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Physical Science International Journal

Generalized Uncertainty Relations in Quantum Mechanics and the Principles of Completeness in Physics

P. G. Castro, J. R. Croca, Marisa Della Gatta, R. N. Moreira

Published Dec 18, 2017• 5 citations
Publisher

Abstract

Focusing on the initial development of quantum mechanics, we will give a brief historical synopsis of the theory foundations, based on the Fourier framework and stating the philosophical conclusions inspired by that same mathematical formalism. We will then proceed, introducing an alternative way of describing the undulatory aspects of quantum entities, using local Gaussian Morlet wavelets. As we shall see, this change implies different philosophical interpretations about quantum reality and, even more, about the contemporary accepted differences between the quantum and the macroscopic realms. From these we will witness the formal and heuristic power of wavelet local analysis applied to the physical description of Nature. The ideas presented in this paper are initial standpoints of what can hopefully be expected to be a more mature and unifying physical theory, still undergoing development.

DOI
10.9734/psij/2017/37038

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Focusing on the initial development of quantum mechanics, we will give a brief historical synopsis of the theory foundations, based on the Fourier framework and stating the philosophical conclusions inspired by that same mathematical formalism. We will then proceed, introducing an alternative way of describing the undulatory aspects of quantum entities, using local Gaussian Morlet wavelets. As we shall see, this change implies different philosophical interpretations about quantum reality and, even more, about the contemporary accepted differences between the quantum and the macroscopic realms. From these we will witness the formal and heuristic power of wavelet local analysis applied to the physical description of Nature. The ideas presented in this paper are initial standpoints of what can hopefully be expected to be a more mature and unifying physical theory, still undergoing development.
The foundations and meaning of quantum theory became a central issue to Albert Einstein and Niels Bohr since the onset of their impassioned debate in the 1920s, enriched by the contributions of many other distinguished scientists and philosophers.The questions are not settled down at all, despite the great achievements of the theory, its impressive accordance with experiment and predictive power.The fundamental and technological applications range from cosmology to biology, with the development of invaluable instruments and the design of new materials.Is quantum mechanics a complete or an incomplete theory?Is there an objective reality independent of the observer or is the reality created by the measurements?Are hidden-variable theories justifiable?Is there a quantum theory founded in a local-causal and non-linear approach that formally contains the orthodox linear theory as a special case?Can such a formulation unify classical and quantum physics?Are Heisenberg's uncertainty relations valid in all cases?Here, the subject is addressed as an adaptation of our contribution to the Colloquium "Quantal aspects in Chemistry and Physics.
After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics persists to this day. Most of these endeavors assume the validity of standard quantum formalism and proceed to ponder the ontic nature of wave functions, operators, and the Schödinger equation. The present essay takes a different approach, more epistemological than ontological. I endeavor to give a heuristic account of how empirical principles lead us to a quantum mechanical description of the world. An outcome of this approach is the suggestion that the notion of discrete quanta leads to the wave nature and statistical behavior of matter rather than the other way around. Finally, the hope is to offer some solace to those older of us who still worry about such things and also to provide the neophyte student of quantum mechanics with physical insight into the mathematically abstract and often baffling aspects of the theory.
We present a historical-epistemological analysis of the foundations of quantum mechanics, highlighting the relationships between quantum mechanics and scientific realism, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of the measurement process in the context of quantum mechanics is underlined as an essential element in providing a coherent description of reality, moving from micro to macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the related ontological problems, the question of the objectification of the wave function, and that of the definition of discernibility. We consider also an overview of the most important alternative proposals to the standard interpretation of quantum mechanics (Copenhagen interpretation), with particular reference to hidden variable theories and other alternatives to standard quantum mechanics philosophical approach, that are modifying the vision of reality, such as the Everett’s many-worlds theory, the QBism and unified holistic approaches, such as the Primordial Dynamic Space.
Nearing a century since its inception, quantum mechanics is as lively as ever. Its signature manifestations, such as superposition, wave-particle duality, uncertainty principle, entanglement and nonlocality, were long confronted as weird predictions of an incomplete theory, paradoxes only suitable for philosophical discussions, or mere mathematical artifacts with no counterpart in the physical reality. Nevertheless, decades of progress in the experimental verification and control of quantum systems have routinely proven detractors wrong. While fundamental questions still remain wide open on the foundations and interpretations of quantum mechanics, its modern technological applications have captured the fascination of the general public and are having a transformative impact on society. This brief article acts as Introduction to a Special Issue in the Philosophical Transactions of Royal Society A, following from a dedicated Scientific Discussion Meeting where these fascinating topics were explored, giving rise to stimulating debates among speakers and audience. The present issue thus aims at conveying the spirit of those discussions.
The contemporary scientific and technological progress builds on the accomplishments of classical mechanics from the 19th century when the so-called 'European scientific method and values' were accepted practically by the whole educated world.Most scientific results and conclusions were reached based on the causal ontological approach proposed in principle already by Plato's Socrates and developed further by Aristotle.Despite the late-modern paradigm shift in science (Galilei, Newton, etc.), the topicality of the ontological approach proposed by Aristotle (II.Analytics) remains.On the other hand, 19th and 20th century philosophers, mainly positivists such as Mach and Avenarius but also Schlick and Carnap, attempted to change this approach to unify scientific knowledge in accordance with an ideological, i.e. positivist outlook on reality.The authors place a special emphasis on the contribution of Rudolf Carnap and his interaction with Martin Heidegger.Three very different theories are applied to physical reality in the present: classical mechanics in the standard macroscopic realm, Copenhagen quantum mechanics in the microscopic realm, and special theory of reality in both realms in the case of systems consisting of objects having higher velocity values.Any explanation or description of transitions between different realms and theories had not been provided until now.Our paper describes the corresponding evolution in the modern period and identifies the underlying false philosophical assumptions and statements existing in today's scientific systems.We will then demonstrate that one common theory for all realms of reality may exist; one that will be based fully on Hamilton equations (only the law