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Some Comments inspired by Dainis Zeps' Quanta Mathematica Instrumentalis

Matti Pitkänen

Published Apr 28, 2011• 0 citations
OpenAlex

Abstract

The ideas introduced by Dainis Zeps in the article Quanta Mathematica Instrumentalis and related articles are discussed in the conceptual framework of Topological Geometrodynamics. The concrete realization for the vision about physics as mathematics is discussed in TGD context and the idea about instrumentalism as key element of mathematics and science is analyzed and criticized. Also the notions of theorem and quantum windows, higher observer, and information field are discussed.

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The ideas introduced by Dainis Zeps in the article Quanta Mathematica Instrumentalis and related articles are discussed in the conceptual framework of Topological Geometrodynamics. The concrete realization for the vision about physics as mathematics is discussed in TGD context and the idea about instrumentalism as key element of mathematics and science is analyzed and criticized. Also the notions of theorem and quantum windows, higher observer, and information field are discussed.
In this thesis I argue that many problems in the philosophy of science and mathematics (in particular, the unreasonable effectiveness of mathematics in physics) can only be addressed within a broader metaphysical framework which provides a coherent world view. I attempt to develop such a framework and draw out its consequences. The attempt is in two parts: first, I develop a speculative framework based on an analogy to set theory; then I combine elements of the framework with ideas from Leibnizian monadology and consistent histories quantum theory to introduce (what I call) quantum monadology. The two parts focus on different aspects of the problem and should be viewed as stages on the way to a final formulation. The inspiration for the thesis came from Plato’s Timaeus and Wigner’s comments on quantum mechanics. As it turned out, Leibniz’s Monadology became a third key source.
Topology is woven into the subtle fabric of quantum theory. Topological concepts and ideas developed starting in the 1980s by the high energy physics and quantum gravity communities, first viewed by many as nothing but aesthetically appealing abstract possibilities, are central components of modern condensed matter physics and play a key role in the field of quantum information and quantum computation. The discovery of integer and fractional quantum Hall effects and, more recently, of topological insulators and superconductors has brought topological quantum matter in the laboratory, with the perspective of realizing functional platforms for topological quantum computation. Rooted in a solid mathematical formalism and spanning its relevance from fundamental questions in quantum gravity and quantum information to practical aspects regarding new materials and platforms for quantum computation, quantum topology is positioned at a fertile confluence of mathematics, physics, and computer and information science. This book focuses on the aspects of quantum topology that are most relevant from the perspective of condensed matter physics and its relation to quantum computation. We start our journey by sketching the relation between topology and quantum physics and summarizing a few basic mathematical concepts that will be used throughout this work. Beyond dry formal definitions, our main goal is to grasp the delicate root that makes the topological quantum world utterly strange and beautiful and follow it into the realm of condensed matter many-body systems.
It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.
Nonlocality seems to be a basic aspect of what it is to be living. Living system is elementary particle-like coherent unit. The phenomenon of memory suggests temporal nonlocality. Also, remote mental interactions, if real, suggest nonlocality. In fact, nonlocality, both spatial and temporal, is the basic element of entire quantum TGD and, in particular, its applications in quantum biology, neuroscience, theory of consciousness and remote mental interactions. In this series of articles, I suggest pictures in Topological Geometrodynamics (TGD). I will begin from empirical findings related to nonlocality rather than problems of General Relativity or of particle physics. The hope is that this could make the basic ideas of TGD easier to grasp. Further, the mathematical framework and its interpretation in current state of TGD are briefly described and some applications of TGD inspired theory of consciousness and quantum biology are discussed.This is Part I of a two-part article.
This book belongs to a series of online books summarizing the recent state Topological Geometrodynamics (TGD) and its applications. TGD can be regarded as a unified theory of fundamental interactions but is not the kind of unified theory as so called GUTs constructed by graduate students at seventies and eighties using detailed recipes for how to reduce everything to group theory. Nowadays this activity has been completely computerized and it probably takes only a few hours to print out the predictions of this kind of unified theory as an article in the desired format. TGD is something different and I am not ashamed to confess that I have devoted the last 32 years of my life to this enterprise and am still unable to write The Rules. I got the basic idea of Topological Geometrodynamics (TGD) during autumn 1978, perhaps it was October. What I realized was that the representability of physical space-times as 4-dimensional surfaces of some higher-dimensional space-time obtained by replacing the points of Minkowski space with some very small compact internal space could resolve the conceptual difficulties of general relativity related to the definition of the notion of energy. This belief was too optimistic and only with the advent of what I call zero energy ontology the understanding of the notion of Poincare invariance has become satisfactory.