Library of Congress Cataloging-in-Publicatlon PrefacePhysics appears to be the only source of fundamental knowledge about the natural world. No other system of thought or methodology has shown any of its systematic explanatory or predictive power. This success has been achieved by a continued attempt at minimalism and reductionism, and it appears that the greatest success has been achieved from the simplest possible foundations. Yet, because we have been obliged to approach the subject by an inductive method, working back from complicated observations to simple explanations, we have still to discover the ultimate foundations on which this whole conceptual scheme has been based. We know that the ultimate theory must be simple, probably extremely simple, but, because it must also be unique, we have no precedent which would help us to make the discovery. Yet the belief that the discovery is possible remains, and has led to many approaches towards a 'unified theory of physics' or a 'theory of everything', none of which seems to be close to success.Obviously, no one expects to succeed instantly with a theory that will simply explain everything. What we would hope to do is to find a process, a systematic way of proceeding with strong indications that we were on the right track. This is what is being aimed at in this book. Positions that are rejected from the outset in the search include model-dependent theories of any kind; the aim of the work is resolutely abstract. One of the particular approaches avoided is the restructuring of particle physics in terms of multidimensional space-time strings or membranes. We can, of course, do this as a mathematical representation, and the procedure for doing so is sketched out in chapters 4, 15 and 18, but a string theory would not be a unified theory, even if we should chance to find out the 'correct' one from the many thousands of possible alternatives. A unified theory has to explain the concept of dimension, as well as the number (why 10? why 11?); it also has to explain space and time, their similarities and differences, and even the use of mathematics to explain physics. But there are also intrinsic difficulties with the approach which explain why it does not offer a true unity. VllZero to Infinity Downloaded from www.worldscientific.com by 34.217.195.47 on 05/12/18. For personal use only. Vlll Zero to InfinityEven the first stage of combining space and time in the simplest way, by adding the single time dimension to space's three in special relativity, causes us problems when we look at quantum mechanics, a theory which appears to be an essential starting-point for all foundational work in physics. Time, unlike space, is simply not an observable in quantum mechanics, though the two quantities are assumed to have identical status in the relativistic 'space-time' concept. When we make the space-time part of an even-more complicated structure, as in general relativity, where 'curvature' is used to eliminate mass or gravity, the problems multiply, and we find singularities, non...
The Foundations of Physical Law by Peter Rowlands, World Scientific, Singapore, 2015, pp. xiv + 247. Scope: monograph, £71 (or ebook £56), ISBN 978-981-4618-37-3 (Hardcover). Level: professional physicists and mathematicians, senior undergraduates, postgraduates.
Library of Congress Cataloging-in-Publicatlon PrefacePhysics appears to be the only source of fundamental knowledge about the natural world. No other system of thought or methodology has shown any of its systematic explanatory or predictive power. This success has been achieved by a continued attempt at minimalism and reductionism, and it appears that the greatest success has been achieved from the simplest possible foundations. Yet, because we have been obliged to approach the subject by an inductive method, working back from complicated observations to simple explanations, we have still to discover the ultimate foundations on which this whole conceptual scheme has been based. We know that the ultimate theory must be simple, probably extremely simple, but, because it must also be unique, we have no precedent which would help us to make the discovery. Yet the belief that the discovery is possible remains, and has led to many approaches towards a 'unified theory of physics' or a 'theory of everything', none of which seems to be close to success.Obviously, no one expects to succeed instantly with a theory that will simply explain everything. What we would hope to do is to find a process, a systematic way of proceeding with strong indications that we were on the right track. This is what is being aimed at in this book. Positions that are rejected from the outset in the search include model-dependent theories of any kind; the aim of the work is resolutely abstract. One of the particular approaches avoided is the restructuring of particle physics in terms of multidimensional space-time strings or membranes. We can, of course, do this as a mathematical representation, and the procedure for doing so is sketched out in chapters 4, 15 and 18, but a string theory would not be a unified theory, even if we should chance to find out the 'correct' one from the many thousands of possible alternatives. A unified theory has to explain the concept of dimension, as well as the number (why 10? why 11?); it also has to explain space and time, their similarities and differences, and even the use of mathematics to explain physics. But there are also intrinsic difficulties with the approach which explain why it does not offer a true unity. VllZero to Infinity Downloaded from www.worldscientific.com by 54.201.150.21 on 05/09/18. For personal use only. Vlll Zero to InfinityEven the first stage of combining space and time in the simplest way, by adding the single time dimension to space's three in special relativity, causes us problems when we look at quantum mechanics, a theory which appears to be an essential starting-point for all foundational work in physics. Time, unlike space, is simply not an observable in quantum mechanics, though the two quantities are assumed to have identical status in the relativistic 'space-time' concept. When we make the space-time part of an even-more complicated structure, as in general relativity, where 'curvature' is used to eliminate mass or gravity, the problems multiply, and we find singularities, non...
Lie superalgebras and the multiplet structure of the genetic code. II. Branching schemes Lie superalgebras and the multiplet structure of the genetic code. I. Codon representations Abstract. We propose that the mathematical structures related to the 'universal rewrite system' define a universal process applicable to Nature, which we may describe as 'Nature's code'. We draw attention here to such concepts as 4 basic units, 64-and 20-unit structures, symmetry-breaking and 5-fold symmetry, chirality, double 3-dimensionality, the double helix, the Van der Waals force and the harmonic oscillator mechanism, and our explanation of how they necessarily lead to self-aggregation, complexity and emergence in higher-order systems. Biological concepts, such as translation, transcription, replication, the genetic code and the grouping of amino acids appear to be driven by fundamental processes of this kind, and it would seem that the Platonic solids, pentagonal symmetry and Fibonacci numbers have significant roles in organizing 'Nature's code'.Biological systems, though operating at the edge of chaos, are extremely ordered, whereas the tendency for nature is to become more disordered. Biology is, in effect, a race between order and entropy with the odds stacked in favour of entropy. So biological systems must create order, i.e. process information, with as much efficiency as possible. Theoretical studies by Freeland and Hurst suggest that the genetic code known on Earth has an extraordinary efficiency; of a million possible codes studied, only one could conceivably have been more efficient. ^"^ The genetic code we have inherited does not seem to be the product of pure chance; and it would appear, in fact, that the efficient processing of information requires certain algebraic and geometric structures, which are also found in systems organized at other scales, in particular, physics.There seems to be evidence that a universal rewrite system operates in nature at a fundamental level. ^"' ' Essentially, this uses a create / conserve process to generate its own system of mathematical structure, based only on the permanent condition of zero totality, and not on any assumed pre-existing number system or algebra. A convenient, but not unique, representation of this mathematical structure is through an infinite Clifford algebra of nested quaternion systems {i\,j\, k^; i2,J2, ^2, etc.), so that the successive units introduced at orders 2, 4, 8, 16, 32, 64 are scalar, pseudoscalar, quaternion, multivariate vector (or complexified quaternion), double quaternion, and multivariate vector quaternion, with respective multiplication factors of
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