wm

This is a preliminary draft from wm, for critical comment, please. It responds to various requests for a classical derivation of the EPR-Bohm correlations which would nullify Bell's theorem. It's off the top of my head; and a more complex denouement might be required (and can be provided) to satisfy mathematical rigour:

(Figure 1) D(a) -<- w(s) [Source] w'(s') ->- D'(b')


Two objects fly-apart [w with property s (a unit-vector); w' with property s' (a unit-vector)] to respectively interact with detectors D (oriented a, an arbitrary unit vector) and D' (oriented b', an arbitrary unit vector). The detectors D (D') respectively project s (s') onto the axis of detector-orientation a (b').

Let w and w' be created in a state such that

(1) s + s' = 0; say, zero total angular momentum. That is:

(2) s' = -s.

Then the left-hand result is a.s and the right-hand result is s'.b'; each a dot-product.

To derive the related correlation, we require (using a recognised notation http://en.wikipedia.org/wiki/Column_vector ), with < ... > denoting an average:

(3) <(a.s) (s'.b')>

(4) = - <(a.s) (s.b')>

(5) = - <[(ax ay az) (sx, sy, sz)] [(sx sy sz) (bx', by', bz')]>

(6) = - (ax ay az) <(sx, sy, sz) (sx sy sz)> (bx', by', bz')

(7) = - (ax ay az) <s.s> (bx', by', bz')

(8) = - (ax ay az) <1> (bx', by', bz')

(9) = - a.b'

(10) = - cos (a, b').

Let s and s' be classical angular-momenta. Then (to the extent that we meet all the Bell-theorem criteria) the result is a wholly classical refutation of Bell's theorem. [It is Bell's constrained realism that we reject; thereby maintaining the common-sense locality clearly evident above.)

E and OE! QED?

Critical comments most welcome, (though I'll be away for a day or so),wm