It is a widespread belief that the Kochen-Specker theorem imposes a contextuality constraint on the ontology of beables in quantum hidden variables theories. On the other hand, after Bell’s influential critique, the importance of von Neumann’s wrongly called ‘impossibility proof’ has been severely questioned. However, Max Jammer, Jeffrey Bub and Dennis Dieks have proposed insightful reassessments of von Neumann’s theorem: what it really shows is that hidden variables theories cannot represent their beables by means of Hermitian operators in Hilbert space. (...) Hereby I show that i) the very same constraint can be derived from Gleason’s theorem, and that ii) if we consider the import of von Neumann’s and Gleason’s theorems, the relevance of the Kochen-Specker theorem for hidden variables theories gets substantially weakened: it does not force them to be contextual in any interesting sense of the term. (shrink)

The recent discovery of the Higgs at 125 GeV by the ATLAS and CMS experiments at the LHC has put significant pressure on a principle which has guided much theorizing in high energy physics over the last 40 years, the principle of naturalness. In this paper, I provide an explication of the conceptual foundations and physical significance of the naturalness principle. I argue that the naturalness principle is well-grounded both empirically and in the theoretical structure of effective field theories, and (...) that it was reasonable for physicists to endorse it. Its possible failure to be realized in nature, as suggested by recent LHC data, thus represents an empirical challenge to certain foundational aspects of our understanding of QFT. In particular, I argue that its failure would undermine one class of recent proposals which claim that QFT provides us with a picture of the world as being structured into quasi-autonomous physical domains. (shrink)

We prove the existence of hidden variables, or, what we call generalized common causes, for finite sequences of pairwise correlated random variables that do not have a joint probability distribution. The hidden variables constructed have upper probability distributions that are nonmonotonic. The theorem applies directly to quantum mechanical correlations that do not satisfy the Bell inequalities.

We critically analyze the rationale of arguments from finetuning and naturalness in particle physics and cosmology, notably the small values of the mass of the Higgs-boson and the cosmological constant. We identify several new reasons why these arguments are not scientifically relevant. Besides laying out why the necessity to define a probability distribution renders arguments from naturalness internally contradictory, it is also explained why it is conceptually questionable to single out assumptions about dimensionless parameters from among a host of other (...) assumptions. Some other numerological coincidences and their problems are also discussed. (shrink)

One implication of Bell’s theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite (...) collection of probability zero events whose disjunction exhausts the space of experimental possibilities. (shrink)

ZusammenfassungFasst man die Ψ‐Funktion in der Quantenmechanik als eine vollständige Beschreibung eines realen Sachverhaltes auf, so ist die Hypothese einer schwer annehm‐baren Fernwirkung impliziert. Fasst man die Ψ‐Funktion aber als eine unvollständige Beschreibung eines realen Sachverhaltes auf, so ist es schwer zu glauben, dass für eine unvollständige Beschreibung strenge Gesetze für die zeitliche Abhängigkeit gelten.‐ A. E.

We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal (...) state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program. (shrink)

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary (...) dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints. (shrink)