The principle of locality: Effectiveness, fate, and challenges

Abstract

The Special Theory of Relativity and Quantum

Quantum Spacetime and Algebraic Quantum Field Theory

“…But even if it were, the formalism would still miss an essential ingredient to be significant: a clear cut algebraic property which replaces Locality and reduces to it in the limit where the Planck length is neglected. As Locality does in the classical Minkowski case [16], this axiom ought to imply most conceptual features of QFT on Quantum Spacetime, independently of the specific form of the interactions.…”

“…But nonlocal effects should be visible only at Planck scales, and vanish fast for larger separations. If Lorentz invariance can be maintained by interactions, a point quite open at present, then we ought to expect that the analysis of the superselection structure, the notion of Statistics, conjugate sectors, the emergence of a compact group of global gauge symmetries, and even the Spin and Statistics Theorem, all deduced on the basis of the Principle of Locality, ought to remain true [16].…”

Nonlocality, no-signalling, and Bellʼs theorem investigated by Weyl conformal differential geometry

“…It is however worth noting that a also a gauge exists where both quantum and gravitational phenomena share the same origin in the metric only. In this particular gauge, that we can call the "Riemann gauge" the geometry is pure Riemann and is entirely governed by the metric tensor 4 . In the Riemann gauge, we have ρ = const., the Weyl vector vanishes and the Weyl curvature reduces to the Riemann curvature built from the the metricḡ ij given byḡ ij = |Ψ(q)| 4 n−2 g ij .…”

“…The connections (4) are invariant under the Weyl conformal gauge transformations [10] g ij → λg ij (7)…”

“…Since the 1935 publication of the famous paper by Einstein -Podolsky -Rosen (EPR), the awkward coexistence within the quantum lexicon of the contradictory terms "locality" and "nonlocality" as primary attributes to quantum mechanics (QM) has been a cause of concern and confusion within the debate over the foundations of this central branch of modern Science [1][2][3][4]. On the other hand, the confirmation by today innumerable experiments, following the first one by Alain Aspect and coworkers, of the paradoxical violation of the Bell inequalities emphasizes the dramatic content of the dispute [5][6][7].…”