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arXiv:2310.04002

A new indeterminacy-based quantum theory

Francisco Pipa

Published Oct 6, 2023• 0 citations
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Abstract

I propose a novel interpretation of quantum theory, which I will call Environmental Determinacy-based (EnDQT). In contrast to the well-known interpretations of quantum theory, EnDQT has the benefit of not adding non-local, superdeterministic, or retrocausal hidden variables. Also, it is not in tension with relativistic causality by providing a local causal explanation of quantum correlations. Furthermore, measurement outcomes don't vary according to, for example, systems or worlds. It is a conservative QT in the sense that, unlike theories such as spontaneous collapse theories, no modifications of the fundamental equations of quantum theory are required to establish when determinate values arise. Moreover, in principle, arbitrary systems can be in a coherent superposition for an arbitrary amount of time. According to EnDQT, at a certain stage of the evolution of the universe, some systems acquire the capacity to have and give rise to other systems having determinate values through an indeterministic process. Furthermore, this capacity propagates via local interactions between systems. When systems are isolated from others that have this capacity, they can, in principle, evolve unitarily indefinitely. EnDQT may provide payoffs to other areas of physics and their foundations, such as cosmology, via the features of the systems that start the chains of interactions.

DOI
10.48550/arxiv.2310.04002

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I propose a novel interpretation of quantum theory, which I will call Environmental Determinacy-based (EnDQT). In contrast to the well-known interpretations of quantum theory, EnDQT has the benefit of not adding non-local, superdeterministic, or retrocausal hidden variables. Also, it is not in tension with relativistic causality by providing a local causal explanation of quantum correlations. Furthermore, measurement outcomes don't vary according to, for example, systems or worlds. It is a conservative QT in the sense that, unlike theories such as spontaneous collapse theories, no modifications of the fundamental equations of quantum theory are required to establish when determinate values arise. Moreover, in principle, arbitrary systems can be in a coherent superposition for an arbitrary amount of time. According to EnDQT, at a certain stage of the evolution of the universe, some systems acquire the capacity to have and give rise to other systems having determinate values through an indeterministic process. Furthermore, this capacity propagates via local interactions between systems. When systems are isolated from others that have this capacity, they can, in principle, evolve unitarily indefinitely. EnDQT may provide payoffs to other areas of physics and their foundations, such as cosmology, via the features of the systems that start the chains of interactions.
In this dissertation, I propose two frameworks to address some important scientific and philosophical issues with quantum theory (QT). First, I propose Environmental Determinacy-based Quantum Theory (EnDQT) and argue that contrary to the other well-known quantum theories, it has the great benefit of being a local, non-relational, and non-superdeterministic/non-retrocausal "interpretation" of quantum theory, or quantum theory (QT). EnDQT has the benefit of being conservative, not modifying the fundamental equations of QT, and, in principle, allowing arbitrary systems to be placed in a coherent superposition for an arbitrary amount of time. Also, EnDQT is able to give a local causal explanation of quantum correlations. Via EnDQT, I also argue that i) QT is local in the sense of not being in conflict with relativity but without the need to adopt a relationalist, a superdeterminist, or a retrocausal approach. I also argue that ii) the notorious measurement problem can be addressed without modifying the quantum formalism, adding hidden variables, or adopting relationalism. Second, I propose Generative Quantum Theory (GQT) as a new ontology for quantum theories and show how it can be implemented via GRW, the MWI and single-world relationalist views, Bohmian Mechanics, hybrid classical-quantum theories, and EnDQT. I also distinguish it from the most discussed ontologies for quantum theories, namely, wavefunction realism and primitive ontology, and argue that it has certain benefits that they lack without some of their costs, such as non-locality. Due to the overall benefits of GQT compared with these widely debated ontological frameworks, and given that GQT, contrary to these frameworks, considers the wavefunction more like a predictor and that quantum indeterminacy plays an important explanatory role, I will argue that iii) the wavefunction is more like a predictor for different possibilities rather than a law or a field in a multidimensional space, and that iv) quantum indeterminacy plays a key explanatory role instead of a derivative role in order to understand QT.
