On the basis of our recent model of a one-dimensional (1D) completed scattering we argue that Leggett's principles of macroscopic realism must and can be extended onto the level of single electrons and atoms. These principles need three quite feasible innovations in quantum mechanics (QM): (1) at the conceptual level, QM must treat a pure time-dependent one-particle state to involve two or more macroscopically distinct alternatives for a particle as a pure {\it combined} one - the intermediate link between a pure {\it elementary} state (indecomposable into macroscopically distinct parts) and statistical mixture; (2) at the mathematical level, QM must provide the presentation of the pure time-dependent combined state as a coherent superposition of macroscopically distinct elementary states (MDESs); (3) at the experimental level, QM must provide for such states two types of measurements - those for observing the interference pattern resulting from the joint action of MDESs, and non-demolishing 'which-way' measurements for scanning the individual properties of MDESs.
On the basis of our recent model of a one-dimensional (1D) completed scattering we argue that Leggett's principles of macroscopic realism must and can be extended onto the level of single electrons and atoms. These principles need three quite feasible innovations in quantum mechanics (QM): (1) at the conceptual level, QM must treat a pure time-dependent one-particle state to involve two or more macroscopically distinct alternatives for a particle as a pure {\it combined} one - the intermediate link between a pure {\it elementary} state (indecomposable into macroscopically distinct parts) and statistical mixture; (2) at the mathematical level, QM must provide the presentation of the pure time-dependent combined state as a coherent superposition of macroscopically distinct elementary states (MDESs); (3) at the experimental level, QM must provide for such states two types of measurements - those for observing the interference pattern resulting from the joint action of MDESs, and non-demolishing 'which-way' measurements for scanning the individual properties of MDESs.
On the basis of our model of a one-dimensional (1D) completed scattering (Russian Physics, 49, p.119 and p.314 (2006)) we argue that the linear formalism of quantum mechanics (QM) respects the principles of the macroscopic realism (J. Phys.: Condens. Matter, 14, R415-R451 (2002)). In QM one has to distinguish two kinds of pure ensembles: pure unentangled ensembles to be macroscopically inseparable, and pure entangled ones to be macroscopically separable. A pure entangled ensemble is an intermediate link between a pure unentangled ensemble and classical mixture. Like the former it strictly respects the linear formalism of QM. Like the latter it is decomposable into macroscopically distinct subensembles, in spite of interference between them; our new model exemplifies how to perform such a decomposition in the case of a 1D completed scattering. To respect macroscopic realism, the superposition principle must be reformulated: it must forbid introducing observables for entangled states.
As contrasted with physicists to idolize Bell's theorem and quantum nonlocality, we argue that quantum mechanics (QM), in reality, respects the principles of a macroscopic realism (PMRs). The current QM to tell us that "... the state of a system can be instantaneously changed by a distant measurement >..." cannot be treated as a physical theory. Its key statements - that the EPR-Bell experiments to violate Bell's inequality verify nonlocality, and nonlocal correlations respect special relativity - are false. Both the EPR-Bell experiments and theorems to support the "non-signalling principle" are based on the implicit assumption that all quantum postulates and, in particular, Born's averaging rule are fully applicable to Cat states. However, this is not the case. Introducing observables (e.g., correlations) for Cat states violates the correspondence principle. Pure (macro- and micro-)Cat states must be governed both by the PMRs and superposition principle. Our (macrorealistic) model of a one-dimensional completed scattering shows how these principles coexist with each other, in the case of a one-electron micro-Cat state.
In an attempt to test the limits of the current interpretation of quantum mechanics, according to which microscopic systems are always in a superposition of states, A. Leggett has proposed the thesis of macrorealism, according to which quantum mechanical superpositions of macroscopically distinct states never occur. Leggett has also shown the basic features of some experimental tests that would decide definitively between quantum mechanics and macrorealism. In this paper I develop an interpretation of macrorealism from which the experimental results can be understood as examples of violations of the principle of induction in which macrorealism rests, opening the door for solving the tension between QM and macrorealism in terms of the backwards causation. According to this interpretation there is no need for appealing to any special role played by either observers or measurement apparatuses in order to explain what differentiates quantum systems from macroscopic ones, a difference that could now be defined partly in terms of their causal and temporal directionality.
