Why the weak nuclear force is short range

Doesn't this "explanation" just shift the question to what is stiffness? Like it refactored the question but didn't actually explain it.

Previously, we had statement "the weak force is short range". In order to explain it, we had to invent a new concept "stiffness" that is treated as a primitive and not explained in terms of other easy primitives, and then we get to "accurately" say that the weak force is short due to stiffness.

I grant the OP that stiffness might be hard to explain, but then why not just say "the weak force is short range -- and just take that as an axiom for now".

What makes me skeptical here is that the author claims that fields have a property that is necessary to explain this, and yet physicists have not given that property a name, so he has to invent one (“stiffness”). If the quantity appears in equations, I find it hard to believe that it was never given a name. Can anyone in the field of physics elucidate?

There is an interesting video essay by the Huygens Optics channel where some simulations of these field effects are considered.

Turning Waves Into Particles https://www.youtube.com/watch?v=tMP5Pbx8I4s

And if unfamiliar, that channel constantly delivers high quality thought provoking content on the nature of light.

>NOTICE THERE IS NO QUANTUM PHYSICS IN THIS DISCUSSION! The short range of the field is a “classical” effect; i.e., it can be understood without any knowledge of the underlying role of quantum physics in our universe. It arises straightforwardly from ordinary field concepts and an ordinary differential equation. Nothing uncertain about it.

It's interesting to me how fuzzy the definition of quantum physics is. For example, I've seen the description of particles as described by a wave function (e.g. electron position and momentum in an atom) labeled as a quantum phenomenon, but have also heard it, as in this quote, as classical, since it's defined by a differential equation; a "classical" wave. In that view, quantum only enters the model when modelling exchange effects, spin, fermion states etc.

With the former definition, as in the article, you see descriptions of the wave nature of matter, replete with Planck's constant, complex wave function representations etc described as classical.

If we wanted to model the universe as a set of equations or a cellular automaton, how complex would that program be?

Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?

I guess I'm trying to figure out the complexity of the task of universe creation, assuming the necessary computational power exists. For example, could it be a computer science high school project for the folks in the parent universe (simulation hypothesis). I know that's a tough question :)

Urgh, I'm half way through this and I hate it.

The problem is it's upfront that "X thing you learned is wrong" but is then freely introducing a lot of new ideas without grounding why they should be accepted - i.e. from sitting here knowing a little physics, what's the intuition which gets us to field "stiffness"? Stiff fields limit range, okay, but...why do we think those exist?

The article just ends the explanation section and jumps to the maths, but fails to give any indication at all as to why field stiffness is a sensible idea to accept? Where does it come from? Why are non-stiff fields just travelling around a "c", except that we observe "c" to be the speed of light that they travel around?

When we teach people about quantum mechanics and the uncertainty principle even at a pop-sci level, we do do it by pointing to the actual experiments which build the base of evidence, and the logical conflicts which necessitate deeper theory (i.e. you can take that idea, and build a predictive model which works and here's where they did that experiment).

This just...gives no sense at all as to what this stiffness parameter actually is, why it turned up, or why there's what feels like a very coincidental overlap with the Uncertainty principle (i.e. is that intuition wrong because actually the math doesn't work out, is this just a different way of looking at it and there's no absolute source of truth or origin, what's happening?)

It seems to me that there is a 1:1 correlation between mass of virtual particle and field stiffness. Given that fact, why isn't it equally correct to say "The field stiffness is caused by the mass of the virtual particle" and "The virtual particle necessarily has mas because the field is stiff"

The author states that "it is short range because the particles that “mediate” the force, the W and Z bosons, have mass;" is misleading as to causality, but I missed the part where they showed how/why it was misleading.

How I learned it, as a mere undergrad, was that the mass of the virtual particle for the field in question determined exactly how long it could exist, just by the uncertainty principle -- much like the way the virtual particles drive Hawking radiation.

In short, a massive virtual particle can exist only briefly before The Accountant comes looking to balance the books. And if you give it a speed of c, it can travel only so far during its brief existence before the books get balanced. And therefore the range of the force is determined by the mass of the force carrier virtual particle.

There's probably some secondary and tertiary "loops" as the virtual particle possibly decays during its brief existence, influencing the math a little further, but that is beyond me.

