[extropy-chat] Cramer on Afshar

Damien Broderick thespike at satx.rr.com
Wed Nov 17 18:59:44 UTC 2004


You probably know about this, Serafino (and it's all mysterious wizardry to 
me), but I repost it from `a student' on sci.physics.research:

============

On the logical derivation side, there has recently been a cool 'exact
uncertainty' way of getting from the classical equations of motion to
the quantum equations, just by adding momentum fluctuations.  This
method (by Hall and Reginatto) doesn't assume wavefunctions, complex
numbers, operators, etc. - they all come out in the wash (see
<http://xxx.lanl.gov/abs/quant-ph/0102069>http://xxx.lanl.gov/abs/quant-ph/0102069; 
there is a nice review at
<http://xxx.lanl.gov/abs/gr-qc/0408098>http://xxx.lanl.gov/abs/gr-qc/0408098, 
which claims to do quantum
gravity as well, and calls the textbook approach 'black magic'!).  The
basic formalism is a sort of classical field theory (it is all in
terms of two fields P and S, rather than position and momentum).

They start with a probability density P(x,t) for an ensemble, and
assume it satisfies an action principle.  So there is a Lagrangian or
Hamiltonian for P(x,t), and a conjugate field S(x,t).  They derive an
extra term for the classical Lagrangian by assuming fluctuations are
added to the classical momentum, with the strength of the momentum
fluctuations depending only on the position uncertainty (this is what
they mean by 'exact uncertainty').  The equations for P and S then
magically turn out to be the same as the Schrodinger equation, if you
define psi=sqrt{P} exp{i S/hbar} (hbar appears as a constant that sets
the scale of the fluctuations).

Actually, I'm not sure if they do general operator theory, but at
least they get the right statistics for position, momentum and energy
(and Bohm showed that all you really need is position - and a linear
meter interaction - to measure anything).





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