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Category theory applied to a radically new but logically essential description of time and space

John Yates

Published Aug 22, 2008• 0 citations
OpenAlex

Abstract

McTaggart's ideas on the unreality of time as expressed in "The Nature of Existence" have retained great interest for many years for scholars, academics and other philosophers. In this essay, there is a brief discussion which mentions some of the high points of this philosophical interest, and goes on to apply his ideas to modern physics and neuroscience. It does not discuss McTaggart's C and D series, but does emphasise how the use of derived versions of both his A and B series can be of great virtue in discussing both the abstract physics of time, and the present and future importance of McTaggart's ideas to the subject of time. Indeed an experiment using human volunteers and dynamic systems modelling which was carried out is described, which illustrates this fact. The Many Bubble Interpretation, which also derives from McTaggart's ideas, is discussed and various examples of its use and effectiveness are referred to. The Schrodinger Cat paradox is essentially resolved in principle, the quantum Zeno effect interpretable, Kwiat's recent result referred to, and the newly discovered reverse Stickgold effect described. \n

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Cambridge University Press eBooks•Apr 17, 2014•0 citations
McTaggart's ideas on the unreality of time as expressed in "The Nature of Existence" have retained great interest for many years for scholars, academics and other philosophers. In this essay, there is a brief discussion which mentions some of the high points of this philosophical interest, and goes on to apply his ideas to modern physics and neuroscience. It does not discuss McTaggart's C and D series, but does emphasise how the use of derived versions of both his A and B series can be of great virtue in discussing both the abstract physics of time, and the present and future importance of McTaggart's ideas to the subject of time. Indeed an experiment using human volunteers and dynamic systems modelling which was carried out is described, which illustrates this fact. The Many Bubble Interpretation, which also derives from McTaggart's ideas, is discussed and various examples of its use and effectiveness are referred to. The Schrodinger Cat paradox is essentially resolved in principle, the quantum Zeno effect interpretable, Kwiat's recent result referred to, and the newly discovered reverse Stickgold effect described. \n
For many years the physical interpretation of quantum theory has been dominated by the “wave-particle duality” attitude of the “Copenhagen school.” This point of view is eloquently described in Bohr's collection of essays on the subject. Despite persistent concerns with apparent paradoxes and limitations to this interpretation (as exemplified by Schrodinger's cat, the paradox of Einstein, Podolsky and Rosen, among others), the Copenhagen view persists de facto in the daily life of the modern physicist. Traditional quantum theory has so successfully explained such a vast amount of data in atomic and molecular physics, solid state physics (and to a lesser extent, elementary particle physics) that little doubt can exist concerning its essential validity. As a consequence of the overwhelming practical success of the “Copenhagen interpretation, ” the latter has acquired the status of dogma. For many years, therefore, most physicists have found it expedient to relegate the puzzling aspects of the theory to philosophers, and mathematicians. Nevertheless, a persistent interest in this subject has produced a significant and fascinating literature, reviewed by Jammer. In recent years, concerns over the proper meaning to be ascribed to quantum theory have produced an increasingly deep and incisive series of investigations. These investigations fall generally into two categories: either (1) discussion of the philosophical content of the theory, or (2) analyses of the mathematical variants of the theory and their connection with differing interpretational schemes. Physicists tend to be detached from a commitment to philosophical issues, because of their realization of the transient character of the meanings attached to theories of the day. As a simple illustration of this we can mention the profound differences between nonrelativistic and relativistic quantum mechanics.
THE conceptual problems raised by the discovery of quantum effects have not been fully resolved after half a century. Part of the reason for this is undoubtedly to be found in the mutual ignorance which prevails between physicists and philosophers. In his book Heisenberg brings together a philosophically inclined temperament with an unrivalled knowledge of physics. The result is a book of very great interest, however much one might disagree with his conclusions. The collection of essays of which the other book is made up is intended to bring crucial conceptual problems in physics especially to the notice of philosophers. The design and intention of the collection is admirable for this is the proper way to overcome the departmentalization of interest that has left the deep conceptual problems still unresolved. Men like Heisenberg who combine philosophical temperament with scientic knowledge of great distinction are rare, and yet the difficulties can only be cleared up by the application of philosophical techniques of analysis to problems which are an intimate and difficult part of physics. A great deal of the interest of Heisenberg's book lies in the very comprehensive account he gives of the origin and growth of the Copenhagen school, and the way the new phenomena forced a largely unwelcome picture of nature upon Bohr and his friends. The most important chapter from a philosophical point of view is that in which Heisenberg defends this interpretation against the attacks to which it has been subjected. The essence of his argument for the interpretation can be summed up in two propositions. (i) The Copenhagen interpretation of physical theory, which depends upon the acceptance of the so-called Principle of Complementarity, is an inevitable and final interpretation. The reason for this is that there are only two possible general models for understanding given physical phenomena; a particle model or a wave model. These are exhaustive and exclusive because the former depends upon discontinuous and the latter upon continuous (using substance here in the traditional philosophical sense). If we find, as we do, that the two fundamental constituents of the universe, matter and radiation, each exhibit two classes of phenomena, one explainable only on a particle model and one on a wave model, then we are compelled to adopt a complementarity hypothesis and give up the idea of finding a single and uniform model for the understanding of phenomena. There are only two kinds of models; they are mutually exclusive; both are required; hence we either despair before an insoluble problem or adopt the Copenhagen interpretation. (2) Any serious criticism of this interpretation must offer an alternative
