Scientific Enlightenment, Div. One Book 2: Human Enlightenment of the First Axial C. Contemporary Revival of the First Axial Examination of the Parallels between Philosophy and Physics Problems with "The Tao of Physics" (2) ACADEMY | previous section | Table of Content | next section | GALLERY

copyright © 2003 by L C. Chin.

"Most reaction channels have several resonance energies, each of them corresponding to the mass of an ephemeral intermediate hadron state which is formed when the energy of the colliding particles reaches the resonance value. In the framework of S-matrix theory, the problem of whether one should call the resonances 'particles' or not does not exist. All particles are seen as intermediate states in a network of reactions." (p. 270, emphasis added.) That is, in the rearrangement of a given hadronic structure or pattern into a different one, or in the self-transforming manifestations of the substrate (measured as energy) in various hadronic states.

In the S-matrix the strong nuclear force "that bind groups of [hadrons] together to form intermediate bound states" (ibid.), although also represented as particles, is not so represented as virtual particles, but rather by "crossing". "To illustrate this property, consider the following [left] diagram picturing the interaction between a proton and a p^-.

taken from Capra, ibid., p. 271

"If this diagram is rotated through 90 degree, and if... the arrows pointing downwards indicate antiparticles, the new diagram [on the right] will represent a reaction between an antiproton and a proton which emerge from it as a pair of pions, the p⁺ being the antiparticle of the p^- in the original reaction. The 'crossing' property... refers to the fact that both these processes are described by the same S-matrix element... [T]he two diagrams represent merely two different aspects, or 'channels', of the same reaction." (p. 271) The same reaction can then be read as direct channel (p + p^- => p + p^-) or cross channel (-p + p => p^- + p⁺). See the top diagram below.

taken from Capra, ibid., p.272

taken from Capra, ibid.

"[Now let us look at the lower diagram above.] The connection between forces and particles is established through the intermediate states in the two channels. In the direct channel of our example, the proton and the p^- can form an intermediate neutron, whereas the cross channel can be made up by an intermediate neutral pion (p⁰). This pion -- the intermediate state in the cross channel -- is interpreted as the manifestation of the force which acts in the direct channel binding the proton and the p^- together to form the neutron. Thus both channels are needed to associate the forces with particles; what appears as a force in one channel is manifest as an intermediate particle in the other." (p. 273)

There is then a certain similarity between the S-matrix and quantum field theory. "In both theories, the forces manifest themselves as particles [neutral pion (a meson) in S-matrix and gluon in field theory] whose mass determines the range of the force, and in both theories they are recognized as intrinsic properties of the interacting particles; they reflect the structure of the particles' virtual clouds in field theory, and are generated by bound states of the interacting particles in S-matrix theory." ( Ibid.) A sensitive issue is touched on here, concerning whether or not there are really any laws of nature at all or whether maybe there are only properties of matter (fermions).

"The main challenge in S-matrix theory is to use this dynamic description [of hadron as an integral part of an inseparable network of reaction] to account for the symmetries which give rise to the hadron patterns and conservation laws discussed [previously]... In such theory, the hadron symmetries would be reflected in the mathematical structure of the S matrix in such a way that it contains only elements which correspond to reactions allowed by the conservation laws. These laws would then no longer have the status of empirical regularities but would be a consequence of the S-matrix structure, and thus a consequence of the dynamic nature of hadrons." (p. 274)

"At present, physicists are trying to achieve this ambitious aim by postulating several general principles [in total, three] which restrict the mathematical possibilities of constructing S-matrix elements and thus give the S-matrix a definite structure... The first [related to relativity]... says that the reaction probabilities (and thus the S matrix elements) must be independent of displacements of the experimental apparatus in space and time, independent of its orientation in space, and independent of the state of motion of the observer... [This] independence of a particle reaction with regard to changes of orientation and displacement in space and time implies the conservation of the total amount of rotation, momentum and energy involved in the reaction...

