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Honoring Epimenides of Crete (±Δx): From Quantum Paradoxes, through Weak Measurements, to the Nature of Time

Eliahu Cohen, Avshalom C. Elitzur

Published Jan 1, 2014• 3 citations
Publisher

Abstract

Quantum temporal peculiarities, involving ordinary and weak measurements, are explored. We introduce the foundations of weak measurement and outline some novel theoretical and experimental predictions derived from it. We then show how weak values, which explicitly depend on both forward and backward evolving state-vectors, can serve as important tools for gaining new insights into the nature of time.

DOI
10.1051/epjconf/20147100028

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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Apr 19, 2016•17 citations
Quantum temporal peculiarities, involving ordinary and weak measurements, are explored. We introduce the foundations of weak measurement and outline some novel theoretical and experimental predictions derived from it. We then show how weak values, which explicitly depend on both forward and backward evolving state-vectors, can serve as important tools for gaining new insights into the nature of time.
The two-state vector formalism provides a complete description of pre- and post-selected quantum systems and has uncovered a host of new quantum phenomena which were previously hidden. The most important feature is that any weak coupling to a pre- and post-selected system is effectively a coupling to a "weak value" which is given by a simple expression depending on the two-state vector. In particular, weak values, are the outcomes of so called "weak measurements" which have recently become a very powerful tool for ultra-sensitive measurements. Using weak values, I will show that the classical limit of quantum mechanics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects.
Interest in weak values has grown steadily since their introduction in 1988, driven by developments in quantum measurement theory and increasing attention to the foundational issues at the heart of quantum mechanics. This thesis undertakes a philosophical investigation into the nature and implications of weak values, with a particular focus on their interpretation and role in creating and resolving quantum paradoxes. Overall, we argue that sequential weak values offer novel conceptual tools for assessing logical consistency in an atemporal fashion, ultimately motivating a shift toward a fundamentally relation-based ontology. Chapter 1 begins by establishing the conceptual and philosophical foundations of the thesis. We argue that performing this conceptual analysis of weak values requires a philosophical methodology informed by the structure of quantum theory and the foundational questions it poses. In Chapter 2, we provide a critical exploration of weak measurement theory and weak values, outlining their historical foundations and development, the experimental context, and interpretative challenges. Through a detailed analysis of paradoxes related to weak values such as the nested interferometer and the quantum Cheshire cat, the chapter argues that weak values reveal spatiotemporally discontinuous trajectories which conflict with classical intuition about particles and their trajectories. We contend that weak values are inherently contextual, as their significance arises in the context of the pre- and post- selections of the system. Chapter 3 develops an original account of ‘particle presence' across time, building on metaphysical notions of persistence. This chapter proposes a way of recovering continuity in paradoxes such as the three-box gendankenexperiment. Our framework offers a means of assessing the persistence of particles through spacetime via sequential weak values which we argue test the logical consistency of propositions across time. We then explore the implications for temporality, developing the key argument of this chapter: presence is defined across durations of time, rather than in discrete spacetime. This raises the possibility of presence without a well-defined causal order. In Chapter 4, the insights developed in the previous chapters are extended to a consideration of Relational Quantum Mechanics (RQM), addressing the longstanding issue of a lack of intersubjective agreement in relational interpretations. Given RQM's rejection of absolutism, this chapter critiques existing attempts at bridging perspectives and proposes a new route to empirical confirmation grounded in the persistence and reliability of observer's memory records. Our two- step model, consisting of internal confirmation via sequential weak values and then a consistency check from a second observer, offers a new approach to confirmation in RQM without rejecting the non-absolutist core of the interpretation. Sequential weak values are re-interpreted as atemporal probes available to the informational observer, distinct from its physical counterpart. This atemporal nature allows them to establish logical consistency across the observer's records and assign credence to them without presupposing a classical temporal order. These results suggest an ontology grounded in primitive relations, rather than one built on temporally ordered events. Chapter 4 thus builds on the contextuality arguments of earlier chapters: just as weak values reveal measurement outcomes to be context-dependent, their sequential and time-symmetric structure exposes temporal contextuality, challenging classical assumptions about fixed causal order and reinforcing the case for a non-classical, relation-based ontology. Finally, in Chapter 5, we conclude by summarising our key results and giving a list of open questions.
Quantum systems usually travel a multitude of different paths when evolving through time from an initial to a final state. In general, the possible paths will depend on the future and past boundary conditions, as well as the system's dynamics. We present a gedankenexperiment where mutually exclusive paths are followed deterministically and simultaneously, by the same system, depending on which measurement was performed. We show how this `paradoxical' behavior is interpreted in the weak measurement formalism where the back action of the measurement cannot be used to account for the strange behavior. To support our predictions we present a method for performing both the strong and weak measurement.
Unlike regular time evolution governed by the Schr\"odinger equation, standard quantum measurement appears to violate time-reversal symmetry. Measurement creates random disturbances (e.g., collapse) that prevent back-tracing the quantum state of the system. The effect of these disturbances is explicit in the results of subsequent measurements. In this way, the joint result of sequences of measurements depends on the order in time in which those measurements are performed. One might expect that if the disturbance could be eliminated this time-ordering dependence would vanish. Following a recent theoretical proposal [Bednorz, Franke, and Belzig, New J. Phys. 15, 023043 (2013)], we experimentally investigate this dependence for a kind of measurement that creates an arbitrarily small disturbance: weak measurement. We perform various sequences of a set of polarization weak measurements on photons. We experimentally demonstrate that, although the weak measurements are minimally disturbing, their time ordering affects the outcome of the measurement sequence for quantum systems.
We study the unique role played in quantum mechanics by non-events or 'counterfactuals'. Our earlier analysis of 'quantum oblivion' has revealed some subtle stages in the measurement process, which may end up in self-cancellation. To these findings, we now add two insights derived by two time-symmetric interpretations of quantum mechanics. (i) Like all quantum interactions, the non-event is formed by the conjunction of forward-plus-backward-evolving wave functions. (ii) Then, it is another feature of such dual evolutions, namely the involvement of negative masses and energies, that enables Nature to make some events 'unhappen' while leaving causal traces.