The Platonic solids and fundamental tests of quantum mechanics | Hacker News Reader

The Platonic solids and fundamental tests of quantum mechanics

quantum-journal.org

43 pointsmathgenius9 comments

Whole article rendered beyond the summary (this link is from the page in the OP):

https://www.arxiv-vanity.com/papers/2001.00188/

Thank you for introducing me to arxiv-vanity. I've always hated reading PDFs of papers on my phone.

> I've always hated reading PDFs of papers on my phone.

I've always hated reading PDFs of papers on a desktop PC as well. It's a horrible format for reading on-screen generally. No automatic text-flow or fit screen by default, fonts are usually too small, too much margin white space etc etc

I agree to that as well. When I'm at my PC/laptop, I usually have my iPad at my side, which with the pencil, is ideal for pdf reading and annotation, so I have less complaints there. If I'm travelling or in bed, the phone is often easier.

But yeah, we really need to move on from formats designed for print. HTML/CSS needs more typesetting options and native math support though for that to be feasible, unfortunately. There's no math typesetting conventions for responsive design yet.

> No automatic text-flow or fit screen by default

Aside: While it's a hack, and only useful if you've a supported e-reader, I've found Koreader does decent reflowings of LaTeX-rendered pdfs these days.

Bell's inequality was used to prove incompatibility between local and hidden variable theories. What's the point of fancier Bell's inequalities?

From the abstract, among other things:

[We] find a Bell inequality that is more robust to noise than the celebrated Clauser-Horne-Shimony-Holt Bell inequality. Finally, we elaborate on the tension between mathematical beauty, which was our initial motivation, and experimental friendliness, which is necessary in all empirical sciences

I can think of several answers:

- Their violation may be more practical to verify experimentally

- They may be less prone to various loopholes

- They may be more beautiful

- They may elucidate something deeper about the structure of quantum mechanics

I don't get it, is there something special about Platonic solids in this context, or can you construct Bell inequalities that are maximally violated along any set of vertices? Randomly gluing two things together isn't "beautiful mathematics," beautiful mathematics is when you discover a connection.

I don't know the physics well enough, but having skimmed the paper it looks like it has something to do with crystallographic point groups[1]. The point sets are invariant under some of these groups, and that symmetry can help you do some calculations. They also seem to make some use of dualities of the solids, which correspond to polyhedra with the same point group. It might have been more interesting to consider all of the point groups, but, again, I don't understand the physics to know why they did what they did.

[1] https://en.wikipedia.org/wiki/Crystallographic_point_group

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