I prefer Mulder and Scully to Bob and Alice when discussing quantum X-Files. :-)
Terry On Mon, Nov 24, 2008 at 12:32 PM, Horace Heffner <[EMAIL PROTECTED]> wrote: > On Nov 24, 2008, at 5:12 AM, Harry Veeder wrote: > >> >>> Quantum untanglement: Is spookiness under threat? >>> >>> >>> * 02 November 2007 >>> * NewScientist.com news service >>> >>> Recent experiments have gone further and tried to establish which >>> of >>> the two ideas has to go: locality or realism. They concluded that >>> we >>> have to abandon the idea of an objective reality (New Scientist, 23 >>> >>> June, p 30). All of this rests on the fundamental assumption that >>> Bell's original argument was sound, and most physicists have >>> accepted >>> his conclusions for 40 years. But if Christian is right, they've >>> been >>> overlooking an alternative all this time. >>> >>> Bell assumed the hidden variables in his argument would be familiar >>> >>> numbers, akin to the value of a velocity or a mass. Such numbers >>> obey >>> the ordinary rules of algebra, including a law that says that the >>> order of multiplication doesn't matter - so that, for example, 2 × >>> 5 >>> equals 5 × 2. This property of multiplication is called >>> commutation. >>> The idea that hidden variables are commuting numbers might seem so >>> basic as to be beyond question, but Christian argues it is >>> important >>> to question this point because mathematicians know that different >>> kinds of variables needn't obey commutative algebra. Take rotations >>> >>> in space, for example. They differ fundamentally from ordinary >>> numbers in one important respect: the order of rotations matters >>> (see >>> Diagram). Rotations do not commute. > > [snip] > > Questioning Bell's theorem, which uses the commutative property to > demonstrate non-locality for results at *every* angle of polarization and > relative orientation of the receiver, is not sufficient to disprove > non-locality. The following proof of non-locality, "EPR and Bell > Revisited", October 2004, is much simpler than Bell's in that the > orientations of Bob's receiver are either identical to Alice's, or fully > orthogonal: > > http://www.mtaonline.net/~hheffner/BellEPR.pdf > > In other words commutation under rotation is not an issue in the proof I > provided in this article. It is merely the *empirical* experimental result > that, regardless of primary orthogonal axes chosen, if Bob and ALice chose > the same axis, the results match 100%, and if they chose orthogonal axes, > the probability of same spin observation is 50%. Beyond this, the analysis > deals only with probabilites, which are ordinary real numbers. > > If *any* experiment demonstrates non-locality, then the universe is > non-local. It is not necessary that Bell's proof be valid for the universe > to be non-local. > > Best regards, > > Horace Heffner > http://www.mtaonline.net/~hheffner/ > > > > >
