Local Properties of Entanglement and Application to Collapse

Abstract

When a quantum system is macroscopic and becomes entangled with a microscopic one, this entanglement is not immediately total, but gradual and local. A study of this locality is the starting point of the present work and shows unexpected and detailed properties in the generation and propagation of entanglement between a measuring apparatus and a microscopic measured system. Of special importance is the propagation of entanglement in nonlinear waves with a finite velocity. When applied to the entanglement between a macroscopic system and its environment, this study yields also new results about the resulting disordered state. Finally, a mechanism of wave function collapse is proposed as an effect of perturbation in the growth of local entanglement between a measuring system and the measured one by waves of entanglement with the environment.Keywords: entanglement, kinetic physics, decoherence, wave function collapse _________ This is a revised version of arxiv.org.quant.phys.13093472, partly rewritten for clarity and with two previous key assumptions reconsidered, page 20: II as still convenient but unnecessary and III as being now proved.It became clear early in the theory of quantum measurements -particularly in Schrödinger's works [1, 2]-that entanglement is the stumbling block forbidding emergence of a unique datum in a measurement. More recently many experiments confirmed this viewpoint by realizing conditions that were similar to a measurement but involved only a few atoms or photons [3]: Von Neumann's standard description of a measurement as a creation of entanglement was found perfectly adequate [4], even when there was decoherence, and there was as predicted no glimpse of collapse in these experiments.An obvious consequence is that collapse, or the emergence of reality, is essentially a macroscopic phenomenon. This conclusion was drawn particularly in the theory of spontaneous collapse at a small but macroscopic scale by Ghirardi, Rimini and Weber [5], but in a form requiring modification in the quantum principles: The existence of a collapse effect with universal range and universal rate was added to these principles, the essential role of this effect being to break down the deadly obstruction from entanglement.But one may also wonder whether entanglement is so total and rigid that a new principle is needed to break it. Is it impossible to look at it more ordinarily as a physical phenomenon needing time for its growth and space for its expansion, rather than remaining an absolute mathematical property of wave functions? This question can stand in some sense as the starting point of the present work.When describing the nature of entanglement, Schrödinger considered an example where two quantum systems A and B, initially independent, begin to interact at some time zero and separate again after some more time [2]. Both systems are initially in a pure state but, although this is still true of the compound system AB after their interaction, it is not

Constitutive Elements of Non-Abelian Gauge Theories

“…, is defined as an associative algebra, such that each element of  is in correspondence with aspects of motion taking place in 4  . There is a subset…”

“…It can be classified by two categories of primitive concepts. One is the material point, specified by a set of local points of 4  and endowed with the content of momentum. The other is the concept of a field, which is a mechanical system with no local characteristics in 4  and not reducible to material point; but in general it is endowed with the content of momentum [27] [28].…”

“…The set of transformation µ ν Λ is the Lorentz-Lie group. With this structure, the manifold 4  is called the Minkowski space,  . CE2.…”

Espaço, Tempo e Estruturas das Teorias do Movimento

“…A importância deste tipo de estudo, mesmo que inicialmente motivado por questões acadêmicas, e não por problemas de aplicações imediatas [1][2][3][4][5][6][7], conduziu a significativas descobertas de natureza conceitual e prática. Um exemplo notório foi a proposição das desigualdades de Bell [8,9], associadas ao desenvolvimento subsequente de conceitos como emaranhamento e teletransporte de estados da radiação; noções fundadoras para a computação e comunicação quânticas [10][11][12][13][14][15].…”