hallucination – creating a perfect axiomatic world – create an aversion towards semantic reality (unNaturalness). It is having its own autonomous aim (entropy) called naturalness !

    If the “semantics” of automation languages conceptually, built on mathematical logic” (UnNaturalness) – then, no way to avoid entropy increase to the degree of total randomness. UNLESS , again a very big one intervene, there will be catastrophe (naturalness) ?

  15. To T. L,OM : If the solution to UN or H are not in the realm of imagination -YET – it would not be problems anymore ……..please think deeper OM.

  16. Hmmm. Intuitively, finely-tuned interaction strengths are what you would expect to see in the vacuum state of a QFT where the couplings between the fields are themselves quantum fields, or perhaps some other sort of quantum observable. Put another way, if the couplings are free to change in a way that minimizes the zero-point energy, you’d expect them to wind up finely-tuned.

    On the other hand, if I understand what you’ve said about the difference between the cosmological constant problem and the naturalness problem correctly, it isn’t immediately obvious that minimizing the zero-point energy would explain the naturalness problem, but it could be worth a try. I’m guessing this is an approach that has already been looked into, or is there an obvious problem that rules it out?