"The second principle [related to quantum theory]... asserts that the outcome of a particular reaction can only be predicted in terms of probabilities and, furthermore, that the sum of the probabilities for all possible outcomes -- including the case of no interaction between the particles -- must be equal to one. In other words, we can be certain that the particle will either interact with one another, or not. This seemingly trivial statement turns out to be, in fact, a very powerful principle, known under the name of 'unitarity', which severely restricts the possibilities of constructing S-matrix elements.

"The third and final principle... is known as the principle of causality. It states that energy and momentum are transferred over spatial distances only by particles, and that this transfer occurs in such a way that a particle can be created in one reaction and destroyed in another only if the latter reaction occurs after the former. The mathematical formulation of the causality principle implies that the S matrix depends in a smooth way on the energies and momenta of the particles involved in a reaction, except for those values at which the creation of new particles becomes possible. At these values, the mathematical structure of the S matrix... encounters what mathematicians call a singularity. Each reaction channel contains several of these singularities, that is, there are several values of energy and momentum in each channel at which new particles can be created. The 'resonance energies' mentioned before are examples of such values. The fact that the S matrix exhibits singularities is a consequence of the causality principle, but the location of the singularities is not determined by it. The values of energy and momentum at which particles can be created are different for different reaction channels and depend on the masses and other properties of the created particles. The locations of the singularities thus reflect the properties of these particles, and since all hadrons can be created in particle reactions, the singularities of the S matrix mirror all the patterns and symmetries of hadrons." (p. 275-6)

"The central aim of S-matrix theory is, therefore, to derive the singularity structure [the location of singularities?] of the S-matrix from the general principles [simply as a matter of self-consistency, i.e. as implicated by these general principles]... [I]t may well be that they are sufficient to determine all the properties of the S-matrix -- and thus all the properties of hadrons -- uniquely. If this turns out to be the case, the philosophical implications of such a theory would be very profound. All three of the general principles are related to our methods of observation and measurement, that is, to the scientific framework. If they are sufficient to determine the structure of hadrons, this would mean that the basic structures of the physical world are determined, ultimately, by the way in which we look at this world. Any fundamental change in our observational methods would imply a modification of the general principles which would lead to a different structure of the S matrix and would thus imply a different structure of hadrons... [That is to say] that the structures and phenomena we observe in nature are nothing but creations of our measuring and categorizing mind" (p. 276-7, emphasis added.)

This profound insight Capra relates again to Eastern mysticism: "The Eastern mystics tell us again and again that all things and events we perceive are creation of the mind arising from a particular state of consciousness and dissolving again if this state is transcended. Hinduism holds that all shapes and structures around us are created by a mind under the spell of maya, and it regards our tendency to attach deep significance to them as the basic human illusion." (Ibid.) The illusion however has a much deeper significance than believing the creations of the mind to be objective and independent of the mind. After all, my hunch is that, even though this ultimate implication of the "bootstrap" hypothesis -- that all the determinateness of nature is simply the result of our being conscious of it -- is very likely to be correct, this consciousness of nature, this measuring and categorizing of it, is probably also "objective" in the sense of "non-arbitrary", i.e. consciousness can be conscious of nature only in the same way, this "illusion" is necessarily the way it is, its structure is necessary. One may note that the first principle -- the irrelevance of changes of orientation and displacements in space and time and of the motion of the observer -- is simply an expression of the law of Conservation, and therefore a logical law of tautology, that "what is" = "what is" and never otherwise. The second principle of "unitarity" -- that something either happens or not -- is again the same logical tautology. The two principles are reducible to the same principle of tautology, and so can just be called "the law of Conservation" pure and simple. The third principle of causality -- that "reacted" or "created" or "destroyed" happens after the "reacting" or "creating" or "destroying" -- is again logical tautology. It says nothing more than if something happens (one state leading to another), it does happen (one state has led to another). The derivation of the singularity structure of the S-matrix from logical tautology -- which we have said, in connection with Parmenides, is the ultimate structure of the Universe -- is what is meant earlier by the derivation of the hadronic structure from the self-consistency of the whole, and is therefore saying that, in addition to there being no laws of nature but only properties of matter, or rather the fixed patterns of the self-transformative manifestation of the substrate, these properties themselves are simply aspects of the law of Conservation, but that is to say that these properties of nature are all aspects of and reducible to absolute Nothingness and are, taken together, nothing at all, if we understand that the law of Conservation guarantees that the Universe, and in fact anything, cannot possibly exist. The illusion is not simply thinking that the determinateness of reality is creation independent of the mind rather than the creation of the mind itself, but that anything has been created at all, that there is any reality at all, subjective or objective or any mixture of the two.