This thesis consists of two parts. Although both are concerned with macroscopic quantum phenomena, I choose to present the two parts quite separately. Macroscopic Quantum Phenomena: Tests of Quantum Mechanics The correctness of quantum mechanics has been verified in numerous situations. A particularly strong test of quantum mechanics was suggested by Bell, who showed that the predictions of all classical theories, based as they are on the assumptions of local realism, contradict those of quantum mechanics. Later work by Greenberger, Horne, and Zeilinger showed that the GHZ phenomena also contradicts all classical theories. Experimental tests of Bells inequality performed to date support quantum mechanics (No experimental test of the GHZ phenomenon has yet been attempted). However, such tests have been so far restricted to microscopic systems in the sense that one particle is at a detector at a time. Our interest here in the first part of this thesis is in tests of quantum mechanics against local realistic theories in macroscopic or mesoscopic systems where there is a significant number of particles incident on each analyser. The states considered in the first two chapters are not simple quantum superpositions of macroscopically distinct states, but we nevertheless show how one can obtain tests of quantum mechanics in situations involving large numbers of particles. A more elementary macroscopic quantum state, and one in which the deviation from classical interpretations is striking, is the Schrodinger Cat state considered by Schrodinger in his famous "Schrodinger Cat" paradox. In Chapter Three we consider a scheme for generating such a state. The Quantum Brownian Motion Master Equation The second section of this thesis involves an examination of various aspects of the Quantum Brownian Motion Master Equation. We begin with a discussion of the recent problem occurring from the study of the quantum Brownian motion (QBM) master equation, which can occur because the QBM master equation is not of the Lindblad form. We examine two specific examples, namely the damped free particle and the two level atom. More specifically, in the case of the evolution of a free particle, we show that the equation of motion for the Wigner function (which is exactly the same as the Fokker-Planck equation for classical Brownian motion) gives unphysical results if the initial position distribution is well localised. In the case of the two level atom we show that unphysical results can also occur even in the steady state. The last chapter of the thesis involves using the quantum Brownian motion master equation to estimate the rate of diagonalisation of the off diagonal elements of a Fermion system. These elements contain the "quantum information" and hence knowledge of how long they exist can determine the type of model required to describe the semiconductor medium. Using a very simplistic approach we can show that there are two main time scales present and for normal parameters one of these is very small. If we neglect electron-electron scattering we can show that the the many electron system solution is simply a product of the one electron solutions.
Entanglement is usually associated with compound systems. We first show that a one-dimensional (1D) completed scattering of a particle on a static potential barrier represents an entanglement of two alternative one-particle sub-processes, transmission and reflection, macroscopically distinct at the final stage of scattering. The wave function for the whole ensemble of scattering particles can be uniquely presented as the sum of two isometrically evolved wave packets to describe the (to-be-)transmitted and (to-be-)reflected subensembles of particles at all stages of scattering. A noninvasive Larmor-clock timing procedure adapted to either subensemble shows that namely the dwell time gives the time spent, on the average, by a particle in the barrier region, and it denies the Hartman effect. As regards the group time, it cannot be measured and hence it cannot be accepted as a measure of the tunneling time. We argue that nonlocality of entangled states appears in quantum mechanics due to inconsistency of its superposition principle with the corpuscular properties of a particle. For example, this principle associates a 1D completed scattering with a single (one-way) process, while a particle, as an indivisible object, cannot take part in transmission and reflection, simultaneously.
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its core concepts (amplitudes, global phases, etc.) can not be directly accessed and its interpretation is still the subject of intense debate, more than 100 years since it was introduced. So, a fundamental question is why this particular mathematical model is the one that nature chooses, if indeed it is the correct model. In the past two decades there has been a renewed effort to determine what physical or informational principles define quantum mechanics. In this paper, recent attempts at establishing reasonable physical principles are reviewed and their degree of success is tabulated. An alternative approach using joint quasi-probability distributions is shown to provide a common basis of representing most of the proposed principles. It is argued that having a common representation of the principles can provide intuition and guidance to relate current principles or advance new principles. The current state of affairs, along with some alternative views are discussed.