Epistemic models of nature prove to be problematic in many settings, particularly in those in which measurement procedures are ill-defined. By contrast, in ontological models of nature, measurement results are independent of the procedure used to obtain them. Quantum mechanics, as a model of nature, is notoriously ambiguous in this regard. If we assume that all measurement results can be expressed in terms of pointer readings, then any useful ontology would need to unambiguously specify the positions of things. But the positions of pointers are ill-defined in many relativistic and cosmological settings. One potential solution to this problem presents itself in the solutions to the Wheeler-DeWitt equation as developed by Hartle and Hawking. In this article we introduce such a model in which these solutions to the Wheeler-DeWitt equation serve as the ontology of the model. We then show that, for any model that admits these solutions as beables, the global preservation of Lorentz invariance is incompatible with global determinism. However, we also show that an Everett-like interpretation that allows for all possible mappings of the matter field to the geometry and for all possible foliations of these mappings as being equally real, might solve this problem.
Epistemic models of nature prove to be problematic in many settings, particularly in those in which measurement procedures are ill-defined. By contrast, in ontological models of nature, measurement results are independent of the procedure used to obtain them. Quantum mechanics, as a model of nature, is notoriously ambiguous in this regard. If we assume that all measurement results can be expressed in terms of pointer readings, then any useful ontology would need to unambiguously specify the positions of things. But the positions of pointers are ill-defined in many relativistic and cosmological settings. One potential solution to this problem presents itself in the solutions to the Wheeler-DeWitt equation as developed by Hartle and Hawking. In this article we introduce such a model in which these solutions to the Wheeler-DeWitt equation serve as the ontology of the model. We then show that, for any model that admits these solutions as beables, the global preservation of Lorentz invariance is incompatible with global determinism. However, we also show that an Everett-like interpretation that allows for all possible mappings of the matter field to the geometry and for all possible foliations of these mappings as being equally real, might solve this problem.
We consider the problem of extracting physical predictions from the wave function of the universe in quantum cosmological models. We state the features of quantum cosmology an interpretational scheme should confront. We discuss the Everett interpretation, and extensions of it, and their application to quantum cosmology. We review the steps that are normally taken in the process of extracting predictions from solutions to the Wheeler-DeWitt equation for quantum cosmological models. Some difficulties and their possible resolution are discussed. We conclude that the usual wave function-based approach admits at best a rather heuristic interpretation, although it may in the future be justified by appeal to the decoherent histories approach.
The article analyzes the principal interpretations of quantum mechanics from the standpoint of an original conception of informational realism. It is shown that these interpretations can be unified within an informational ontology in which fundamental status is accorded to informational invariants of quantum constraints that are common to all empirically equivalent interpretations of quantum mechanics. A distinction is proposed between two informational layers: epistemic information (measurement data and the updating of knowledge on their basis) and ontic information (invariant structures and constraints). The first layer varies across interpretations, whereas the second is preserved, which explains their experimental equivalence. The proposed informational ontology is compared with other realist approaches, and its advantages are formulated and argued for. It is shown that all the interpretations considered, despite often incompatible philosophical foundations and worldviews, are equally dependent on a certain set of informational invariants, which prove to be primary with respect to any particular interpretation. This can be explained either by the fact that a unified descriptive model of real physical processes at the quantum level is still unknown, or – as argued in the present article – by the claim that the fundamental level consists of informational constraints, and that different descriptions are equivalent, with their differences explained by distinct perspectives. The novelty and contribution of the article consist in proposing an operational definition of a falsifiable class of invariants and constraints on operations that are stable under changes of perspective; providing a unified translational vocabulary for interpretations in terms of the two informational layers; showing that their empirical equivalence is explained by the preservation of the same ontic layer; and formulating a criterion for distinguishing interpretations from alternative theories. Taken together, this allows informational ontology to be regarded as a meta-position with respect to these interpretations.
The aim of this thesis is to better understand the features of quantum matter that makes quantum gravity so hard to reach. In Chapter 3, we present two general models of decoherence, without specifying any Hamiltonian. The first one makes decoherence naturally appear as a geometrical phenomenon between reservoirs of dimensions. The second one specifically tackles the question of why, in a universe where decoherence is ubiquitous, things are not frozen by the quantum Zeno effect. In Chapter 4, we discuss the ontological problem of quantum physics, usuallyreferred to as the ‘measurement problem’. Our aim in this chapter is not to give a solution, but rather to formulate the problem independently of any interpretation of quantum mechanics, in the light of the theory of decoherence. In Chapter 5, a new ingredient is introduced in the discussion: spacetime. After investigating the apparent incompatibility between quantum mechanics and special relativity, we present a program of research and a toy model designed to build a backgroundless notion of position within the quantum formalism.
Ψ-epistemic models of quantum mechanics imply that the quantum state does not correspond to physical reality, but instead reflects the observer's knowledge of the underlying quantum system. The epistemic view of the quantum state has the potential to shed light on several foundational problems of quantum theory and has attracted considerable attention in the literature. On the other hand, the Pusey-Barrett-Rudolph theorem demonstrated that broad classes of ψ-epistemic models must lead to predictions that deviate from those of quantum mechanics. Although the original theorem involved entangled joint measurements on composite systems, alternative no-go theorems involving measurements on single quantum systems were developed shortly thereafter. Experimental investigations of the deviations predicted by ψ-epistemic models from quantum mechanics are still ongoing. So far, such tests have been performed within the framework of non-relativistic quantum mechanics and predominantly rely on quantum information based measurement procedures. In this work, we show that ψ-epistemic models can give rise to deviations from standard quantum field-theoretic predictions through modifications of polarized scattering cross sections and decay widths. Our results do not require a relativistic formulation of ontological models or of the Harrigan-Spekkens criterion; the essential assumption is merely that measurements implemented through relativistic processes can still be represented within the ontological framework by well-defined response functions and probabilities. The present work constitutes a proof-of-principle study demonstrating that particle physics tests of the ontological status of the quantum state are possible and that ψ-epistemic models may exhibit experimentally distinguishable signatures in particle phenomenology.
