‘Alien calculus’ could save particle physics from infinities • Hacker News Board

Re: ‘Alien calculus’ could save particle physics from infinities

#11

Post by pa7x1 » Fri, Apr 07, 2023, 9:05 AM UTC

adastra22 wrote: post #5

hilbert42 wrote: post #2

Finding a way around the problem of infinities in perturbative quantum theory/QFT would not only put the science on a more sound mathematical footing but would also greatly benefit it in other ways. It seems to me that with a rigorous mathematical foundation it's likely phenomena will emerge that would never have been obvious without it. We can only hope the 'discovery' of Écalle's work leads us along that path.

Is t the problem of quantum gravity related? Does this being us closer to a grand unified theory?

It's related in the sense that the vanilla attempts to quantize gravity lead to infinities as described in the article. But the nature of these infinities is more troubling in the case of quantum gravity than those found in the rest of the theories that compose the Standard Model. Infinities appear very early in the series expansion of quantized gravity, at second order of the series expansion for the free theory. And the techniques developed by physicists to deal with them ( https://en.wikipedia.org/wiki/Renormalization ) do not work at all.

It's possible that the mathematical techniques being developed here only work for renormalizable theories. In which case they wouldn't work at all for Quantum Gravity. This would likely signal that there is something else missing that is needed to build a quantum theory of gravity.

Re: ‘Alien calculus’ could save particle physics from infinities

#12

Post by axilmar » Fri, Apr 07, 2023, 9:18 AM UTC

Sincere question: could it be that the underlying structure of the universe is really simple but since we have no idea what it is we have to use exotic mathematics for it?

Re: ‘Alien calculus’ could save particle physics from infinities

#13

Post by yuuuuyu » Fri, Apr 07, 2023, 9:23 AM UTC

omeysalvi wrote: post #9

I really appreciate how writers at Quanta turn extremely complex and dry topics into a pleasurable read by mixing simple analogies with history. I really admire the skill it takes to break down these topics and make them fascinating for someone with no understanding of them, such as me.

All soon to be obsoleted by ChatGPT. /s

(I agree with your point and share your appreciation.)

Re: ‘Alien calculus’ could save particle physics from infinities

#14

Post by eximius » Fri, Apr 07, 2023, 9:39 AM UTC

Is the implication that each nonperturbative term represents a specific kind of field interaction? Thus would there be a finite set of nonperturbative terms that, if exhaustively found, would render the trans-series convergent?

Re: ‘Alien calculus’ could save particle physics from infinities

#15

Post by thriftwy » Fri, Apr 07, 2023, 9:48 AM UTC

Using different math approach is super fruitful.

For example, alternating current in presense of capaciators and induction coils is well handled by switching to imaginary (complex) resistance/current/voltage calculation, and transition processes in electric chains are handled by operational calculus.

If we used differential equations to solve these, which indeed look natural for these tasks, we will not be able to accomplish any calculations without a PhD.

Re: ‘Alien calculus’ could save particle physics from infinities

#16

Post by froggychairs » Fri, Apr 07, 2023, 9:52 AM UTC

yuuuuyu wrote: post #13

omeysalvi wrote: post #9

I really appreciate how writers at Quanta turn extremely complex and dry topics into a pleasurable read by mixing simple analogies with history. I really admire the skill it takes to break down these topics and make them fascinating for someone with no understanding of them, such as me.

All soon to be obsoleted by ChatGPT. /s (I agree with your point and share your appreciation.)

Sarcasm aside. Even the output from GPT-4 is quite bland and generic. Very good for performing tasks (I.e convert a blob of text into a knowledge graph or generate X code), but quite awful at the elegant prose we see at play

Wonder how long before that’s solved. Hard to believe training on such large swathes of the web doesn’t result a compressed generic representation of language within its weights.

Re: ‘Alien calculus’ could save particle physics from infinities

#17

Post by simonh » Fri, Apr 07, 2023, 10:03 AM UTC

froggychairs wrote: post #16

yuuuuyu wrote: post #13

Earlier quoted context omitted.

All soon to be obsoleted by ChatGPT. /s (I agree with your point and share your appreciation.)

Sarcasm aside. Even the output from GPT-4 is quite bland and generic. Very good for performing tasks (I.e convert a blob of text into a knowledge graph or generate X code), but quite awful at the elegant prose we see at play Wonder how long before that’s solved. Hard to believe training on such large swathes of the web doesn’t result a compressed generic representation of language within its weights.

It seems like there’s a tension. On the one hand generating the most likely sequence of tokens maximises the chance the response will make sense and be relevant. On the other hand it also guarantees you will get the most bland and unimaginative response.

Re: ‘Alien calculus’ could save particle physics from infinities

#18

Post by simonh » Fri, Apr 07, 2023, 10:10 AM UTC

axilmar wrote: post #12

Sincere question: could it be that the underlying structure of the universe is really simple but since we have no idea what it is we have to use exotic mathematics for it?

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.

Re: ‘Alien calculus’ could save particle physics from infinities

#19

Post by criddell » Fri, Apr 07, 2023, 10:18 AM UTC

axilmar wrote: post #12

Sincere question: could it be that the underlying structure of the universe is really simple but since we have no idea what it is we have to use exotic mathematics for it?

Some think the underlying structure of the universe is mathematics. That is, the universe isn’t merely describe by mathematics, but it is a mathematical structure.

Re: ‘Alien calculus’ could save particle physics from infinities

#20

Post by tourgen » Fri, Apr 07, 2023, 10:24 AM UTC

criddell wrote: post #19

axilmar wrote: post #12

Sincere question: could it be that the underlying structure of the universe is really simple but since we have no idea what it is we have to use exotic mathematics for it?

Some think the underlying structure of the universe is mathematics. That is, the universe isn’t merely describe by mathematics, but it is a mathematical structure.

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