Investigations into the Nature of Matter
I love teaching at every level. By my young class at Priory School in Jamaica, I was not seen as a great disciplinarian.
I did however make a considerable effort to instill an interest and a fair confidence in mathematics which are not always present in
eleven year old children.
I love learning science and mathematics and was absolutely delighted to be able to work under Ed Corrigan as a research student at Durham Univertsity.
Ed is a World-renouned string theorist who helped me to understand a little of some current areas of research in this fast developing field of mathematical physics.
Our search for deep truth and wisdom never ends. I love learning science and all philosophy and continue my life-long search for a better understanding of anything and everything.
Theoretical Elementary Particle Theory
Stuff is made of molecules, molecules are made of atoms, atoms are made of electrons and nuclei, nuclei are made of protons and neutrons. So far so good.
Protons and electrons are held together by exchange of virtual photons. Protons and neutrons are held together by exchange of virtual pions. Protons and neutrons (and pions) are made of up and down quarks. These quarks are held together by virtual gluons. OK so far?
The theory, called the Standard Model, is awesome and fantastically well verified. But it is incomplete because it leaves out gravitation.
Now we believe that everything is string: electrons, quarks, photons, gluons, .. everything. String Theory appears to be able to incorporate the Standard Model and gravitation.
If so, it is a theory of EVERYTHING, unifying Quantum Field Theory, which already incorporates Special Relativity,
and General Relativity which is Einstein's theory of gravitation and cosmology.
Knots in String Theory
If particles are loops of vibrating string, what gives them their stability? Perhaps the string is knotted and therefore cannot simply shrink to a point. This is the proposal made in my paper, Torus Knots are Rigid String Instantons, published in 1989. Since then, knotted solutions have been found in many
unexpected places, including Maxwell's Equations of electromagnetism.
String, Membranes and Lumps
If a stringy model of matter seems to work so well, what about a membrane model, or a lumpy 3-dimensionally extended model (string being a 1-dimensionally extended version of a point particle)?
In my second publication, Self-Dual Lumps and Octonions, a new theory of everything in 8 dimensions is proposed and a new set of quaternionic knotted solutions is sought.
A Grand Unified Tour of Physics
Less ambitious solutions
have been found, but the doubly self-dual, knotted quaternionic lumps in octonionic space-time which were fully described in Self-Duality and Extended Objects and were explained at the University of the West Indies, Jamaica, are tantalizingly close
to an infinite hierarchy of knotted lumps in 8 dimensions by analogy with the infinite hierarchy of torus knots in 4 dimensions discovered earlier.
Extended Objects and the Standard Model of Particle Physics
Our world only has three space and one time dimension you might say. In fact, soon after Einstein proposed his theory of four dimensional curved space-time, Kaluza demonstrated that electromagnetism could be incorporated into a five dimensional version of general relativity where one of the dimensions is curled up very tightly. By this mechanism the extra dimensions required in standard string theory are wrapped up in various ways in the search for a natural way to include all the nuances of the standard model.
Quantised Rigid Super p-Branes .. even Love might succumb to Quantum Physics.
One lesson that we have learnt from the standard model is that deep symmetries lead to physical forces. For example, electromagnetic forces are related to symmetries among unit length complex numbers, and strong nuclears
forces are related to symmetries between 3 by 3 matrices of complex numbers which have determinant one and are equal to the complex conjugate of their transpose.
Here is some blue sky thinking for you:
Consider objectively two butterflies fluttering around one another and imagine that this demonstration of 'animal magnetism' is ultimately explicable in terms of some deep symmetry. Of course there is already
an obvious symmetry between the two butterflies. They are the same species, they look the same, talk the same and smell the same, but we are searching for a mathematical account
of their attraction to one another. While it might seem more satisfactory to seek an account of what is happening in terms of the colour and scent experiences of the individual butterflies, perhaps
their behaviour is better understood as a quantum superposition of possible states requiring a completely different mode of explanation. They have the same genetic origins - their gnomes are almost identical. There is at least quantum entanglement if not clear fundamental physical attraction ...
♥ ♥ ♥ YOU are
Special ♥ ♥ ♥
proof that you are special, but you have chosen to ignore it because
your theories tell you otherwise.
says scientific theories cannot be proved, only at best confirmed. But surely
individual observations, the plain facts, must be believed if they
are immediately verifiable. Of course Feyerabend says that every fact is theory-laden.
But some facts are so striking that one feels obliged to believe
are true, independent of any particular theory, or perhaps it would
be better to say dependent on every reasonable theory.
