Probing the Meaning of Quantum Mechanics

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• CONTENTS

Kolmogorov’s axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another context. As the respective probabilities need not (but, depending on the physical/model realization, can) be of the Born rule type, this generalizes approaches to quantum probabilities by Aufféves and Grangier, which in turn are inspired by Gleason’s theorem.

In the last five years of his life Itamar Pitowsky developed the idea that the formal structure of quantum theory should be thought of as a Bayesian probability theory adapted to the empirical situation that Nature’s events just so happen to conform to a non-Boolean algebra. QBism too takes a Bayesian stance on the probabilities of quantum theory, but its probabilities are the personal degrees of belief a sufficiently-schooled agent holds for the consequences of her actions on the external world. Thus QBism has two levels of the personal where the Pitowskyan view has one. The differences go further. Most important for the technical side of both views is the quantum mechanical Born Rule, but in the Pitowskyan development it is a theorem, not a postulate, arising in the way of Gleason from the primary empirical assumption of a non-Boolean algebra. QBism on the other hand strives to develop a way to think of the Born Rule in a pre-algebraic setting, so that it itself may be taken as the primary empirical statement of the theory. In other words, the hope in QBism is that, suitably understood, the Born Rule is quantum theory’s most fundamental postulate, with the Hilbert space formalism (along with its perceived connection to a non-Boolean event structure) arising only secondarily. This paper will avail of Pitowsky’s program, along with its extensions in the work of Jeffrey Bub and William Demopoulos, to better explicate QBism’s aims and goals.

It is suggested that the “B” in QBism rightfully stands for Bohr. The paper begins by explaining why Bohr seems obscure to most physicists. Having identified the contextuality of physical quantities as Bohr’s essential contribution to Kant’s theory of science, it outlines the latter, its own contextuality (human experience), and its decontextualization. In order to preserve the decontextualization achieved by Kant’s theory, Bohr seized on quantum phenomena as the principal referents of atomic physics, all the while keeping the universal context of human experience at the center of his philosophy. QBism, through its emphasis on the individual experiencing subject, brings home the intersubjective constitution of objectivity more forcefully than Bohr ever did. If measurements are irreversible and outcomes definite, it is because the experiences of each subject are irreversible and definite. Bohr’s insights, on the other hand, are exceedingly useful in clarifying the QBist position, attenuating its excesses, and enhancing its internal consistency.

Werner Heisenberg, Erwin Schrödinger and Wolfgang Pauli exhibited in their works a strong and insistent interest in Greek philosophy. And this interest — they claimed — was not at all separated from their investigations into the new quantum theory. Heisenberg directly affirmed that “one could hardly make progress in modern atomic physics without a knowledge of Greek natural philosophy”. What does this claim mean? Why do these central figures in the development of quantum mechanics saw the Greeks as their main inspiring source? Why do they took them as a model for contemporary science, even over their modern predecessors of Enlightenment? This work attempts to answer these questions focusing on three main reasons: the revision of atomism, the recasting of the meaning of “understanding” in physics, and the critique of separations in science.

The scientific realist wants to read the metaphysical picture of reality through our best fundamental physical theories. The traditional way of doing so is in terms of objects, properties, and laws of nature. For instance, there are families of fundamental particles individuated by their properties of mass and charge, which determine how they move. One could call this view an object-oriented metaphysics grounded on properties. In this paper, I wish to present an alternative view that one can dub a thin object-oriented metaphysics grounded on structure: there are fundamental entities with no fundamental properties other than the one(s) needed to specify their nature. I argue that my view has several advantages over the received one. In particular, I compare my proposal to the traditional view in the quantum domain and I argue that my view provides a better fit for both approaches to quantum metaphysics, namely the primitive ontology program and wave-function realism.

Whether quanta exist or not is a complex question that engages with a variety of issues in the realism/anti-realism debate and concerning the interpretation of quantum mechanics, ranging from the kinds of commitments and requirements needed to determine the existence of quantum particles to the sorts of empirical and instrumental control of the relevant phenomena. In this paper, I argue that one need not settle the issue of the existence of quanta to determine their objectivity, that is, to settle whether they are what they are independently of what one takes them to be. The objectivity of quanta is a separate issue from those concerning their existence and metaphysical specification of the kind of thing quanta are. Along the way, I discuss the similarities and differences between mathematical objectivity and the objectivity of quanta, and consider the role that the framework in which quanta are formulated plays in addressing the issue of their objectivity. In the end, the objectivity of quanta and their existence are importantly different. One can hold on to the former while being agnostic about the latter.