As Capra has presented, then, from the S-matrix describing the hadronic behavior emerges gradually a view of matter and force in general that "nature cannot be reduced to fundamental entities, such as elementary particles or [even -- in contrast to the quantum theory of the Standard Model --] fundamental fields. It has to be understood entirely through its self-consistency, with its components being consistent both with one another and with themselves. This... is known as the 'bootstrap' hypothesis... [Here] the universe is seen as a dynamic web of interrelated events. None of the properties of any part of this web is fundamental; they all follow from the properties of the other parts, and the overall consistency of their mutual interrelations determines the structure of the entire web... [Here there are] no fundamental entities whatsoever -- no fundamental laws, equations or principles". (p. 285-6) The universe as simply a network of interrelations, "[t]he properties of any part are determined, not by some fundamental law, but by the properties of all other parts." (p. 290) This implies the vision of "interpenetration" or "mutual embodiment", that "every part 'contains' all the others", the "notion of 'all in each and each in all'" (p. 292), or "the provocative phrase, 'every particle consists of all other particles'." (p. 295) This interpenetration goes even to include space-time, i.e. "objects as events whose mutual interpenetration can only be understood if one realizes that space and time, too, are interpenetrating." (p. 299) Together with the insight that "all... theories of natural phenomena, including the 'laws' they describe, are creations of the human mind; properties of our conceptual map of reality, rather than of reality itself" (p. 287), all this means that "'explaining' nature just means to show its unity; that, ultimately, there is nothing to explain." (p. 291)

Two strands of the bootstrap hypothesis need therefore to be distinguished.

(1) Concerning the nature of Nature, the bootstrap teaches, in regard to hadronic structure, that, "[r]ather than 'containing' one another, hadrons 'involve' one another in the dynamic and probabilistic sense of S-matrix theory, each hadron being a potential 'bound state' of all sets of particles which may interact with one another to form the hadron under consideration. In that sense, all hadrons are composite structure whose components are again hadrons, and none of them is any more elementary than the others. [Force being represented, as in quantum field theory, by the exchange of particles,] these exchanged particles are again hadrons. Each hadron, therefore, plays three roles: it is a composite structure, it may be a constituent of another hadron, and it may be exchanged between constituents [as force] holding a structure together... [Here is 'crossing' relevant.] Each hadron is held together by forces associated with the exchange of other hadrons in the cross channel, each of which is, in turn, held together by forces to which the first hadron makes a contribution. Thus, 'each particle helps to generate other particles, which in turn generate it'... [This is the self-generation of the hadronic structure by 'bootstrap'. That is to say, with respect to this self-generation] there is only one way in which it can be achieved... only one possible self-consistent set of hadrons -- the one found in nature." (p. 296) What this means is that there is simply the substrate engaging in self-movements which are manifested as hadronic structures (and other fermionic structures, if one succeeds in "bootstrapping" not just strong but weak force, electromagnetism and gravity and eventually all space-time and everything as well) and which are mutually "implicated" because, after all, they are all aspects of the same substrate. This substrate, furthermore, is simply Conservation, so that all its self-manifestations, taken together, say nothing at all, but just "substrate = substrate"; this is the meaning of self-consistency, i.e. that all these "properties" of matter are just aspects of Conservation, or more generally, Tautology as the structure of the Universe. Finally, this substrate, as Conservation, if taken to its logical conclusion, is simply Nothingness -- confirmed by the fact that the total energy of everything in the Universe seems canceled out by the negative energy of gravity -- so that all properties are, taken together and at last, evened out into the Tautology of Nothingness: "nothing = nothing". Even at this level, leaving the implication of consciousness aside, all existence is just an illusion.

