The conventional quantum theory gives no real, that is, independent of the observer, natural description. If it is required that it must give an absolute reality of the natural phenomena at least in the macroscopic region, then the quantum theory must be changed. One possibility of that kind is discussed. A model of a quantum theory, which for small systems agrees with the usual theory, but for large systems deviates so much from them that the absolute reality of macroscopic size remains steady, is described. This was achieved by means of an additional term in the motion equation for the density matrix. This additional term plays no role for the small system. For macroscopic ion of the density matrix as if'' all macroscopic size of the system was observed perennially. (tr-auth)
The conventional quantum theory gives no real, that is, independent of the observer, natural description. If it is required that it must give an absolute reality of the natural phenomena at least in the macroscopic region, then the quantum theory must be changed. One possibility of that kind is discussed. A model of a quantum theory, which for small systems agrees with the usual theory, but for large systems deviates so much from them that the absolute reality of macroscopic size remains steady, is described. This was achieved by means of an additional term in the motion equation for the density matrix. This additional term plays no role for the small system. For macroscopic ion of the density matrix as if'' all macroscopic size of the system was observed perennially. (tr-auth)
It is assumed that the quantum state that may describe a macroscopic system at a given instant of time is one of the eigenstates of the reduced density matrix calculated from the wave function of the system plus its environment. This implies that the above quantum state is a member of a special orthonormed set of states. Using a suitable Monte-Carlo simulation, this property is shown to be consistent with the extremely small standard deviation for the coordinates and the momenta of macroscopic systems. Consequences for statistical mechanics and possible observable effects are discussed.
An explicit model allowing a unified description of microscopic and macroscopic systems is exhibited. First, a modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in far-away spatial regions and induces an evolution agreeing with classical mechanics. This dynamics also allows a description of the evolution in terms of trajectories. To set up a unified description of all physical phenomena, a modification of the dynamics, with respect to the standard Hamiltonian one, is then postulated also for microscopic systems. It is shown that one can consistently deduce from it the previously considered dynamics for the center of mass of macroscopic systems. Choosing in an appropriate way the parameters of the so-obtained model one can show that both the standard quantum theory for microscopic objects and the classical behavior for macroscopic objects can all be derived in a consistent way. In the case of a macroscopic system one can obtain, by means of appropriate approximations, a description of the evolution in terms of a phase-space density distribution obeying a Fokker-Planck diffusion equation. The model also provides the basis for a conceptually appealing description of quantum measurement.
Despite its power as the conceptual basis for a huge range of physical phenomena in atomic and subatomic physics, quantum mechanics still suffers from a lack of clarity regarding the physical meaning of its fundamental theoretical concepts, such as those of quantum state and of quantum theoretical quantities or variables , dealt with by the known mathematical-theoretical rules. These concepts have generally been considered as not giving a direct description of physical systems, for they do not correspond to what is usually understood by `physical states' or `physical properties', notably characterized by definite numerical values such as those obtained from measurement. The situation has been tentatively expressed in terms of various `interpretations', conceived not only with regard to the physical meanings of mathematical quantities, but also in connection with philosophical statements about `physical reality'. The question of whether or not quantum theoretical quantities describe definite physical systems existing in nature has therefore generally been considered as beyond the possibilities of physics, because of the definitions that are commonly taken for `physical state' and `physical quantity'. We sketch the main ideas on this problem and propose a possible way out of the puzzle, in terms of an extension of the meaning given to the concepts of the physical state and physical quantity of a system, which would allow one, without any theoretical change in quantum mechanics, to speak consistently of real quantum systems as having definite physical properties .
For systems which obey quantum mechanics, the formulation of the problem of treating large numbers of particles is, of course, somewhat different than it is for classical systems. The microscopic description of the system is provided by a wave function which (in the absence of spin) is a function of the classical coordinates { q i }. The mathematical model is provided by a Hamiltonian operator H which is often obtained from the corresponding classical Hamiltonian by the replacement p i → ( ħ /i)(∂/∂ q i ). In other cases the form of the Hamiltonian operator is simply postulated. The microscopic dynamics are provided by the Schrödinger equation i ħ (∂Ψ/∂ t ) = H Ψ which requires as initial condition the knowledge of the wave function Ψ({ q i }, t ) at some initial time t 0 . (Boundary conditions on Ψ({ q i }, t ) must be specified as part of the description of the model as well.) The results of experiments in quantum mechanics are characterized by operators, usually obtained, like the Hamiltonian, from their classical forms and termed observables. Operators associated with observables must be Hermitian. In general, the various operators corresponding to observables do not commute with one another. It is possible to find sets of commuting operators whose mutual eigenstates span the Hilbert space in which the wave function is confined by the Schrödinger equation and the boundary conditions. A set of such (time independent) eigenstates, termed ψ ν ( q ), is a basis for the Hilbert space.
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.
It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to be extended by one beable (hidden variable), i. e., a quantum observable with always definite values in nature (but usually only statistically given in the quantum state). Localization is taken as the most plausible beable. The paradoxical aspects of conventional QM take now a different form. Suitably defining the notion of "subject" fully within the QM formalism, proving the quantum conditional subsystem-state theorem, and choosing the relative-decoherence interpretation of QM, the paradoxes formally disappear, leaving one with decoherence relative to the definite values of the beable; thus being only appearance, not absolute reality in QM. Relative to a different subject one has perseverance of coherence. Hence, in this approach it is claimed that decoherence and coherence, both exist in reality, but are not "seen" by the same subject, and "subject" is, in this interpretation, indispensable. The two mentioned, apparently contradictory phenomena, are in this way decoupled from each other, contradiction is avoided, and any one of the two can be treated in the way that is usual in QM.