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 (nor beauty queens).
I love learning science and mathematics and was absolutely delighted to be able to work under Ed Corrigan as a research student at Durham University.
Ed is a world-renouned string theorist who helped me to understand a little of some current areas of his research in this fast-developing, extensive and literally fantastic field of mathematical physics.
Our search for deep truth and wisdom never ends. I love learning all science and philosophy and continue my life-long search for a better understanding of anything and everything, including matter and the elusive nature and origin of mind.
Theoretical Elementary Particle Theory
All the physical stuff that we are familiar with on Earth is made of atoms and molecules (which are themselves made of atoms). Atoms are made of electrons and nuclei;
atomic nuclei are composed of protons and neutrons. So far so good.
Protons and point electrons are oppositely charged particles held together in an atom by electromagnetic forces through exchange of virtual photons.
Protons and neutrons are held together in the nucleus by nuclear forces through exchange of virtual pions. Protons and neutrons (and pions) are made of up
and down quarks. Three of these point quarks are held together inside nucleons through the strong interactions by way of exchange of virtual gluons.
Quantum Field Theory underlies this descriptive understanding of material point particles.
The fundamental mathematical account is called the Standard Model. This is a magnificent,
beautiful and absolutely amazing model of particle physics which is fantastically well verified by experiment. Here
are the first pages of my own naive programmatic version of the model (full DERIVE program here). The Standard Model, for all its successes, is nevertheless clearly incomplete because it leaves out gravitation
entirely and has about 20 free parameters such as all the particle masses, which are generated but not quantified by the Higgs mechanism.
The point to be appreciated here is that nobody knows how to combine Einstein's classical theory with the Standard Model quantum theory. A quantum theory is ultimately
a theory of quantised fields in space-time, but space-time itself is not quantised in that theory. Space-time is not quantised in Einstein's theory. These two pillars of
modern physics, General Relativity and the Standard Model of particle physics, are based on very different branches of mathematics, Riemannian geometry and Hilbert space respectively, which are not easily merged into a single unified theory.
Everything may not ultimately be made of point particles. This line of thinking has led some theoretical physicists to suggest that matter may ultimately be
string-like: electrons, quarks, photons, gluons, .. everything, at root, is more like a vibrating string than a point particle. What makes this proposal of particular
interest is that the resulting
String Theory appears to be able, in principle, to incorporate both the
Standard Model and gravitation. If so, it is potentially 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 - the part of physics which is missing from the Standard Model. This is potentially a monumental achievement
with unlimited potential for science and humanity. My brief summary of Quantum Field Theory for philosophers might be helpful here.
I have also produced an amusing introduction to Special Relativity here in the form of a fictitious ancient Greek dialogue between Socrates and Meno (or his slave) incorporating APL notation.
Knots in String Theory
If particles are loops of vibrating string, what gives them their stability? The tension in the string can shrink the loop to a point. Perhaps the string is knotted and therefore cannot collapse indefinitely. This is the proposal made in my paper, Torus Knots are Rigid String Instantons, published in 1989. Since then, knotted topologies have been found in many
unexpected places, including Maxwell's equations of electromagnetism, atomic physics, nuclear physics, gravitation and Skyrme theory, as well as superfluids and superconductors in condensed matter physics. Large-scale knots have even been found in astronomical bodies, but not yet in cosmic strings. Knotted models of physical systems have been investigated by a number of great physicists from verified the validity of knots (or even string theory) in fundamental physics.
String, Membranes and Lumps
If a stringy model of matter seems potentially 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 published work, 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. Unfortunately the existence of these solutions has not yet been established although I believe they will be found. These functions would form an infinite hierarchy of quaternionic solutions to octonionic equations of motion - functions which would be interesting in themselves even if it turned out that they were not representative of any physical system.
A Grand Unified Tour of Physics
Less ambitious lumpy solutions
have been found to the new equations of motion, but the doubly-self-dual knotted quaternionic lumps in octonionic space-time which were thoroughly described in Self-Duality and Extended Objects and were explained in a talk to the Physics Department at the University of the West Indies, Jamaica, are tantalizingly close
to a hierarchy of knotted lumps in 8 dimensions by analogy with the infinite hierarchy of torus knots in 4 dimensions discovered earlier.