The self-generation of the hadronic structure (the singularity structure) from the only possible self-consistency of the S-matrix avoids the postulation of any sort of further constituents for the hadrons such as quarks. In the 1960s when the experimental detection of quarks as such seemed simply impossible, the bootstrap hypothesis was a serious viable alternative. "But by the 1970s experiments on so-called deep elastic scattering had given increasingly direct evidence for point-like constituents inside particles like protons" which were routinely identified as quarks. (Stephen Wolfram, notes for Chapter 9 in A New Kind of Science.) Since then the bootstrap hypothesis focused the attention of only a minority in the physics community while the majority followed the quark-model of quantum chromodynamics with the quarks bound in hadrons by gauge bosons of the strong force (gluons) which was incorporated into the Standard Model.

The view that laws of physics were simply properties of matter similarly remained un-orthodox. Alan Guth, for example, in an interview, found flaws in this view in its implication that "if there is no matter, then there are no properties." (Discover, Vol. 23. No 4. April 2002.) This contradicted Guth's speculation, in accordance with his inflationary model, on how the Universe may have come into being from nothing. To this he added that "quantum theory holds that objects can appear and disappear according to specific laws and the behavior of an absent object is just as predictable as the behavior of a present one... If laws are just properties of objects... how can those laws continue to operate when the object is not really there?" (Ibid.) This contradiction may not necessarily stand, since the creation of the enormous amount of matter that makes up the Universe from virtually nothing (a small, ordinary vacuum fluctuation) through the mechanism of inflation does not, as Guth emphasizes often, imply violation of the law of Conservation because at the same time that the matter was increased ("inflated" shall we say) during the inflationary era, this increase was exactly canceled out by the gravitation field that they created which, of course, was negative energy. If the derivation of the properties of matter from the self-consistency of self-movements of the substrate means, as has been argued, that they are simply aspects of and evened out in the Conservation of Nothingness, then they are properties of nothingness, and in fact are nothing, somewhere and somehow mutually canceled out in their "self-consistency", which is then something like supersymmetry. The laws, or rather properties, therefore continue to operate even when nothing is there and before the Universe is created out of nothing, because they are really properties of Nothingness which is the substrate for existence, because, even while we observe these properties at the moment, nothing really is there: the Universe is nothing fundamentally, as Guth himself repeatedly emphasizes.

"But Guth [however] argues that quantum theory... seems to imply independent laws. 'If you bang two electrons together with enough energy, you produce protons. If there are no independent laws, then all the properties of protons must somehow be 'known' by the electrons. By extension every elementary particle must carry around enough information to create the entire universe. I find that difficult to believe." (Ibid.) This actually is exactly the bootstrap hypothesis, that every elementary particle in fact contains the whole Universe, since in its self-consistency with the rest of the Universe and with itself it "implicates" the whole Universe. A "bootstraper" would probably have no problem making such assertion in that he or she would not "believe in" the existence of elementary particles as such.

