Christopher G. Timpson

Quantum Mechanics on Spacetime I: Spacetime State Realism

What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism. We elaborate the sense in which wave-function realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism, a view which takes the states associated to spacetime regions as fundamental. This approach enjoys a number of beneficial features, although, unlike wave-function realism, it involves non-separability at the level of fundamental ontology. We investigate the pros and cons of this non-separability, arguing that it is a quite acceptable feature, even one which proves fruitful in the context of relativistic covariance. A companion paper discusses the prospects for combining a spacetime-based ontology with separability, along lines suggested by Deutsch and Hayden. 1 Introduction 2 Prolegomena 3 Wave-function Realism 4 Problems with Wave-function Realism 5 Spacetime State Realism 6 Locality 7 Non-unitary Dynamics on the Spacetime Ontology 8 Relativity and Poincaré Covariance 9 Finding the Appearances 10 Conclusion 1 Introduction 2 Prolegomena 3 Wave-function Realism 4 Problems with Wave-function Realism 5 Spacetime State Realism 6 Locality 7 Non-unitary Dynamics on the Spacetime Ontology 8 Relativity and Poincaré Covariance 9 Finding the Appearances 10 Conclusion

On a supposed conceptual inadequacy of the Shannon information in quantum mechanics

Abstract Recently, Brukner and Zeilinger (Phys. Rev. Lett. 83(17) (2001) 3354) have claimed that the Shannon information is not well defined as a measure of information in quantum mechanics, adducing arguments that seek to show that it is inextricably tied to classical notions of measurement. It is shown here that these arguments do not succeed: the Shannon information does not have problematic ties to classical concepts. In a further argument, Brukner and Zeilinger compare the Shannon information unfavourably to their preferred information measure, I( p → ) , with regard to the definition of a notion of “total information content.” This argument is found unconvincing and the relationship between individual measures of information and notions of “total information content” investigated. We close by considering the prospects of Zeilingers Foundational Principle as a foundational principle for quantum mechanics.

Why special relativity should not be a template for a fundamental reformulation of quantum mechanics

In a comparison of the principles of special relativity and of quantum mechanics, the former theory is marked by its relative economy and apparent explanatory simplicity. A number of theorists have thus been led to search for a small number of postulates - essentially information theoretic in nature - that would play the role in quantum mechanics that the relativity principle and the light postulate jointly play in Einsteins 1905 special relativity theory. The purpose of the present paper is to resist this idea, at least in so far as it is supposed to reveal the fundamental form of the theory. It is argued that the methodology of Einsteins 1905 theory represents a victory of pragmatism over explanatory depth; and that its adoption only made sense in the context of the chaotic state state of physics at the start of the 20th century - as Einstein well knew.

Nonlocality and information flow: The approach of Deutsch and Hayden

Deutsch and Hayden claim to have provided an account of quantum mechanics which is particularly local, and which clarifies the nature of information transmission in entangled quantum systems. In this paper, a perspicuous description of their formalism is offered and their claim assessed. It proves essential to distinguish, as Deutsch and Hayden do not, between two ways of interpreting the formalism. On the first, conservative, interpretation, no benefits with respect to locality accrue that are not already available on either an Everettian or a statistical interpretation; and the conclusions regarding information flow are equivocal. The second, ontological, interpretation, offers a framework with the novel feature that global properties of quantum systems are reduced to local ones; but no conclusions follow concerning information flow in more standard quantum mechanics.