Descartes showed one could doubt almost everything, except for this
one thing, I AM. One cannot doubt that one exists because
existence is a prerequisite of this thought. "Cogito, ergo
sum." (I think, therefore I am.) The proof that you are special is this; as far as you
know, without introducing any metaphysical (untestable)
assumptions, yours may be the only consciousness in the universe.
Wherever you go, from birth to death, it will go with you. It
is absolutely attached to you which makes you absolutely different
from everyone else in the world, from your point of view. This
point of view is the only one you have and, although you may deeply
empathise with others, even other animals, you will forever remain
you. You are ABSOLUTELY special and you cannot deny that.
One is unique and absolutely different from every other person.
This scientific observation, that there is only one direct consciousness, is
ignored, degraded and even derided in conventional physics.
What is consciousness? That is a hard question.
Who is conscious? That's easier to answer, is it not?
Everyone is conscious, are they not? Descartes pointed out
that one can only prove one's own consciousness to oneself. No
one else can prove that you are conscious, and you cannot prove that
anyone else but yourself is conscious. Consciousness, by
virtue of its very nature, is something that one can only observe
internally, in oneself. The assumed consciousness of others is
an implication of a theory which says, "You are not so special, you
are so like everyone else and everyone is very like you."
Basic science has tended to support this view because the laws of
nature are demonstrably the same for everyone. This is indeed
an axiom of general relativity: The fundamental laws of
physics are necessarily the same for all observers. But what
if the laws of nature turn out to be merely tautologous, necessary
truths of the logic of the mathematical foundations, and therefore
turn out to have no physical content other than that this is the way
things must be? What then?
All meaning resides in the light of awareness.
The conditions under which an observation is made, the
boundary conditions, dictate the meaning of reality, not the laws.
laws of nature appear to be tautologies;
if so, only the boundary conditions contain real meaning.
We are getting used to being told that geometry is empirical, and now that logic is
Instead consider that the laws are theorems and circumstances prescribe everything.
What is consciousness? It is this immediate experience.
It is not about what was or what will be. It is about this
here and now awareness. This is it. This is where
consciousness is – always in the present; compared with memories of
awareness, or assumptions of awareness, or endowments of awareness
in others. We naturally endow fellow citizens with
consciousness – their equivalent of our experience. However,
this is a metaphysical presumption which is not testable except by
inference from a normal perspective. From a purely empirical
stance, there is and can only be one consciousness, only one
immediate and present reality, only one fountain of direct
awareness. All other hypothetical consciousnesses are
metaphysical assumptions without scientific basis, except in so far
as our philosophy of science presupposes them. Hearsay and
rhetoric will convince us of other minds - a complex tangle of
states leading to complex behaviour patterns - but consciousness is
certainly singularly mine, is it not?
According to my view of quantum mechanics, alluded to
in Philosophical Problems
of Quantum Ontology and elaborated in
Unity Consciousness and the Perfect Observer, the state of a system is only
determinable through consciousness. If not immediately
observed then the state is a superposition of all classically
possible states. This means, in particular, that the states of
mind of other people have to be considered as superstates - a
hypothesis that should have testable consequences. This view could
be labelled solipsistic pantheism because there is
only one consciousness in the universe (hence solipsistic), and that
which is experienced is a phenomenal unity emerging from a complex
noumenal state underlying all reality. That noumenon we may
call Nature (or Goddess) or God (hence pantheism).
To be more precise, the noumenon of Kant might be
understood as being represented by a complex function or set of
complex functions which reside in a Hilbert space of states.
Nothing like this is entertained as physics in Newton's natural
philosophy where everything is in terms of real numbers and real
functions of real numbers. Operators which act in this Hilbert
space may be associated with Kantian phenomena by projecting real
measurable numbers out of the function or group of functions in
Hilbert space. Kant's forms of perception and categories of
understanding may be identified with an array of sensory operators
such as we have on board with our 5 senses.
Consequences of this view might be
comprehensible to a psychologist as well as a physicist.
First the angle that is comprehensible to the physicist.
Consider the attractive force between two oppositely electrically
charged particles circling round one another. This force is
ultimately deducible from the assumption that the state of the
system, the complex function in Hilbert space, has a certain
symmetry called U(1) invariance (meaning you can multiply the state by
exp(iθ) and get the same observables). The U(1) invariance of the
electromagnetic field implies conserved electric charges.
Non-zero charges attract or repel one another. Similarly
consider the attractive force between two differently colored quarks
circling round each another. This 'strong force' is ultimately
deducible from the assumption that the state of the system has a
certain symmetry called SU(3) invariance. (And the heavenly bodies
attract as a result of GL4 symmetry of space-time.)
Thus symmetries engender forces in physics.
Now consider objectively two butterflies fluttering
around one another and imagine that this animal magnetism is
ultimately explicable in terms of some deep symmetry. Of
course there is already an obvious symmetry between the butterflies.
They are the same species, they look the same, talk the same and
even smell the same, but we are looking for a description that is
deeper than that. While it might seem more satisfactory to seek an
account of what is happening in terms of the colour and scent
experiences of the individual butterflies, perhaps their experience
is better understood as a quantum superposition of possible states
requiring a completely different mode of explanation. They
have the same genetic origins, their gnome is almost identical.
Could this symmetry appear as a force? Could quantum identity principles
introduce superposition or interference or entanglement at a deeper
level of explanation?
The theory might be called "G2 Love".
G2 is a wonderful symmetry with, as yet, no definite
application in the real world. Nevertheless you can do the
same mathematical tricks with G2 as are done with U(1)
and SU(3) and produce a theory of deep and complicated forces.
Since love is a real and powerful force in human lives, let
us look for human dimensions that might fit in with this objective
way of looking at human relations. The search for the
dimensions of the mind is not a new quest but the mathematics of G2
might be a much needed guide. This theory has a classical
(real) version and so can be discussed without involving relativity
or some of the more abstruse quantum ideas such as intrinsic spin or
anti-matter. This is non-relativistic Yang-Mills theory with G2
However quantum ideas are still vital. Consider
Schroedinger's cat. The cat cannot be said to be alive or dead
until observed, in von Neumann's mathematical formulation of quantum
mechanics. Wigner's friend observes the cat, and now he too
cannot be said to have seen a live cat or seen a dead cat.
Until one knows the result of the wicked experiment oneself, the
complete mathematical description of the world does not involve a
cat which is alive, nor one which is dead. The cat and indeed
the mind of Wigner's friend are in an entangled state with respect
to the question of the health of the cat. For a fuller
explanation, see the account in
Philosophical Problems of
Quantum Ontology, chapter 2.
The usual interpretation of Wigner's friend rests on
the fact that we believe the friend when he tells us that he was
never in a superposition of two states, one seeing a live cat and
another seeing a dead cat. This led Wigner to conclude that,
at least by the time the information has arrived at his friend's
consciousness, the state of the cat has already 'collapsed'.
This is not the interpretation given here. (I went to Princeton in
the summer of 1974 to talk to Eugene Wigner about this very point of his
paradox, but unfortunately he was not in his room at the university
when I visited.) Consider instead, that the only reality is
ones immediate conscious experience, and all that is implied by that
experience. The state is an evolving complex function and only
when directly observed by you can many properties that were
previously entangled be said to have real values. Even other
minds must be treated like this. B.F.Skinner showed that, by
focusing entirely on behaviour, one can completely ignore the
possibility of consciousness in many psychological experiments without a
complete loss of substance in psychology. Now we must view
other minds like a quantum computer with superpositions of many
entangled possibilities. The resulting behaviour may require
the combination of many classical alternatives to explain it.
It is worth noting here that Einstein, Tolman and Podolski showed
that determining the state of a quantum system now does not imply
that the past can have all quantum uncertainty squeezed out of it,
and that John Archebald Wheeler (whom I wrote to in 1976 and who was good enough to
reply with a kind and
sympathetic letter) showed with a delayed choice experiment that state
'collapse' cannot be assumed to happen at the moment of the nominal
event. Inferences about the past, in particular about the past
state of mind of a friend, can not be made glibly, and without
reference to a physical theory. But remember how Wheeler
helped Feynman to understand that there might be only one electron
in the universe, similarly we might be able to go from a conception
of many minds to just one mind by an analogous route of quantum
In the quantum version of G2
Love, two minds are each considered as
superpositions of states. These superstates interact by way of
exchange of the 14 virtual bosons corresponding to the Yang-Mills
theory of G2
interaction symmetry. What classically we describe as exchange
of visual or audio information and even exchange of chemicals such
as pheromones, now we must describe in a new way given only that
which we ourselves know, and without the classically assumed
substrate of an infinity of assumptions about the precise state of an underlying
objective reality. Thus, for example, butterflies, which have
huge eyes (although they can see only red, green and yellow) might be
assumed to attract simply by sight of the bright wing colours.
But butterflies have been around for over 100 million years and are
probably even more complicated and more subtle than that.
Butterflies don't have mouths or noses, but they can smell with
their antennae and they can taste with their feet.
What is more, they can communicate with molecular scent.
Male butterflies can release pheromone chemicals from their
abdomen and attract females by this "song".
The mind of a butterfly might have a simpler deeper less disjointed
(due to the multitude of artificial experimental arrangements
involved in human analysis of butterflies) comprehension. They
might see communication as transferring a mental state by exchange of some
particular intermediate boson, rather like nucleons interact by
exchange of pions. If we knew all about butterflies, this
theory of communication (love is perfect communication) might
not seem so far fetched. For example,
it is said that butterflies can orient themselves both in
latitude and in longitude and that they can be seen to
cooperate with ant colonies. We easily forget one
consequence of Bell's theorem, that correlation between quantum
states is significantly greater than one can imagine from a
classical perspective. Nature may have found ways of using
this while we can hardly imagine what it signifies.
General relativity takes Riemannian
geometry and applies it to flat Minkowski 4D space-time.
Quantum theory takes Hilbert space theory and applies it to
Lagrangian dynamics. Both these applications of new
mathematics lead to completely new understandings of the world which
are incomprehensible to traditional Western metaphysics. Is it
possible that Eastern metaphysics could provide a new foundation for our understanding?
Western philosophers such as A.C.Grayling are beginning to take
Indian philosophy seriously, partly because they have discovered
that not all schools of Indian philosophy are mystical - some are
realist and even atheistic. But what we are looking for is
ways to understand the world which can accommodate lack of
determinism, lack of locality, increased correlation and perhaps a
big change in what we mean by reality. As Einstein did to
geometry, even logic has been taken down from the shelf of a priori
truths. (I went to talk to Hilary Putman in Harvard about quantum
logic in 1974, but he was not there at the time.) It is the traditional
mystical schools of Indian philosophy such as
Yoga that are most likely to enlighten the West. I went to
visit Fritjov Capra at Imperial College in order to understand
better his ideas on some connections between particle physics
(mostly S-matrix theory, the fashion at the time) and Eastern
philosophy. (Unfortunately he was away too.) In order to
discover more about Indian philosophy, in 1978 I went to the
Radhakrishnan Institute at the University of Madras where they
had a course that included Indian logic and Indian epistemology.
Unfortunately they seemed more interested in Wittgenstein. In
any case I was not able to stay in India for long because the banks
would not transfer my savings from Edinburgh.
The original motivation of both religion and science is
to make sense of the world. Through history,
religion has at many times been hijacked by those in power for
political purposes and the original message has been corrupted or
lost. Lee Smolin has recently suggested that science might be
suffering from political influences today. Science and
religion would not be enemies if both were completely honest because
both have some truth and neither have all of the truth.
Usually religion is condemned for being unscientific,
but yoga is said to be a science in India. There are many
branches of yoga, including hatha, raja, karma, bhakti, jnana,
kundalini, kriya, mantra and tantra yoga to name a few. I am
initiated in Transcendental Meditation and in the Ananda Marga
movement. TM in particular argues for the scientific approach
to yoga, or union. The primary branch of yoga, raja
yoga, has eight limbs, or stages, to union: yama or loss of ego,
niyama or purity, asana or posture, pranayama or breath control,
pratyahara or withdrawal, dharana or concentration, dhyana or
meditation and samadhi or union. Jnana yoga follows the path
of knowledge. Bhakti yoga follows the path of love. The
Greeks had four different concepts of love: agape, philia, storge
and eros. The love of bhakti yoga is most like agape, the love
that consumes, the highest and purest form of love. Bhakti
yoga follows essentially the same path as raja yoga but with Krishna
as the vehicle of union through perfect love. Christianity
follows the Bhakti path with Jesus as its consummation.
Where are we trying to get to? - to a new understanding through a higher
level of consciousness!
There is a scientific observation that is ignored by
science and recognised by religion. One faces the world from
within, looking out. The approach of science has been to
discount this truth as contingent, necessary perhaps in order to
progress, but contingent to the final goal of an objective
description of the world, independent of all souls. The
approach of religion is clearly different. The true basis of
religion is intuitive experience rather than blind faith and belief.
Individual souls are taken to be central to the description and
the final understanding of the world. There is some evidence that
science and religion are beginning to see the other's point of view.
Some cosmologists see that an anthropic principle may be the answer
to their science, while some modern yogis see psychopharmacology as holding
the key to their religion. Philosophy and religion are venerable
attempts to understand the world but they must take full
account of modern science to continue to develop. Similarly,
modern science must not reject all past thinking because they need a
new foundation themselves.
Metaphysical religious dictates such as uniteing
of a human with God is not consistent with Islamic philosophy
or pseudo-scientific pronouncements such as cannabis causes psychosis
don't help at all in the search for real understanding.
So I have written
a little black book in which I have tried to
explain what might help. I have tried to explain what I
understand by quantum theory and how this theory might change our
perception of ourselves and the world. It is a simple book but
it is not an easy book, at least not until the simplicity is
accepted. Please read it and then study
the meaning of quantum ontology further.
A theory of
everything unifies all ideas into a coherent understanding.
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