This talk starts from basic relativistic particle dynamics and shows how gravity and electromagnetism may be added. Building on this foundation, quantum fields are introduced and the standard model is outlined. Then string theory, rigid string and knots are explained until finally my problem related to quaternionic knots and a Theory Of Everything is posed.
Extended Objects and the Standard Model of Particle Physics
Our world has just four dimensions, three space and one time, not eight dimensions, you might protest. In fact, soon after Einstein proposed his theory of four dimensional curved space-time,
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, such as Calabi-Yau compactification, in the search for a natural
way to include all the nuances of the standard model. To date, no satisfactory wrapping has been found, but if one were found, the consequences could be absolutely momentous.
Quantised Rigid Super p-Branes .. even Love might succumb to Quantum Physics.
One lesson that we learn 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 (preserves volume) and are equal to the complex conjugate of their transpose (preserves probability). So, for example, conservation of energy is derived from the symmetry of physical systems with respect to time translations. Conservation laws derive directly from symmetries, and symmetries imply conservation laws. This follows from Noether's Theorem which lurks in the mathematical foundations of the Standard Model.
Now here is some real 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 even (probably) smell the same, but we are searching for a mathematical account
of their attraction towards 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 by us 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 must be at least some quantum entanglement if not a fundamental physical force as a result of the deep genetic symmetry between them - between each and every cell. Read on ...
A theory of everything unifies all ideas into a coherent understanding.
♦ ♦ ♦ YOU are Special ♦ ♦ ♦
proof that you are absolutely special, but you have chosen to ignore that because
the current theories tell you otherwise.
claims scientific theories cannot be proved, only at best confirmed. But surely
individual observations, the plain facts, must be believed if they
are immediately verifiable. Paul Feyerabend argues that every fact is theory-laden.
they are true independent of any particular theory, or rather, perhaps, dependent on every reasonable theory.
But some facts are so striking that one feels obliged to believe
René Descartes showed how one could doubt almost everything except for the first person singular of the verb to be; I AM. One cannot doubt that one exists because
existence is a prerequisite for understanding 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 is the only consciousness in the universe.
Wherever you go, from birth to death, it goes 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 consciousness, is
ignored, degraded and even derided in conventional physics and most Western philosophy.
WHO is Conscious?
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 to oneself one's own consciousness. 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 strongly support this view because the laws of
nature are demonstrably the same for everyone. This is indeed
an explicit 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 mere tautologies - 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?
The Meaning of Anything
All meaning resides in the light of awareness.
The conditions under which an observation is made, the
boundary conditions, not the laws, dictate the meaning of reality.
laws of nature appear to be tautologies;
if so, only the boundary conditions contain real meaning.
We are getting used to the idea that geometry is empirical, and then that logic is
Now consider that laws are theorems and circumstances prescribe everything meaningful.
What is consciousness? Consciousness 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 the normal paradigm. From a purely empirical
stance, there is and can only conceivably 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, experience and
rhetoric will convince us of other minds - a complex tangle of
states leading to complex behaviour patterns - but consciousness is
certainly singularly solely one's own, is it not?
Consciousness in Quantum Mechanics
According to my interpretation of quantum mechanics, alluded to obliquely
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 may be regarded as superposition of all classical
outcomes. This means, in particular, that the states of
mind of other people have to be considered generally as superpositions of states - 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 might
call Nature in Herself, or God (hence pantheism).
Reality to Complexity
To be more precise, the noumenon of
Immanuel Kant might now 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 specified 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 quantum operators
such as we have on board through our five senses.
Consequences of this view might be
relevant to a psychologist as well as a quantum physicist.
First the angle that is comprehensible to the physicist.
Consider the attractive force between two oppositely electrically
charged particles circling around 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 (symmetry) of the
electromagnetic field implies conserved electric charges.
Opposite charges attract 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 oppositely gendered butterflies fluttering
around one another and imagine that this animal magnetism is
ultimately explicable in terms of some deep symmetry of nature. Of
course there is already an obvious symmetry between the butterflies.
They look 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 behaviour
is better understood in terms of a quantum superposition of possible states
requiring a completely different mode of explanation. They are the same species. They have the same genetic origins; their genomes are almost identical.