The Grammar of Teleportation

Whilst a straightforward consequence of the formalism of non-relativistic quantum mechanics, the phenomenon of quantum teleportation has given rise to considerable puzzlement. In this paper, the teleportation protocol is reviewed and these puzzles dispelled. It is suggested that they arise from two primary sources: (1) the familiar error of hypostatizing an abstract noun (in this case, ‘information’) and (2) failure to differentiate interpretation dependent from interpretation independent features of quantum mechanics. A subsidiary source of error, the simulation fallacy, is also identified. The resolution presented of the puzzles of teleportation illustrates the benefits of paying due attention to the logical status of ‘information’ as an abstract noun. 1. Introduction2. The quantum teleportation protocol 2.1Some information-theoretic aspects of teleportation 2.1.1Preamble 2.1.2Application to teleportation3. The puzzles of teleportation4. Resolving (dissolving) the problem 4.1The simulation fallacy5. The teleportation process under different interpretations 5.1Collapse interpretations:Dirac/von Neumann, GRW 5.2No collapse and no extra values: Everett 5.3No collapse, but extra values: Bohm 5.3.1A note on active information 5.4Ensemble and statistical viewpoints6. Concluding remarks Introduction The quantum teleportation protocol 2.1Some information-theoretic aspects of teleportation 2.1.1Preamble 2.1.2Application to teleportation 2.1Some information-theoretic aspects of teleportation 2.1.1Preamble 2.1.2Application to teleportation 2.1.1Preamble 2.1.2Application to teleportation The puzzles of teleportation Resolving (dissolving) the problem 4.1The simulation fallacy 4.1The simulation fallacy The teleportation process under different interpretations 5.1Collapse interpretations:Dirac/von Neumann, GRW 5.2No collapse and no extra values: Everett 5.3No collapse, but extra values: Bohm 5.3.1A note on active information 5.4Ensemble and statistical viewpoints 5.1Collapse interpretations:Dirac/von Neumann, GRW 5.2No collapse and no extra values: Everett 5.3No collapse, but extra values: Bohm 5.3.1A note on active information 5.3.1A note on active information 5.4Ensemble and statistical viewpoints Concluding remarks

Philosophy of Quantum Information and Entanglement: Information, immaterialism, instrumentalism: Old and new in quantum information

We live, we are told, in an information age. We are told this, perhaps, less often than once we were; but no doubt only because the phrase has become worn from use. If ours is an age of information, then quantum information theory is a field propitiously in tune with the spirit of the times: a rich and sophisticated physical theory that seeks to tame quantum mysteries (no less!) and turn them to ingenious computational and communication ends. It is a theory that hints, moreover, at the possibility of finally rendering the quantum unmysterious; or at least, this is a conclusion that many have been tempted to draw. And yet, for all its timeliness, some of the most intriguing of the prospects that quantum information science presents are to be found intertwining with some surprisingly old and familiar philosophical themes. These themes are immaterialism and instrumentalism; and in this essay we shall be exploring how these old ideas feature in the context of two of the most tantalizing new questions that have arisen with the advent of this field: Does quantum information theory finally help us to resolve the conceptual conundrums of quantum mechanics? And does the theory indicate a new way of thinking about the world—one in which the material as the fundamental subject matter of physical theory is seen to be replaced by the immaterial: information? The moral I will suggest is that it is only once the influence of these old ideas is explicitly recognised for what it is and treated accordingly that one can begin to hope ∗I would like to thank the organisers for the invitation to speak at the Boston Colloquium and to contribute to this resulting volume. This paper draws on material discussed in Timpson (2004, 2008b). †christopher.timpson@bnc.ox.ac.uk

Quantum Computers: the Church-Turing Hypothesis Versus the Turing Principle

Following the development of quantum computers, a question has arisen regarding the relation between the basis of the classical theory of computation and the quantum theory. Here I argue against Deutsch’s claim that a physical principle, the Turing principle, underlies the famous Church-Turing hypothesis. I also discuss the computational analogy and emphasize a certain line of argument suggesting it may be misplaced. Finally, I assess Deutsch’s claims for the dependence of mathematics upon empirical science, claims that arise as a consequence of his conception of computation and his adherence to the computational analogy.

The applicability of Shannon information in quantum mechanics and Zeilinger's foundational principle

Recently, Brukner and Zeilinger have presented a number of arguments suggesting that the Shannon information is not well defined as a measure of information in quantum mechanics. If established, this result would be highly significant, as the Shannon information is fundamental to the way we think about information not only in classical but also in quantum information theory. On consideration, however, these arguments are found unsuccessful; I go on to suggest how they might be arising as a consequence of Zeilinger’s proposed foundational principle for quantum mechanics.

Building with quantum correlations

Abstract‘Correlations without correlata’ is an influential way of thinking of quantum entanglement as a form primitive correlation which nonetheless maintains locality of quantum theory. A number of arguments have sought to suggest that such a view leads either to internal inconsistency or to conflict with the empirical predictions of quantum mechanics. Here we explicate and provide a partial defence of the notion, arguing that these objections import unwarranted conceptions of correlation properties as hidden variables. A more plausible account sees the properties in terms of Everettian relative states. The ontological robustness of entanglement is also defended from recent objections.

What Is the Lesson of Quantum Computing

It would be a mistake to seek for a singlelesson that the advent of quantum computing has provided: the theory is rich in both physics and computer science terms. But my quarry is a, or perhaps the, central conceptualpoint that we should draw; and it concerns putative shifts in our understanding of the Church- Turing hypothesis inspired by reflection on quantum computation.