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arXiv:2503.19079 · Foundations of Physics

Weak Particle Presence

Bethany Terris

Published Mar 25, 2025• 2 citations
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Abstract

Abstract The concept of presence has been extensively explored in philosophy, yet the notion of particle presence within quantum theory remains under-examined. In this article, we explore particle presence through an analysis of a paradox arising from weak measurements. We show that the classical intuition about particle presence involves an erroneous logical combination of propositions from single-time weak values, leading to inconsistencies that result in the deduction of discontinuous trajectories. Instead, we argue that by treating presence as a property defined across time by measuring sequential weak values, the discontinuity paradox is resolved, providing a coherent, non-classical account of particle presence. We discuss some advantages and drawbacks of this account, and consider applications to other cases of trajectory discontinuity.

DOI
10.1007/s10701-025-00837-2

Related papers

Weak values in quantum mechanics : conceptual questions

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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.

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In the paper "Does the weak trace show the past of a quantum particle?" [arXiv:2109.14060v2], it is argued that null weak values of the spatial projectors are inadequate to infer the presence of a quantum particle at an intermediate time between preparation and detection. This conclusion relies on two arguments - (i) the role of the disturbance induced by a weak measurement, and (ii) classical-like features like continuous paths that must purportedly be associated with a quantum particle presence. Here we first show that (i) arises from a misunderstanding of null weak values by putting forward a simple counter-example that highlights that the relevant quantities to examine are the vanishing amplitudes, not the wavefunction. Then we briefly argue that enforcing classical pre-conditions in order to account for quantum properties during unitary evolution is unlikely to lead to a consistent understanding of quantum phenomena.

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Weak measurement criteria for the past of a quantum particle

B. E. Y. Svensson

Vaidman, Phys.Rev. A 87, 052104 (2013), has proposed a weak value criterion for the past of a quantum particle, and applied it to photons in a particular setup of nested Mach-Zehnder interferometers. From his analysis, he draws some astonishing conclusions regarding which arms of the setup the photons populate. I argue that the weak values Vaidman employs as weak tracers in his analysis cannot be used in this case and that, consequently, the conclusions he draws cannot be upheld. The reason is that weak values are defined as a limit which in this case turns out to be discontinuous. I propose instead a weak mean value criterion which avoids these shortcomings.

arXiv:1407.4613•Jul 17, 2014•1 citation
Abstract The concept of presence has been extensively explored in philosophy, yet the notion of particle presence within quantum theory remains under-examined. In this article, we explore particle presence through an analysis of a paradox arising from weak measurements. We show that the classical intuition about particle presence involves an erroneous logical combination of propositions from single-time weak values, leading to inconsistencies that result in the deduction of discontinuous trajectories. Instead, we argue that by treating presence as a property defined across time by measuring sequential weak values, the discontinuity paradox is resolved, providing a coherent, non-classical account of particle presence. We discuss some advantages and drawbacks of this account, and consider applications to other cases of trajectory discontinuity.
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.
In the paper "Does the weak trace show the past of a quantum particle?" [arXiv:2109.14060v2], it is argued that null weak values of the spatial projectors are inadequate to infer the presence of a quantum particle at an intermediate time between preparation and detection. This conclusion relies on two arguments - (i) the role of the disturbance induced by a weak measurement, and (ii) classical-like features like continuous paths that must purportedly be associated with a quantum particle presence. Here we first show that (i) arises from a misunderstanding of null weak values by putting forward a simple counter-example that highlights that the relevant quantities to examine are the vanishing amplitudes, not the wavefunction. Then we briefly argue that enforcing classical pre-conditions in order to account for quantum properties during unitary evolution is unlikely to lead to a consistent understanding of quantum phenomena.
The notion of the trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum observable, can offer a possible description of trajectory on account of its statistical nature. In this paper, we explore the physical significance provided by this “weak trajectory” by considering various situations where interference takes place simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment is available. These include the double slit experiment and Lloyd's mirror, where in the former case it is argued that the real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak trajectory holds universally under the complex probability defined from the given transition process. These features remain essentially unaltered in the case of Lloyd's mirror where interference occurs with a single slit.
Quantum mechanical weak values of projection operators have been used to answer which-way questions, e . g . to trace which arms in a multiple Mach–Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I show that this procedure might lead to logical inconsistencies in the sense that different methods used to answer composite questions, like “Has the particle traversed the way X or the way Y ?”, may result in different answers depending on which methods are used to find the answer. I illustrate the problem by considering some examples: the “quantum pigeonhole” framework of Aharonov et al. , the three-box problem, and Hardy’s paradox. To prepare the ground for my main conclusion on the incompatibility in certain cases of weak values and logic, I study the corresponding situation for strong/projective measurements. In this case, no logical inconsistencies occur provided one is always careful in specifying exactly to which ensemble or sample space one refers. My results cast doubts on the utility of quantum weak values in treating cases like the examples mentioned.
Nondestructive weak measurements (WMs) made on a quantum particle are useful in order to extract information as the particle evolves from a prepared state to a finally detected state. The physical meaning of this information has been open to debate, particularly in view of the apparent discontinuous trajectories of the particle recorded by WMs. In this work we investigate the properties of vanishing weak values for projection operators as well as general observables. We then analyze the implications when inferring the past of a quantum particle. We provide a nonoptical example for which apparent discontinuous trajectories are obtained by WMs. Our approach is compared to previous results.
Vaidman, Phys.Rev. A 87, 052104 (2013), has proposed a weak value criterion for the past of a quantum particle, and applied it to photons in a particular setup of nested Mach-Zehnder interferometers. From his analysis, he draws some astonishing conclusions regarding which arms of the setup the photons populate. I argue that the weak values Vaidman employs as weak tracers in his analysis cannot be used in this case and that, consequently, the conclusions he draws cannot be upheld. The reason is that weak values are defined as a limit which in this case turns out to be discontinuous. I propose instead a weak mean value criterion which avoids these shortcomings.