In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of “quantum theory from five reasonable axioms.” Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy's assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his work can be easily reconciled with a Bayesian interpretation of quantum probability.

In QBism the wave function does not represent an element of physical reality external to the agent, but represent an agent’s personal probability assignments, reflecting his subjective degrees of belief about the future content of his experience. In this paper, I argue that this view of the wave function is not consistent with protective measurements. The argument does not rely on the realist assumption of the ψ-ontology theorems, namely the existence of the underlying ontic state of a quantum system.

Particle theories intend to describe the fundamental constituents from which all matter is constructed and the interactions among them. These constituents include atoms and molecules as well as their subatomic constituents, nuclei and their component parts including elementary particles. We consider an alternative to the usual particle theories, but dealing with the same phenomena. We call these theories ‘QT’s’. This is an attempt to provide a formal description of the essential features of elementary particle theories within the framework of metatheoretical (...) structuralism. (shrink)

Recently I posted a paper entitled “External observer reflections on QBism”. As any external observer, I was not able to reflect all features of QBism properly. The comments I received from one of QBism’s creators, C. A. Fuchs, were very valuable to me in better understanding the views of QBists. Some of QBism’s features are very delicate and extracting them from articles of QBists is not a simple task. Therefore, I hope that the second portion of my reflections on QBism (...) might be interesting and useful for other experts in quantum foundations and quantum information theory. In the present paper I correct some of my earlier posted critical comments on QBism. At the same time, other critical comments gained new validation through my recent deeper understanding of QBists views on a number of problems. (shrink)

Quantum mechanics is a theory whose foundations spark controversy to this day. Although many attempts to explain the underpinnings of the theory have been made, none has been unanimously accepted as satisfactory. Fuchs has recently claimed that the foundational issues can be resolved by interpreting quantum mechanics in the light of quantum information. The view proposed is that quantum mechanics should be interpreted along the lines of the subjective Bayesian approach to probability theory. The quantum state is not the physical (...) state of a microscopic object. It is an epistemic state of an observer; it represents subjective degrees of belief about outcomes of measurements. The interpretation gives an elegant solution to the infamous measurement problem: measurement is nothing but Bayesian belief updating in a analogy to belief updating in a classical setting. In this paper, we analyze an argument that Fuchs gives in support of this latter claim. We suggest that the argument is not convincing since it rests on an ad hoc construction. We close with some remarks on the options left for Fuchs' quantum Bayesian project. (shrink)

Meyer, Kent and Clifton (MKC) claim to have nullified the Bell-Kochen-Specker (Bell-KS) theorem. It is true that they invalidate KS's account of the theorem's physical implications. However, they do not invalidate Bell's point, that quantum mechanics is inconsistent with the classical assumption, that a measurement tells us about a property previously possessed by the system. This failure of classical ideas about measurement is, perhaps, the single most important implication of quantum mechanics. In a conventional colouring there are some remaining patches (...) of white. MKC fill in these patches, but only at the price of introducing patches where the colouring becomes ``pathologically'' discontinuous. The discontinuities mean that the colours in these patches are empirically unknowable. We prove a general theorem which shows that their extent is at least as great as the patches of white in a conventional approach. The theorem applies, not only to the MKC colourings, but also to any other such attempt to circumvent the Bell-KS theorem (Pitowsky's colourings, for example). We go on to discuss the implications. MKC do not nullify the Bell-KS theorem. They do, however, show that we did not, hitherto, properly understand the theorem. For that reason their results (and Pitowsky's earlier results) are of major importance. (shrink)

This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and the (...) claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe its manifestation. (shrink)

According to Relational Quantum Mechanics the wave function \ is considered neither a concrete physical item evolving in spacetime, nor an object representing the absolute state of a certain quantum system. In this interpretative framework, \ is defined as a computational device encoding observers’ information; hence, RQM offers a somewhat epistemic view of the wave function. This perspective seems to be at odds with the PBR theorem, a formal result excluding that wave functions represent knowledge of an underlying reality described (...) by some ontic state. In this paper we argue that RQM is not affected by the conclusions of PBR’s argument; consequently, the alleged inconsistency can be dissolved. To do that, we will thoroughly discuss the very foundations of the PBR theorem, i.e. Harrigan and Spekkens’ categorization of ontological models, showing that their implicit assumptions about the nature of the ontic state are incompatible with the main tenets of RQM. Then, we will ask whether it is possible to derive a relational PBR-type result, answering in the negative. This conclusion shows some limitations of this theorem not yet discussed in the literature. (shrink)

