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" (1)
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2003 by L. C. C.

We have enumerated the principles regarding the understanding of philosophy: 1. the reading of philosophy has to be comparative: philosophy West cannot be understood except when compared to philosophy East and vice versa; 2. the reading of philosophy has to be thermodynamic; 3. philosophy cannot be understood unless its parallels are sought with science (physics). This is why Fritjof Capra's popular book concerns us, as his approach is essentially wrong, and understanding how this is so will provide a good lesson as to how to correctly construct the parallels between philosophy and physics.

Fritjof Capra's exposition of the parallels between Eastern philosophy and modern physics in his The Tao of Physics starts with the dominant trends in contemporary physics -- quantum field theory and relativity -- and then moves into the less prevalent trend of S-matrix and "bootstrap hypothesis". The following will be critical of his seemingly revolutionary stance in defending the less prevalent trend.

Emptiness and Form. The unity of reality offered by modern theoretical physics is: (1)"the material objects are not distinct entities, but are inseparably linked to their environment"; (2) "their properties can only be understood in terms of their interaction with the rest of the world" (p. 209). (2) relates to relativity or Mach's principle of inertia, i.e. the motion of one object -- such as its inertia, its "resistance against being accelerated" -- has meaning only because of its relationship with other objects in the universe: "When a body rotates, its inertia produces centrifugal forces... but these forces appear only because the body rotates 'relative to the fixed stars'" (p. 209).

(1) is at issue here. The elementary particles of the Standard Model are each field. This is quantum field theory, where "the classical contrast between solid particles and the space surrounding them is completely overcome. The quantum field is seen as... fundamental..., a continuous medium which is present everywhere in space [i.e. it fills the universe]. Particles are merely local concentrations of the field of energy... which come and go, thereby losing their individual character and dissolving into the underlying field" (p. 210), matter being "the region of space in which the field is extremely intense" (p. 211). For example, electron "is merely a small domain of the electrical field within which the field strength assumes enormously high values, indicating that a comparatively huge field of energy is concentrated in a very small space. Such an energy knot, which by no means is clearly delineated against the remaining field, propagates through empty space like a water wave across the surface of a lake" (p. 213). Force, such as electromagnetic force between two electrons approaching each other, is "interaction", represented by the emission of photon by one electron and the absorption of it by the other. Both then deflect from one another. The force-carrying boson, photon, is itself just the surface oscillation of a underlying field, the electromagnetic field.

The space-time diagrams in quantum field theory ("world-lines") that we have seen so far, together with the mathematical expression associated with them and "which allows one to calculate the probability for the corresponding process [in the diagram] to occur", were first established in 1949 by Richard Feynman.

"This unity and interrelation between a material object and its environment" shown by quantum field theory coincides with eastern mysticism. The mystical void is like a field: "As the Upanishad says: 'Tranquil, let one worship it, as that from which he came forth, as that into which he will be dissolved, as that in which he breathes"(p. 212). Note that this Upanishad is itself an expression of the memory of the first law, that substratum, under-lying (hupokeimenon) of the Ionian physicists. Then Capra cites also the Neo-Confucian Chang-Tsai: "When the chi [air] condenses, its visibility becomes apparent so that there are then the shapes [of individual things]. When it disperses, its visibility is no longer apparent and there are no shapes. At the time of its condensation, can one say otherwise than that this is but temporary? But at the time of its dispersing, can one hastily say that it is then non-existent?" (p. 214) The parallel that Capra sees between the view of the Eastern sages and the modern quantum field theory lies therefore in the coincidence between the "field" and the "substratum", and the Eastern sages arrived at this substratum -- the overcoming of the opposition between material object and its environment, as he would call it -- through the memory of conservation, the driving motor of philosophic enlightenment everywhere.

