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Understanding the pointer states

Carlos Alexandre Brasil

Published Jan 1, 2015• 12 citations
OpenAlex

Abstract

Abstract: In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in Everett's relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett's thesis. In this article, we review the measurement process according to von Neumann, Everett's relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek's primordial paper that consolidated the concept of pointer states, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems-one representing the main system, the other the measurement apparatus-and a thermal bath-representing the environment-we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses

Related papers

Understanding the pointer states

Carlos Alexandre Brasil, Leonardo Andreta de Castro

Abstract In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in Everett’s relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett’s thesis. In this article, we review the measurement process according to von Neumann, Everett’s relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek’s primordial paper that consolidated the concept of pointer states, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems—one representing the main system, the other the measurement apparatus—and a thermal bath—representing the environment—we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.

arXiv:1508.04101•European Journal of Physics•Sep 8, 2015•13 citations

Measurement in Quantum Mechanics: Decoherence and the Pointer Basis

Anu Venugopalan

Quantum Mechanics represents one of the greatest triumphs of the scientific enterprise of the twentieth century. The stunning success of quantum theory has led to many revolutionary inventions and its extraordinary concepts describe the heart of several important real world applications like transistors and lasers. The theory makes accurate predictions about a wide range of physical phenomena and has historically withstood the tests and scrutiny of every experimental investigation. However, inspite of the fact that quantum theory is widely regarded by the scientific establishment as the fundamental theory of nature and is immensly successful and useful, its conceptual framework makes many predictions which are difficult to comprehend “classically. The theory is, pardoxically, powerful and confusing at the same time. Quantum theory’s unusual predictions originate from its basic formailsm which involves concepts like probability amplitudes and the linear superposition principle(Dirac, 1947). The quantum view appears abstract and counterintuitive and at odds with classical perceptions. Many of the conceptual problems of quantum mechanics are encompassed in what is known as the quantum measurement problem(Peres, 1986; von Neumann, 1932; Wheeler & Zurek, 1983). Conventionally, the measurement paradox is supposedly ’resolved’ by forcing a notion of a sudden collapse of the state vector of the system being measured. However, the nature of this mechanism is at odds with the basic tenets of quantum mechanics and hence may lie outside its realm thus questioning the validity of the theory it self. Closely related with the problem of measurement in quantum mechanics is the question of its connection with the emergence of classicality and the elusive boundary between quantum and classical worlds. What is the connection between the ‘classical’ and the ‘quantum’ worlds? Is there a definite relationship? Are classical mechanics and quantum mechanics two mutually exclusive incompatible theories or are they two aspects of the same underlying philosophy? Classical objects are eventually composed of elements of the microworld which can be described quantum mechanically. So, how and where can there be a boundary between the two worlds? In the following section we begin by introducing the quantum measurement problem. In the next section we will discuss attempts to understand and explain away the underlying paradoxes in quantum theory as highlighted in the quantum measurement problem and the question of the quantum-classical connection. From among the various explanations that seek a resolution to the conceptual problems of quantum mechanics, we focus on the ‘environment induced decoherence theory’ an approach that employs the methods developed by several authors to analyse the quantum mechanics of Measurement in Quantum Mechanics: Decoherence and the Pointer Basis

InTech eBooks•Feb 22, 2012•2 citations

Decoherence and the measurement problem

Hervé Zwirn C

The problem of measurement taken at face value shows clearly that there is an inconsistency inside the quantum formalism.The phenomenon of decoherence is often presented as a solution to it.A widely debated question is to decide between two different interpretations.The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate.For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed and so, to explain the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears.In this case, explaining why only one single definite outcome is observed remains to do.In this paper, we examine arguments for and against both interpretations and defend a position according to which the outcome that is observed is relative to the observer in close parallel to the Everett interpretation.

