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Investigations into the Nature of Matter

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Priory School
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.
Durham Maths
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, extensive field of mathematical physics.
Ghosts
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 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 is 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 fabulous 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 J.C.Maxwell, Lord Kelvin and G.P.Tait to modern Fields Medalists Ed Witten and Vaughan Jones. No one has yet proved the validity of knots (or even string theory) in fundamental modern physics.

String, Membranes and Lumps

Drum 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 the 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, 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, 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 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 (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.

Now 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 even 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 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 is at least quantum entanglement if not clear fundamental physical attraction as a result of the deep genetic symmetry between them. Read on ...

    A theory of everything unifies all ideas into a coherent understanding.

♦ ♦ ♦   YOU are Special   ♦ ♦ ♦

     You have proof that you are special, but you have chosen to ignore that because your theories tell you otherwise. Popper 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. Feyerabend says that every fact is theory-laden. But some facts are so striking that one feels obliged to believe they are true independent of any particular theory, or rather, perhaps, dependent of every reasonable theory. Descartes showed how one could doubt almost everything, except for this one thing, 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.

The ultimate 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 quantal.
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 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 5 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 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 behaviour is better understood in terms of 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 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 this deep symmetry and may adopt collective, unified behaviour, as in Fermi-Dirac statistics.)

♥ ♥ ♥   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 Archebald Wheeler (whom I wrote to in 1976 and who was good enough to reply with akind 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 basid 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 Vedanta and 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 exact, 42) in its account of life, the universe and everything.

     Vedanta states that अटमन is बरमन, 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 UCPO flyer 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 to the centre of understanding, where it was before Copernicus or Galileo, Leucippus or Democritus, Katyayana or Kanada. Unaccounted for 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 and satisfy all of humanity. Can you entertain a genuine mysticism beyond flat atomism, logicism, structuralism, functionalism or even existentialism? Because there is indeed a mystery.

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