We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal (with or without signalling, dynamical or non-dynamical), future-input-dependent, atemporal and all-at-once, not always with the same meaning or context. Sometimes, these models are assumed to be deterministic, sometimes not, the word deterministic has been given different meanings, and different notions of causality have been used when classifying them. This has created much confusion in the literature, and we hope that the terms proposed here will help to clarify the nomenclature. The general model framework that we will propose may also be useful to classify other interpretations and modifications of quantum mechanics. This document grew out of the discussions at the 2022 Bonn Workshop on Superdeterminism and Retrocausality.
We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal (with or without signalling, dynamical or nondynamical), future-input-dependent, atemporal and all-at-once, not always with the same meaning or context. Sometimes, these models are assumed to be deterministic, sometimes not, the word deterministic has been given different meanings, and different notions of causality have been used when classifying them. This has created much confusion in the literature, and we hope that the terms proposed here will help to clarify the nomenclature. The general model framework that we will propose may also be useful to classify other interpretations and modifications of quantum mechanics. This document grew out of the discussions at the 2022 Bonn Workshop on Superdeterminism and Retrocausality.
A number of writers have been attracted to the idea that some of the peculiarities of quantum theory might be manifestations of 'backward' or 'retro' causality, underlying the quantum description. This idea has been explored in the literature in two main ways: firstly in a variety of explicit models of quantum systems, and secondly at a conceptual level. This note introduces a third approach, intended to complement the other two. It describes a simple toy model, which, under a natural interpretation, shows how retrocausality can emerge from simple global constraints. The model is also useful in permitting a clear distinction between the kind of retrocausality likely to be of interest in QM, and a different kind of reverse causality, with which it is liable to be confused. The model is proposed in the hope that future elaborations might throw light on the potential of retrocausality to account for quantum phenomena.
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
N 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-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.
Gisin has provided an argument for the conclusion that no covariant nonlocal model can reproduce the operational statistics observed in Bell experiments. Gisin's argument applies only to deterministic models and we argue that proposed generalizations of the argument beyond determinism based solely on statistical notions are unconvincing, as they lack the resources to formulate a satisfactory notion of no-retrocausality. We introduce the framework of frame-indexed causal models in order to extend Gisin's argument to the genuinely probabilistic case. Frame-indexed causal models associate potentially different causal models with different reference frames while requiring corresponding operational variables to agree runwise. Within this framework, we establish two no-go results based on Gisin's argument. First, we show that no empirically adequate frame-indexed causal model can jointly satisfy Independent Settings, No-Retrocausality, and Causal Lorentz Invariance. Second, it is established that this result continues to hold when Causal Lorentz Invariance is weakened to Lorentz Invariance of Causal Connections, which requires only the skeleton of the causal structure to remain invariant, thereby allowing the direction of causal influence to depend on the choice of reference frame. These results are discussed in the context of relativistic interpretations of quantum theory and nonclassical causal inference.
One of the basic assumptions underlying Bell's theorem is the causal arrow of time, having to do with temporal order rather than spatial separation. Nonetheless, the physical assumptions regarding causality are seldom studied in this context, and often even go unmentioned, in stark contrast with the many different possible locality conditions which have been studied and elaborated upon. In the present work, some retrocausal toy-models which reproduce the predictions of quantum mechanics for Bell-type correlations are reviewed. It is pointed out that a certain toy-model which is ostensibly superdeterministic-based on denying the free-variable status of some of quantum mechanics' input parameters-actually contains within it a complete retrocausal toy-model. Occam's razor thus indicates that the superdeterministic point of view is superfluous. A challenge is to generalize the retrocausal toy-models to a full theory-a reformulation of quantum mechanics-in which the standard causal arrow of time would be replaced by a more lenient one: an arrow of time applicable only to macroscopically-available information. In discussing such a reformulation, one finds that many of the perplexing features of quantum mechanics could arise naturally, especially in the context of stochastic theories.