An elementary introduction to the geometry of quantum states with a picture book | Hacker News Reader

An elementary introduction to the geometry of quantum states with a picture book

arxiv.org

57 pointsblopeur9 comments

Maybe I clicked the wrong link but I would hardly call that PDF a picture book

As with “elementary” you have to see this in the broader context of Quantum Mechanics, a truly weird and Byzantine theoretical architecture. Anything that isn’t pages of bra-ket notation with occasional words “naturally follows from...” is elementary. Anything that isn’t just a load of linear algebra, but includes the odd diagram is a “picture book.”

Quantum Mechanics, it’s amazing, but it’s hard to wade into.

Are there opportunities for improving its representational design?

It’s possible to do this subsets of stuff, but rewriting QM in a better way is at least as difficult as rewriting the linear algebra of hermitian operators in a way that is easily palatable.

While QM is somewhat of a new development, linear algebra has been around for nearly 150+ years in its roughly modern form (and far longer in less general forms, since around the classical Islamic empire). It is possible we now have better abstractions, but this is also generally unclear.

No. The stuff that exists works well enough, and isn't anywhere near as complicated as what it represents so it's not worth changing it

The equations next to the diagrams, it will take a million years for me to understand them.

If you start now - and you get hooked - give it a year or two and you'll be there

Why do mathematicians and physicist use the words “elementary” and “introduction” for advanced textbooks in the field? Is it to flex intellectual powress?

“Elementary” doesn’t mean “what you learned in elementary school,” although it is publically perceived as such.

Almost universally, in almost every text I’ve read, it means “use tools that are well-known to people with an undergraduate degree in a related field, or simple extensions thereof.” (There are some cheeky counter-examples, such as Weil’s Basic Number Theory, but this is far more rare.)

In the same way you cannot expect someone who has never seen a circuit or understand logic gates to construct a processor, you cannot expect someone without any mathematical maturity (e.g. basic linear algebra and calculus) to use QM in any fashion other than understand the most basic of constructions.

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