Comment by Timwi

The author isn't inventing anything. He's just dumbing it down in an extreme way so that non-physicists could have the faintest hope of understanding it. Wich seems odd, because if you actually want to understand any of this you should prepare to spend two or three years in university level math classes first. The truth is that in reality all this is actually a lot more complex. In the Higgs field (or any simple scalar field for that matter) for example, there is a free parameter that we could immediately identify as "mass" in the way described in the article. But weirdly enough, this is not the mass of the Higgs boson (because of some complicated shenanigans). Even more counterintuitive, fermionic (aka matter) fields and massive bosonic fields (i.e. the W and Z bosons mentioned in the article) in the Standard Model don't have any mass term by themselves at all. They only get something that looks (and behaves) like a mass term from their coupling to the Higgs field. So it's the "stiffness" of the Higgs field (highly oversimplified) that gives rise to the "stiffness" of the other fields through complex interactions governed by symmetries. And to put it to the extreme, the physical mass you can measaure in a laboratory is something that depends on the energy scale at which you perform your experiments. So even if you did years of math and took an intro to QFT class and finally think you begin to understand all this, Renormalization Group Theory comes in kicks you back down. If you go really deep, you'll run into issues like Landau Poles and Quantum Triviality and the very nature of what perturbation theory can tell us about reality after all. In the end you will be two thirds through grad school by the time you can comfortably discuss any of this. The origin of mass is a really convoluted construct and these low-level discussions of it will always paint a tainted picture. If you want the truth, you can only trust the math.

He addresses this in the comments. The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments.

Roughly put:

- A particle is a "minimum stretching" of a field.

- The "stiffness" corresponds to the energy-per-stretch-amount of the field (analogous to the stiffness of a spring).

- So the particle's mass = (minimum stretch "distance") * stiffness ~ stiffness

The author's point is that you don't need to invoke virtual particles or any quantum weirdness to make this work. All you need is the notion of stiffness, and the mass of the associated particle and the limited range of the force both drop out of the math for the same reasons.

It does have a name, it's called "coupling." A spring (to physicists all linkages are springs :-) ) couples a pair of train cars, and a coupling constant attaches massive fields to the higgs field.

The longer I read the article, the more "stiffness" feels like mass. In Lagrangians, the quantity saying how stiff it is is precisely the mass term, vide https://en.wikipedia.org/wiki/Scalar_field_theory.

At the same time, the author does not give any different definition; he says it's "stiffness". In the comment, he writes:

> The use of a notion of “stiffness” as a way to describe what’s going on is indeed my personal invention. Physicists usually just call the (S^2 phi) part of the equation a “mass term.” But that’s jargon, since this thing doesn’t give mass to the field; it just gives mass to its particles, which exist only in the context of quantum physics. The word “mass term” also doesn’t explain what’s going on physically. My view is that “stiffness” conveys the basic physical sense of what is happening to the field, an effect it has even without accounting for quantum physics.

So well, it is mass. Maybe not mass one may think about (in physics, especially Quantum Field Theory, there are a few notions of mass, which are not the same as what we set on a scale), but I feel the author is overzealous about not calling it "mass (term)".

So, I am not convinced unless the author shows a way to have massive particles carrying a long-term interaction (AFAIK, not possible) or massless particles giving rise to short-term interactions (here, I don't know QFT enough so that it might be possible). But the burden of proof is on the inventor of the new term.

> If the quantity appears in equations, I find it hard to believe that it was never given a name.

It does have a name: mass!

What I'm skeptical of is that this "stiffness" is somehow logically or conceptually prior to mass. Looking at the math, it just is mass. The term in the equation that this author calls the "stiffness" term is usually just called the "mass" term.

I will go one deeper. Are fields (quantum fields) even real, or just a model ?

It's nonsense. The fact that the particle is massive is a direct cause of the fact that the interactions are short ranged.

The nuance is this: Naturally, in a field theory the word "particle" is ill-defined, thus the only true statement one can make is that: the propagator/green function of the field contains poles at +-m, which sort of hints at what he means by stiffness.

As a result of this pole, any perturbations of the field have an exponential decaying effect. But the pole is the mass, by definition.

The real interesting question is why Z and W bosons are massive, which have to do with the higgs mechanism. I.e., prior to symmetry breaking the fields are massless, but by interacting with the Higgs, the vacuum expectation value of the two point function of the field changes, thus granting it a mass.

In sum, whoever wrote this is a bit confused and just doesn't have a lot of exposure to QFT