The opposition between bootstrap and quantum chromodynamics seems to remind of the opposition in the early history of quantum theory between Heisenberg's complex matrix mechanics of 1925 and Schroedinger's wave mechanics of 1926.¹ "The wave mechanics appealed to many physicists because it seemed to do everything that matrix mechanics could do but much easier and seemingly without giving up the visualization of orbits within atom." (Exhibition on Heisenberg by American Institute of Physics.) Eventually "[i]n May 1926 Schroedinger published a proof that matrix and wave mechanics gave equivalent results: mathematically they were the same theory." (Ibid.) Likewise the bootstrap and quantum chromodynamics could just be two different ways of looking at the same thing, and both approaches could imaginably lead to an unified theory of Nature, the one through self-consistency among observed phenomena and the other through further reduction to elementary constituents like strings of the supersymmetric string theories. In this way one seems the functional approach and the other the structural: the bootstrap, by ignoring fundamental constituent entities but dealing only with the surface interactions (the effects or functions of these constituent entities) and deriving them from logical self-consistency or mutual implications, seems, for example, like the explanation of human psychology by reference to id, ego, and super-ego, which represent psychological forces, i.e. functions or effects produced by the underlying neurological structures of neurons and their communications through neuro-transmitters; whereas quantum chromodynamics derives the same interactions by reference to an underlying structure called quarks, which is like the neurological explanation of human psychology in terms of neuro-transmitters. In the case of psychology the structural (neurological) approach has also triumphed over the functional (e.g. psychoanalytic) approach. This is lamented by Capra as the inherent tendency in Western culture to always "reduce" things to their "building blocks" -- although here we see this tendency as more or less universal among humans. In physics both can be the same, however, in explanatory (i.e. descriptive or representational) power that is -- if they should both succeed in the representation of hadronic structure and be proven mathematically equivalent. But if the quarks are "found", then the structural model would seem preferable because, just as in the Schroedinger's wave mechanics, it digs deeper into the structure of Reality by allowing the "visualization" of the "deeper reality".

Capra reminds us that bootstrap has succeeded in "representing" the quark structure in a functional way. It has shown that the self-transformative flow of the substrate measured as energy proceeds in particularly well-defined patterns that produce "the two-ness associated with mesons and the three-ness associated with baryons. This is the dynamic [i.e. functional] equivalent to the statement that hadrons consist of quarks." (Ibid., p. 318) The topological classification of "the order in the interconnectedness of subatomic processes" (i.e. in the self-transformative flow of energy) within the S-matrix produces "only a few special categories of ordered relationships... compatible with the well-known properties of the S-matrix. These categories of order are precisely the quark patterns observed in nature. Thus, the quark structure appears as manifestation of order and necessary consequence of self-consistency, without any need to postulate quarks as physical constituents of hadrons." (Ibid.) This is the functional approach to hadronic structure, in difference from the structural approach of the actual postulation of things called quarks to explain hadronic behavior.

Even in the structural approach, however, the ultimate goal seems to be the complete derivation of laws of nature as it has revealed from its very framework, without the need for postulation of any extra variables not "implicated" by the structure of the framework itself. This is the same, in essence, as the self-consistency of the bootstrap. The supersymmetric string theory, if it succeeds in "representing" everything (fermions, bosons, and gravity) in one package (string vibration), should "implicate" all laws governing the workings of these fermions, etc. within its very structure. In supersymmetry, all fermions, bosons, and gravity should all even each other out in the Conservation of Nothingness -- so that, in accordance with the law of Conservation, there really is nothing afterall, before and after creation. Whether through bootstrap or the traditional structural approach, the conclusion should be the same: the parallel between philosophy and physics is the discovery of the Truth of existence: existence is but an illusion. The advance of physics from philosophy -- the advantage of the historical approach to the problem of existence (working backward through the history of the Universe) over the synchronic approach of the Logos -- lies in the former's ability to offer a description -- a representation, and an exact, i.e. quantitative one at that -- of the manner in which we do not exist and come to our non-existence masqueraded as existence, i.e. in what way our existence is canceled out -- this the philosophy does not tell: it says only that we don't exist.

Whether my presentation of the current trend of theoretical physics is correct or not, this is how we should look for the parallels between physics and philosophy. We have to ignore Capra's assertion that Eastern philosophers' view of nature as an interrelated whole engaging in self-transformative cosmic dance is also reached (confirmed) in the world-picture revealed by modern physics, for this sort of world view is trivial. The philosophers, East or West, look for the eternally-remaining-the same behind this endless series of change or "cosmic dance" and arrive at the conclusion that empirical (temporal and spatial) existence is simply illusion and the timeless eternal substrate behind the only reality -- and that this substrate may be nothing at all. We need to inquire if physics reveals the same.

