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Entanglement --- a higher order symmetry
1  Istituto Universitario Sophia
Academic Editor: Douglas Singleton


On October 4, 2022, the Nobel prize for physics was awarded to Alain Aspect, John Clauser and Anton Zeilinger for their experimental work related to quantum entanglement, a controversial topic dating back to a famous research paper published in 1935 by Einstein, Podolsky and Rosen (EPR). Elementary particles sometimes form entangled pairs. For example, two electrons in a singlet state have equal and opposite spin values if placed in a magnetic field, resulting in a sum of zero angular momentum. Consequently, if we were to model these paired electrons on the computer, we might be tempted to imagine two spheres rotating in opposite directions along a fixed axis analogous to the Earth's daily motion. However, we cannot consider elementary particles in this way since there is no fixed axis and their motion cannot be cloned. The axes change as the direction of the magnetic field change. When the spin of each entangled particle is measured in an arbitrary direction, we discover that they have equal and opposite values but until the experiment is carried out there is no preferred spin axis. In contrast to Einstein’s notion of locality, the work of Aspect, Clauser and Zeilinger motivated by Bell’s inequality suggests that quantum entanglement violates “locality.” Unfortunately, for many authors, “non-locality” has come to mean that there is “action at a distance” and that communication is faster than the speed of light. I would like to offer an alternative approach in which “non-locality” neither means faster than light communication nor does it mean that there are hidden parameters in Einstein’s sense. It will be shown that EPR entangled states constitute a higher order symmetry that are SL(2,C) invariant (and hence Lorentz invariant) and that the Pauli Exclusion Principle is a consequence of this new approach to entanglement.

Keywords: Entanglement, SL(2,C) symmetry, Pauli Exclusion Principle
Comments on this paper
Andras Kovacs
It is very interesting work. Among the various attempts to explain/derive the Pauli exclusion principle, I find this derivation to be the most understandable and mathematically precise.
An interesting, and not widely known aspect of these derivations: the actual particle spin value does not play a role in the Pauli exclusion mechanism.