A large number of physicists now admit that quantum mechanics is a non-local theory. The EPR argument and the many experiments showing the violation of Bell’s inequalities seem to have confirmed convincingly that quantum mechanics cannot be local. Nevertheless, this conclusion can only be drawn inside a standard realist framework assuming an ontic interpretation of the wave function and viewing the collapse of the wave function as a real change of the physical state of the system. We show that this (...) standpoint is not mandatory and that if the collapse is not considered an actual physical change it is possible to recover locality. (shrink)

What does quantum physics tell us about the nature of reality, specifically the parts of reality we do not directly perceive called hidden variables? One may think it could tell us a lot because of our enhanced technological sensing abilities that delve into the realms that quantum physics covers so well. Surprisingly, it seems to surround us in a deeper mystery rather than reveal more of nature's secrets. It seems that we cannot escape from philosophical consideration when dealing with what (...) is hidden in quantum physics. In Part I we will look at how Epistemology and Ontology bear upon Hidden Variables. In Part II we will consider Hidden Variables in the light of Contextuality, and Non-Classicality. Inevitably questions of subjectivity and objectivity arise in dealing with states of observation. How should we think about these states? Perhaps it is a question of the meaning associated with our knowledge of a state-that is, a question of ontology or epistemology. The issue of ontic and epistemic states is particularly important when considering hidden variables in quantum physics because, as one may argue, the interpretation of quantum states as either ontic or epistemic will naturally lead to different assumptions about how reality is constructed; if it is constructed or not. It also raises the question of what attributes we are able to observe simultaneously and that brings contextuality into the discussion. If it turns out that reality is constructed contextually what does that imply about ontological realism? If on the other hand reality is constructed non-contextually what does that imply about ontological realism? Many implications can arise when considering these questions from a quantum physical point of view. In this paper I shall discuss how quantum physics provides some answers to these questions by considering quantum physical states and their measurements. (shrink)

This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on (...) and summarize the highlights of the individual contributions. (shrink)

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological (...) and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics. (shrink)

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

This paper puts forward an ontology that is indebted to QBism, Kant, Bohr, Schrödinger, the philosophy of the Upanishads, and the evolutionary philosophy of Sri Aurobindo. Central to it is that reality is relative to consciousness or experience. Instead of a single mind-independent reality, there are different poises of consciousness, including a consciousness to which “we are all really only various aspects of the One”. This ontology helps clear up unresolved issues in the philosophy of science, such as arise from (...) the reification of quantum states or from disregard of the universal context of science, which is human experience. It further helps clear up unresolved issues in the philosophy of mind, in particular the problem of intentionality and the dilemma posed by the mutual inclusion of self and world. (shrink)

The year 2019 witnessed the 20th Jubileum of the Växjö conference series on quantum foundations and probability in physics. This has been the longest running series of conferences on the subject in history. Many old and new friendships were forged at Linnaeus University and the beautiful surrounding lakes of Småland, where once yearly everyone gathers to renew the debate and report their latest progress. 2019 also represents the Porcelain Anniversary—18 years—of the point of view on quantum theory known as QBism. (...) In this regard, the 2001 meeting in the series was pivotal in more ways than one. Not only did it instigate Fuchs’s break [1] from the earlier (Jaynes style) “objective Bayesianism” and neo-Copenhagen thinking of Caves et al. [2], but it was the first meeting at an international scale to indicate that the quantum information revolution might have something genuine to contribute to quantum foundational thought. That meeting set the pace far beyond Växjö by the participation of a number of luminaries of quantum information: The late Asher Peres, Daniel Greenberger, David Mermin, Herbert Bernstein, Carlton Caves, Rüdiger Schack, Richard Jozsa, Benjamin Schumacher, and John Smolin. One could almost hear a battle cry echo from the woods, “Quantum foundations from quantum information or die!” The foundations debate had turned so stale by the time, it would surely die without an influx of new thinking. (shrink)

A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure.