The Foundations of Physical Law 9258hc_9789814618373_tp.indd 1 15/7/14 9:57 am May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory PST˙ws This page intentionally left blank Peter Rowlands University of Liverpool, UK The Foundations of Physical Law World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 9258hc_9789814618373_tp.indd 2 15/7/14 9:57 am Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Control Number: 2014018315 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. THE FOUNDATIONS OF PHYSICAL LAW Copyright © 2015 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-4618-37-3 In-house Editor: Ng Kah Fee Typeset by Stallion Press Email: [email protected] Printed in Singapore KahFee - The Foundations of Physical Law.indd 1 12/9/2014 10:45:57 AM August 30, 2014 16:44 The Foundations of ... - 9in x 6in b1877-fm pagev Preface The success of physics as the ultimate explanation of everything in the world around us has been phenomenal, but we still have a major problem: we can’t formulate the story from the beginning. We have laws of physics, funda- mental particles, and concepts like space and time, but we don’t have any understanding of their foundations. We don’t know where they come from or why they are there. This, of course, is not for want of trying: the search for the ultimate foundations of human knowledge of the world is one of the biggest quests ever undertaken, and it is certainly one of the most expensive, requiring massive international collaborations and incredibly sophisticated facilities. On the experimental side, the search has been successful beyond all expectation, but the results have been disappointing to many because they have repeatedly confirmed existing theories — quantum mechanics, the Standard Model of particle physics, general relativity — without sug- gesting any new direction leading towards a more general unification. We seem to be no nearer to solving the foundational problems than we were when the Standard Model of particle physics first reached its most complete form around 1973. I am not convinced that finding ‘new physics’ would actually help to solve the problems of the old, and I don’t think our failure to date has anything to do with the lack of resources or with the subject’s inherent difficulty. I think it is a question of mind-set. It seems to me that we may have been asking the wrong questions or perhaps asking the right questions in the wrong way. We haven’t properly accepted that if tried and trusted techniques fail to give us answers, then perhaps we need to try new ones. In that sense, the primary aim of this book is to devise a methodology for a subject that we would like to exist but have not yet really attempted to create. v August 30, 2014 16:44 The Foundations of ... - 9in x 6in b1877-fm pagevi vi The Foundations of Physical Law It is remarkable that, for all its importance, the foundations of physics has virtually no recognition as a subject in its own right. It has never been seen as a branch of physics of equal importance as quantum mechanics, particle physics or relativity. It has no place in most university physics courses, and has no legion of PhD students working out details to be tested by experiment. For whatever reason, the subject is not entirely ‘respectable’. You can’t do it in the hard-edged way that most of physics is done, and so it is very difficult to write a paper that the most pres- tigious journals would accept. Even though John Bell and others have made it acceptable to talk in a certain way about the foundations of quantum mechanics, it still doesn’t take us very far in explaining the foundations of physics itself. Quantum mechanics is still a given in all the discussions, it isn’t explained in a more fundamental way. In fact, one of the problems with our failure to define the foundations of physics as a separate subject is the fact that many people think that founda- tional results can be obtained by extending existing areas, such as quan- tum mechanics, particle physics, general relativity or cosmology. Expe- rience tells us that they cannot. Foundational ideas have to be simpler than the subjects they are explaining. Extending existing ideas that are already complicated will not bring us nearer to the more primitive starting points. Nevertheless, for all the general lack of appreciation of the kind of the- ory needed to explain the foundations of physics and physical law, the desire for such a theory is very strong. My own experience is that students usually enter physics because they really want to know where everything comes from, and that a course which really explains how the search for the foundations should be carried out would come the closest to fulfilling this need. And it is not only physicists and physics students who would benefit from such knowledge for the desire to understand origins and fundamental explanations is part of a much more general human requirement. Clearly, a book or a course of lectures on such a subject, if it reached a deeper level than current investigations would seem to allow, would be of interest to a great number of people. So, what can one say that is new and positively useful if so many attempts have failed to make any headway? Perhaps we could begin by defining a few negatives — things we want to avoid. The list would certainly include, among other things, major challenges to existing theo- ries, model-dependent ideas, theories that are more complicated than the ideas we are trying to explain, and ideas which are not sufficiently generic. August 30, 2014 16:44 The Foundations of ... - 9in x 6in b1877-fm pagevii Preface vii We could also focus on some ideas which seem to reflect successful previous approaches: minimalism, a high (and preferably total) degree of abstrac- tion, simplicity, symmetry and recurring patterns. In effect, our experience suggests that we need to think in a way that maximises the second list and minimises the first. Even if we adopt such a programme, there is no guarantee that we will be successful, but I would like to suggest that there isn’t even a possibility of success if we don’t. Nevertheless, this is still not fully understood. Theories are still being produced which do not respect the principles of minimalism and abstraction. By consciously setting out on a path which privileges them, we are already formulating a methodol- ogy which, even in this very generalised and simplified form, is diverging from many of the existing approaches towards fundamental theory. The aim of this book is to show that such a methodology can lead to successful results. Even in purely conventional terms, the version of quan- tum mechanics that emerges from more abstract foundations using argu- ments based largely on symmetry appears to be more powerful and effec- tive than alternative versions. Many significant results in physics follow purely from relatively simple arguments privileging symmetry. A generic kind of physics can be constructed from a combination of pure abstrac- tion, symmetry and mathematics without any model-dependent or empir- ical input. Even gravity and particle physics can be treated in this purely abstract way. It seems to me important that we take the most successful generic the- ories and try to find their constituent elements, rather than treat them as elementary and fundamental in themselves. Ultimately, there should be no separate ‘physical’ constituency to which mathematics is merely applied. At the fundamental level, physics has to be about the simplest ideas, and, almost by definition, these must be the most abstract. This necessarily forces us in the direction of pure mathematics, although (as will be pro- posed at the end of the last chapter) this mathematics may incorporate ideas which have yet to be written down. We should also expect even familiar areas of physics to look different in a fundamental context while preserving their standard forms at the more complex levels at which they are currently known. This is especially true of general relativity, which, as Einstein developed it, became a purely abstract theory not based on any specifically physical assumptions, and the struc- tures of fundamental particles where the empirically-observed properties clearly have an abstract generic foundation in symmetry principles which have not yet been completely uncovered. As in other areas, the proposed August 30, 2014 16:44 The Foundations of ... - 9in x 6in b1877-fm pageviii viii The Foundations of Physical Law treatment of these subjects at the fundamental level leads to extremely interesting possibilities at the level of observation. In the case of general relativity, the abstract treatment in Chapter 8 leads to the conclusion that the validity of the theory will extend well beyond the limits currently assumed, together with a prediction of dark energy produced long before its experimental discovery which is very close to the currently observed numerical value.