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A review of quantum mechanics in a minimum-length scenario.

K. C. Lemos Filho

Published Mar 31, 2017• 0 citations
OpenAlex

Abstract

Quantum theory has shown to be well succeded since its birth at the beginning of the last century. But new ideas that emerged in the physics scenario can change some of quantum mechanics fundamentals, one of these ideas is the existence of a minimun measurable length. In this work we will review the main changes in quantum mechanics arising from the existence of this minimum length.

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Quantum theory has shown to be well succeded since its birth at the beginning of the last century. But new ideas that emerged in the physics scenario can change some of quantum mechanics fundamentals, one of these ideas is the existence of a minimun measurable length. In this work we will review the main changes in quantum mechanics arising from the existence of this minimum length.
We reconsider some important foundational problems of quantum mechanics. After reviewing the measurement problem and discussing its unavoidability, we analyze some proposals to overcome it. This analysis leads us to reconsider the current debate on our best theory, i.e. quantum mechanics itself. We stress that, after the remarkable interest and the many efforts which have lead, in the last years of the past century, to a revival of the subject, and, more important, to new interesting results, we are now witnessing a re-emergence of the vague and unprofessional positions which have characterized the debate in the second quarter of the XXth century. In particular we consider as extremely serious the fact that a completely mistaken position concerning the real meaning of Bell's theorem seems to have been taken by many scientists in the field.
These lectures will cover all of physics. Since we believe that the behavior of systems of many particles can be understood in terms of the interactions of a small number of particles, we shall be concerned primarily with the latter. Bearing in mind that the present theories need modifications or revision to account for observed phenomena, we shall want to consider the foundation of quantum mechanics in their most general form. This is so we can get some idea of the minimum assumptions (and their character) which we use to formulate those parts of the theory we use in dealing with the new phenomena of the strange particles.
This is a brief review of the history and development of quantum theories. Starting from the experimental findings and theoretical results which marked the crisis of the classical framework, I overview the rise of axiomatic quantum mechanics through matrix and wave mechanics. I discuss conceptual problems such as the measurement problem that led scientific realists to explore other, more satisfactory, quantum theories, as well as Bell’s theorem and quantum nonlocality, concluding with a short review of relativistic theories.
What is 'the nature of reality’? This thought has occupied the minds of scientists and philosophers since time immemorial. This issue is examined scientifically, that, how the views of scientists and western philosophers have undergone a dramatic change over a period of time. This may then answer whether spacetime is a reality of nature or if it is just a figment of our imagination in which to view this cosmos! The article begins with the thoughts of Democritus, and the other Greek philosophers, continuing with the ideas of Copernicus, Galileo and Kepler. With the thoughts of Bacon, Descartes and Isaac Newton, the rise of the ‘mechanical world view’ later the decline of this view is discussed when the phenomenon in optics, electricity and magnetism could not be explained. Then the concept of ‘field’ was evolved, culminating in ‘Maxwell’s equations of electromagnetic fields’.The beginning of twentieth century saw the evolution of the concepts of ‘relativity’, by Einstein, and the birth of ‘quantum theory’, starting with the idea of ‘quanta’, originated by Planck in 1900. The first three decades of the 20th century saw great breakthroughs in the world of theoretical physics - totally new ideas on ‘the nature of reality’ were being conceived. Large numbers of fundamental particles were discovered in the ensuing years. However, not much progress indeed was made in answering some of the most fundamental questions about the existence of human life and the nature of reality. Some interesting ideas on ‘biocentrism’ have now evolved. Biocentrism, along with the ideas of quantum theory and the concept of consciousness, may answer some of the intricate questions about the nature of reality; these will be discussed at length. These concepts will then be viewed from the perspective of Indic thoughts. The ‘Vedic’ and ‘Upanishadic’ knowledge from Indian scriptures may probably answer even more clearly some of the most intriguing questions about the existence of life and the ‘nature of reality’ itself.Beginning of twentieth century saw the evolution of the concepts of ‘Relativity’, by Einstein, and the birth of ‘Quantum Theory’, starting with the idea of ‘Quanta’, originated by Planck in 1900. The first three decades of 20th century saw the great breakthroughs in the world of theoretical physics. Absolutely new ideas on ‘The Nature of Reality’ were being conceived. Large number of fundamental particles was discovered in the ensuing years. But not much progress indeed took place in answering some of the most fundamental questions on existence of human life and the nature of reality. Some interesting ideas on ‘Biocentrism’ have now evolved. Biocentrism along with the ideas of Quantum Theory and the concept of Consciousness may answer some of the intricate questions on nature of reality; these will be discussed at length. These concepts will then be viewed from perspective of Indic thoughts. The ‘Vedic’ and ‘Upanishadic’ knowledge from Indian scriptures may probably answer even more clearly some of the most intriguing questions on the existence of life and the ‘Nature of Reality’ itself.
The first objective of this chapter is to briefly review some of the basic ideas about the structure of matter, in particular the concepts of microscopic physics, in order to recall the knowledge gained in previous physics (and chemistry) courses and make it more precise. Our review will be very concise, and most statements will be made without any proof or detailed discussion. A second objective is to give a brief description of some of the crucial stages in the early development of quantum physics. We shall not follow the strict historical order of this development or present the arguments used at the beginning of the last century by the founding fathers of quantum mechanics; rather, we shall stress the concepts which we shall find useful later on. Our last objective is to give an elementary introduction to some of the basic ideas, like those of a quantum particle or energy level, that will reappear throughout this text. We shall base our review on the Bohr theory, which provides a simple, though far from convincing, explanation of how energy levels are quantized and how the spectrum of the hydrogen atom arises. This chapter should be reread later on, once the basic ideas of quantum mechanics have been made explicit and illustrated by examples. From the practical point of view, it is possible to skip the general considerations of Sections 1.1 and 1.2 at the first reading and begin with Section 1.3, returning to those two sections later on as needed.