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
) [Source] w'
) ->- D'
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
) onto the axis of detector-orientation a
be created in a state such that
= 0; say
, zero total angular momentum. That is:
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:
(4) = - <(a.s
(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
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