The effect of stiffness can also be represented by stretchability of the string. Picking up a string with a free end will result in the same shape described by adding stiffness. A fanciful analogy might be a chain of springs with constant k2 where each spring junction is anchored to the ground with a spring with constant k1. If k2>>k1 the entire spring chain lifts in a gentle arc when a spring is lifted. If k1>>k2, only the springs near the pulling point really stretch and displace. It’s these kinds of simple analogies that engage our intuition. I still however cannot envision a mechanical analogy to demonstrate wavicles.

The top of fig 3 doesn't accurately represent a string pulled down in the middle. A string pulled down in the middle would have no curve to it in the legs unless some force is acting on it, it would look like a V.

> Only stiff fields can have standing waves in empty space, which in turn are made from “particles” that are stationary and vibrating. And so, the very existence of a “particle” with non-zero mass is a consequence of the field’s stiffness.

It's really difficult to reconcile "standing waves in empty space" with "stiff fields". If the space is truly empty, then the field seems to be an illusion?

If we think about fields as the very old concept of aether, then it actually makes more intuitive sense. Stiffness then becomes simply the viscosity of the aether.

But I don't think this is where this article is trying to get us!!

The real answer is we don't know or otherwise some kind of anthropic argument, i.e. the weak force has the range it does becuase otherwise we wouldn't have this kind of universe with people in it pondering why the weak force is the way it is.

Seems generally unhelpful to say 'the weak force is short range because it's field is stiffer!' When you can then immediately say 'well why is the weak force's field stiffer?'

This article goes to great contortions to avoid talking about electroweak theory or spontaneous symmetry breaking, both of which have decent Wikipedia articles, and are crucial to understanding what's going on here. Spontaneous symmetry breaking of the electroweak interaction and the Higgs mechanism is the reason _why_ the W and Z have mass. The article throws up a "who knows?" at this. When you write down the field equations for a massive boson field, you get an additional m^2 term in the denominator of the propagator, which contributes a e^(-r/m) term to the interaction force at low energy, such as the decay of a neutron or a weak-mediated nuclear decay.

Is there an ELI5 version of this? I think the article tries, and it's always cool to see physics described from a different vantage point.

My ELI5 version would be: fields with a massive gauge boson are "dragged down" in energy by the mass of the boson, so interactions propagate as if they have negative energy. What does a negative energy wave propagation look like? Similar negative energy wave propagations in physics are evanescent waves and electron tunneling, both of which have exponential drop-off terms, so it makes sense to see an exponential factor in massive boson interactions.

This is a lot of words to say that the field oscillations (i.e., particles) require very high energy. This shows up as the mass-(energy) of the particle, or stiffness of the field; take your pick.

Whether you call that stiffness or mass is a little beside the point IMO -- it shows up in the Yukawa force as an exponential dependence on that parameter which means the force quickly decays to zero unless the parameter is 0.

The reason is because of the anthropic principle. If it wasn't short range, we probably wouldn't exist and there would be no consciousness to observe it.

Stiffness just seems to be rewriting mass as a different term. Only things with mass have stiffness, stiffness is exactly proportional to mass, light isn’t stiff…

This particular article has a prelude on the same website

https://profmattstrassler.com/2025/01/10/no-the-short-range-...

One thing that confused me at the very beginning is, the author says the weak force is weak because it is short range. But the strong force is also short range.

> Google’s AI, for instance, and also here — that the virtual particles with mass actually “decay“

Do virtual particles decay?

"For the subtleties of different meanings of “mass”, see chapters 5-8 of my book.]"

Isn't this called "equivocation" in logic?

TLDR; It is short range primarily because the underlying fields (those of the W and Z bosons) are “stiff,” causing any disturbance to die off exponentially at distances much smaller than an atom’s diameter. In quantum language, that same stiffness manifests as the nonzero masses of the W and Z bosons, so their corresponding force does not effectively propagate over long distances—hence it appears “weak” and short-range.

"In a quantum world such as ours, the field’s waves are made from indivisible tiny waves, which for historical reasons we call “particles.” Despite their name, these objects aren’t little dots; see Fig. 8."

Does anyone know when physicists realized that the world is not made of indivisible units called "particles" but waves? Is there a specific experiment or are we talking about the results of many experiments?

As an aside, is there conclusive evidence to say that no aether exists, or are we just saying it doesn't exist because a handful of tests were conducted to match what we thought this aether would behave like and the tests came back negative?

PSA: it's "fib," not "phib"