A point to note here is that every nucleon, and indeed every particle, is surrounded by a cloud of virtual particles that, according to the uncertainty principle, are constantly being produced out of no where (within the range of time Dt the energy is uncertain within DE so that potentially extra energy might exist to create virtual particles) and then reabsorbed into the nucleon or particle (because the extra energy has to be returned after time Dt). "Every nucleon is surrounded by such a cloud of virtual mesons which live only for an exceedingly short period of time... when two nucleons come so near to each other that their meson clouds overlap, some of the virtual particles may not go back to be absorbed by the nucleon which originally created them, but may 'jump across' to be absorbed by the other nucleon. This is how the exchange processes arise which constitute the strong interactions. This picture shows clearly that the interaction between particles, and thus the forces between them, are determined by the composition of their virtual clouds... Thus the electromagnetic forces are due to the presence of virtual photons 'within' charged particles, whereas the strong interactions between nucleons arise from the presence of virtual pions and other mesons 'within' the nucleons. In field theory, the forces between particles appear as intrinsic properties of the particles." (p. 220) An important point is asserted here, that the laws of nature are only properties of matter. This will play out in a significant way later on. (Note also that in the Standard Model with quarks the strong force is represented by gluons and not mesons. Capra is probably leaning toward the rejection of quark model here.)

The Cosmic Dance. The difference between two types of hadrons: "all baryons have distinct antiparticles, whereas a meson can be its own antiparticles" (p. 229).

"The processes of creation and destruction occurring in the world of particles [in super collider]... also include the creation and destruction of virtual particles which are exchanged in particle interactions and do not live long enough to be observed. Take, for example, the creation of two pions in a collision between a proton and an antiproton. [In space-time diagram:]

"It shows the world lines of the proton and the antiproton which collide at one point in space and time, annihilating each other and creating the two pions (p+ and p-). This diagram, however, does not give the full picture. The interaction between the proton and the antiproton can be pictured as the exchange of a virtual neutron...

"Similarly, the process... where four pions are created in a proton-antiproton collision can be pictured as a more complicated exchange process involving the creation and destruction of three virtual particles; two neutrons and one proton.

"The situation becomes... infinitely more complex when we remember that each of the particles involved in the interactions emits and re-absorbs virtual particles incessantly. A proton, for example, will emit and reabsorb a neutron pion every now and then; at other times, it may emit a p+ and turn into a neutron which will absorb the p+ after a short while and transform itself back into the proton. [Note the conservation of charge in these two transformations and in all others as well.]

"A negative pion, to take another example, may create a neutron plus an antiproton which then annihilate one another to re-establish the original pion:

"It is important to realize that all these processes follow the laws of quantum theory, and thus are tendencies, or probabilities, rather than actualities. Every proton exists potentially, i.e. with a certain probability, as a proton plus a p0, as a neutron plus a p+, and in many other ways... Much more complicated patterns arise when the virtual particles create other virtual particles, thus generating a whole network of virtual interactions. [From Kenneth Ford's The World of Elementary Particles:]

"Ford is not the only physicist to have used phrases like 'dance of creation and destruction' and 'energy dance'. The ideas of rhythm and dance naturally come into mind when one tries to imagine the flow of energy going through the patterns that make up the particle world." (p. 236 - 241)

How all these particles are merely "maya -- not fundamental, but illusory and ever-changing"! (p. 242-3)

"According to quantum field theory, all interactions between the constituents of matter take place through the emission and absorption of virtual particles. More than that, the dance of creation and destruction is the basis of the very existence of matter, since all material particles 'self-interact' by emitting and reabsorbing virtual particles. Modern physics has thus revealed that every subatomic particle not only performs an energy dance, but also is an energy dance..." (p. 244)

It is important to note -- and such is philosophic -- that throughout all these dances the total amount of energy that "dances" and the total charge of the particles are always conserved -- remain ever the same.

Quark Symmetry. To find out whether the nucleons like protons and neutrons are themselves composite or not, they are smashed in super collisions. "When this is done, however, the resulting fragments are never 'smaller pieces' of the original particles. Two protons, for example, can break up into a great variety of fragments when they collide with high velocities, but there will never be fractions of a proton among them. The fragments will always be entire hadrons which are formed out of the kinetic energies and masses of the colliding proton... We are dealing here with a crucially relativistic situation where dynamic energy patterns are dissolved and rearranged, and the static concepts of composite objects and constituent parts cannot be applied to these patterns." (p. 249) Only, to remember, the total amount of energy will remain constant. Furthermore, this is where the study of hadrons diverges into the quark model on the one hand and the bootstrap on the other.

"The notion of symmetry played an important role in this research [into the regularities in the hardron world revealed by super collisions]...

