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.
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.