The fundamental physical theories that interpret and explain behaviour of matter in nature are dependent on several unobservables and insensibles in their construction. While a rigorous natural philosophy cannot take them for granted, there does not seem to be a way of avoiding such unobservables in our theories. While a program to banish all unobservables from physical theory is unlikely to succeed, and perhaps even unnecessary, they are both the strong and weak points of the theoretical descriptions of physical nature. Analyzing them for empirical and philosophical consistency and integrity is always a promising path towards a better theory. In this paper, I examine the nature of physical reality in the context of unobservables in physics and discuss three examples. One is about the apparent loss of physical reality due to the need for a consistent quantum mechanical representation. The second example deals with the conflict between the assumed reality of quantum fields, so fundamental and essential to our standard physics worldview, and the dynamics of the observable universe. The third deals with an all-important difference between conventional modern physics constructed in the unreal and unobservable empty `space' and an empirically and logically determined physics with matter-filled universe as its arena. The acknowledgment of the observable matter-filled universe necessitates reformulation of dynamics with total relativity. Not surprisingly, this paradigm with its universal cosmic links also holds human concepts of harmony and beauty.
The interplay between non-relativistic quantum theory and metaphysics has generated radically opposed interpretations for quantum theory: Niels Bohr's 'orthodox' interpretation, and Einstein's 'realist' one. Out of this debate emerged the classical first-generation paradoxes of quantum theory: Schrodinger's Cat and the Einstein-Podolsky-Rosen paradoxes. And more recently a range of new paradoxes has emerged from the work of J.S. Bell which questions the `local' nature of quantum theory, prefiguring a return either to an action-at-a-distance metaphysics or to a radically holistic conception of matter. This book outlines the contours of these debates, and presents an interpretation of quantum theory which, while metaphysically realist, resolves most of the paradoxes. This interpretation takes quantum systems to be fuzzy particles, piloted by fields of propensities which are represented by density operators on Hilbert space; and constitutes, in part, a return to an earlier view of quantum systems advanced by De Broglie, Schrodinger, Born, and Einstein. A book for philosophers and physicists who are interested in the philo sophy o f science.
The fundamental physical theories that interpret and explain behaviour of matter in nature are dependent on several unobservables and insensibles in their construction.While a rigorous natural philosophy cannot take them for granted, there does not seem to be a way of avoiding such unobservables in our theories.While a program to banish all unobservables from physical theory is unlikely to succeed, and perhaps even unnecessary, they are both the strong and weak points of the theoretical descriptions of physical nature.Analyzing them for empirical and philosophical consistency and integrity is always a promising path towards a better theory.In this paper, I examine the nature of physical reality in the context of unobservables in physics and discuss three examples.One is about the apparent loss of physical reality due to the need for a consistent quantum mechanical representation.The second example deals with the conflict between the assumed reality of quantum fields, so fundamental and essential to our standard physics worldview, and the dynamics of the observable universe.The third deals with an allimportant difference between conventional modern physics constructed in the unreal and unobservable empty 'space' and an empirically and logically determined physics with matter-filled universe as its arena.The acknowledgment of the observable matter-filled universe necessitates reformulation of dynamics with total relativity.Not surprisingly, this paradigm with its universal cosmic links also holds human concepts of harmony and beauty.
What is time? This book explores the hypothesis that time is discrete rather than continuous. Time is an enigma, so we should expect some metaphysics and philosophy to creep into the discussion. Our inclination is to avoid those disciplines as much as possible, so let us deal with them right now. Metaphysics and philosophy deal with statements and conjectures that cannot be empirically validated. In those disciplines there are constant references to absolutes such as existence, good and bad, and suchlike without further qualification, as if everyone accepted them as meaningful concepts. Absolutes are the key things we wish to avoid. For the record, we define an absolute statement as one that is considered to be true regardless of any caveats or criteria, i.e., context-free. In contrast, a contextual statement has a truth value that is meaningful only relative to its particular context. The idea that physical truth can be contextual is an unfamiliar and uncomfortable one to physicists conditioned to believe that the laws of physics transcend the context of observation because they can be empirically validated. In fact, that is a circular line of reasoning. Every experiment is defined by its own context and experimentalists have to work hard to create that context: the search for the Higgs particle at the Large Hadron Collider did not happen overnight.