For the last hundred years, philosophers and physicists alike have been obsessed with the quest of comprehending the mysteries of quantum mechanics. I’ll argue that those who still pursue an understanding of quantum riddles are burdened with a classical view of reality and fail to truly embrace the fundamental quantum aspects of nature.

It is well known that correlations produced by common causes in the past cannot violate Bell’s inequalities. This was emphasized by Bell in his celebrated example of Bertlmann’s socks. However, if common causes are induced by the very measurement process i.e., actualized at each run of a joint measurement, in a way that depends on the type of joint measurement that is being executed (hence, the common causes are contextually actualized), the resulting correlations are able to violate Bell’s inequalities, thus providing a simple and general explanation for the origin of quantum correlations. We illustrate this mechanism by revisiting Bertlmann’s socks example. In doing so, we also emphasize that Bell’s inequalities, in their essence, are about demarcating ‘non-induced by measurements’ (non-contextual) from ‘induced by measurements’ (contextual) common causes, where the latter would operate at a non-spatial level of our physical reality, when the jointly measured entangled entities are microscopic in nature.

The view exists that Bell-tests would only be about local incompatibility of quantum observables and that quantum non-locality would be an unnecessary concept in physics. In this note, we emphasize that it is not incompatibility at the local level that is important for the violation of Bell-CHSH inequality, but incompatibility at the non-local level of the joint measurements. Hence, non-locality remains a necessary concept to properly interpret the outcomes of certain joint quantum measurements.

The ontological meaning of the wave function is an important problem in the metaphysics of quantum mechanics. The conventional view is wave function realism, according to which the wave function represents a real physical field in a fundamental high-dimensional space. In this chapter, I present a new analysis of the meaning of the wave function, and the analysis suggests a particle ontological interpretation of the wave function. According to this interpretation, the wave function of a quantum system describes the state of random discontinuous motion of particles in three-dimensional space, and in particular, the modulus squared of the wave function gives the probability density that the particles appear in every possible group of positions in space. Moreover, I argue that the difference between particle ontology and field ontology may result in different predictions under certain reasonable assumption, and it is the former, not the latter, that is consistent with the predictions of quantum mechanics. Finally, I discuss similar pictures of motion of particles suggested by others. It is argued that Bell’s Everett (?) theory also implies the picture of random discontinuous motion of particles.

This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section 2 presents the traditional discussion of metaphysical underdetermination regarding the individuality and non-individuality of quantum particles. Section 3 discusses three reactions to it found in the literature: eliminativism about individuality; conservatism about individuality; eliminativism about objects. Section 4 wraps it all up with metametaphysical considerations regarding the epistemology of metaphysics of science.

In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of Quantum Mechanics (QM). We attempt to show why this is not an “obvious” nor “self evident” problem for the theory of quanta but a direct consequence of the empirical-positivist understanding of physical theories in terms of (binary) observations when applied to the orthodox linear formalism of QM. In contraposition, we discuss a representational realist account of both physical ‘theories’ and ‘measurement’ which goes back to the works of Einstein, Heisenberg and Pauli. After presenting a critical analysis of Bohr’s definitions of ‘measurement’ we continue to discuss the way in which several contemporary approaches to QM — such as decoherence, modal interpretations and QBism — remain — still today — committed to Bohr’s general methodology. Finally, in order to expose the inconsistencies present within the (empirical-positivist) presuppositions responsible for creating the quantum measurement problem we show how following these same set of presuppositions it is easy to derive a completely analogous paradox for the case of classical mechanics.

I outline Bell’s vision of the “great enterprise” of science, and his view that conventional teachings about quantum mechanics constituted a betrayal of this enterprise. I describe a proposal of his to put the theory on a more satisfactory footing, and review the subsequent uses that have been made of one element of this proposal, namely Bell’s transition probabilities regarded as fundamental physical processes.