Superselection Rules
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Arxiv:Quant-Ph/0105127V3 19 Jun 2003
DECOHERENCE, EINSELECTION, AND THE QUANTUM ORIGINS OF THE CLASSICAL Wojciech Hubert Zurek Theory Division, LANL, Mail Stop B288 Los Alamos, New Mexico 87545 Decoherence is caused by the interaction with the en- A. The problem: Hilbert space is big 2 vironment which in effect monitors certain observables 1. Copenhagen Interpretation 2 of the system, destroying coherence between the pointer 2. Many Worlds Interpretation 3 B. Decoherence and einselection 3 states corresponding to their eigenvalues. This leads C. The nature of the resolution and the role of envariance4 to environment-induced superselection or einselection, a quantum process associated with selective loss of infor- D. Existential Interpretation and ‘Quantum Darwinism’4 mation. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite II. QUANTUM MEASUREMENTS 5 of the environment. Einselection enforces classicality by A. Quantum conditional dynamics 5 imposing an effective ban on the vast majority of the 1. Controlled not and a bit-by-bit measurement 6 Hilbert space, eliminating especially the flagrantly non- 2. Measurements and controlled shifts. 7 local “Schr¨odinger cat” states. Classical structure of 3. Amplification 7 B. Information transfer in measurements 9 phase space emerges from the quantum Hilbert space in 1. Action per bit 9 the appropriate macroscopic limit: Combination of einse- C. “Collapse” analogue in a classical measurement 9 lection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselec- III. CHAOS AND LOSS OF CORRESPONDENCE 11 tion replaces quantum entanglement between the appa- A. Loss of the quantum-classical correspondence 11 B. -
April 2010 Contents
International Association of Mathematical Physics News Bulletin April 2010 Contents International Association of Mathematical Physics News Bulletin, April 2010 Contents Reflections on the IAMP Geography 3 Aharonov-Bohm & Berry Phase Anniversaries 50/25 5 The 25th anniversary of the founding of HARL 8 An interview with Huzihiro Araki 10 Shing-Tung Yau the Wolf Prize laureate 2010 in Mathematics 14 News from the IAMP Executive Committee 22 A new associated member: PIMS 26 Bulletin editor Valentin Zagrebnov Editorial board Evans Harrell, Masao Hirokawa, David Krejˇciˇr´ık, Jan Philip Solovej Contacts [email protected] http://www.iamp.org Cover photo (courtesy of Professor A.Tonomura): From double-slit experiment to the Aharonov-Bohm effect. See a comment at the end of the page 7. The views expressed in this IAMP News Bulletin are those of the authors and do not necessary represent those of the IAMP Executive Committee, Editor or Editorial board. Any complete or partial performance or reproduction made without the consent of the author or of his successors in title or assigns shall be unlawful. All reproduction rights are henceforth reserved, mention of the IAMP News Bulletin is obligatory in the reference. (Art.L.122-4 of the Code of Intellectual Property). 2 IAMP News Bulletin, April 2010 Editorial Reflections on the IAMP Geography by Pavel Exner (IAMP President) The topic of today’s meditation was inspired by complaints of American colleagues about the shaky position our discipline enjoys in the U.S. True, such woes are ubiquitous since com- petition for resources in science was and will always be tough. -
Einselection Without Pointer States
Einselection without pointer states Einselection without pointer states - Decoherence under weak interaction Christian Gogolin Universit¨atW¨urzburg 2009-12-16 C. Gogolin j Universit¨atW¨urzburg j 2009-12-16 1 / 26 Einselection without pointer states j Introduction New foundation for Statistical Mechanics X Thermodynamics X Statistical Mechanics Second Law ergodicity equal a priory probabilities Classical Mechanics [2, 3] C. Gogolin j Universit¨atW¨urzburg j 2009-12-16 2 / 26 Einselection without pointer states j Introduction New foundation for Statistical Mechanics X Thermodynamics X Statistical Mechanics Second Law ergodicity ? equal a priory probabilities Classical Mechanics ? [2, 3] C. Gogolin j Universit¨atW¨urzburg j 2009-12-16 2 / 26 Einselection without pointer states j Introduction New foundation for Statistical Mechanics X Thermodynamics X Statistical Mechanics [2, 3] C. Gogolin j Universit¨atW¨urzburg j 2009-12-16 2 / 26 Einselection without pointer states j Introduction New foundation for Statistical Mechanics X Thermodynamics X Statistical Mechanics * Quantum Mechanics X [2, 3] C. Gogolin j Universit¨atW¨urzburg j 2009-12-16 2 / 26 quantum mechanical orbitals discrete energy levels coherent superpositions hopping Einselection without pointer states j Introduction Why do electrons hop between energy eigenstates? C. Gogolin j Universit¨atW¨urzburg j 2009-12-16 3 / 26 discrete energy levels hopping Einselection without pointer states j Introduction Why do electrons hop between energy eigenstates? quantum mechanical orbitals coherent superpositions C. Gogolin j Universit¨atW¨urzburg j 2009-12-16 3 / 26 Einselection without pointer states j Introduction Why do electrons hop between energy eigenstates? quantum mechanical orbitals discrete energy levels coherent superpositions hopping C. -
