Scott: What I really want is one coherent theory that accounts for how information about a physical system may be extracted given the physical laws that govern it. Then we can concentrate on the non-information parts of physics (maybe such as the electron mass, etc.); I guess because I’m a physicist primarily, I want to be able to cleanly say “this is necessary because of maths and logical thinking” and so get to the “real” physics. A man can dream, can’t he? :p

]]>From the abstract: *… It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.*

Compare your paper—especially its general outlook—with Entropic Dynamics (gr-qc/0109068), and the more recent gr-qc/0508108, plus other papers by the same author on quantum theory, statistical mechanics, and Bayesian inference.

]]>I hopped over here from the general abstract nonsense cafe, and really (complexly?) enjoyed this lecture on the origin of quantum mechanics. If you’re up for a light read on how to get quantum mechanics from information theory and complex probabilities, I wrote up this simple minded paper on it a few months ago:

http://arxiv.org/abs/physics/0605068

It exactly parallels the derivation of the probability distribution of a canonical ensemble, with a twist.

Best,

Garrett

Bill’s comment was helpful too.

]]>Looking ahead to Scott’s next post, you might justly have criticized our engineering group for having a faith-based belief that science and technology can be deployed in service of “freedom, security, education, and enterprise ” (per the syllabus).

You might justly have asked, what guarantees can you offer that quantum science and technology will not be deployed in service of “oppression, terror, mind-control, and hegemony”?

Our QSE Group has an answer to this, but it’s a highly imperfect answer. Namely, we have deliberately embraced open models of research, system engineering, and equity, in order to expose ourselves us to the Madisonian checks and balances of public scrutiny, a free-market economy, and democratic elections.

These checks and balances admittedly can be only a partial remedy to faith-based belief in our own rationality and morality. ðŸ™‚

]]>Physicist Albert Optimist is trying to calculate Cosh[x] (in Mathematica notation). Upon discovering an integral expressions for Cosh[x], and evaluating it by the method of stationary phase, he obtains the leading expression Cosh[x] ∼Exp[x]/2, and he verifies that his expression is highly accurate for x = 3/2 Pi, having a relative error of only 0.00008.

Hugely pleased, Albert publishes a paper asserting, by analytic continuation, that Cosh[I 3/2 Pi]∼-I/2 to high accuracy. The correct answer is, of course, zero.

Where did Albert go wrong in his analytic continuation?

]]>(Layperson: “You mean he *thought* he had a proof, but he *didn’t*?”

Mathematician: “Dude.”)

No doubt there are simpler proofs than Wiles found, but were there a *dramatically* simpler proof, it would’ve been found already.

*… The final, correct proof uses the standard constructions of modern algebraic geometry, which involve the category of schemes.*

*Because Wiles’s proof relies mainly on techniques developed in the twentieth century, most mathematicians agree that Wiles’s proof is not the same as Fermat’s proof. Some mathematicians believe that Fermat did not actually prove the theorem or that his proof was flawed like other early attempts. However, there are other mathematicians who believe that Fermat really did prove the theorem with seventeenth-century techniques. Although Andrew Wiles has already proved that the theorem is true, some mathematicians who believe that Fermat did prove the theorem continue to search for an elementary proof.*

(Actually, I thought hardly anybody believed Fermat actually had a proof, but never mind…)

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