arXiv subjects
Publications and source records attributed to Simon Kochen.
We strengthen the Free Will Theorem, which proved the spontaneity of particles, based on the free will of the experimenter. The new result is unconditional, and does not require the experimenter's free will to prove the particles' spontaneity.
Many physicists believe that the EPR experiment exhibits instantaneous non-local effects. I argue below that an application of Born's Rule to EPR shows no such instantaneous effects and that EPR is consistent with full Lorentz invariance. I then discuss how it is possible to understand the EPR correlations for non-commuting spin components without recourse to non-local effects. Finally, I use these results to discuss the Free Will Theorem, which I formulate in a new way.
We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by interactions with other systems. We apply the canonical definitions of the concepts of classical physics of observables, states, combined systems, symmetries, and dynamics to derive the standard quantum characterizations, including the Schr\"odinger equation and the von Neumann-L\"uder's Projection Rule. This manifestly consistent reconstruction of quantum mechanics is then used to discuss and resolve the dilemmas of the orthodox interpretation.
We strengthen "The Free Will Theorem" [1] in several ways, by replacing the axiom FIN by a weaker axiom MIN, and also by allowing the particles' responses to depend on past half-spaces rather than on on past light cones. This change allows us to directly apply our theorem to relativistic theories of the GRW type.
We prove a no-triplets theorem for spin 1 particles, which implies a strengthened form of the no-cloning theorem.
We show that the authors in the title have erred in claiming that our axiom FIN is false by conflating it with Bell locality. We also argue that the predictions of quantum mechanics, and in particular EPR, are fully Lorentz invariant, whereas the Free Will Theorem shows that theories with a mechanism of reduction, such as GRW, cannot be made fully invariant.
We respond to Stephen Adler's comments on our paper "The Free Will Theorem",and add some further observations.
On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.
The Copenhagen Interpretation describes individual systems, using the same Hilbert space formalism as does the statistical ensemble interpretation (SQM). This leads to the well-known paradoxes surrounding the Measurement Problem. We extend this common mathematical structure to encompass certain natural bundles with connections over the Hilbert sphere S. This permits a consistent extension of the statistical interpretation to interacting individual systems, thereby resolving these paradoxes. Suppose V is a physical system in interaction with another system W. The state vector of V+W has a set of polar decompositions with a vector q of complex coefficients. These are parameterized by the right toroid T of amplitudes q, and comprise a singular toroidal bundle over S, which comprises the enlarged state space of V+W. We prove that each T has a unique natural convex partition yielding the correct SQM probabilities. In the extended theory V and W synchronously assume pure spectral states according to which member of the partition contains q. The apparent indeterminism of SQM is thus attributable to the effectively random distribution of initial phases.