Physics Commons^™

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

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

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, …

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The “Quantal Newtonian” Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen–Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a “probability amplitude.” A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or “Quantal Newtonian” Laws obeyed by each electron. These Laws, derived from …

What Is A Photon? Foundations Of Quantum Field Theory, Charles G. Torre

All Physics Faculty Publications

This is a brief, informal, and relatively low-level course on the foundations of quantum field theory. The prerequisites are undergraduate courses in quantum mechanics and electromagnetism.

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The 'Quantal Newtonian' Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a ‘probability amplitude’. A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper we present a new perspective on such determinism. The ideas are based on the equations of motion or ‘Quantal Newtonian’ Laws obeyed by each electron. These Laws, derived from the …

Limits On Parameter Estimation Of Quantum Channels, Vishal Katariya

LSU Doctoral Dissertations

The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We begin by describing the classical task of parameter estimation that we build upon. In its most basic form, parameter estimation is the task of obtaining an estimate of an unknown parameter from some experimental data. This experimental data can be seen as a number of samples of a parameterized probability distribution. In general, the goal of such a task is to obtain an estimate of the unknown parameter while minimizing its error.

We study the task of estimating unknown parameters which …

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.

Patrick Aidan Heelan’S The Observable: Heisenberg’S Philosophy Of Quantum Mechanics, Paul Downes

Research Resources

The publication of Patrick Aidan Heelan’s The Observable, with forewords from Michel Bitbol, editor Babette Babich and the author himself, offers a timely invitation to reconsider the relation between quantum physics and continental philosophy.

Patrick Heelan does so, as a contemporary of and interlocutor with Werner Heisenberg on these issues, as a physicist himself who trained with leading figures of quantum mechanics (QM), Erwin Schrödinger and Eugene Wigner. Moreover, Heelan highlights Heisenberg’s interest in phenomenology as ‘a friend and frequent visitor of Martin Heidegger’ (55). Written originally in 1970 and unpublished then for reasons Babich explicates in her foreword, …

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

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 …

An Introduction To Supersymmetric Quantum Mechanics, Vincent R. Siggia

Theses and Dissertations

In this thesis, the general framework of supersymmetric quantum mechanics and the path integral approach will be presented (as well as the worked out example of the supersymmetric harmonic oscillator). Then the theory will be specialized to the case of supersymmetric quantum mechanics on Riemannian manifolds, which will start from a supersymmetric Lagrangian for the general case and the special case for S2. Afterwards, there will be a discussion on the superfield formalism. Concluding this thesis will be the Hamiltonian formalism followed by the inclusion of deforma- tions by potentials.

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

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

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 …

Exomol Line List – Xxi. Nitric Oxide (No), Andy Wong, Sergei N. Yurchenko, Peter Bernath, Holger S.P. Müller, Stephanie Mcconkey, Jonathan Tennyson

Chemistry & Biochemistry Faculty Publications

Line lists for the X ²Pi electronic ground state for the parent isotopologue of nitric oxide (¹⁴N¹⁶O) and five other major isotopologues (¹⁴N¹⁷O, ¹⁴N¹⁸O, ¹⁵N¹⁶O, ¹⁵N¹⁷O and ¹⁵N¹⁸O) are presented. The line lists are constructed using empirical energy levels (and line positions) and high-level ab initio intensities. The energy levels were obtained using a combination of two approaches, from an effective Hamiltonian and from solving the rovibronic Schrödinger equation variationally. The effective Hamiltonian model was obtained through a fit …

Combinatorial Algorithms For Perturbation Theory And Application On Quantum Computing, Yudong Cao

Open Access Dissertations

Quantum computing is an emerging area between computer science and physics. Numerous problems in quantum computing involve quantum many-body interactions. This dissertation concerns the problem of simulating arbitrary quantum many-body interactions using realistic two-body interactions. To address this issue, a general class of techniques called perturbative reductions (or perturbative gadgets) is adopted from quantum complexity theory and in this dissertation these techniques are improved for experimental considerations. The idea of perturbative reduction is based on the mathematical machinery of perturbation theory in quantum physics. A central theme of this dissertation is then to analyze the combinatorial structure of the perturbation …

Art As A Tool In Quantum Mechanics, Zachary Vealey

Oglethorpe Journal of Undergraduate Research

Revolutions in scientific thought often have substantial societal consequences, however, cultural assimilation of the new idea is contingent on a widespread understanding. Historically recent developments in modern physics, such as quantum mechanics and general relativity, suffer from their notoriously perceived difficulty, thus hindering cultural assimilation. To address this issue, art can serve as a useful complement to a student studying quantum mechanics - especially through its interpretation of delocalized electron density. A cross-disciplinary approach affords a greater diversity in participation and consequently results in a broader scientific outreach.

Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall

Randall W. Hall

Feynman’s path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4–Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born–Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results …

Quantum Computers Are Coming And Will Be Able To Solve Complex Aviation And Aerospace Problems, Nihad E. Daidzic

Aviation Department Publications

No abstract provided.

Elements Of The Mathematical Formulation Of Quantum Mechanics, Keunjae Go

Senior Honors Papers / Undergraduate Theses

In this paper, we will explore some of the basic elements of the mathematical formulation of quantum mechanics. In the first section, I will list the motivations for introducing a probability model that is quite different from that of the classical probability theory, but still shares quite a few significant commonalities. Later in the paper, I will discuss the quantum probability theory in detail, while paying a brief attention to some of the axioms (by Birkhoff and von Neumann) that illustrate both the commonalities and differences between classical mechanics and quantum mechanics. This paper will end with a presentation of …

Naïve Physics And Quantum Mechanics: The Cognitive Bias Of Everett’S Many-Worlds Interpretation, Andrew Lang

College of Science and Engineering Faculty Research and Scholarship

We discuss the role that intuitive theories of physics play in the interpretation of quantum mechanics. We compare and contrast naïve physics with quantum mechanics and argue that quantum mechanics is not just hard to understand but that it is difficult to believe, often appearing magical in nature. Quantum mechanics is often discussed in the context of "quantum weirdness" and quantum entanglement is known as "spooky action at a distance." This spookiness is more than just because quantum mechanics doesn't match everyday experience; it ruffles the feathers of our naïve physics cognitive module. In Everett's many-worlds interpretation of quantum mechanics, …

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

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 …

Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu

Asim Gangopadhyaya

We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h.

Spin-Dependent Two-Color Kapitza-Dirac Effects, Scot Mcgregor, Wayne Cheng-Wei Huang, Herman Batelaan, Bradley Allan Shadwick

Department of Physics and Astronomy: Faculty Publications

In this paper we present an analysis of the spin behavior of electrons propagating through a laser field. We present an experimentally realizable scenario in which spin-dependent effects of the interaction between the laser and the electrons are dominant. The laser interaction strength and incident electron velocity are in the nonrelativistic domain. This analysis may thus lead to novel methods of creating and characterizing spin-polarized nonrelativistic femtosecond electron pulses.

Discrete Excitation Spectrum Of A Classical Harmonic Oscillator In Zero-Point Radiation, Wayne Cheng-Wei Huang, Herman Batelaan

Department of Physics and Astronomy: Faculty Publications

We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.

Differentiability Of Correlations In Realistic Quantum Mechanics, Alejandro Cabrera, Edson De Faria, Enrique Pujals, Charles Tresser

Publications and Research

We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed …

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

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.