‘Alien calculus’ could save particle physics from infinities

Fyi, this is from the french. "Alien" is a bad translation. The better word is "stranger". Alien just sounds more scifi, akin to how "alien hand syndrome" is the more scifi translation of le mans etrangers, which is best translated as "stranger's hand".

https://www.webmd.com/brain/what-is-alien-hand-syndrome

Typically in physics we derive laws from principles. For example, the law of conservation of momentum is derived from the principle of translation invariance.

Nobody calls the Standard Model a law, for example. The modern view is that the Standard Model is a low-energy effective field theory.

But, whatever supplants the SM, we still expect the principle of translation invariance to hold.

Until, that is, we have evidence for a paradigm shift. If we discover physics that really can't be described, for example, by dynamics happening in a geometric space, then we'll have to give up that principle. Strongly-coupled stringy dynamics seems to have non-geometric phases, for example.

So our statement of laws is more a description of the current best paradigm (say, the operating system), rather than our best model (the program).

Yes, but you very quickly run out of steam.

Moreover, we know the perturbative series does not converge for many theories.

For QED, for example, the radius of convergence must be 0, by an argument due to Dyson. Roughly:

1. The perturbative series is an analytic function of the fine structure constant α, which is proportional to the electron charge squared.

2. Like charges repel and therefore α>0. If like charges attracted the vacuum would be unstable against the continuous creation of electron-positron pairs from the vacuum and the electrons going to one part of the universe and the positrons to the other.

3. Because of this instability the series converges for no α0 either.

> 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.

Or perhaps better "foreigner", legal alien, someone from over the border.

The alien derivative is an operation which moves you from one sector to another. A bit like crossing a branch cut.