[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.

[_yb2s]

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.

[devnullbrain]

As a rule, I think physics should be expected to make less sense the further it gets from the human scale. It's not because it's inherently more complex, it's because we benefit from millions of years of brains evolving to understand what we can see and touch.

[openrisk]

The universe does not owe us explainability in terms of everyday intuition.

You don't just "find some math that fits the data" the way you would mechanically tune the parameters of a given mathematical model to fit empirical data.

Indeed finding a mathematical formulation that seems to describe a corner of reality with any fidelity is such an extraordinary thing that physicists have always puzzled about why it is even possible!

Now it turns out that these mathematical inventions "work" even when our intuition (built on experiences around human scale) cannot quite grasp them. This is the case both in the realms of the very small (quantum) and very big (relativity).

This doesnt mean that at some point we might not find deeper mathematical abstractions that "work better" (e.g., this was the string theory ambition) but the practical result would still be every bit "shut up and calculate".

[l33tman]

This is far from the truth in particle physics. The symmetries we've found there (together with the Lorentz symmetry from special relativity) guides and constrains the math very strongly, to the degree that it allows you to predict the photon and the other force-carrying particles, and it even allowed predicting the existence and mass of the weak force carriers (discussed in the article) along with the Higgs mechanism that gives masses to them and most of the other particles. This is certainly a triumph of the Standard Model.

There are limits to how much you can do though, I mean at some point it's going to be "just math that fits reality". If you try to enumerate the number of mechanisms and realities that could give a decent enough diversity of composition that life can arise in some form, there's going to be more than our universe possible.

[bsder]

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

Well, you build "intuition" via "experience"--generally lots of experience to get small amounts of intuition.

> 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"

Well, the math needs to fit the data and have predictive power. That "predictive" side is really important and is what sets "science" apart from everything else.

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

Sure. But wouldn't the world be incredibly boring if we had it all figured out?

[cellular]

In my gravity simulations, on my YouTube, i found the short weak force distance was the same needed to avoid opposite charges from gaining so much speed that the next iteration's position wouldn't slow the electron down after passing the proton!

Imagine my surprise!!

We might live in a simulation!

[pas]

care to link to your YT videos?

[monadINtop]

I think its more than "we just found some math that fits the data" in the sense that its not just a case of adding some terms to match an observed curve - for example like with Rayleigh-Jeans' law vs Wein's Approximation of blackbody radiation and eventually Max Planck's solution by quantizing energy to the curve match experiment, without actually having anything else to say about it.

Spiritually it feels more like what happened later, when people took the idea of quantized energy seriously and began finding ways to make it a theoretically consistent theory which also required a radical new approach of disregarding old intuitive assumptions about the way the most fundamental things worked solely to obey a new abstract, esoteric, purely theoretical framework (an approach which was sometimes controversial especially with experimentalists).

But of course this new theory of quantum mechanics turned out to be immensely successful in totally unprecedented ways, in a manner similar to Relativity and it's "theory first" origin with trying to ensure mathematical consistency of Maxwell's equations and disregarding anything else in the way (and eventually with Einstein's decade long quest to find a totally covariant general theory that folded gravity into the mix).

With physics the more I dug into "why" it was rarely the case that it was "just because", the justification was nearly always some abstract piece of math that I wasn't equipped to understand at the time but was richly rewarded later on when I spent the time studying in order to finally appreciate it.

The first time I solved Schrodinger Equation for a hydrogen atom, I couldn't see why anyone could've bothered to try discovering how to untangle such a mess of a differential equation with a thousand stubborn terms and strange substitutions (ylm??) and spherical coordinate transformations - all for a solution I had zero intuition or interest in. After I had a better grasp of the duality between those square integrable complex functions and abstract vector spaces I found classical QM elegant in an way I wasn't able to see before. When basic Lie theory and representations was drilled into my head and I had answered a hundred questions about different matrix representations of the SU(n) and S0(3) groups and their algebras and how they were related, it finally clicked how naturally those ylm angular momentum things I saw before actually arose. It was spooky how group theory had manifested in something as ubiquitous and tangible as the structure of the periodic table. After drudging through the derivation of QFT for the first time, when I finally understood what was meant by "all particles and fields that exist are nothing more than representations of the Poincare-Spacetime Algebra", I felt like Neo when everything turned into strings of code. And there's no point describing what it was like when Einstein's field equations clicked, before then I never really got what people meant by the beauty of mathematics or physics.

I guess its not really the answer "why" things are, but the way our current theories basically constrain nearly everything we see (at least from the bottom up) from a handful of axioms and cherry-picked coupling constants, the rest warped into shape and set in stone only by the self-consistency of mathematics, I feel like that's more of a "why" than I would've ever assumed answerable, and maybe more of one than I deserve.

[_yb2s]

I only got as far as "solved Schrodinger equation for a hydrogen atom" and never got to the next stage you describe with physics.

In a sense, I think your explanation is consistent with mine, but with the deeper context of math being a language itself, and the math itself being a more satisfactory explanation to someone with a greater intuition for what the equations actually mean. I can pump through all of the major equations in physics and explain almost anything I want with them, but it always just feels like rote application of algebra rules to completely arbitrary seeming formulas- nothing like what you describe. Frankly, I think I was more interested in girls than studying when I was a physics student decades ago, and I could probably get a lot more out of it revisiting this stuff now.

However, I do still think there is a real chance that we are missing something big that would fit all of these pieces together with qualitative explanations. Personally, I think Julian Barbour is likely on the right path with his timeless physics, but if so it will need a lot more research and development.