3 ms·
I haven't yet read the actual papers linked to be article, but I'm confused what the big breakthrough is here, the article is very light on specifics. The gene
by jeffwass 12y ago
I haven't yet read the actual papers linked to be article, but I'm confused what the big breakthrough is here, the article is very light on specifics.
The generalized uncertainty principle is nothing but an application of the 'Schwartz Inequality' to two non-commuting operators. Specifically, if the commutator [A,B] = iC for operators A and B (C can be an operator or scalar, i is sqrt(-1) to preserve Hermitian-ness), then the product of uncertainties Delta A x Delta B >= <C>/2. Where Delta A = sqrt(<A^2> - <A>^2) and <A> is the expectation value of A for a given wave function, and [A,B] = AB - BA.
The wave function itself is the fundamental driver behind the wave-particle duality. And the generalized uncertainty principle just follows downstream from mathematical application. I don't see why the article (not the papers though) is saying they're two unrelated things.
FYI, this brings back annoying memories from one of my midterm exams in grad level quantum mechanics. Five questions to solve in one hour. And one question alone was to derive the generalized uncertainty relation from first principles.
- HCIdivision17 12y agoOk, cool. That explains nicely the feeling I was getting. (And your note reminds me of some of the QM and modern physics tests I had as well - I didn't take grad work, but I still remember thinking, "Man, we spent hours deriving some of the stuff, and I've got... less than 10 minutes. Whelp...")