Abstract Given an ontological model of a quantum system, a “genuine measurement,” as opposed to a quantum measurement, means an experiment that determines the value of a beable, i.e., of a variable that, according to the model, has an actual value in nature before the experiment. We prove a theorem showing that in every ontological model, it is impossible to measure all beables. Put differently, there is no experiment that would reliably determine the ontic state. This result shows that the positivistic idea that a physical theory should only involve observable quantities is too optimistic.
Quantum nonlocality has been a long-standing and fascinating problem in the foundations of quantum theory since its proof by the Bell inequality. It seems to contradict our intuitive picture of space-time and thus urges us to reconsider its foundation. With the advent of quantum information science, it has attracted renewed interest from a fundamental point of view as well as from a quantum information-theoretic one. Another fundamental question on the nature of quantum theory is how we understand what quantum states represent. (Quantum states hereafter refer to pure states.) This is also a long-standing problem since the early days of quantum theory. Roughly speaking, there are two conflicting views on this matter: one is ontology and the other is epistemology. Ontological models of quantum theory are models in which we assume some underlying reality for physical systems and require that all the predictions of quantum theory should be reproduced. The ontological models are divided into two categories, depending on which views the models are based on, ontology or epistemology. In the models based on ontology, quantum states represent the underlying reality in some sense, and different quantum states correspond to different realities. In the models based on epistemology, quantum states do not necessarily correspond to the underlying realities, and even different quantum states can be consistent with a common underlying reality. The former type of ontological models of quantum theory is called 1⁄4-ontic. The latter is called 1⁄4-epistemic. Thus, it might be rather confusing that ontological models are classified further into 1⁄4-ontic models and 1⁄4-epistemic ones. We use these terms here in accordance with the recent literature on quantum foundations. (For details of these notions in the ontological models of quantum theory, see the paper by Harrigan and Spekkens.) Quite recently, the question just mentioned has been answered by Pusey et al., and one of the above models has been refuted. It was shown that 1⁄4-epistemic models are inconsistent with the predictions of quantum theory. In other words, epistemological views on quantum states turned out to be false as long as we assume some underlying reality for physical systems. Therefore, only 1⁄4-ontic models of quantum theory are valid for describing quantum systems. This significantly advances our understanding on the nature of quantum states. It is expected that various conclusions will be drawn from this fact. In this paper, we will discuss a connection with nonlocality. The above two fundamental questions, nonlocality and the nature of quantum states, are intimately connected, and the connection was first implicitly recognised by Einstein in the early days of quantum theory. In a private correspondence with Schrodinger, Einstein constructed a fascinating argument that relates the above two. (That argument is distinctly different from the well-known EPR argument.) Recently, it was revisited and reconstructed in accordance with more rigorous notions in quantum foundations. Nonlocality is usually shown by violations of Bell inequalities. (Bell inequalities hereafter include all the subsequent developments such as the CHSH inequality.) Even if it is not clear whether the models of quantum theory are 1⁄4-ontic or 1⁄4-epistemic, we can prove nonlocality just by showing the violation of Bell inequalities. However, the above argument originated by Einstein implies that if we know the models are 1⁄4-ontic in advance (as we do now), we can prove nonlocality in a simpler way without Bell inequalities. (This argument had been known in quantum foundations before the refutation of 1⁄4-epistemic models.) Nonlocality is rigorously defined as a violation of the notion of local causality defined by Bell. Showing the violation of Bell inequalities is one way of demonstrating the violation of local causality. Since the simpler proof initiated by Einstein directly demonstrates the violation of local causality, it is a more straightforward proof of nonlocality from a conceptual point of view. In the following, we will see that this simple argument of nonlocality without Bell inequalities can be used to show multipartite nonlocality as well. Before moving onto multipartite cases, first let us define the necessary notions for presenting our result. First of all, we assume that there exists a complete specification of the properties of a physical system, which we refer to as the ontic state of that system. The ontic states represent the underlying realities and are not necessarily equal to ordinary quantum states. (In other words, the ontic states correspond to hidden variables.) Ontological models of quantum theory are models that assume ontic states and reproduce all the predictions of quantum theory. An important question is how ontic states correspond to quantum states in quantum theory. In order to frame the question accurately, we need the notion of an epistemic state, which represents the relation between them. Suppose we prepare a physical system in a quantum state 1⁄4. Although the system is uniquely specified as 1⁄4 in quantum theory, there still remains a possibility that it allows a more detailed specification in the ontic state space, in which case many different ontic states turn out to be consistent with 1⁄4. The relation between ontic states and the preparation procedure, P1⁄4, is described by a conditional probability distribution over the ontic state space, pð jP1⁄4Þ, which we refer to as an epistemic state. In general, the preparation P can be a preparation of a physical system in a mixed sate. Unless there exists a one-to-one correspondence between ontic states and quantum states, the probability distribution spreads over . (See Fig. 1.) The question of whether an ontological model is 1⁄4-ontic or 1⁄4-epistemic is concerned with the behaviour of the epistemic states for two distinct preparations of quantum states. Consider two distinct preparations of quantum states, Journal of the Physical Society of Japan 82 (2013) 055003