For today’s post, I’ve added a bit more information to the article that I’m gradually writing on “naturalness”. So far, in that article and an accompanying one, I have

- explained what “naturalness” means in this context;
- given you a first glimpse of what people mean when they say “the Standard Model appears unnatural”;
- tried to clarify, in a side article, what quantum fluctuations of quantum fields are, and how these fluctuations contribute lots of energy to ordinary, empty space — creating a naturalness puzzle called the “cosmological constant problem’‘.

And now the next installment of the article on Naturalness and the Standard Model provides additional knowledge that you’ll need, if you want to understand the argument that suggests the Standard Model *(the highly successful equations used to predict the behavior of the known particles and forces)* is an apparently unnatural (i.e., highly atypical) theory.

Specifically, the new section of the article explains how the Higgs field’s average value, and the Higgs particle’s mass, are determined *(as for any similar field)* by how the energy of empty space — to which the above-mentioned quantum fluctuations are a crucial contributor — depends on the Higgs field itself.

Yes, this is a long story — but so central to current “conventional wisdom” about the universe that we’d better go through it carefully. By the next installment, we should be getting to the heart of the matter.

Matt, your invitation for other possibly novel solutions for the “hierarchy problem” invites an idea about why the Higgs field is locked at a relatively small value.

“The solution to the hierarchy problem involves a completely novel mechanism. Easy to say — but got any ideas? Arkani-Hamed gave us two examples of mechanisms which he had studied that he couldn’t make work — but perhaps someone else can do better.”

So here is my half baked idea, not entirely novel, as it is a composite of several older theories jumbled together: Should a large volume in three dimensional space, (make it universal in size to avoid boundary questions) be filled with charge that has the property of mutually repelling all other charge. Generally easier to visualize as point charged particles. Now, although the pressure and volume energy is large the total average field is near zero as long as the point charges are stationary. That is the charge in any direction is balanced by the charge in the opposite direction. However, this would be unstable because the effective shape of stationary point charges is spherical. And point charges in motion relative to all surrounding point charges take on a shape that packs more efficiently than stationary point charges thus reducing the pressure and volume energy. Any change in kinetic energy of the charge elements (increase or decrease) would reduce the packing efficiency and increase the pressure. This kinetic charge structure generates a non zero field. Or you can view it the other way around and say this universal non zero field produces the charge.