No-go theorems for \psi-epistemic models based on a continuity assumption

The quantum state \psi is a mathematical object used to determine the probabilities of different outcomes when measuring a physical system. Its fundamental nature has been the subject of discussions since the inception of quantum theory: is it ontic, that is, does it correspond to a real property of the physical system? Or is it epistemic, that is, does it merely represent our knowledge about the system? Assuming a natural continuity assumption and a weak separability assumption, we show here that epistemic interpretations of the quantum state are in contradiction with quantum theory. Our argument is different from the recent proof of Pusey, Barrett, and Rudolph and it already yields a non-trivial constraint on \psi-epistemic models using a single copy of the system in question.Comment: Version 1 contains both theory and an illustrative experiment. Version 2 contains only the theory (the experiment with expanded discussion will be posted separatly at a later date). The main novelty of Version 2 is a detailed comparison in appendix 2 with L. Hardy arXiv:1205.14396. Version 2 is 6 pages of text and 1 figure; v3: minor change

Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System

Here we review and extend central limit theorems for highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck process results within a totally deterministic framework. These results illustrate that the contamination of experimental data by "noise" may, under certain circumstances, be alternately interpreted as the signature of an underlying chaotic process.Comment: 65 pages, 8 figure

On the fate of Lorentz symmetry in loop quantum gravity and noncommutative spacetimes

I analyze the deformation of Lorentz symmetry that holds in certain noncommutative spacetimes and the way in which Lorentz symmetry is broken in other noncommutative spacetimes. I also observe that discretization of areas does not necessarily require departures from Lorentz symmetry. This is due to the fact that Lorentz symmetry has no implications for exclusive measurement of the area of a surface, but it governs the combined measurements of the area and the velocity of a surface. In a quantum-gravity theory Lorentz symmetry can be consistent with area discretization, but only when the observables ``area of the surface" and "velocity of the surface" enjoy certain special properties. I argue that the status of Lorentz symmetry in the loop-quantum-gravity approach requires careful scrutiny, since areas are discretized within a formalism that, at least presently, does not include an observable "velocity of the surface". In general it may prove to be very difficult to reconcile Lorentz symmetry with area discretization in theories of canonical quantization of gravity, because a proper description of Lorentz symmetry appears to require that the fundamental/primary role be played by the surface's world-sheet, whose "projection" along the space directions of a given observer describes the observable area, whereas the canonical formalism only allows the introduction as primary entities of observables defined at a fixed (common) time, and the observers that can be considered must share that time variable.Comment: 59 pages, LaTe

Optional Stopping with Bayes Factors: a categorization and extension of folklore results, with an application to invariant situations

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings that various authors give to this claim: (1) stopping rule independence, (2) posterior calibration and (3) (semi-) frequentist robustness to optional stopping. We then prove theorems to the effect that these claims do indeed hold in a general measure-theoretic setting. For claims of type (2) and (3), such results are new. By allowing for non-integrable measures based on improper priors, we obtain particularly strong results for the practically important case of models with nuisance parameters satisfying a group invariance (such as location or scale). We also discuss the practical relevance of (1)--(3), and conclude that whether Bayes factor methods actually perform well under optional stopping crucially depends on details of models, priors and the goal of the analysis.Comment: 29 page