Weak realism, counterfactuals, and decay of geometry at small scales

Abstract

Two typical entanglements will be shown to stand on opposite sides on the issue of \emph{instrumental realism}, the issue of whether (as for EPR in the original form or EPRB, Bohm's versions using spin) or not (as for GHZ) observables have values that preexist measurement. Instrumental realism in the EPR context helps us prove that in some special circumstances, one can get simultaneous knowledge of two conjugate quantities, which in particular make sense together. This shatters the axiomatic presentation of Quantum Mechanics. This simultaneous knowledge of two conjugate quantities elaborates on 1935 work by Schr{ö}dinger, hence the name, \emph{Schr{ö}dinger Unorthodoxy Theorem}, given to the second main result that is easily deduced from the result on instrumental realism. Once the axiomatic edifice of Quantum Mechanics is broken, we can let go the completeness of the wave function as suggested in EPR, and hold fast on locality. The EPR paper of mid-1935 gets here contrasted, from a new point of view, with a 1936 text where Einstein avoids using counterfactuals. Counterfactuals get a precise definition and the corresponding concept is used all along, but may be new under an old name. We provide a short critical review of Bell's 1964 paper. Then, a small modification of arguments for the Schr{ö}dinger Unorthodoxy Theorem will let appear a simple conservation law, combined with the Malus Law, as the origin of the correlation in Bell's version of EPRB: this is our third main result. As the fourth main result, a last use of the concept of counterfactual yields the decay of geometry at small enough scale. This opens a new world of interpretation of aspects of Quantum Mechanics, aspects that range from measurement and the need of classical physics to views on what realism should mean in microphysics.