Could this deep symmetry appear as a force? Could quantum identity principles
introduce superposition or interference or entanglement at a deeper
level of explanation? (Likewise, all the cells in one's body, having identical DNA,
might be united through deep symmetry and may adopt a collective, unified behaviour, as in instances of, for example,
♥ ♥ ♥ Love is Perfect Communication ♥ ♥ ♥
The theory might be called "G2 Love".
G2 is a beautiful 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 a quantum (complex) version and can be discussed without involving relativity
or some of the more abstruse quantum ideas such as intrinsic spin or
anti-matter. This is a non-relativistic Yang-Mills theory with G2 symmetry.
However quantum ideas are vital. Take
Schroedinger's cat. According to von Neumann's mathematical formulation of quantum
mechanics, the cat cannot be said to be alive or dead
until observed. 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: Superstates and Consciousness.
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 famously 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 Archibald 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. 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
logic based on the identity of archetypal ideas.
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) more unified comprehension. They
might enact communication by transferring a mental state through 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 being defined as 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. Don't forget one basic
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 correlation while we can hardly imagine what it signifies.
Could love itself succumb to an exact characterisation?
♠ ♣ ♠ New and Ancient Understanding ♣ ♠ ♣
General relativity takes Riemannian
geometry and applies it to flat Minkowski 4D space-time.
Quantum theory takes Hilbert space theory and applies it to
classical 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 loss of
determinism, lack of locality, increased correlation, and perhaps a
big change in what we mean by reality itself. 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, I went to the
Radhakrishnan Institute at the University of Madras in 1978 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 Indian 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 today from political rather than religious influences while others
argue that the latest theories are "not even wrong". Science and
religion would not be enemies if both were completely open and honest because
both have some truth and neither have all of the truth.
Often religion is condemned for being unscientific,
but yoga is said to be a science and a religion 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 also in the Ananda Marga
movement. TM in particular argues for the scientific approach
to yoga, or union. The primary branch of yoga, Patanjali's 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 to union through perfect love. Christianity generally
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!
Samadhi has been described as the state of being aware of one's existence without thinking. This is a state of mind, apparently foreign to Cartesian thinking, which adherents over millennia have claimed can be attained by scientific training and practice. I approached yoga, a practical philosophy that purports to be true and valid, with the aim of understanding the quantum world. This is perfectly reasonable and justifiable when Western philosophy has been reduced to ridicule (albeit exactly 42) in its account of life, the universe and everything.
Vedanta states that "Atman is Braman", loosely translated as "the self is everything". This encapsulates a fundamental scientific observation that is thoroughly ignored by hard 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 Vedic religion is clearly different. The basis of
Hinduism is intuitive experience rather than blind faith and belief in ridiculous unfounded dogmas.
According to Vedanta, 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 afford an answer
to their science, while some modern yogis see psychopharmacology as holding
a key to their religion. Philosophy and religion consist of venerable
attempts to understand the world, but they must take full
account of modern science in order to continue to develop. Similarly,
modern science must not reject all past thinking because they now clearly need a
new foundation themselves.
Metaphysical religious dictates such as uniting
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 of our modern world and the new revelations of science.
So I have written a little black book, UNITY CONSCIOUSNESS AND THE PERFECT OBSERVER: Quantum Understanding Beyond Reason and Reality, in which I have tried
to explain what I understand by quantum theory and how this theory might change our perception of ourselves and the world. The book attempts to convey a philosophy involving a paradigm shift from logic to quantum logic and from reality (real numbers) to complexity (complex numbers). You might also review my previous work, Philosophical Problems of QUANTUM ONTOLOGY, for a more traditional critical background on the meaning of quantum thoery.
I attempt to reinstate the soul at the centre of understanding, where it was before Copernicus or Kepler, Leucippus or Democritus, Katyayana or Kanada. Unaccounted by them, our forms of perception and categories of understanding are preset through evolution to give us our normal perspective. With extended senses (scientific instruments) has come new knowledge and new understanding whose meaning surely can, and must, help to enlighten all of humanity and satisfy his curiosity.
Can you entertain a mysticism beyond atomism, logicism, structuralism, functionalism and existentialism or postmodernism? If probability is to be fundamental, there is an everlasting unquenchable incomprehensible mystery in the depths of modern science.