Quantum Physics For Everybody 145
fiziko writes in with a self-described "blatant self-promotion" of a worthwhile service for those wishing to go beyond Khan Academy physics: namely Bureau 42's Summer School. "As those who subscribe to the 'Sci-Fi News' slashbox may know, Bureau 42 has launched its first Summer School. This year we're doing a nine-part series (every Monday in July and August) taking readers from high school physics to graduate level physics, with no particular mathematical background required. Follow the link for part 1."
Re:So far, I'm not impressed (Score:4, Informative)
With the exception of gravity, of course
Re:No mathematical background? (Score:2, Informative)
A Hilbert space is a complete vector space with a scalar (dot) product. The "complete" just means that any infinite sequence of items such that the distance between two successive ones goes to zero has a limit (the set of rational numbers is NOT complete). A trivial example is normal Euclidian 3D space.
You don't need to explain anything about functions in order to explain Hilbert space, because any Euclidian space is a Hilbert space. When you do know about functions, you just show that any linear differential equation generates a Hilbert space with functions as it's points, and you can show that it is infinite dimensional if you need to. You just have to realize that there is a difference between configuration space ('where', commonly denoted as x, y, z) and wave-function space ('state', commonly denoted as psi or phi in quantum mechanics). The integration is performed in configuration space, and that's always finite-dimensional; the solutions to Schrodinger's equation are vectors in wave-function space, and you can write them as infinite sums.
There will always be problems when you actually have to go through the quantitative stuff. Each generation learns things in a certain order, using certain conventions. And, the fields being so vast, it's very easy to make it hard for the students in some areas, while making it easy in other areas.
Re:No mathematical background? (Score:4, Informative)
It's hit the concepts dealt with at the graduate level, but I left the math out to make those concepts accessible to people who don't have the heavy mathematical background. I'm half way through writing next year's summer school (linear algebra, full mathematical glory, ending with tensors), and the 2012 curriculum will be Einstein's Relativity and have two parts to each lesson. The first part will be all conceptual, like this, and the second part will have all of the math. 2013 will be real analysis, 2014 assessment theory, and years beyond that haven't been pinned down. The "Bureau 42 teaches" link at the side has everything along these lines listed, with links if they've already been posted.
Re:So far, I'm not impressed (Score:1, Informative)
In GR, gravity is not a force.
Re:No mathematical background? (Score:5, Informative)
Actually, I was working on the ATLAS detector that is in place at the LHC when I started writing for Bureau 42 almost 10 years ago. And I don't know how we profit off of something that's free...
My philosophy (which is in lesson nine, and probably should have come sooner; lesson one is more focused on why we need quantum mechanics, and the rest develops over time) is that the concepts and ideas of physics are represented by the math, but not defined by them. Math can certainly point out directions to look at and avenues to explore, and indicate connections between ideas we hadn't previously noticed, but as a student, I always found that the worst possible reason for a physics phenomenon was "because the math says so." This is about getting those ideas across for people who want to learn about the ideas. The ideas covered in the last two lessons are not typically introduced before grad school. (Lesson one starts at the high school level, which is all I wanted to assume from my audience.) Will you be a researcher when you're done? No. Will you have a better understanding of popular science articles relating to quantum physics? I certainly hope so.
Re:No mathematical background? (Score:3, Informative)
Okay, I can see that point. I admit the language used was imprecise; I was trying to balance between describing what I was doing and keeping it short enough to work as a Slashdot snippet. Perhaps I leaned too far one way. The source article specifies "graduate level physics concepts" instead of just "graduate level physics." This was a submission issue, rather than a source material issue.