Counterfactuals, i.e., events that could have occurred but eventually did not, play a unique role in quantum mechanics in that they exert causal effects despite their non-occurrence. They are therefore vital for a better understanding of quantum mechanics (QM) and possibly the universe as a whole. In earlier works, we have studied counterfactuals both conceptually and experimentally. A fruitful framework termed quantum oblivion has emerged, referring to situations where one particle seems to "forget" its interaction with other particles despite the latter being visibly affected. This framework proved to have significant explanatory power, which we now extend to tackle additional riddles. The time-symmetric causality employed by the Two State-Vector Formalism (TSVF) reveals a subtle realm ruled by "weak values," already demonstrated by numerous experiments. They offer a realistic, simple and intuitively appealing explanation to the unique role of quantum non-events, as well as to the foundations of QM. In this spirit, we performed a weak value analysis of quantum oblivion and suggest some new avenues for further research.
Counterfactuals, i.e., events that could have occurred but eventually did not, play a unique role in quantum mechanics in that they exert causal effects despite their non-occurrence. They are therefore vital for a better understanding of quantum mechanics (QM) and possibly the universe as a whole. In earlier works, we have studied counterfactuals both conceptually and experimentally. A fruitful framework termed quantum oblivion has emerged, referring to situations where one particle seems to "forget" its interaction with other particles despite the latter being visibly affected. This framework proved to have significant explanatory power, which we now extend to tackle additional riddles. The time-symmetric causality employed by the Two State-Vector Formalism (TSVF) reveals a subtle realm ruled by "weak values," already demonstrated by numerous experiments. They offer a realistic, simple and intuitively appealing explanation to the unique role of quantum non-events, as well as to the foundations of QM. In this spirit, we performed a weak value analysis of quantum oblivion and suggest some new avenues for further research.
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.
Among the (in)famous differences between classical and quantum mechanics, quantum counterfactuals seem to be the most intriguing. At the same time, they seem to underlie many quantum oddities. In this article, we propose a simple explanation for counterfactuals, on two levels. Quantum Oblivion (QO) is a fundamental type of quantum interaction that we prove to be the origin of quantum counterfactuals. It also turns out to underlie several well-known quantum effects. This phenomenon is discussed in the first part of the article, yielding some novel predictions. In the second part, a hypothesis is offered regarding the unique spacetime evolution underlying QO, termed Quantum Hesitation (QH). The hypothesis invokes advanced actions and interfering weak values, as derived first by the Two-State-Vector Formalism (TSVF). Here too, weak values are argued to underlie the familiar "strong" quantum values. With these, an event that appears to have never occurred can exert causal effects and then succumb to QO by another time-evolution involving negative weak values that eliminate them. We conclude with briefly discussing the implications of these ideas on the nature of time.
While quantum reality can be probed through measurements, the Two-State Vector Formalism (TSVF) reveals a subtler reality prevailing between measurements. Under special pre- and post-selections, odd physical values emerge. This unusual picture calls for a deeper study. Instead of the common, wave-based picture of quantum mechanics, we suggest a new, particle-based perspective: Each particle possesses a definite location throughout its evolution, while some of its physical variables (characterized by deterministic operators, some of which obey nonlocal equations of motion) are carried by "mirage particles" accounting for its unique behavior. Within the time interval between pre- and post-selection, the particle gives rise to a horde of such mirage particles, of which some can be negative. What appears to be "no-particle", known to give rise to interaction-free measurement, is in fact a self-canceling pair of positive and negative mirage particles, which can be momentarily split and cancel out again. Feasible experiments can give empirical evidence for these fleeting phenomena. In this respect, the Heisenberg ontology is shown to be conceptually advantageous compared to the Schrödinger picture. We review several recent advances, discuss their foundational significance and point out possible directions for future research.
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.
A simple quantum interaction is analyzed, where the paths of two superposed particles asymmetrically cross, while a detector set to detect an interaction between them remains silent. Despite this negative result, the particles' states leave no doubt that a peculiar interaction has occurred: One particle's momentum is changed while the other's remains unaffected, in apparent violation of momentum conservation. Revisiting the foundations of the standard quantum measurement process offers the resolution. Prior to the macroscopic recording of no interaction, a brief critical interval (CI) prevails, during which the particles and the detector's pointer form a subtle entanglement which immediately dissolves. It is this self-cancellation, henceforth "quantum oblivion (QO)," that lies at the basis of some well-known intriguing quantum effects. Such is interaction-free measurement (IFM)1 and its more paradoxical variants like Hardy's Paradox2 and the quantum liar paradox.3 Even the Aharonov–Bohm (AB) effect4 and weak measurement (WM)5 turn out to belong to this group. We next study interventions within the CI that produce some other peculiar effects. Finally, we discuss some of the conceptual issues involved. Under a greater time-resolution of the CI, some non-local phenomena turn out to be local. Momentum is conserved due to the quantum uncertainties inflicted by the particle–pointer interaction, which sets the experiment's final boundary condition.
Many counterfactual predictions are made by quantum theory, such as quantum tunneling and violations of Bell’s inequalities. Experimental verifications of these predictions demonstrate that quantum theory is reliable for the microscopic world. Despite its widespread application, consistent theoretical interpretations of quantum theory remain a challenge. Recently, Aharonov et al. proposed several new and intriguing counterfactuals based on quantum weak measurement and interaction-free measurement, such as the quantum violation of the pigeonhole principle and the departure of physical properties from particles, also known as the quantum Cheshire cat effect. These counterfactuals garnered considerable interest. Although no common consensus has been reached, many pioneering experiments have already been conducted in light of these theoretical proposals. Furthermore, these counterfactuals and the key concepts underlying them, weak measurement and interaction-free measurement, open up a whole new way of thinking about and understanding the strange quantum theory. Herein, our aim is to provide a unified perspective on these counterfactuals. The theoretical ideas, particularly the fundamental quantum concepts underlying these counterfactuals, are the focus of our attention. First, we present concise and insightful introductions to weak measurement and interaction-free measurement, which are the two key fundamental constructions for discussing all of the following quantum counterfactuals. Next, we discuss the quantum violation of the pigeonhole principle in depth, explicitly demonstrating that the key idea leading to the violation is destructive quantum interference between the possible paths of two particles traveling along the same path. Then, two key proposals of the quantum Cheshire cat effect are examined based on weak values of certain physical properties. Both proposals are built around interaction-free measurement, and the departure of physical properties from their bodies is realized based on the quantum Zeno effect. After introducing the weak measurement and weak value, the non-locality in the quantum Cheshire cat effect can be dismissed, and the physical properties leave the body continuously with infinitesimal quantum amplitudes. Meanwhile, during the departure, the total property in the entire space remains invariant. Finally, we present our conclusion on quantum counterfactuals, arguing that when coherent processes are endowed with concrete physical properties, counterfactuals are unavoidable. Throughout our discussions, we try to elaborate on the key roles played by the quantum concepts, quantum amplitudes, and quantum coherence in these counterfactuals. The idea behind weak measurement and weak value is that information about a coherent process can be obtained with sufficiently weak coupling. In other words, a quantum coherent process becomes observable with a weak measurement and even acquires a specific property quantified by a weak value. When compared to our conventional understanding of quantum coherent processes, this is a mind-boggling viewpoint. The idea behind interaction-free measurement is that weak amplitudes can cause large system evolution even if they cannot transport the body of the system, which is also astonishing! This demonstrates the enormous power of infinitesimal quantum amplitudes in quantum communication and computation. Therefore, all quantum counterfactuals provide new perspectives to further investigate these fundamental quantum concepts.