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/
