Perhaps an approach trying to actually explain the Feynman propagators would be more helpful? Either way, I agree that if someone wanted to understand this all properly it requires a university education + years of postgrad exposure to the delights of QED / electroweak theory. If anyone here wants a relatively understandable deep dive, my favourite books are Quantum Field Theory for the Gifted Amateur [aka graduate student] by Stephen Blundell [who taught me] and Tom Lancester [his former graduate student], and also Quarks and Leptons by Halzel and Martin. It is not a short road.
> ...causing a growing rift between scientists and the normal population.
True.
Now, to my 'craft' (GRC). I lately catch myself speaking like Peter Thiel, taking 20-30 second 'silences', build in my mind what I want to say, 'translate it' to simple(r) English, and then slowly say it out loud to make sure I pave the path with mental & verbal stepping stones without using any jargon.
I very well understand what I want to say, but the gap between in the knowledge and the use of language puts the onus to the explainer.
Ie: “I can’t explain it in terms of something else you’re more familiar with because I don’t understand it terms of anything else you’re more familiar with.”
How so? It's the standard equation for a scalar (spin zero) field.
EDIT: yes I tried pasting it in to Gemini, 4o, and Claude. Only Claude was able to zero-shot create the latex and an html wrapper that renders it, and open the html preview on iOS. It worked great.
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.
Then why not just call it "mass"? That's what it is. How is the notion of "stiffness" any better than the notion of "mass"? The author never explains this that I can see.
I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking. Mass as a term is particle-centric.
It seems these minimum-stretching could also be thought of as a “wrinkle”. It’s a permanent deformation of the field itself that we give the name to, and thus “instantiate” the particle.
Eye opening.
"Stiffness" to me isn't a field term or a particle term; it's a condensed matter term. In other words, it's a name for a property of substances that is not fundamental; it's emergent from other underlying physics, which for convenience we don't always want to delve into in detail, so we package it all up into an emergent number and call it "stiffness".
On this view, "stiffness" is a worse term than "mass", which does have a fundamental meaning (see below).
> Mass as a term is particle-centric.
Not to a quantum field theorist. :-) "Mass" is a field term in that context; you will see explicit references to "massless fields" and "massive fields" all over the literature.
Mass is a bad term because it's loaded with so many meanings and equivalences already. But also in the kindest and most accurate reading here it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does, which was the whole point of the article.
No, because no physicist tries to argue that "color" is an appropriate term because of some physical interpretation that involves actual physical properties of colored objects.
This author, OTOH, appears to be arguing that "stiffness" is a better term than "mass" because of some physical interpretation that involves actual physical properties of stiff objects. An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors.
> it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does
I'm not sure the explanation of that in terms of "stiffness" is any better, because in the setting where the term "stiffness" comes from, there is no such thing as what this author calls a "floppy" object. So his explanation only "explains" the behavior of forces associated with massive gauge bosons at the price of throwing away an explanation of the behavior of forces associated with massless gauge bosons.
They do, there are 3 and they add up like primary colors, so all 3 make stuff colorless. That's why those names were chosen. Because of similarities with color we know from color theory.
> there is no such thing as what this author calls a "floppy" object
It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope because nothing holds remote parts of the rope in place. The only way for a wrinkle to exist in such rope is to travel at "rope speed". If there's stiffness then a wrinkle can travel at any speed or none at all, because it can oscilate without moving, which is rest energy (mass). So it explains all bosons.
What's great with this analogy is that it coveys that both mass and force range arise from a single term of the equation. There's really no causal connection between them. Neither limited range causes mass nor mass causes limited range. They both come from a single intrinsic field "quality".
There's also no anti-blue color in color theory but it's easy to imagine it so you can intuitively understand its behavior.
Not instantly; the force you apply at one point still has to be transmitted through the rope. And if the rope is unattached and not taut, it won't transmit force well at all, and you have very limited control over how the rest of the rope will move when you pull on one part.
I don't see how any of this is a useful analogy to how massless gauge bosons work in forces like electromagnetism.
That's fine. No analogy works for everybody.
In the unit analysis that is most natural to quantum field theory, it's mass.
For this discussion it makes sense call the "mass" of a field "stiffness" instead, since it's not known a priori that it corresponds to particle mass.
Here the "stiffness" is interpreted as the effect of nearby charges "screening" a perturbing "bare" charge of the opposite sign. If you solve the equation you find the that effective electric field produced by the bare charge is like that of the usual point charge but with a factor exp(-r/λ). So, the effect of the "stiffness" term is reducing the range of the electric interactions to λ, which is called the Debye length. see this illustration [1].
Interestingly, if you look at EM waves propagating in this kind of system, you find some satifying the dispersion relation ω² = k²c² + ω_p² [2]. With the usual interpretation E=ℏω, p=ℏk you get E² = (pc)² + (mc²)², so in a sense the screening is resulting in "photons" gaining a mass.
[1]: https://en.wikipedia.org/wiki/File:Debye_screening.svg
[2]: https://en.wikipedia.org/wiki/Electromagnetic_electron_wave#...
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.
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.
If you are referring to the claim in the article that goes along with the equation E = m c^2, that claim is the author's personal interpretation, which I don't buy. The mass appears in the dispersion relation whether the particle is at rest or not. "Rest mass" is an outdated term for it; a better term is "invariant mass", i.e., it's the invariant associated with the particle's 4-momentum. Or, in field terms, it's the invariant associated with the dispersion relation of the field and the waves it generates.
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
But I don't particularly like the whole "mass vs not mass" discussion as it's pointless
Recognizing correct analogies is not easy and it's insanely powerful educational tool.
Incredible.
https://scholar.google.com/citations?user=19WGkFsAAAAJ&hl=en
be sure to check past the first 20 papers or so, like, oh, say his 1990 paper with Michael Peskin (438 citations), a copy of which can be found at <https://www.slac.stanford.edu/pubs/slacpubs/5250/slac-pub-53...>.