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arXiv:1911.08586 · Scientific Reports

A microscopic model of wave-function dephasing and decoherence in the double-slit experiment

Satish Ramakrishna

Published Oct 25, 2021• 3 citations
arXivHTMLPDF

Abstract

The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.

DOI
10.1038/s41598-021-99995-2

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The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.
The act of measurement on a quantum state is supposed to collapse the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schr\odinger's equation. There are two general approaches to the study of wave-function collapse: one called the consistent or decoherent histories approach and the other, the environmental decoherence approach, which studies the effect of the environment upon the quantum system, to explain wave-function collapse. In the environmental decoherence approach, one usually studies a Markovian-approximated Master equation to study the time-evolution of reduced density matrix and obtains the long-term dependence of the off-diagonal elements of this matrix. We do not make a Markovian assumption and study a particularly simple and calculable example. We find, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential, which is a new result (the long-term behavior is, of course, still exponential). This allows one to connect the Fermi-golden rule quadratic-in-time behavior of a transition probability to the exponential long-time behavior of a collapsing wave-function.
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring system and a measured one. These properties result directly from the Schrödinger equation. They cannot be formulated in terms of observables, do not affect the wave functions themselves but express their history in an irreversible way. They carry a specific new kind of local probabilities, which evolve with a finite velocity under nonlinear wave equations. The second category of results extends these local properties to the case of a macroscopic system and its environment. Fluctuations in their interaction are predicted then and generate a specific incoherence in the quantum state of the system. These two kinds of effects act together when a macroscopic measuring system interacts with a measured system and with an environment. Their combination yields then an explicit and effective mechanism of collapse, with a random behavior resulting from random incoherence. Born's basic probability rule for the results of measurements turns out then simply a consequence of quantum dynamics. Some conjectures still enter into the derivation of these effects, which one may recognize to look hardly credible at first sight. They fit however so well together that one proposes a more thorough investigation of their approach as a promising strategy for a self-contained explanation of collapse.
Quantum decoherence in all its locus of essence, and expression is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. Detrimental ramifications, and pernicious implications of this dephasing leads to classical or probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse (the reduction of the physical possibilities into a single possibility as seen by an observer. Here it is to be noted that perception is not the reality and what you see is not what you see ;what you do not see is what you do not see; what you see is what you do not see ;and what you do not see is what you see.)… Thus in all its wide ranging manifestations, it justifies the propositional subsistence and corporeal reality that justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a perceptual field   of quantum starting point and it determines the location of the quantum-classical boundary. Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents transitive states, substantive sub states and determinate orientation different elements in the quantum superposition of the system and environment's wavefunction from interfering with each other. Decoherence has been a subject of active research since the 1980s. Decoherence can be viewed as the principal frontier of diurnal dynamics that results in loss of information from a system into the environment (often modeled as a heat bath), since every system is loosely coupled with the energetic state of its surroundings, with particularistic predicational pronouncements. . Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion). Thus, the dynamics of the system aphorism and anecdote of the system alone are irreversible. As with any coupling, entanglements are generated in its theme and potentialities between the system and environment, which have the effect of sharing quantum information with—or transferring it to—the surroundings. It is a blatant and flagrant misconception that collapse of wave function is attributable and ascribable to wave function collapse; Decoherence does not generate actual wave function collapse. It only provides an explanation for the appearance of the wavefunction collapse, as the quantum nature of the system leaks into the environment. So, the wave function collapse is the figment of the observer’s imagination, product of puerile prognostication and resultant orientationality of his phantasmagoria.  One cannot have the apodictic knowledge of reality that is; components of the wavefunction are decoupled from a coherent system, and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue. This is a very important pharisaical provenience and plagenetious precocity with all the disembodied resemblances of the system in total form; specifically, decoherence does not attempt to explain the measurement problem. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the of precisely one state in the ensemble.Decoherence represents a challenge for the practical realization of quantum computers, since they are expected to rely heavily on the undisturbed evolution of quantum coherences. Simply put; they require that coherent states be preserved and that decoherence is managed, in order to actually perform quantum computation. In the following we give a model for decoherence of the environment, coupled quantum states, at determinate and differential levels ,internal resonance in coupled spin systems, and the conflict in the Quantum state operations and decoupling. KEY WORDS Coupled quantum states, Quantum mechanics