A Model-Theoretic Interpretation of Environmentally-Induced
A model-theoretic interpretation of environmentally-induced superselection Chris Fields 815 East Palace # 14 Santa Fe, NM 87501 USA fi[email protected] November 28, 2018 Abstract The question of what constitutes a “system” is foundational to quantum mea- surement theory. Environmentally-induced superselection or “einselection” has been proposed as an observer-independent mechanism by which apparently classical sys- tems “emerge” from physical interactions between degrees of freedom described com- pletely quantum-mechanically. It is shown here that einselection can only generate classical systems if the “environment” is assumed a priori to be classical; einselection therefore does not provide an observer-independent mechanism by which classicality can emerge from quantum dynamics. Einselection is then reformulated in terms of positive operator-valued measures (POVMs) acting on a global quantum state. It is shown that this re-formulation enables a natural interpretation of apparently-classical systems as virtual machines that requires no assumptions beyond those of classical arXiv:1202.1019v2 [quant-ph] 13 May 2012 computer science. Keywords: Decoherence, Einselection, POVMs, Emergence, Observer, Quantum-to-classical transition 1 Introduction The concept of environmentally-induced superselection or “einselection” was introduced into quantum mechanics by W. Zurek [1, 2] as a solution to the “preferred-basis problem,” 1 the problem of selecting one from among the arbitrarily many possible sets of basis vectors spanning the Hilbert space of a system of interest. Zurek’s solution was brilliantly simple: it transferred the preferred basis problem from the observer to the environment in which the system of interest is embedded, and then solved the problem relative to the environment. -
Decoherence and the Transition from Quantum to Classical—Revisited
Decoherence and the Transition from Quantum to Classical—Revisited Wojciech H. Zurek This paper has a somewhat unusual origin and, as a consequence, an unusual structure. It is built on the principle embraced by families who outgrow their dwellings and decide to add a few rooms to their existing structures instead of start- ing from scratch. These additions usually “show,” but the whole can still be quite pleasing to the eye, combining the old and the new in a functional way. What follows is such a “remodeling” of the paper I wrote a dozen years ago for Physics Today (1991). The old text (with some modifications) is interwoven with the new text, but the additions are set off in boxes throughout this article and serve as a commentary on new developments as they relate to the original. The references appear together at the end. In 1991, the study of decoherence was still a rather new subject, but already at that time, I had developed a feeling that most implications about the system’s “immersion” in the environment had been discovered in the preceding 10 years, so a review was in order. While writing it, I had, however, come to suspect that the small gaps in the landscape of the border territory between the quantum and the classical were actually not that small after all and that they presented excellent opportunities for further advances. Indeed, I am surprised and gratified by how much the field has evolved over the last decade. The role of decoherence was recognized by a wide spectrum of practic- 86 Los Alamos Science Number 27 2002 ing physicists as well as, beyond physics proper, by material scientists and philosophers. -
Decoherence, Einselection, and the Quantum Origins of the Classical
REVIEWS OF MODERN PHYSICS, VOLUME 75, JULY 2003 Decoherence, einselection, and the quantum origins of the classical Wojciech Hubert Zurek Theory Division, LANL, Mail Stop B210, Los Alamos, New Mexico 87545 (Published 22 May 2003) The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ‘‘Schro¨ dinger-cat states.’’ The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between -
Arthur Strong Wightman (1922–2013)
Obituary Arthur Strong Wightman (1922–2013) Arthur Wightman, a founding father of modern mathematical physics, passed away on January 13, 2013 at the age of 90. His own scientific work had an enormous impact in clar- ifying the compatibility of relativity with quantum theory in the framework of quantum field theory. But his stature and influence was linked with an enormous cadre of students, scientific collaborators, and friends whose careers shaped fields both in mathematics and theoretical physics. Princeton has a long tradition in mathematical physics, with university faculty from Sir James Jeans through H.P. Robertson, Hermann Weyl, John von Neumann, Eugene Wigner, and Valentine Bargmann, as well as a long history of close collaborations with colleagues at the Institute for Advanced Study. Princeton became a mecca for quantum field theorists as well as other mathematical physicists during the Wightman era. Ever since the advent of “axiomatic quantum field theory”, many researchers flocked to cross the threshold of his open office door—both in Palmer and later in Jadwin—for Arthur was renowned for his generosity in sharing ideas and research directions. In fact, some students wondered whether Arthur might be too generous with his time helping others, to the extent that it took time away from his own research. Arthur had voracious intellectual appetites and breadth of interests. Through his interactions with others and his guidance of students and postdocs, he had profound impact not only on axiomatic and constructive quantum field theory but on the de- velopment of the mathematical approaches to statistical mechanics, classical mechanics, dynamical systems, transport theory, non-relativistic quantum mechanics, scattering the- ory, perturbation of eigenvalues, perturbative renormalization theory, algebraic quantum field theory, representations of C⇤-algebras, classification of von Neumann algebras, and higher spin equations. -
'Einselection' of Pointer Observables
‘Einselection’ of Pointer Observables: The New H-Theorem? Ruth E. Kastner † 16 June 2014 to appear in Studies in History and Philosophy of Modern Physics ABSTRACT. In attempting to derive irreversible macroscopic thermodynamics from reversible microscopic dynamics, Boltzmann inadvertently smuggled in a premise that assumed the very irreversibility he was trying to prove: ‘molecular chaos.’ The program of ‘Einselection’ (environmentally induced superselection) within Everettian approaches faces a similar ‘Loschmidt’s Paradox’: the universe, according to the Everettian picture, is a closed system obeying only unitary dynamics, and it therefore contains no distinguishable environmental subsystems with the necessary ‘phase randomness’ to effect einselection of a pointer observable. The theoretically unjustified assumption of distinguishable environmental subsystems is the hidden premise that makes the derivation of einselection circular. In effect, it presupposes the ‘emergent’ structures from the beginning. Thus the problem of basis ambiguity remains unsolved in Everettian interpretations. 1. Introduction The decoherence program was pioneered by Zurek, Joos, and Zeh, 1 and has become a widely accepted approach for accounting for the appearance of stable macroscopic objects. In particular, decoherence has been used as the basis of arguments that sensible, macroscopic ‘pointer observables’ of measuring apparatuses are ‘einselected’ – selected preferentially by the environment. An important application of ‘einselection’ is in Everettian or ‘Many Worlds’ Interpretations (MWI), a class of interpretations that view all ‘branches’ of the quantum state as equally real. MWI abandons the idea of non-unitary collapse and allows only the unitary Schrödinger evolution of the quantum state. It has long been known that MWI suffers from a ‘basis arbitrariness’ problem; i.e., it has no way of explaining why the ‘splitting’ of worlds or of macroscopic objects such as apparatuses and observes occurs with respect to realistic bases that one would expect. -
Decoherence and Einselection in Equilibrium in an Adapted Caldeira Leggett Model
Decoherence and einselection in equilibrium in an adapted Caldeira Leggett model Andreas Albrecht Center for Quantum Mathematics and Physics (QMAP) and Department of Physics UC Davis Seminar University of Nottingham April 4, 2019 Supported by the US Department of Energy 4/4/19 A. Albrecht Nottingham seminar 1 Outline 1. Motivations 2. Introduction to einselection and the toy model 3. Einselection in equilibrium (technical explorations and overall assessment) 4. Eigenstate Einselection Hypothesis (if there is time) 5. Conclusions 4/4/19 A. Albrecht Nottingham seminar 2 Outline 1. Motivations 2. Introduction to einselection and the toy model 3. Einselection in equilibrium (technical explorations and overall assessment) 4. Eigenstate Einselection Hypothesis (if there is time) With A. Arrasmith 5. Conclusions 4/4/19 A. Albrecht Nottingham seminar 3 Outline 1. Motivations 2. Introduction to einselection and the toy model 3. Einselection in equilibrium (technical explorations and overall assessment) 4. Eigenstate Einselection Hypothesis (if there is time) 5. Conclusions 4/4/19 A. Albrecht Nottingham seminar 4 Comments on the arrow of time in cosmology (at board) 4/4/19 A. Albrecht Nottingham seminar 5 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc. 4/4/19 A. Albrecht Nottingham seminar 6 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc. ➔ Explore the process of einselection in a toy model, relate to AoT, etc. 4/4/19 A. Albrecht Nottingham seminar 7 Q: What features of the universe are correlated with classicality? • Arrow of time? • Locality? • Etc.Related to the emergence of classical ➔ Explore the process of einselection in a toy model, relate to AoT, etc. -
Solutions in Constructive Field Theory