(2) Concerning the connection between consciousness and the structure of reality. Capra has said that the complete derivation of the singularity structure of the hadron world as a matter of self-consistency from the three general principles of observation means that the properties of matter (the laws of nature) are simply the result of our ways of looking at it. He cites Geoffrey Chew, the pioneer of bootstrapping: "Carried to its logical extreme [i.e. bootstrapping beyond hadrons to everything else], the bootstrap conjecture implies that the existence of consciousness, along with all other aspects of nature, is necessary for self-consistency of the whole." (Ibid., p. 300) This extreme form of the anthropic principle -- that the Universe evolves in such a way that it shall eventually become conscious of itself -- is truly -- at long last for Capra! -- philosophic thinking expressed in physics. However, Capra continues: "This view, again, is in perfect harmony with the views of the Eastern mystical traditions which have always regarded consciousness as an integral part of the universe. In the Eastern view, human beings, like all other life forms, are parts of an inseparable organic whole. Their intelligence, therefore, implies that the whole, too, is intelligent. Man is seen as the living proof of cosmic intelligence; in us, the universe repeats over and over again its ability to produce forms through which it becomes consciously aware of itself." (Ibid. Emphasis added.) Capra again passes over the Greeks and fails to notice that the pre-Socratics again and again call the cosmos nous, i.e. intelligence, in their expression of pantheism. This truly philosophic insight in the form of anthropic principle nonetheless deserves special attention.

"In modern physics, the question of consciousness has arisen in connection with the observation of atomic phenomena. Quantum theory has made it clear that these phenomena can only be understood as links in a chain of processes, the end of which lies in the consciousness of the human observer. In the words of Eugene Wigner, 'it was not possible to formulate the laws of [quantum theory] in a fully consistent way without reference to consciousness.' The pragmatic formulation of quantum theory used by the scientists in their work does not refer to their consciousness explicitly. Wigner and other physicists have argued, however, that the explicit inclusion of human consciousness may be an essential aspect of future theories of matter." (Ibid.)

What quantum physics has specifically revealed is that the very observation, measurement, and detection of Nature disrupts the latter in its "pure state" so that the latter only appears to observation and measurement in definite ways. The anthropic principle of Capra together with its reference to quantum physics therefore seems to involve a relationship of mutual implication between consciousness and the structure of the Universe of which it is conscious, i.e. the loss of purity, of innocence in the gain of structure, determinateness by the Universe in its consciousness of itself.

We may start from the simpler case in chemistry. There the degree of temperature of an object is indicative of (or just is) the kinetic energy of the atoms or molecules making up the object. Hence even in solid state the atoms in the solid are not motionless but vibrate around themselves, since the solid has always a degree of temperature associated with it. "There is a temperature to which we can extrapolate, absolute zero, at which, theoretically, the motion of the atoms and molecules would stop... [But s]ince light, electromagnetic radiation, is required to see an object and light hitting an object gives it energy, as soon as one is able to see an object at absolute zero, it is not at absolute zero anymore from the new energy. Any other means of detection would add energy to the material at absolute zero. An object at absolute zero would be as hard to keep as a lump of antimatter... Practically, we can cool something down to temperatures approaching absolute zero, but we cannot get to that theoretical point, nor can we achieve temperatures below that point." (From chemtutor.com.)

That the observation of material at absolute zero necessarily disrupts it and so negates the absolute zero reflects the fact that consciousness itself is a process in the Universe, that its existence involves the flow of energy, so that the motionless state of atoms at absolute zero with no flow of energy is incompatible with the co-existence with it of consciousness being conscious of it. If somewhere in the Universe there is a region of absolute zero temperature, then this region is the unconsciousness of the Universe in the sense that it is theoretically impossible for the Universe to ever become conscious of this region of it. The self-consciousness of the Universe (through us, for example) requires its own existence beyond absolute zero degree of temperature to ensure the flow of energy which makes possible any form of (self-)consiousness (of the Universe). We are here reminded of Parmenides again. So thus the goddess spake to the young Parmenides:

Non-Being is not knowable nor speakable, because knowing itself involves Being, it is a process of Being.