How Renormalization Saved Particle Physics | Hacker News Reader

How Renormalization Saved Particle Physics

quantamagazine.org

57 pointstheafh17 comments

The concept underlying renormalization/invariance as we now understand it, is a fundamental and profoundly beautiful idea about the very nature of what it means to make a model for a phenomenon. Essentially:

A theory is nothing but a way to turn (a finite number of) measurements into predictions.

The number of degrees of freedom in some putative model might be infinite, but all/most of them will be common between the observed context and the prediction context; it’s only the difference between those two that matters. And renormalization theory provides certain bookkeeping tools to track & ensure that, which then makes tractable the task of predicting.

> A theory is nothing but a way to turn (a finite number of) measurements into predictions.

That's a very nice way of putting it. Is there a particular book, lecture, or other resource you could recommend for this interpretation of theorizing?

I'd also love a recommendation here!

That particular statement is something I made up once I finally understood what was going on; I’ve not seen any references which explain it quite that way. If there are any specific leading questions, I might try to unwrap that intuition here; otherwise it’s a little difficult and I’ll need to think harder to cook up a nice motivating example :-)

That said, Simon Dedeo has a relatively accessible set of online lectures which explain the concepts behind renormalization and broader connections to ideas in computing and other fields, without needing as much heavy machinery as a typical theoretical physics treatment. I haven’t watched it, but in general I appreciate his pedagogy, so here’s the playlist: https://www.youtube.com/playlist?list=PLF0b3ThojznTzAA7bfLWh...

Renormalization is a beautiful hack, but it is a hack.

Let's take infinity, subtract other infinitites add a bit of alchemy and here is our prediction. <- from mathematical perspective this is a very sketchy business.

But it works. And it works in other fields. For example in the theory of phase transitions (I have PhD on the topic :))

And it is pretty common in Physics to work with sketchy constructions for decades before mathematicians catch up.

I love the example of "Generalized Functions" (examples are Delta function and Step Function) that were widely in Physics decades before a consistent mathematical theory was developed.

I hope, at some point we will have a similar story with Renormalization theory.

Well, that's how this was discovered, as a clever hack that worked. In the 1940s.

But it was subsequently understood much better, in the 70s. There are no infinities involved in thinking about renormalisation group flow.

That progress seems like exactly the story the article is trying to tell.

It's indeed not so different from the story of calculus. You don't even need Dirac, the very basic idea of calculus is a hack for dividing zero by zero without getting confused, which later got nicely cleaned up to became respectable mathematics.

Hey, I think we’ve had a good understanding of renormalization group for at least a couple of decades! It might have been considered a hack before that, but I think by now we appreciate exactly what role it plays, and how to exploit it to the best of our abilities (Eg: effective field theories). See my other top-level comment for an interpretation.

Btw, what was your thesis on? :-) PS: My thesis also touched on some of these ideas, but from the hep-th side.

Following the links in the article, it seems it's about:

https://ncatlab.org/nlab/show/Schwinger-Tomonaga-Feynman-Dys...

leading to:

https://ncatlab.org/nlab/show/perturbative+algebraic+quantum...

The first link is indeed relevant, but the second is emphatically not what physicists talk about when they talk about QFT. (It is generally true that nLab usually lacks perspective, to put it mildly, and the corresponding Wikipedia articles are likely more information.)

For a description of the differences, I suggest this paper (link is to a preprint version): http://philsci-archive.pitt.edu/8890/1/critique_sep10.pdf. The author also gave a talk on it which was recorded and put on YouTube.

> the second is emphatically not what physicists talk about when they talk about QFT

Thanks many times. It looked weird to me too, but I've thought "well, some fringe theoretical physicists -- metaphysics topics".

"Quantum" attracts everything.

> renormalization’s hostility to microscopic details works against the efforts of modern physicists who are hungry for signs of the next realm down

No, it doesn't. It simply says "your tools are good down to about here; beyond this point, you must use different tools." That's all.

Ken Wilson wrote a beautiful popular article on the renormalization group for SciAm in 1979.

https://websites.pmc.ucsc.edu/~wrs/Project/2014-summer%20sem...

So, the need for the renormalization group could be seen as Nature's answer to reductionism. Emergent phenomena can (and perhaps should) be treated independently.

@dang: Could we get a title change to "How Renormalization Saved Particle Physics"?

It's interesting, you can see in the URL that at some point the article was named "How Renormalization Saved Particle Physics". My guess is that an editor changed it to make it more comprehensible / clickbaity.

I found it less click-baity and more a sly reference to the perception of the theory by its contemporaries (particularly Feynman in his QED book):

"…is technically called ‘renormalization.’ But no matter how clever the word, it is what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory [...][...] is self-consistent. It’s surprising that the theory still hasn’t been proved self-consistent one way or the other by now; [...][...] What is certain is that we do not have a good mathematical way to describe the theory of quantum electrodynamics: such a bunch of words…" - Feynman, QED 1985

kudos to /u/acqq for the links in their comment.

Sure.

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