Quantum theory is often cited as being one of the most empirically validated theories in terms of its predictive power and precision. These attributes have led to numerous scientific discoveries and technological advancements. However, the precise relationship between quantum and classical physics remains obscure. The prevailing description is known as decoherence theory, where classical physics emerges from a more general quantum theory through environmental interaction. Sometimes referred to as the decoherence program, it does not solve the quantum measurement problem. We believe experiments performed between the microscopic and macroscopic world may help finish the program. The following considers a free electron that interacts with a surface (the environment), providing a controlled decoherence mechanism. There are non-decohering interactions to be examined and quantified before the weaker decohering effects are filtered out. In the first experiment, an electron beam passes over a surface that’s illuminated by low-power laser light. This induces a surface charge redistribution causing the electron deflection. This phenomenon’s parameters are investigated. This system can be well understood in terms of classical electrodynamics, A second experiment tests decoherence theory by introducing a nanofabricated diffraction grating before the surface. The electron undergoes diffraction through the grating, but as the electron passes over the surface it’s predicted by various physical models that the electron will lose its wave interference property. Image charge based models, which predict a larger loss of contrast than what is observed, are falsified (despite experiencing an image charge force). A theoretical study demonstrates how a loss of contrast may not be due to the irreversible process decoherence, but dephasing (a reversible process due to randomization of the wavefunction’s phase). To resolve this ambiguity, a correlation function on an ensemble of diffraction patterns is analyzed after an electron undergoes either process in a path integral calculation. The diffraction pattern is successfully recovered for dephasing, but not for decoherence, thus verifying it as a potential tool in experimental studies to determine the nature of the observed process.
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.
Abstract: The quantum measurement problem has been the deepest conceptual difficulty since the birth of quantum mechanics. Standard quantum mechanics accepts wavefunction collapse as an independent postulate but never provides a physical explanation. The decoherence approach attributes collapse to the interaction between the system and its environment, but faces two fundamental limitations: the “infinite regress” problem and the “insufficiency of decoherence” problem. Within the framework of the Self-Construction Theory (SCT), this paper provides a complete resolution of the measurement problem. The core thesis is that quantum measurement is not a fundamental process independent of the laws of physical evolution, but rather a local manifestation of constructive renormalization—the scale evolution of the spacetime complex field KKK from microscopic degrees of freedom to macroscopic effective descriptions. The origins of wavefunction collapse, decoherence, and the Born rule receive a unified first‑principles interpretation in this framework. SCT’s spontaneous decoherence mechanism is the key to the resolution. Constructive renormalization inherently involves information loss—the integrated‑out microscopic degrees of freedom no longer exist in the macroscopic effective description. During a measurement, the measuring apparatus possesses a huge number (∼1023\sim10^{23}∼1023) of microscopic degrees of freedom. When the apparatus interacts with the measured system, constructive renormalization triggers information compression of these degrees of freedom—the apparatus can no longer distinguish which branch of the superposition it is in, and quantum coherence is thus spontaneously lost. No “external environment” is needed—the constructive renormalization dynamics of spacetime itself is the ultimate source of decoherence, thereby completely solving the “infinite regress” problem. Among the probability distribution given by the Born rule, the weights of non‑maximal probability branches are further suppressed by information compression under the huge number of microscopic degrees of freedom, so that macroscopic observers can perceive only a definite outcome in the effective description. The information loss caused by constructive renormalization is ontological—it does not rely on any approximation or truncation, thus fundamentally solving the “insufficiency of decoherence” problem. The Born rule—that measurement outcomes occur with probabilities given by the squared amplitudes—is directly derived from the constructive integral structure in SCT. In the constructive renormalization limit, interference terms between different configurations are naturally suppressed by off‑diagonal phase randomization, and the system automatically switches to a classical probabilistic description. In the diagonal density matrix representation, the squared amplitude is the only natural weight that is simultaneously real and non‑negative. Hence the Born rule is not an additional postulate of quantum mechanics but a necessary and unique manifestation of the relative frequencies of the constructive integral in the constructive renormalization limit. This derivation is rigorous within the mathematical framework of constructive renormalization—it does not rely on any approximations or truncations. SCT’s quantum measurement theory is deeply unified with the black hole information paradox. The “collapse” in quantum measurement and the “information loss” in black hole evaporation are different manifestations of the same core mechanism—the redistribution of information due to constructive renormalization—in two extreme physical situations. In quantum measurement, information is redistributed into the degrees of freedom of the macroscopic apparatus; in black hole evaporation, information is redistributed into the time‑point configurations on the horizon. This unification is the strongest proof of the universality of constructive renormalization as an information‑processing mechanism. Keywords: quantum measurement; spontaneous decoherence; constructive renormalization; Born rule; wavefunction collapse; information redistribution; Self-Construction Theory