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.
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.
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.
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.
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.
What is the true meaning of quantum superposition? Can a particle genuinely reside in several places simultaneously? These questions lie at the heart of this paper which presents an updated survey of some important stages in the evolution of the three-boxes paradox, as well as novel conclusions drawn from it. We begin with the original thought experiment of Aharonov and Vaidman, and proceed to its non-counterfactual version. The latter was recently realized by Okamoto and Takeuchi using a quantum router. We then outline a dynamic version of this experiment, where a particle is shown to "disappear" and "re-appear" during the time evolution of the system. This surprising prediction based on self-cancellation of weak values is directly related to our notion of Quantum Oblivion. Finally, we present the non-counterfactual version of this disappearing-reappearing experiment. Within the near future, this last version of the experiment is likely to be realized in the lab, proving the existence of exotic hitherto unknown forms of superposition. With the aid of Bell's theorem, we prove the inherent nonlocality and nontemporality underlying such pre- and post-selected systems, rendering anomalous weak values ontologically real.
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.
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.