Reply to Comments of Bassi, Ghirardi, and Tumulka on the Free Will 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.Comment: We sharpen our theorem by replacing axiom FIN by a weaker axiom MIN to answer the above authors' objection

Bell-Type Quantum Field Theories

In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Psi|^2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to "second quantization." As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field.Comment: 53 pages LaTeX, no figure

The "Unromantic Pictures" of Quantum Theory

I am concerned with two views of quantum mechanics that John S. Bell called ``unromantic'': spontaneous wave function collapse and Bohmian mechanics. I discuss some of their merits and report about recent progress concerning extensions to quantum field theory and relativity. In the last section, I speculate about an extension of Bohmian mechanics to quantum gravity.Comment: 37 pages LaTeX, no figures; written for special volume of J. Phys. A in honor of G.C. Ghirard

Reduced coherence in double-slit diffraction of neutrons

In diffraction experiments with particle beams, several effects lead to a fringe visibility reduction of the interference pattern. We theoretically describe the intensity one can measure in a double-slit setup and compare the results with the experimental data obtained with cold neutrons. Our conclusion is that for cold neutrons the fringe visibility reduction is due not to decoherence, but to initial incoherence.Comment: 4 pages LaTeX, 2 figure

Another Proof of Born's Rule on Arbitrary Cauchy Surfaces

In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born's rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $\Sigma$, then the observed particle configuration on $\Sigma$ is a random variable with distribution density $|\Psi_\Sigma|^2$, suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.Wilhelm Schuler-Stiftung Tuebingen, DAAD (Deutscher Akademischer Austauschdienst

Feynman's Path Integrals and Bohm's Particle Paths

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schroedinger's equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation.Comment: 4 pages LaTeX, no figures; v2 shortened a bi

Are All Particles Identical?

We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same particle, just as spin-up and spin-down do. The implications of this viewpoint can be best appreciated within Bohmian mechanics, a precise formulation of quantum mechanics with particle trajectories. The implementation of this viewpoint in such a theory leads to trajectories different from those of the usual formulation, and thus to a version of Bohmian mechanics that is inequivalent to, though arguably empirically indistinguishable from, the usual one. The mathematical core of this viewpoint is however rather independent of the detailed dynamical scheme Bohmian mechanics provides, and it amounts to the assertion that the configuration space for N particles, even N ``distinguishable particles,'' is the set of all N-point subsets of physical 3-space.Comment: 12 pages LaTeX, no figure