Proceedings of Frontiers of Fundamental Physics 14 — PoS(FFP14)•Sep 15, 2016•3 citations

Reconstructing Reality: Environment-Induced Decoherence, the Measurement Problem, and the Emergence of Definiteness in Quantum Mechanics

Hanneke Janssen

This work is a critique of the program of "environment-induced decoherence" as advocated by Zurek, Zeh and Joos, among others. In particular, the alleged relevance of decoherence for a solution of the "measurement problem" is subjected to a detailed philosophical analysis. In the first chapter, an attempt is made to unravel what exactly this "measurement problem" amounts to for the decoherence theorists. The second chapter reviews the standard decoherence literature. The third chapter starts with a brief discussion of the philosophical implications of the decoherence program, followed by a non-standard reconstruction of the decoherence argument that aims to uncover some (mostly hidden) assumptions underlying the approach. It is argued that different subsets of these assumptions result in different versions of the decoherence argument. Next, these assumptions are investigated in more detail, and a number of open problems for the decoherence approach is formulated, in addition to the well-known "problem of outcomes". These problems concern the interpretational relevance of the preferred basis, the role and status of the ignorance interpretation of mixed states, imperfect decoherence and the role of the environment and the definition of subsystems. The fourth chapter addresses the question to what extent the embedding of decoherence in an Everett-like interpretational framework, such as Zurek's "existentional interpretation" and Wallace's structural-realistic version of the many-worlds interpretation, helps to resolve these problems. The main conclusions are formulated in the fifth chapter. Namely: 1) decoherence cannot address the "preferred-basis problem" without adding new interpretational axioms to the standard formalism, 2) the the locality principle (that says that the environment is the "irrelevant" part and should therefore be ignored) is not only problematic but also interpretationally superfluous, 3) the decoherence approach, when formulated in terms of the standard interpretation of quantum mechanics, is predicated on a solution of the "problem of outcomes" and thus cannot claim to account (even partially) for the latter, and 4) that the results of the decoherence program do not increase the plausibility of a realist interpretation of the quantum state.

•Aug 1, 2008•13 citations

Does Decoherence Select the Pointer Basis of a Quantum Meter?

Abraham G. Kofman, Gershon Kurizki

The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.

Entropy•Jan 10, 2022•3 citations

Quantum measurement

Franck Laloë

The process of measurement plays an important role in quantum theory. Measurements can be direct, if the physical system S interacts directly with the measurement apparatus M (as we have assumed until now), or indirect. In the latter case, the physical system first interacts with an ancillary system B , which may have a space of states that is very different from that of S , for instance much larger; after this interaction has finished, M is used to perform a measurement on B , without any direct interaction with A . Because S is then “protected” from any direct interaction with the measurement apparatus, the state of S is not necessarily strongly modified, and may even be only weakly affected. In both cases, the process implies entanglement between several physical systems. In this chapter, we study how this entanglement is created and used for measurements as well as the notion of weak and continuous measurements. These questions play an important role in several of the interpretations of quantum mechanics that we discuss in Chapter 10. Direct measurements The Von Neumann model of quantum measurement [4] provides a general frame for describing the process in terms of correlations appearing (or disappearing) in the state vector associated with the whole system S + M . In this model, the two systems S and M are initially described by a product state ∣ψ 0 〈 and interact during the time of measurement, so that they become entangled; they then reach a final state ∣ψ′〈 and do not interact anymore.

