Absence of evidence for entanglement in a three-photon Greenberger-Horn-Zeilinger type experiment
Résumé
A famous experiment by Pan et al. (Nature 403, 515 (2000)) on a three-photon Bell state is considered to prove the existence of entanglement without relying on Bell inequalities. We show that the theory this proof is based on contains errors in the calculations that are beyond repair. Indeed, the formalism to describe the internal dynamics of electrons (at rest) and photons in quantum mechanics is based on the representations of the rotation group. For electrons, who have spin 1/2, the representation is SU(2), for photons, who have spin 1 it is SO(2). Rotations are just a subject of elementary Euclidean geometry, which does not contain any physics, let alone "quantum magic". Therefore all quantum paradoxes that oppose classical mechanics and QM (when it is purely based on the algebra of SU(2)), can only be due to logical errors and a lack of understanding of the group representation theory. The three-photon Bell state is extended but not non-local and as such does not imply a "spooky action at a distance". (This version supersedes the previous version which contained an error).
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