Re:An elementary introduction to the geometry of quantum sta...
by Pharmakon on Sunday January 27, 2019 @02:36PM
(#19013365)
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.
Re:An elementary introduction to the geometry of quantum sta...
by LolWolf on Sunday January 27, 2019 @05:14PM
(#19014082)
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.
Re:An elementary introduction to the geometry of quantum sta...
by hackernewsacct on Sunday January 27, 2019 @05:29PM
(#19014141)
Why do mathematicians and physicist use the words “elementary” and “introduction” for advanced textbooks in the field? Is it to flex intellectual powress?
Re:An elementary introduction to the geometry of quantum sta...
by LolWolf on Sunday January 27, 2019 @05:51PM
(#19014253)
“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.
Quantum Mechanics, it’s amazing, but it’s hard to wade into.
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.
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.