The Foundations of Physical Law

262 Pages·2014·1.824 MB·English

by  Peter Rowlands

The
Foundations
of
Physical Law
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Peter Rowlands
University of Liverpool, UK
The
Foundations
of
Physical Law
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
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THE FOUNDATIONS OF PHYSICAL LAW
Copyright © 2015 by World Scientific Publishing Co. Pte. Ltd.
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ISBN 978-981-4618-37-3

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Preface
Thesuccessofphysicsastheultimateexplanationofeverythingintheworld
aroundushasbeenphenomenal,butwestillhaveamajorproblem:wecan’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
biggestquestseverundertaken,anditiscertainlyoneofthemostexpensive,
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
whentheStandardModelofparticlephysicsfirstreacheditsmostcomplete
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
havebeenaskingthewrongquestionsorperhapsaskingtherightquestions
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
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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
explanationsispartofamuchmoregeneralhumanrequirement.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
Wecouldalsofocusonsomeideaswhichseemtoreflectsuccessfulprevious
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
complexlevelsatwhichtheyarecurrentlyknown.Thisisespeciallytrueof
generalrelativity,which,asEinsteindevelopedit,becameapurelyabstract
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
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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. The suggested abstract sym-
metry structure for fundamental particles in Chapter 9, generated by the
convergence of four quite different approaches, makes predictions concern-
ing grand unification within the range of future experimental verification
using large colliders.
While the work described in these chapters forms part of a long-term
research project whose most significant publication is a book entitled Zero
to Infinity: The Foundations of Physics, published by World Scientific in
2007, the immediate origin was a course of lectures given in the Physics
Department at the University of Liverpool, which were attended by under-
graduate and postgraduate students in addition to members of staff, and
whichwereanexperimenttowardsseeingifacourseonwhatwasessentially
an entirely new subject would generate the expected interest. The book is
intended at creating a convenient basis for those who wish to work in the
subject or to develop their interests in this area.
Before 1997, the overall research project was a solitary enterprise
and much of it still is. This was the origin of the material outlined in
Chapters 1–4, and the basis of the work on quantum mechanics, particle
physics and gravity in Chapters 5–9. After that period, John Cullerne col-
laborated with me on aspects of quantum mechanics and particle physics.
At the same time, I began to work with Bernard Diaz on the univer-
sal rewrite system, and with Peter Marcer on a computational systems
approach, both of which appear in Chapter 10. A further extensive collab-
oration with Vanessa Hill on biology is largely discussed elsewhere, but the
table on pp. 202–3, which here refers to fundamental particles, is a result
of our discussion of a generic algebraic-geometric patterning observable in
many aspects of nature.
The details of these, and several other collaborations, are discussed
in Zero to Infinity, but I would like to draw attention to the enrich-
ment of the work that they have produced. I would also like to mention
the continuing support from a number of members of Liverpool’s Physics
Department, in particular from Mike Houlden and John Dainton. I would
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Preface ix
finally like to thank Dave Law and Christian Faber, who filmed and edited
the lectures delivered and have made them available to anyone who is
interested.
Peter Rowlands
Physics Department
University of Liverpool
June 2014