[metacritic12]

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".

[ajkjk]

I think it's a big improvement. Stiffness is something you can picture directly, so the data -> conclusions inference "stiffness" -> "mass and short range" follows directly from the facts you know and your model of what they mean. Whereas "particles have mass" -> "short range" requires someone also telling you how the inference step (the ->) works, and you just memorize this as a fact: "somebody told me that mass implies short range". You can't do anything with that (without unpacking it into the math), and it's much harder to pattern-match to other situations, especially non-physical ones.

It seems to me like the right criteria for a good model is:

* there are as few non-intuitable inferences as possible, so most conclusions can be derived from a small amount of knowledge

* and of course, inferences you make with your intuition should not be wrong

(I suppose any time you approximate a model with a simpler one---such as the underlying math with a series of atomic notions, as in this case---you have done some simplification and now you might make wrong inferences. But a lot of the wrongness can be "controlled" with just a few more atoms. For instance "you can divide two numbers, unless the denominator is zero" is such a control: division is intuitive, but there's one special case, so you memorize the general rule plus the case, and that's still a good foundation for doing inference with)

[BrandoElFollito]

Intuition does not work in quantum mechanics. Intuition is based on observations at your scale, and this breaks dramatically at quantum levels. So this is not a good criterium.

[lilyball]

Besides the fact that stiffness shows up as a term in the equations, stiffness is a concept that can be demonstrated via analogy with a rubber sheet, and so lends itself to a somewhat more intuitive understanding.

Also, the math section demonstrated how stiffness produces both the short-range effect and the massive particles, so instead of just handwaving "massive particles is somehow related to the short range" the stiffness provides a clear answer as to why that's the case.

[drdec]

If you read far enough into the math-y explanations, stiffness is a quantity in the equations. That makes it more than a hand waving explanation in my book.

[exmadscientist]

In addition to what the sibling comments have said, the "axiom" is actually the term in the equations. That is, fundamentally, where this all comes from. "Stiffness" is just a word coined to help describe the behavior that arises from a term like this. Everything flows from having that piece in the math, so if you start there and with nothing else, you can reinvent everything else in the article. (Though it will take you a while.)

You might also ask where that term comes from. It really is "axiomatic": there is no a priori explanation for why anything like that should be in the equations. They just work out if you do that. Finding a good explanation for why things have to be this way and not that way is nothing more and nothing less than the search for the infamous Theory of Everything.

[UniverseHacker]

This is often I think a really unsatisfying thing about physics. Usually the qualitative descriptions don't quite make sense if you think very hard about them- and if you dig deeper it's often just "we found some math that fits our experimental data" - and ultimately that is as much as we know, and most attempts at explaining it conceptually are conjecture at best.

When I was a physics undergrad, most of my professors were fans of the "shut up and calculate" interpretation of quantum mechanics.

Ultimately, this is probably just a symptom of still not having yet discovered some really important stuff.

[scotty79]

'Stiffness' is a better concept because it can be used to explain behavior of all forces of finite and infinite range and why force mediators can have mass or not.

If you need to assume some axiomatic concept it's better to assume one that can used to derive a lot of what is observed.

[cellular]

I don't think electric force is necessarily shorter distance than gravity.

But electric charges cancel out each other over big regions, while gravity never cancels.

[seanhunter]

Not a physicist, but in classical mechanics stiffness is just the proportionality of some restorative force (ie the extent to which something tries to bounce back when you push it). It definitely would be overkill to make it an axiom.

So say you have a spring if you compress it, it pushes because it wants to go back to its natural length and likewise if you stretch it there is a restorative force in the opposite direction. The constant of proportionality of that force (in N/m) is the stiffness of the spring, and the force from the spring[1] is something like F=-k x with x being the position measured from the natural length of the spring and k being the stiffness. So not knowing anything about electromagnetism I read this and thought about fields having a similar property like when you have two magnets and you push like poles towards each other, the magnetic field creates a restorative force pushing them apart and the constant is presumably the stiffness of the field.

But obviously I’m missing a piece somewhere because as you can see the force of a spring is proportional to distance whereas here we’re talking about something which is short-range compared to gravity and gravity falls off with the square of distance so it has to decay more rapidly than that.

Edit to add: in TFA, the author defines stiffness as follows:

   For a field, what I mean by “stiffness” is crudely this: if a field is stiff, then making its value non-zero requires more energy than if the field is not stiff.

So this coincides with the idea of restorative force of something like a spring and is presumably why he's using this word.

[1] Hooke’s law says the force is actually H = k (x-l)ŝ where k is stiffness, l is the natural length of the spring and ŝ is a unit vector that points from the end you’re talking about back towards the centre of the spring.

[neutronicus]

A simple, classical case where "stiff" fields arise is electrostatic plasma physics.

Electrons are tiny and nuclei are huge, so you have a bunch of mobile charge carriers which cost energy to displace to an equilibrium position away from their immobile "homes". A collection of test charges moving "slowly" through the plasma (not inducing B field, electrons have time to reach equilibrium positions) will produce exponentially decaying potentials like in the article. If you want to read more, this concept is called "Debye Screening"

Anyway, this might be a more helpful approach than trying to imagine a spring - a "stiff" field equation is an equation for a field in a medium that polarizes to oppose it, and you can think of space as polarizing to oppose the existence of a Z Boson in a way that it doesn't polarize to oppose the existence of a photon.

[pishpash]

Because you may get something else out of stiffness besides this explanation? Usually that's how a level deeper explanation works.