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At the moment your comment is the only text containing the string "quantum" -- and in a quotation, at that. Enough with the negatives, let's move on to the imaginaries!

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Sun Mar 23rd, 2008 at 01:33:14 AM EST
[ Parent ]
Actually, you can do a lot of quantum mechanics in an arbitrary Rig (Ring without negatives). And a lot of graph theory and statistical mechanics and is also quantum mechanics in a Rig.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 08:14:53 AM EST
[ Parent ]
Ack. Semirings. Yet another bunch of algebras I didn't know about (as such). Now you've made me curious:
  • "A lot of quantum mechanics" omits what?
  • An "arbitrary rig", not non-negative reals? (Is this all about counting states, not describing them or their transitions?)
  • Do you intend that "a lot of graph theory and statistical mechanics and is also quantum mechanics in a Rig" be read as saying that "a lot of graph theory...is also quantum mechanics"?
  • Are complex numbers uniquely necessary for quantum mechanics, or just a convenience?
  • Why do I keep reading about so many mathematical structures that I can't remotely claim to understand?
  • How can anyone (other than a Republican) still support the Clinton candidacy?
I see that Baez has (of course) touched on some of the earlier questions in this list.

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Sun Mar 23rd, 2008 at 03:12:24 PM EST
[ Parent ]
Well, where do you think I got this stuff from? You think I invented it?
  • "A lot of quantum mechanics" omits squaring the result to get a probability.
  • There are more Rigs that just the nonnegative reals, basically subsets (closed under addition and multiplication) of matrices with nonnegative real entries.
  • No, I intend to say that the mathematical structure of flow in networks, of minimal paths in networks, of statistical mechanics at finite and zero temperature, and quantum mechanics, is that of combinatorics on Rigs.
  • I have no idea whether complex numbers are necessary for quantum mechanics, but given their algebraic completeness once you have characteristic zero you might as well assume your Rig consists of matrices with complex entries. I guess, for convenience.
  • Where do you keep reading about mathematical structures you can't remotely claim to understand?
  • There will always be people who identify with her over the other candidates.
BTW, did you get my e-mail?


It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 03:25:34 PM EST
[ Parent ]
After reading a bit on the web, I assumed that you had invented this stuff at a time when you were incredibly young, but gotten no credit. The sufferings of genius.

  • "'A lot of quantum mechanics' omits squaring the result to get a probability." Fair enough, but with a chemical mindset in this diary, one would miss having wavefunctions and amplitudes. On the other hand, given the vast amount of quantum mechanics, I suppose that omitting lot leaves a lot that is not omitted. Just not the sort of QM that I crunch on this machine.

  • "There are more Rigs than just the nonnegative reals..." Indeed, and some of them are, well, cheesy. (To speak non-technically for a moment.) At the bottom of the barrel, "The simplest example of a semiring which is not a ring is the commutative semiring B formed by the two-element Boolean algebra," and nearby are other lame Rigs mentioned in Wikipedia

  • "Where do you keep reading..."? TWF, of course, for starters!

  • "No, I intend to say..." What you say is, I expect, entirely correct and, in principle, enlightening.

Re. your e-mail: Did you get my response? After the conversation I promised, she suggested considering citizen sector options, and minimizing the gap, on strategic/marketing grounds.

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Tue Mar 25th, 2008 at 02:46:22 AM EST
[ Parent ]
  • You still get "diffusion of states" and "probability densities", just not wave propagation (you need i for that, I think).
  • What can I say, mathematicians tend to use lame examples when asked to make arcane structures concrete. I think matrices or nonnegative reals are a better meta-example, with the advantage of being universal.
  • TWF? I can't be held responsible for that.
  • "You expect" and "in principle"? Ask some questions!
I replied to your e-mail.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Tue Mar 25th, 2008 at 09:32:58 AM EST
[ Parent ]
Technically, you could do away with i entirely in QM and not lose generality. But then you'd be stuck with 4th order differential equations. At least that's what one of our Optics profs claimed. I never checked myself, because you do not want to do 4th order PDEs anyway, unless you're a mathmatician or some (other) kind of masochist.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Mar 25th, 2008 at 02:41:11 PM EST
[ Parent ]
Well, a complex differential equation can always be written as a real differential equation of twice the order.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Wed Mar 26th, 2008 at 03:07:01 AM EST
[ Parent ]

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