Working entirely within the Schroedinger paradigm, meaning wavefunction only, I present a modification of his theory that prevents formation of macroscopic dispersion (MD; "cats"). The proposal is to modify the Hamiltonian based on a method introduced by Steven Weinberg in 1989, as part of a program to test quantum mechanics at the atomic or nuclear level. By contrast, the intent here is to eliminate MD without affecting the predictions of quantum mechanics at the microscopic scale. This restores classical physics at the macro level. Possible experimental tests are indicated and the differences from previous theories discussed. In a second paper, I will address the other difficulty of wavefunction physics without the statistical (Copenhagen) interpretation: how to explain random outcomes in experiments such as Stern-Gerlach, and whether a Schroedingerist theory with a random component can violate Bell's inequality.
Working entirely within the Schroedinger paradigm, meaning wavefunction only, I present a modification of his theory that prevents formation of macroscopic dispersion (MD; "cats"). The proposal is to modify the Hamiltonian based on a method introduced by Steven Weinberg in 1989, as part of a program to test quantum mechanics at the atomic or nuclear level. By contrast, the intent here is to eliminate MD without affecting the predictions of quantum mechanics at the microscopic scale. This restores classical physics at the macro level. Possible experimental tests are indicated and the differences from previous theories discussed. In a second paper, I will address the other difficulty of wavefunction physics without the statistical (Copenhagen) interpretation: how to explain random outcomes in experiments such as Stern-Gerlach, and whether a Schroedingerist theory with a random component can violate Bell's inequality.
In the first paper of this series, I introduced a non-linear, Hamiltonian, generalization of Schroedinger's theory that blocks formation of macroscopic dispersion ("cats"). But that theory was entirely deterministic, and so the origin of random outcomes in experiments such as Stern-Gerlach or EPRB was left open. Here I propose that Schroedinger's wavefunction has a random component and demonstrate that such an improvised stochastic theory can violate Bell's inequality. Repeated measurements and the back-reaction on the microsystem are discussed in a toy example. Experiments that might falsify the theory are described.
Paper I of this series introduced a nonlinear version of quantum mechanics that blocks cats, and paper II postulated a random part of the wavefunction to explain outcomes in experiments such as Stern-Gerlach or EPRB. However, an ad hoc extra parameter was assumed for the randomness. Here I provide some analytic and simulation evidence that the nonlinear theory exhibits sensitive dependence on initial conditions in measurement scenarios, perhaps implying that the magnitude of randomness required is determined by structural features of the model, and does not require a free parameter.
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.
In the Schrödinger-cat gedanken experiment a cat is in a quantum superposition of two macroscopically distinct states, alive and dead.The paradoxical interpretation of quantum mechanics is that the cat is not in one state or the other, alive or dead, immediately prior to its measurement. Because of this apparent defiance of macroscopic reality, quantum superpositions of states macroscopically distinct have generated much interest. Here we address the issue of proving a contradiction with macroscopic reality objectively, through the testable predictions of quantum mechanics. We consider the premises of macroscopic reality (that the ``cat'' is either ``dead'' or ``alive'', the measurement indicating which) and macroscopic locality (that simultaneous measurements some distance away cannot induce the macroscopic change, ``dead'' to ``alive'' and vice versa, to the ``cat''). The predictions of quantum mechanics for certain states, generated using states exhibiting continuous variable entanglement, are shown to be incompatible with the predictions of all theories based on this dual premise. Our proof is along the lines of Bell's theorem, but where all relevant measurements give macroscopically distinct results.
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schroedinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. We also discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics.
Quantum measurement theory addresses several problems. All of them arise from applying a microscopically valid theory to the macroscopic domain. The most famous is the Schrödinger cat example in which the ordinary use of quantum rules suggests a superposition of macroscopically different states, something we do not seem to experience. Another problem is the Einstein-Podolsky-Rosen (EPR) paradox in which a fundamental quantum concept, entanglement, creates subtle and non-classical correlations among remote sets of measurements. Although it seems mere word play to observe that such an apparent micro-macro conflict ought to be viewed as a problem in statistical mechanics—by virtue of the way that discipline is defined—until recently the importance of this observation was seldom recognized. The founders, Bohr, Schrödinger, Heisenberg, Einstein did not emphasize this direction, but over the years the realization that measurement necessarily involves macroscopic objects—objects with potentially mischievous degrees of freedom of their own—began to be felt. For me this was brought home by the now classic fourth chapter of Gottfried's text on quantum mechanics. He takes up the following problem. The density matrix ρ 0 for a normalized pure state is ρ 0 = |ψ〉 〈ψ|. It follows that Tr ρ 0 = Tr ρ 0 2 = 1. After a non-trivial measurement, the density matrix ρ is supposed to be diagonal in the basis denned by the measured observable, with Tr ρ = 1 but Tr ρ 2 < 1.