The received view in foundations and philosophy of physics holds that if we reject supplementing quantum theory (QT) with certain hidden variables and consider that unitary QT is correct and universal, we should adopt a relationalist interpretation of QT. Relationalist interpretations relativize measurement outcomes to, for example, worlds, systems, agents, or reference frames. It includes the Many-Worlds Interpretation, Relational Quantum Mechanics, and QBism. These interpretations have potential costs connected with their relationalism that make them unattractive. Thus, if there exists a non-relational non-hidden variable universal intepretations of QT, it should be taken seriously. I will present an interpretation of this kind called Environmental Determinacy-based or EnD Quantum Theory (EnDQT), which goes beyond relationalism and the received view. EnDQT circumvents relationalism by constructing an account of indeterminate and determinate values and underlying quantum properties that is not relational while maintaining unitary non-hidden variable universal QT. In situations where a relationalist assumes that measurement outcomes are relativized, such as in the extended Wigner's friend scenarios, according to EnDQT there aren't determinate outcomes but systems with non-relational indeterminate values. In this approach, determinate values arose at some point in time through certain systems and persist due to them via certain interactions represented by certain networks. When there is isolation from the rest of the systems that belong to these networks, such as inside the friend's lab in the extended Wigner's friend scenarios, indeterminate values non-relationally arise inside. I will discuss other independent good reasons for adopting EnDQT, including providing a local causal explanation of Bell correlations and novel empirical posits represented by these networks.
I present and defend a new ontology for quantum theories (or ``interpretations'' of quantum theory) called Generative Quantum Theory (GQT). GQT postulates different sets of features, and the combination of these different features can help generate different quantum theories. Furthermore, this ontology makes quantum indeterminacy and determinacy play an important explanatory role in accounting for when quantum systems whose values of their properties are indeterminate become determinate. The process via which determinate values arise varies between the different quantum theories. Moreover, quantum states represent quantum properties and structures that give rise to determinacy, and each quantum theory specifies a structure with certain features. I will focus on the following quantum theories: GRW, the Many-Worlds Interpretation, single-world relationalist theories such as Relational Quantum Mechanics, Bohmian Mechanics, hybrid classical-quantum theories, and Environmental Determinacy-based (EnD) Quantum Theory. I will argue that GQT should be taken seriously because it provides a series of important benefits that current widely discussed ontologies lack, namely, wave function realism and primitive ontology, without some of their costs. For instance, it helps generate quantum theories that are compatible with relativistic causality, such as EnD Quantum Theory. Also, GQT has the benefit of providing new ways to compare and evaluate quantum theories, which may lead to philosophical and scientific progress.
Abstract It is often claimed that quantum mechanics entails that there is indeterminacy in the world, in the sense that physical systems can lack a precise value for a property. Indeed, a radical form of indeterminacy, in which systems have almost none of the properties we normally attribute to them, can be shown to follow from a particular interpretation of quantum mechanics—the bare theory. However, the bare theory is shown to be incoherent. Still, a more limited form of indeterminacy can be located in spontaneous collapse, hidden variables, and many-worlds theories. This indeterminacy is unlike that which arises classically, having nothing to do with ordinary forms of vagueness or the composition of large objects out of smaller parts. Indeterminacy in quantum mechanics can perhaps be avoided, but there seems little reason to do so.
In this dissertation, we explore two alternatives to quantum nonlocality in a single-universe framework: superdeterminism and retrocausality. These models circumvent Bell's theorem by violating the assumption that the hidden variables are uncorrelated with the measurement settings. In Chapter 1, we introduce superdeterminism and prepare the groundwork for our results in Chapter 2. We start from a review of the topic, focussing on the various qualitative criticisms raised against superdeterminism in the literature. We identify the criticism of 'superdeterministic conspiracy' by Bell as the most serious, and introduce nonequilibrium extensions of superdeterministic models in an attempt to formalise the criticism. We study the different properties of these models, and isolate two conspiratorial features. First, the measurement statistics depend on the physical system used to determine the measurement settings. Second, the