How a "Hidden" Constant of the Motion Can Explain Einstein's "Spooky Action at a Distance"
See how a
Common Cause, Constant of the Motion, and Spherical Symmetry are needed to produce the
perfectly correlated (and random) outcomes of two-particle Bell experiments.
Abstract
Whether a calcium cascade or a spontaneous parametric down-conversion, the spins of two entangled particles are projected into a singlet state whose wave function is spherically symmetric with total spin zero. As the particles travel to the distant measurement devices the total spin zero is conserved in the absence of environmental interactions and is a constant of the motion. As long as the two measurement devices are set at the (pre-agreed upon) same angle, they will have planar symmetry. Their measurement angle can then be arbitrary and the interactions will still produce perfectly correlated results. The argument by Bohm1 and Mermin2 that particles spins would need to be defined in all three x, y, z directions (which of course is impossible) is not correct. The requirement is that there be no preferred direction at entanglement and a single arbitrary direction chosen for the two measurements.
1. Bohm, D. and Y. Aharonov, Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky, Physical Review vol.108, no.4, Nov.15, 1957
2. D. Mermin,
Preface
Albert Einstein in 1905 had concerns that lasted for decades about what he thought were
instantaneous interactions or "influences" between quantum particles that he thought had been long "
separated." In 1947 he called it "spooky action at a distance." Such events are today called "
nonlocal" or "
entangled."
Today hundreds of experiments with two entangled particles confirm that measurements made at arbitrarily large separations show the two particles' properties are
perfectly correlated, even though the individual particle properties are found to be
random, an unusual combination of
determined and
indeterministic.
Widely separated events, happening
simultaneously in a frame of reference including the entanglement preparation at the center between the particles, can give the
false appearance of one event influencing the other at speeds much greater than the velocity of light.
Despite Einstein's great physical insight, and despite his deep understanding of conservation principles and mathematical and geometrical symmetries,
he may have introduced a false asymmetry into a symmetric situation.
In the 1935
Einstein-Podolsky-Rosen paper, the properties measured were momentum and position, which are
continuous variables. Since
David Bohm in 1952, the entangled properties studied are spin angular momentum, which have
discrete values much easier to measure.
Bohm proposed "hidden variables" might be found traveling along "
locally" with the particles to explain their perfect correlations. No working physical model for such hidden variables has been proposed.
Entanglement experiments are usually described with two widely separated experiments at points A and B with experimenters, Alice and Bob, typically located symmetrically about the center C where two particles become entangled.
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