[simonh]

That’s quite possible. A lot of what we think of as fundamental physics might turn out to be emergent behaviour.

In fact that’s pretty much the story of the development of physics. It turns out Newtonian mechanics is emergent from Relativity. Maxwells equations are emergent from quantum mechanics. The behaviour of bosons is emergent from the behaviour of quarks.

As I understand it there are theoretical reasons to suspect that quarks do not have any decomposition though. We’ll see.

[gus_massa]

> The behaviour of _bosons_ is emergent from the behaviour of quarks.

I think you mean

> The behaviour of _hadrons_ is emergent from the behaviour of quarks.

--

Anyway, back to your main idea, the problem is that most of the times the new underlaying theory is even worse than the original one

> Newtonian mechanics is emergent from Relativity

For Newtonian Mechanics you need only basic calculus. For General Relativity you need curvature, tensors, two definitions of derivatives and other nasty stuff. [I never saw the details, but it's in my todo list.]

> Maxwells equations are emergent from quantum mechanics

Well, electromagnetism is just the local gauge invariance of the U(1) group. The idea is very simple but each word in that sentence needs like one semester to be decoded. [I saw the calculations a long time ago. I don't remember the details, but I remember the general idea. I wrote a comment with a oversimplified version https://news.ycombinator.com/item?id=8189346 )

> there are theoretical reasons to suspect that quarks do not have any decomposition though.

My favorite reason is that for a classic small ball, the ratio of the magnetic moment to the inertia moment is 1 (once you fix some nasty details about units), but for an elementary quantum particle it is 2. For composite particles, there is no theoretical value. https://en.wikipedia.org/wiki/G-factor_(physics)

The experimental value for protons is 5.5 and for Neutrons is 3.8, that is not surprising because we are sure they are composed particles.

For Electrons and Muons it's slightly more than 2, but we understand that difference quite well (but not perfectly, and that is related to the main point of the article here).

I don't think it has been measured directly for Quarks, but my guess is that it's used in some parts of the calculation of some Feynman diagrams, and if it were very different from 2 someone would have noticed.

[simonh]

Yes Hadrons sorry. Posting in a hurry.

>most of the times the new underlaying theory is even worse than the original one

Oh quite. Macroscopic emergent behaviour is often apparently simpler than the underlying causes and is in some way a generalisation of them.

[gus_massa]

It's strange because from galaxies to protons/neutrons/electrons it looks like the underlying theory is simpler. But if you try to look inside the protons it gets nastier each time you go down in the ladder of theories.

[esperent]

> It turns out Newtonian mechanics is emergent from Relativity.

However relativity is far more complex than Newtonian physics.

[evanb]

The kinds of physical influences that are allowed in Newtonian physics are more general than those allowed in relativity. Relativity requires physics to satisfy constraints.

Which is more complex depends on what you mean. There are fewer laws in the possibility space of generally-relativistic physics than Newtonian physics. So, which metric is more important? Less pleasant calculations or a larger search space?

Your comment suggests you weigh the calculational simplicity more heavily, but most physicists would come down on the other side of the issue.

[esperent]

> most physicists would come down on the other side of the issue.

What's your reason for saying this? I'm more on the mathematical side of things so I don't know that many physicists. But it's been my understanding that equations that are extremely difficult to solve, impossible to solve except numerically, or involve infinities that can't be explained, are a major pain point for physicists. I mean, that's the entire premise of this article.

[evanb]

My reasons are

- I'm a professional physicist and most people I know professionally think this way. People like symmetry, it helps clarify things, simplify things, provides powerful principles. If the cost is practical difficulties, well, that's just the cost of doing business; the physical understanding offered by simpler rules is beneficial. I know at least 2 people mentioned in the article would agree with that.

- I have no conceptual problem saying that the only solutions are numerical in nature if the principles are clear. Nobody promised physics should be easy. In fact some of the people mentioned in the article also have shown how their formal understanding might unlock better numerical methods!

- Some infinities are worse than others, and a modern effective field theory perspective makes me not worry about most examples.* With a Wilsonian understanding, renormalization is perfectly simple to understand. For theories which have perturbative UV fixed points you can formulate a lattice discretization which flows to that fixed point and you never encounter any infinity along the way.

Theories without a perturbative UV fixed point, well, that's where the trouble lies. Either there is no UV fixed point, in which case the theory is not valid for all energy scales and the troubling divergences point to an energy scale beyond which your theory is invalid. Or there IS a UV fixed point but it can only be found nonperturbatively.

Handed a QFT with no perturbative UV fixed point, how should you decide?

Well, one step back: should you, as a physicist, care?

For instance, why should we worry whether QED as a standalone theory is UV-complete? We know that in the real world electrodynamics mixes with the weak force at high energy. So whether QED as a standalone theory is UV-complete is a question that I'm not worried about. It is an interesting mathematical question, and that can only be answered with new techniques, such as resurgence. For standalone QED it's a question of pure mathematics, as far as anyone can tell. That's what these tools are good for, at the moment.

HOWEVER. I do admire the program of trying to show that more quantum field theories even exist mathematically, beyond the handful that we already know (which tend to have exotic properties). That seems important to me. But if it's false that's ALSO extremely interesting, it suggests that there are additional principles that we ought to understand.

* except for gravity, where the divergences are SO bad that even the EFT approach has problems.

[peteradio]

Theoretical physicists are like enterprise architects, there seems to be a preference for generality of prescription over practical experimentation/implementation.

[eternalban]

This could the universe's way of telling us that knowledge requires work, mathematically speaking.

[simonh]

That’s an interesting point, but I don’t think the complexity gradient from underlying causes to macroscopic effects always goes the same way. The macroscopic dynamic effects of an earthquake on a building can be modelled fairly easily. Trying to model the earthquake’s dynamics through the earth at the molecular level is a lost cause though.