formal no-signalling constraints are violated although there is no causal connection between the wings. We quantify in Chapter 2 the two conspiratorial features that we found in Chapter 1. We consider a Bell scenario where, in each run and at each wing, the experimenter chooses one of NNN devices to determine the local measurement setting. We then show that a superdeterministic model of the scenario has to finely tuned such that measurement statistics do not depend on the physical system used to determine the measurement settings. This quantifies the first form of conspiracy identified in Chapter 1 as a fine tuning. We also show that a superdeterministic model of the scenario requires arbitrarily large correlations, quantified in terms of a formal entropy drop and in terms of mutual information, to be set up by the initial conditions. Such correlations are required to ensure that the devices that the hidden variables are correlated with are coincidentally the same as the devices in fact used for every run at each wing. This quantifies the second form of conspiracy identified in Chapter 2 as an arbitrary large correlation. Nonlocal and retrocausal models turn out to be non-conspiratorial according to both approaches, thereby singling out `conspiracy' as a unique, problematic feature of superdeterminism. In Chapter 3, we change tracks to focus on retrocausality. Our results regarding retrocausal models are, in contrast to superdeterminism, positive. We first show how to construct a local, ψ\psiψ-epistemic hidden-variable model of Bell correlations with wavefunctions in physical space by a retrocausal adaptation of the originally superdeterministic model given by Brans. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. Lastly, we argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. In Chapter 4, focus on the question whether retrocausal models can utilise their relativistic properties to account for relativistic effects on entangled systems. We consider a hypothetical relativistic Bell experiment, where one of the wings experiences time-dilation effects. We show that the retrocausal Brans model, introduced in Chapter 3, can be easily generalised to analyse this experiment, and that it predicts less separation of eigenpackets in the wing experiencing the time-dilation. This causes the particle distribution patterns on the photographic plates to differ between the wings -- an experimentally testable prediction of the model. We discuss the difficulties faced by other hidden variable models in describing this experiment, and their natural resolution in our model due to its relativistic properties. Lastly, we argue that it is not clear at present, due to technical difficulties, if our prediction is reproduced by quantum field theory. We conclude that if it is, then the retrocausal Brans model predicts the same result with great simplicity in comparison. If not, the model can be experimentally tested.
The collapse of the wave function remains one of the deepest puzzles in quantum mechanics. The Schrödinger equation is unitary and time-reversal symmetric, yet measurement requires an additional postulate that is neither—and we have no physical explanation for why. Existing interpretations either deny that collapse is real (Many-Worlds), treat it as purely subjective (QBism), or add stochastic noise by hand without deriving it from fundamental principles (GRW, CSL). We demonstrate that collapse is a real physical process requiring fundamentally irreversible dynamics. No purely unitary, time-symmetric theory can account for the objective suppression of macroscopic superpositions—irreversibility must be built into the dynamics from the start. We introduce a minimal extension of quantum mechanics through coupling to a universal scalar field (the I-field) governed by an explicit time-asymmetric field equation. Collapse emerges objectively through deterministic dissipative dynamics, with no reference to observers, measurement devices, or stochastic noise. By integrating out the I-field degrees of freedom, we derive effective Lindblad dynamics for quantum systems. The collapse rate scales quadratically with system mass, ensuring microscopic quantum coherence remains intact while macroscopic superpositions are dynamically suppressed. Unlike stochastic collapse models (GRW/CSL), the mechanism is deterministic and produces no spontaneous heating. Unlike gravitational collapse proposals (Diósi-Penrose), it provides explicit field equations rather than heuristic arguments. Unlike environmental decoherence, the irreversibility is fundamental rather than effective. The theory respects relativistic causality and makes testable predictions for current and near-future experiments in matter-wave interferometry, optomechanical systems, and molecular interferometry. Observation of mass-dependent decoherence without accompanying stochastic heating would provide strong evidence for the I-field mechanism. The framework establishes irreversibility as a fundamental interaction rather than an emergent phenomenon, providing a unified physical origin for both wave function collapse and the quantum arrow of time.