Author: Matt Strassler

I’m still early on in my attempts to explain the “naturalness problem of the Standard Model” and its implications.  A couple of days ago I explained what particle physicists mean by the term “natural” — it means “typical” or “generic”.  And I described how, at least from one naive point of view, the Standard Model (the equations we use to describe the known elementary particles and forces) is unnatural.  Indeed any theory is unnatural that has a

• a spin-zero particle (in the Standard Model, the newly discovered Higgs particle), which
• is very lightweight in the following sense: it has a very very low mass-energy compared to the energy at which gravity becomes a strong force, and which
• isn’t accompanied (in the Standard Model specifically) by other related particles that also have small masses.

But I didn’t actually explain any of this yet; I just described it.

Specifically, I didn’t start yet to explain what causes the Standard Model to be unnatural.  This is important to do, because, as many attentive readers naturally complained, my statements about the unnatural aspect of the Standard Model was based on a rather arbitrary-sounding statistical argument, and story-telling, which is hardly enough for scientific discussion.  Patience; I’ll get there, not today but probably the next installment after today’s.

To see why the argument I gave is actually legitimate (which doesn’t mean it is right, but if it’s wrong it’s not for a simple reason you’ll think of in five minutes), it is necessary to look in a little bit more detail at one of the most fundamental aspects of quantum field theory: quantum fluctuations, and the energy they carry.  So for today I have written an article about this, reasonably complete.

Be prepared — the article runs headlong into the only naturalness problem in particle physics that is worse than the naturalness problem of the Standard Model (the one I wrote about on Tuesday)!  I am referring to the “cosmological constant problem”.  In a nutshell:

• we can calculate that, in any typical quantum field theory with gravity, the amount of energy in empty space (often called `dark energy’) should be huge, and we know of no way to avoid having it in a typical somewhat-realistic theory of the universe,
• yet measurements of the cosmos — in fact, the very existence of a large and old universe — assure that, if Einstein’s theory of gravity is basically right, then instead of a huge amount of `dark energy’, there’s just a very small amount — not much more than the total amount of mass-energy [E=mc² energy] found in all the matter that’s scattered thinly throughout the universe.

After you’ve read about quantum fluctuations and the cosmological constant problem, and have a bit of a sense as to why it is so hard to make it go away, we can go back to the Standard Model, and try to understand the naturalness problem that is associated with the Higgs particle and field.  It all has to do with another aspect of quantum fluctuations — the fact that their energy depends on, and therefore helps determine, the average value of the Higgs field.