Solutions in Constructive Field Theory Leif Hancox-Li ∗ [email protected] June 7, 2016 Abstract Constructive field theory aims to rigorously construct concrete, non-trivial solutions to Lagrangians used in particle physics, where the solutions satisfy some relevant set of axioms. I examine the relationship of solutions in constructive field theory to both axiomatic and Lagrangian quantum field theory (QFT). I argue that Lagrangian QFT provides conditions for what counts as a successful constructive solution, and that it provides other information that guides constructive field theorists to solutions. Solutions matter because they describe the behavior of QFT systems, and thus what QFT says the world is like. Constructive field theory, in incorporating ingredients from both axiomatic and Lagrangian QFT, clarifies existing disputes about which parts of QFT are philosophically relevant and how rigor relates to these disputes. ∗I thank Bob Batterman and Michael Miller for comments and encouragement. Several anonymous referees also contribued valuable comments. Copyright Philosophy of Science 2016 Preprint (not copyedited or formatted) Please use DOI when citing or quoting 1 Introduction To date, philosophers of quantum field theory (QFT) have paid much attention to roughly two kinds of QFT: axiomatic approaches to algebraic QFT (Halvorson and Muger,¨ 2006), and Lagrangian-based QFT as used by particle physicists (Wallace, 2006). Comparatively less attention, however, has been paid to constructive QFT, an approach that aims to rigorously construct non-trivial solutions of QFT for Lagrangians and Hamiltonians that are important in particle physics, ensuring that such solutions satisfy certain axioms. In doing so, constructive QFT mediates between axiomatic approaches to QFT and physicists’ Lagrangian-based QFT. -
Decoherence: an Explanation of Quantum Measurement
Decoherence: An Explanation of Quantum Measurement Jason Gross\ast Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139-4307 (Dated: May 5, 2012) The description of the world given by quantum mechanics is at odds with our classical experience. Most of this conflict resides in the concept of \measurement". After explaining the originsof the controversy, and introducing and explaining some of the relevant mathematics behind density matrices and partial trace, I will introduce decoherence as a way of describing classical measurements from an entirely quantum perspective. I will discuss basis ambiguity and the problem of information flow in a system + observer model, and explain how introducing the environment removes this ambiguity via environmentally-induced superselection. I will use a controlled not gate as a toy model of measurement; including a one-bit environment will provide an example of how interaction can pick out a preferred basis, and included an N-bit environment will give a toy model of decoherence. I. INTRODUCTION function over each independent observable. Moreover, the law of superposition, which states that any linear For any physicist who learns classical mechanics before combination of valid quantum states is also valid, gives quantum mechanics, the theory of quantum mechanics at rise to states that do not seem to correspond to any clas- first appears to be a strange and counter-intuitive wayto sical system anyone has experienced. The most famous describe the world. The correspondence between classical example of such a state is that of Schr\"odinger'shypo- experience and quantum theory is not obvious, and has thetical cat, which is in a superposition of being alive been at the core of debates about the interpretation of and being dead. -
Decoherence and the Transition from Quantum to Classical—Revisited
Decoherence and the Transition from Quantum to Classical—Revisited Wojciech H. Zurek This paper has a somewhat unusual origin and, as a consequence, an unusual struc- ture. It is built on the principle embraced by families who outgrow their dwellings and decide to add a few rooms to their existing structures instead of starting from scratch. These additions usually “show,” but the whole can still be quite pleasing to the eye, combining the old and the new in a functional way. What follows is such a “remodeling” of the paper I wrote a dozen years ago for Physics Today (1991). The old text (with some modifications) is interwoven with the new text, but the additions are set off in boxes throughout this article and serve as a commentary on new developments as they relate to the original. The references appear together at the end. In 1991, the study of decoherence was still a rather new subject, but already at that time, I had developed a feeling that most implications about the system’s “immersion” in the environment had been discovered in the preceding 10 years, so a review was in order. While writing it, I had, however, come to suspect that the small gaps in the land- scape of the border territory between the quantum and the classical were actually not that small after all and that they presented excellent opportunities for further advances. Indeed, I am surprised and gratified by how much the field has evolved over the last decade. The role of decoherence was recognized by a wide spectrum of practicing physicists as well as, beyond physics proper, by material scientists and philosophers.