Cambridge University Press eBooks•Aug 30, 2012•0 citations
Abstract: In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in Everett's relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett's thesis. In this article, we review the measurement process according to von Neumann, Everett's relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek's primordial paper that consolidated the concept of pointer states, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems-one representing the main system, the other the measurement apparatus-and a thermal bath-representing the environment-we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses
Abstract In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in Everett’s relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett’s thesis. In this article, we review the measurement process according to von Neumann, Everett’s relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek’s primordial paper that consolidated the concept of pointer states, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems—one representing the main system, the other the measurement apparatus—and a thermal bath—representing the environment—we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.
Quantum Mechanics represents one of the greatest triumphs of the scientific enterprise of the twentieth century. The stunning success of quantum theory has led to many revolutionary inventions and its extraordinary concepts describe the heart of several important real world applications like transistors and lasers. The theory makes accurate predictions about a wide range of physical phenomena and has historically withstood the tests and scrutiny of every experimental investigation. However, inspite of the fact that quantum theory is widely regarded by the scientific establishment as the fundamental theory of nature and is immensly successful and useful, its conceptual framework makes many predictions which are difficult to comprehend “classically. The theory is, pardoxically, powerful and confusing at the same time. Quantum theory’s unusual predictions originate from its basic formailsm which involves concepts like probability amplitudes and the linear superposition principle(Dirac, 1947). The quantum view appears abstract and counterintuitive and at odds with classical perceptions. Many of the conceptual problems of quantum mechanics are encompassed in what is known as the quantum measurement problem(Peres, 1986; von Neumann, 1932; Wheeler & Zurek, 1983). Conventionally, the measurement paradox is supposedly ’resolved’ by forcing a notion of a sudden collapse of the state vector of the system being measured. However, the nature of this mechanism is at odds with the basic tenets of quantum mechanics and hence may lie outside its realm thus questioning the validity of the theory it self. Closely related with the problem of measurement in quantum mechanics is the question of its connection with the emergence of classicality and the elusive boundary between quantum and classical worlds. What is the connection between the ‘classical’ and the ‘quantum’ worlds? Is there a definite relationship? Are classical mechanics and quantum mechanics two mutually exclusive incompatible theories or are they two aspects of the same underlying philosophy? Classical objects are eventually composed of elements of the microworld which can be described quantum mechanically. So, how and where can there be a boundary between the two worlds? In the following section we begin by introducing the quantum measurement problem. In the next section we will discuss attempts to understand and explain away the underlying paradoxes in quantum theory as highlighted in the quantum measurement problem and the question of the quantum-classical connection. From among the various explanations that seek a resolution to the conceptual problems of quantum mechanics, we focus on the ‘environment induced decoherence theory’ an approach that employs the methods developed by several authors to analyse the quantum mechanics of Measurement in Quantum Mechanics: Decoherence and the Pointer Basis
The problem of measurement taken at face value shows clearly that there is an inconsistency inside the quantum formalism.The phenomenon of decoherence is often presented as a solution to it.A widely debated question is to decide between two different interpretations.The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate.For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed and so, to explain the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears.In this case, explaining why only one single definite outcome is observed remains to do.In this paper, we examine arguments for and against both interpretations and defend a position according to which the outcome that is observed is relative to the observer in close parallel to the Everett interpretation.
This work is a critique of the program of "environment-induced decoherence" as advocated by Zurek, Zeh and Joos, among others. In particular, the alleged relevance of decoherence for a solution of the "measurement problem" is subjected to a detailed philosophical analysis. In the first chapter, an attempt is made to unravel what exactly this "measurement problem" amounts to for the decoherence theorists. The second chapter reviews the standard decoherence literature. The third chapter starts with a brief discussion of the philosophical implications of the decoherence program, followed by a non-standard reconstruction of the decoherence argument that aims to uncover some (mostly hidden) assumptions underlying the approach. It is argued that different subsets of these assumptions result in different versions of the decoherence argument. Next, these assumptions are investigated in more detail, and a number of open problems for the decoherence approach is formulated, in addition to the well-known "problem of outcomes". These problems concern the interpretational relevance of the preferred basis, the role and status of the ignorance interpretation of mixed states, imperfect decoherence and the role of the environment and the definition of subsystems. The fourth chapter addresses the question to what extent the embedding of decoherence in an Everett-like interpretational framework, such as Zurek's "existentional interpretation" and Wallace's structural-realistic version of the many-worlds interpretation, helps to resolve these problems. The main conclusions are formulated in the fifth chapter. Namely: 1) decoherence cannot address the "preferred-basis problem" without adding new interpretational axioms to the standard formalism, 2) the the locality principle (that says that the environment is the "irrelevant" part and should therefore be ignored) is not only problematic but also interpretationally superfluous, 3) the decoherence approach, when formulated in terms of the standard interpretation of quantum mechanics, is predicated on a solution of the "problem of outcomes" and thus cannot claim to account (even partially) for the latter, and 4) that the results of the decoherence program do not increase the plausibility of a realist interpretation of the quantum state.
The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.
The process of measurement plays an important role in quantum theory. Measurements can be direct, if the physical system S interacts directly with the measurement apparatus M (as we have assumed until now), or indirect. In the latter case, the physical system first interacts with an ancillary system B , which may have a space of states that is very different from that of S , for instance much larger; after this interaction has finished, M is used to perform a measurement on B , without any direct interaction with A . Because S is then “protected” from any direct interaction with the measurement apparatus, the state of S is not necessarily strongly modified, and may even be only weakly affected. In both cases, the process implies entanglement between several physical systems. In this chapter, we study how this entanglement is created and used for measurements as well as the notion of weak and continuous measurements. These questions play an important role in several of the interpretations of quantum mechanics that we discuss in Chapter 10. Direct measurements The Von Neumann model of quantum measurement [4] provides a general frame for describing the process in terms of correlations appearing (or disappearing) in the state vector associated with the whole system S + M . In this model, the two systems S and M are initially described by a product state ∣ψ 0 〈 and interact during the time of measurement, so that they become entangled; they then reach a final state ∣ψ′〈 and do not interact anymore.