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Full-Text Articles in Physics
Conservation Laws And The Foundations Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Conservation Laws And The Foundations Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a recent paper, [Y. Aharonov, S. Popescu, D. Rohrlich, Proc. Natl. Acad. Sci. U.S.A.118 e1921529118 (2021)], it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature and it can and must be revisited to address the issue of conservation/nonconservation in individual cases. Specifically, in the above paper, an experiment was presented in which it can be proven that in some individual cases, energy is not conserved, despite being conserved statistically. It was felt however that this is worrisome and …
Uncertainty From The Aharonov–Vaidman Identity, Matthew S. Leifer
Uncertainty From The Aharonov–Vaidman Identity, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article, I show how the Aharonov–Vaidman identity A|ψ>=<A⟩|ψ>+ΔA| ψ⊥A> can be used to prove relations between the standard deviations of observables in quantum mechanics. In particular, I review how it leads to a more direct and less abstract proof of the Robertson uncertainty relation ΔAΔB≥12|< [A,B]>| than the textbook proof. I discuss the relationship between these two proofs and show how the Cauchy–Schwarz inequality can be derived from the Aharonov–Vaidman identity. I give Aharonov–Vaidman based proofs of the Maccone–Pati uncertainty relations …
Is There Causation In Fundamental Physics? New Insights From Process Matrices And Quantum Causal Modelling, Emily Adlam
Is There Causation In Fundamental Physics? New Insights From Process Matrices And Quantum Causal Modelling, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article we set out to understand the significance of the process matrix formalism and the quantum causal modelling programme for ongoing disputes about the role of causation in fundamental physics. We argue that the process matrix programme has correctly identified a notion of ‘causal order’ which plays an important role in fundamental physics, but this notion is weaker than the common-sense conception of causation because it does not involve asymmetry. We argue that causal order plays an important role in grounding more familiar causal phenomena. Then we apply these conclusions to the causal modelling programme within quantum foundations, …
Failed Attempt To Escape From The Quantum Pigeon Conundrum, Yakir Aharonov, Shrobona Bagchi, Justin Dressel, Gregory Reznik, Michael Ridley, Lev Vaidman
Failed Attempt To Escape From The Quantum Pigeon Conundrum, Yakir Aharonov, Shrobona Bagchi, Justin Dressel, Gregory Reznik, Michael Ridley, Lev Vaidman
Mathematics, Physics, and Computer Science Faculty Articles and Research
A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with pre- and postselection is clarified.
On Conservation Laws In Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
On Conservation Laws In Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
Conservation laws are one of the most important aspects of nature. As such, they have been intensively studied and extensively applied, and are considered to be perfectly well established. We, however, raise fundamental question about the very meaning of conservation laws in quantum mechanics. We argue that, although the standard way in which conservation laws are defined in quantum mechanics is perfectly valid as far as it goes, it misses essential features of nature and has to be revisited and extended.
The Nature Of The Heisenberg-Von Neumann Cut: Enhanced Orthodox Interpretation Of Quantum Mechanics, Ashok Narasimhan, Deepak Chopra, Menas Kafatos
The Nature Of The Heisenberg-Von Neumann Cut: Enhanced Orthodox Interpretation Of Quantum Mechanics, Ashok Narasimhan, Deepak Chopra, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the issue of the Heisenberg-von Neumann cut in light of recent interpretations of quantum eraser experiments which indicate the possibility of a universal Observer outside space-time at an information level of existence. The delayed-choice aspects of observation, measurement, the role of the observer, and information in the quantum framework of the universe are discussed. While traditional double-slit experiments are usually interpreted as indicating that the collapse of the wave function involves choices by an individual observer in space-time, the extension to quantum eraser experiments brings in some additional subtle aspects relating to the role of observation and what …
Completely Top–Down Hierarchical Structure In Quantum Mechanics, Yakir Aharonov, Eliahu Cohen, Jeff Tollaksen
Completely Top–Down Hierarchical Structure In Quantum Mechanics, Yakir Aharonov, Eliahu Cohen, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest “atoms”? In this paper we answer these questions in the negative for a specific class of systems and measurements. After a general introduction of the topic, we present the main idea with a simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to surprising effects within atomic and electromagnetic systems. A general construction based on preand postselected ensembles is then suggested, wherein the Nbody …
The Participating Mind In The Quantum Universe, Menas Kafatos, Keun-Hang Susan Yang
The Participating Mind In The Quantum Universe, Menas Kafatos, Keun-Hang Susan Yang
Mathematics, Physics, and Computer Science Faculty Articles and Research
The Orthodox interpretation of quantum mechanics, which followed the Copenhagen Interpretation but was enhanced by primarily Werner Heisenberg and John von Neumann into a fully developed theory, brought in, among others, the role of measurement, available choices and response of the quantum system. It is, more consistent and clear than other interpretations of quantum mechanics as it provides account of the interactions of observers with the external world. As such, the Orthodox interpretation does a lot more than just account for physical interactions in the atomic world, which was the original goal of quantum mechanics in the early part of …
Sheaf Theoretic Formulation For Consciousness And Qualia And Relationship To The Idealism Of Non-Dual Philosophies, Menas Kafatos, Goro Kato
Sheaf Theoretic Formulation For Consciousness And Qualia And Relationship To The Idealism Of Non-Dual Philosophies, Menas Kafatos, Goro Kato
Mathematics, Physics, and Computer Science Faculty Articles and Research
Questions about the nature of reality, whether Consciousness is the fundamental reality in the universe, and what is Consciousness itself, have no answer in systems that assume an external reality independent of Consciousness. Ultimately, the ontological foundation of such systems is the absolute division of subject and object. We advocate instead what we consider to be an approach that is in agreement with the foundation of quantum reality, which is based on Rāmānuja’s version of Vedanta philosophy and non-dual Kashmir Śaivism. Quantum mechanics opened the door to consciousness, but it cannot account for consciousness. However, the quantum measurement problem implies …
Preserving Entanglement During Weak Measurement Demonstrated With A Violation Of The Bell–Leggett–Garg Inequality, T. C. White, J. Y. Mutus, Justin Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, John M. Martinis
Preserving Entanglement During Weak Measurement Demonstrated With A Violation Of The Bell–Leggett–Garg Inequality, T. C. White, J. Y. Mutus, Justin Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, John M. Martinis
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak measurement has provided new insight into the nature of quantum measurement, by demonstrating the ability to extract average state information without fully projecting the system. For single-qubit measurements, this partial projection has been demonstrated with violations of the Leggett–Garg inequality. Here we investigate the effects of weak measurement on a maximally entangled Bell state through application of the Hybrid Bell–Leggett–Garg inequality (BLGI) on a linear chain of four transmon qubits. By correlating the results of weak ancilla measurements with subsequent projective readout, we achieve a violation of the BLGI with 27 s.d.s. of certainty.
