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, …

The Effect Of Damping By An Environment On Emergence Of Classicality, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The role of dissipation with respect to a microscopic superposition of quantum states is investigated by means of master equations. This has implications for the study of the emergence of classicality from the quantum level. In particular, it illustrates why it is difficult to observe a macroscopic quantum state. The role of the environment is assumed by the measuring apparatus. A pure state is reduced to a mixture in the pointer basis of the system by means of the interaction with the apparatus. It is the intention that this type of analysis will have applications to experiments which are designed …

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.

A New Look At The Quantum Liouville Theorem, P. T. Leung, G. I. Ni

Physics Faculty Publications and Presentations

We clarify certain confusions in the literature of the density operator in quantum mechanics, and demonstrate that the quantum Liouville theorem has the same form in both the Schrodinger and the Heisenberg pictures. Our starting point is to treat the density operator as an observable which has its specific time dependence in each of the two pictures. It is further shown that such a formulation will provide the exact correspondence between classical and quantum statistical mechanics with the Liouville theorem being interpreted as a conservation law, which is derivable from the equation of motion only in the quantum case.

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 …

Building Confidence In The Dirac Δ-Function, Asim Gangopadhyaya, Constantin Rasinariu

Constantin Rasinariu

In this note we present an example from undergraduate quantum mechanics designed to highlight the versatility of the Dirac δ-function. Namely, we compute the expectation value of the Hamiltonian of a free particle in a state described by a triangular wave function ψ(x). Since the first derivative of ψ(x) is piecewise constant, and because this Hamiltonian is proportional to the second order spatial derivative, students often end up finding the expectation value to be zero—an unphysical answer. This problem provides a pedagogical application of the Dirac δ-function. By arriving at the same result via alternate pathways, this exercise reinforces students’ …

Beyond Density Functional Theory: The Multiconfigurational Approach To Model Heterogeneous Catalysis, Samuel J. Stoneburner, Carlo Alberto Gaggioli, Christopher J. Cramer, Laura Gagliardi

Educator Scholarship

Catalytic processes are crucially important for many practical chemical applications. Heterogeneous catalysts are especially appealing because of their high stability and the relative ease with which they may be recovered and reused. Computational modeling can play an important role in the design of more catalytically active materials through the identification of reaction mechanisms and the opportunity to assess hypothetical catalysts in silico prior to experimental verification. Kohn-Sham density functional theory (KS-DFT) is the most used method in computational catalysis because it is affordable and it gives results of reasonable accuracy in many instances. Furthermore, it can be employed in a …

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 …

Building Confidence In The Dirac Δ-Function, Asim Gangopadhyaya, Constantin Rasinariu

Physics: Faculty Publications and Other Works

In this note we present an example from undergraduate quantum mechanics designed to highlight the versatility of the Dirac δ-function. Namely, we compute the expectation value of the Hamiltonian of a free particle in a state described by a triangular wave function ψ(x). Since the first derivative of ψ(x) is piecewise constant, and because this Hamiltonian is proportional to the second order spatial derivative, students often end up finding the expectation value to be zero—an unphysical answer. This problem provides a pedagogical application of the Dirac δ-function. By arriving at the same result via alternate pathways, this exercise reinforces students’ …

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 …

Gravitationally Induced Quantum Superposition Reduction With Large Extra Dimensions, Jonas R. Mureika

Jonas Mureika

A gravity-driven mechanism (``objective reduction'') proposed to explain quantum state reduction is analyzed in light of the possible existence of large extra dimensions in the ADD scenario. By calculating order-of-magnitude estimates for nucleon superpositions, it is shown that if the mechanism at question is correct, constraints may be placed on the number and size of extra dimensions. Hence, measurement of superposition collapse times ({\it e.g.} through diffraction or reflection experiments) could represent a new probe of extra dimensions. The influence of a time-dependent gravitational constant on the gravity-driven collapse scheme with and without the presence of extra dimensions is also …

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 …

Foundations, 1, David Peak

Foundations

Quantum mechanics is money

Text message and take a picture with your smart phone; watch a movie on your Blu-ray player; get the bar code on your bag of chips scanned; obtain an MRI image of your aching shoulder; take a ride on a maglev train. None of these—and countless other—things would be possible without quantum mechanics! Leon Lederman, Nobel Prize winning physicist, is widely quoted as saying that 1/3 of the world’s economy is due to quantum mechanics. Lederman’s estimate is actually probably too low, but what surely is the case is that computers, lasers, and superconducting magnets (to …

The Classical Limit Of Entropic Quantum Dynamics, Anthony V. Demme

Physics

The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ~ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and …

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, …