Constraints on Determinism: Bell Versus Conway–Kochen

Foundations of Physics, 2015

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell's theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell's theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wavefunctions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold.

Physical Review Letters, 2015

Hidden-variable models aim to reproduce the results of quantum theory and satisfy our classical intuition. Their refutation is based on deriving predictions that are different from those of quantum mechanics. Here instead we study the mutual consistency of apparently reasonable classical assumptions. We introduce a version of the delayed-choice experiment which combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity (an assertion that quantum systems at any moment are either particles or waves, but not both). These three ideas are incompatible with any theory, not only quantum mechanics.

Quantum Reports

In a sequence of papers, Marian Kupczynski has argued that Bell’s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi’s concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell–CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski’s claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell–CHSH inequality is violated, so, despite any other possible imperfections of such experime...

The Bell-Kochen-Specker conditions (BKS) for a deterministic noncontextual hiddenvariable model are wonderfully simple to state, deal with just one-dimensional projectors on a Hilbert space H and make no reference to a probabilistic phase space or quantum system. They only ask for an assignment of zero or one to every projector such that the assignment respects orthogonal resolutions of the identity. Various nogo results in the literature show that the pair of statements {BKS is valid; dim H ≥ 3} are inconsistent. Here we show, more radically, that the pair actually contradicts the dimensionality of the space itself, by implying that there can exist at most a single onedimensional projector acting on H. Our derivation involves only elementary inner product spaces. It is non-probabilistic, inequality-free, state independent, does not use entanglement, and is simultaneously valid in all dimensions three or greater. of the BKS conditions, that is, in exploring different kinds of deterministic models, or indeed, exploration of contextual models or suitable hybrids.

Theoria, 2024

Bell's inequality is an empirical constraint on theories with hidden variables, which Einstein, Podolsky and Rosen argued are needed to explain observed perfect correlations if keeping locality. One way to deal with the empirical violation of Bell's inequality is by openly embracing nonlocality, in a theory like the pilot-wave theory. Nonetheless, recent proposals have revived the possibility that one can avoid nonlocality by resorting to superdeterministic theories. These are local hidden variables theories which violate statistical independence which is one assumption of Bell's inequality. In this paper I compare and contrast these two hidden variable strategies: the pilot-wave theory and superdeterminism. I show that even if the former is nonlocal and the other is not, both are contextual. Nonetheless, in contrast with the pilot-wave theory, superdeterminist contextuality makes it impossible to test the theory (which therefore becomes unfalsifiable and unconfirmable) and renders the theory uninformative (measurement results tell us nothing about the system). It is questionable therefore whether a theory with these features is worth its costs.

The context dependence of Bell local hidden variable theory is reconsidered both in its mathematical and physical justification. The compatibility of the context dependence of individual measurement results with the context independence of the statistics of measurement results is shown to warrant the consistency of the Bell framework with respect to the Gleason no-hidden-vari ables theorem. Finally, a sharp distinction between context dependence and (any form of) nonlocal dependence is defended on the background of some recent algebraic proofs of nonlocality.

Knowledge and Values, ed. Adam Świeżyński, Wyd. UKSW, Warszawa 2011, pp. 73–94., 2011

The paper revisits the old controversy over causality and determinism and argues, in the first place, that non˗deterministic theories of modern science are largely irrelevant to the philosophical issue of the causality principle. As it seems to be the ‘moral’ of the uncertainty principle, the reason why a deterministic theory cannot be applied to the description of certain physical systems is that it is impossible to capture such properties of the system, which are required by a desired theory. These properties constitute what is called ‘the state’ of a system. However, the notion of a state of a system is relative: it depends on a particular theory which one would like to use to describe given kinds of phenomena. This implies that, even in the case where the desired state of a system is fundamentally impossible to be captured, neither ontological nor epistemological determinism may be excluded. Some following critical considerations are also offered with regard to the claim that uncertainty is “rooted in the things themselves”. The cradle of modern discussions about causality and determinism is, of course, quantum mechanics. Because, as it appears, a judgment on deterministic or non˗deterministic character of a theory can be made only after some interpretation of this theory has been given, the paper briefly reminds some chosen interpretations of quantum mechanics (Schrödinger's, probabilistic, statistical, Copenhagen, and the interpretation of quantum ensembles). Many of such interpretations, offered in the past, have now been rejected, and some gained more credibility than the others. Nonetheless, even the claim that indeterminism is irremovable from the description of the micro-world doesn't imply the rejection of the most general formula of the philosophical causality principle. There is no direct implication between theses of the epistemology of scientific knowledge and those of the ontology of the real world.

Springer Proceedings in Mathematics & Statistics

This paper aims to motivate Bell's notion of local causality by means of Bayesian networks. In a locally causal theory any superluminal correlation should be screened off by atomic events localized in any so-called shielder-off region in the past of one of the correlating events. In a Bayesian network any correlation between non-descendant random variables are screened off by any so-called d-separating set of variables. We will argue that the shielder-off regions in the definition of local causality conform in a well defined sense to the d-separating sets in Bayesian networks.

2021

The paper is concentrated on the special changes of the conception of causalityfrom quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by the conservation of quantum information and in accordance with Born’s interpretation; (3) it introduces inverse causality, “backwards in time”, observable “forwards in time” as the fundamentally random probability density distribution of all possible measurements of any physical quantity in quantum mechanics; (4) it involves a kind of “bidirectional causality” unifying (4.1) the classical determinism of cause and effect, (4.2) the probabilistic causality of quantum me...

arXiv (Cornell University), 2012

Although the concept of an observing device with memory is very simple and definable in terms of algorithmic machine, it is not compatible with a predictive theory involving this concept. This is sufficient to show that Physics as a whole cannot be deterministic; moreover, using the Conway-Kochen Free Will Theorem [1] and the simple logical proof of it we gave in [2], we show, without any need of free will or observer's freedom, that Quantum Mechanics are neither deterministic and that no extension of the theory, e.g. by hidden variables, can be deterministic. [1] J.Conway and S.Kochen, The Strong Free Will Theorem, AMS, vol 56/2, p.226-232, Providence, February 2009. [2] I.Reznikoff, A Logical Proof of the Free Will Theorem, arXiv: 1008.3661v1 [quant-ph] 21 Aug 2010 (http://arxiv.org/abs/1008.3661) The results solve a long-standing open problem in Physics and particularly in Quantum Mechanics, and therefore should be of large interest to the scientific community. The paper is in the spirit of the Congress in Mathematical Modelling in Physics in so far that we consider Physics as a deductive theory (in the logical meaning). Moreover, the mechanistic notion of a machine with memory introduces a presumably very fruitful new notion in Physics.