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Mathematics, Physics, and Computer Science Faculty Articles and Research
Retrocausal models of quantum mechanics add further weight to the conflict between causality and the possible existence of free will. We analyze a simple closed causal loop ensuing from the interaction between two systems with opposing thermodynamic time arrows, such that each system can forecast future events for the other. The loop is avoided by the fact that the choice to abort an event thus forecasted leads to the destruction of the forecaster's past. Physical law therefore enables prophecy of future events only as long as this prophecy is not revealed to a free agent who can otherwise render it …
Weak Values Obtained In Matter-Wave Interferometry, Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Hartmutt Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa
Weak Values Obtained In Matter-Wave Interferometry, Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Hartmutt Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak values, introduced more than 25 years ago, underwent a metamorphosis from a theoretical curiosity to a powerful resource in photonics for exploring foundations of quantum mechanics, as well as a practical laboratory tool. Due to the tiny coherence volume of particles used in matter-wave optics, a straightforward implementation of weak measurements is not feasible. We have overcome this hurdle by developing a method to weakly measure a massive particle's spin component. A neutron optical approach is realized by utilizing neutron interferometry, where the neutron's spin is coupled weakly to its spatial degree of freedom. Here, we present how one …
Fundamental Mathematics Of Consciousness, Menas Kafatos
Fundamental Mathematics Of Consciousness, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We explore a mathematical formalism that ties together the observer with the observed in the view that Consciousness is primary, operating through three principles which apply at all levels, the essence of qualia of experience. The formalism is a simplified version of Hilbert space mathematics encountered in quantum mechanics. It does, however, go beyond specific interpretations of quantum mechanics and has strong philosophical foundations in Western philosophy as well as monistic systems of the East. The implications are explored and steps for the full development of this axiomatic mathematical approach to Consciousness are discussed.
Mapping The Optimal Route Between Two Quantum States, S. J. Weber, A. Chantasri, Justin Dressel, Andrew N. Jordan, K. W. Murch, I. Siddiqi
Mapping The Optimal Route Between Two Quantum States, S. J. Weber, A. Chantasri, Justin Dressel, Andrew N. Jordan, K. W. Murch, I. Siddiqi
Mathematics, Physics, and Computer Science Faculty Articles and Research
A central feature of quantum mechanics is that a measurement result is intrinsically probabilistic. Consequently, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance1 to chemical synthesis2. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories3, 4, 5 of a superconducting circuit that evolves under the …
Quantum Non-Barking Dogs, Sara Imari Walker, Paul C. W. Davies, Prasant Samantray, Yakir Aharonov
Quantum Non-Barking Dogs, Sara Imari Walker, Paul C. W. Davies, Prasant Samantray, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Quantum weak measurements with states both pre- and post-selected offer a window into a hitherto neglected sector of quantum mechanics. A class of such systems involves time dependent evolution with transitions possible. In this paper we explore two very simple systems in this class. The first is a toy model representing the decay of an excited atom. The second is the tunneling of a particle through a barrier. The post-selection criteria are chosen as follows: at the final time, the atom remains in its initial excited state for the first example and the particle remains behind the barrier for the …
New Insights On Emergence From The Perspective Of Weak Values And Dynamical Non-Locality, Jeff Tollaksen
New Insights On Emergence From The Perspective Of Weak Values And Dynamical Non-Locality, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article, we will examine new fundamental aspects of "emergence" and "information" using novel approaches to quantum mechanics which originated from the group around Aharonov. 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" …
Point–Counterpoint: Can Anything Be Learned From Surveys On The Interpretations Of Quantum Mechanics?, Matthew S. Leifer, Nathan Harshman
Point–Counterpoint: Can Anything Be Learned From Surveys On The Interpretations Of Quantum Mechanics?, Matthew S. Leifer, Nathan Harshman
Mathematics, Physics, and Computer Science Faculty Articles and Research
"In what follows, Matt Leifer and Nathan Harshman present opposing views on the value of surveys on foundational attitudes towards quantum mechanics. Three such surveys were recently published and their results are summarized in Table 1. Matt takes the `point,’ arguing that such surveys are not useful, while Nathan takes the `counterpoint.’ A complete set of references for both is given at the end."