"In particle physics, symmetries are associated with many other operations besides reflections [an image that can be cut into two parts that are exact mirror image of each other] and rotations [like Yin-Yang symbol that looks the same after being rotated through a certain angle], and these can take place not only in ordinary space (and time), but also in abstract mathematical spaces. They are applied to particles, or groups of particles, and since the particles' properties are inseparably linked to their mutual interactions, the symmetries also apply to the interactions, i.e. to the processes in which the particles are involved. The reason that these symmetry operations are so useful lies in the fact that they are closely related to 'conservation laws'. Whenever a process in the particle world displays a certain symmetry, there is a measurable quantity which is 'conserved';... These quantities provide elements of constancy in the complex dance of subatomic matter... Some quantities are conserved in all interactions, others only in some of them, so that each process is associated with a set of conserved quantities. Thus the symmetries in the particles' properties appear as conservation laws in their interactions." (p. 252, emphasis added.)

"There are four basic conservation laws which seem to be observed in all processes, three of them being connected with simple symmetry operations in ordinary space and time. [1] All particle interactions are symmetric with respect to displacements in space -- they will look exactly the same whether they take place in London or New York. [2] They are also symmetric with respect to displacements in time, which means they will occur in the same way on Monday or on Wednesday. The first of these symmetries is connected with the conservation of momentum, the second with the conservation of energy. This means that the total momentum of all particles involved in an interaction, and their total energy (including all their masses), will be exactly the same before and after the interaction. [3] The third basic symmetry is one with respect to orientation in space. In a particle collision, for example, it does not make any difference whether the colliding particles approach each other along an axis oriented north-south or east-west.1 As a consequence of this symmetry, the total amount of rotation involved in a process (which includes the spins of the individual particles) is always conserved. [4] Finally, there is the conservation of electric charge... the total charge carried by all particles involved in an interaction remains constant." (p. 252)

The S-Matrix and bootstrap. In the study of hadrons and their strong (nuclear) interactions the S-matrix appears ("originally proposed by Heisenberg in 1943" p. 262) as an alternative to the Feynmanian world-lines of field theory. "The S-matrix is a collection of probabilities for all possible reactions involving hadrons. It derives its name from the fact that one can imagine the whole assemblage of possible hadron reactions arranged in infinite array of the kind mathematicians call a matrix... In practice,... one is never interested in the entire collection of hadron processes, but always in a few specific reactions. Therefore, one never deals with the whole S matrix, but only with those of its parts, or 'elements', which refer to the processes under consideration... [For example,] two particles, A and B, undergo a collision to emerge as two different particles, C and D... [T]hese S-matrix diagrams are very different from the Feynman diagrams of field theory. They do not picture the detailed mechanism of the reaction, but merely specify the initial and final particles. The standard process A + B -> C + D, for example, might be pictured in field theory as the exchange of virtual particle V [right diagram below], whereas in S-matrix theory, one simply draws a circle without specifying what goes on inside it. [left diagram below] Furthermore, the S-matrix diagrams are not space-time diagrams, but more general symbolic representations of particle reactions. These reactions are not assumed to take place at definite points in space and time, but are described in terms of the velocities... [momenta]... of the incoming and outgoing particles." (p. 262-3)

the different representations of the same reaction: S-matrix (left) and Feynmanian world-line (right). Capra, ibid.

"Due to the uncertainty principle, the uncertainty of a particle's velocity will increase as its region of interaction is localized more sharply, and consequently, the amount of its kinetic energy will be increasingly uncertain. Eventually, this energy will become large enough for new particles to be created... and one can no longer be certain of dealing with the original reaction... S-matrix theory bypasses this problem by specifying the momenta of the particles and remaining sufficiently vague about the region in which the reaction occurs." (p. 263-4) Hadrons here are not objects but reaction processes, i.e. "manifestation of the interaction between various processes of measurement" (ibid.), and these processes are four dimensional (space-time) patterns.

"A neutron, for example, may participate in two successive reactions involving different particles; the first, say, a proton and a p-, the second a S- and a K+. The neutron thus interconnects these two reactions... into a larger process... [(a) in the first figure below] Each of the initial and final particles in this process will be involved in other reactions; the proton, for example, may emerge from an interaction between a K+ and a L [(b) in the first figure below]; the K+ in the original reaction may be linked to a K- and a p0 [the second figure below]; the p- to three more pions. [the second figure below]" (p. 264-5.) Note that "[t]he interconnections in such a network cannot be determined with certainty, but are associated with probabilities. Each reaction occurs with some probability, which depends on the available energy and on the characteristics of the reaction, and these probabilities are given by the various elements of the S matrix." (Ibid.)

(from Capra, ibid.,p. 265-6)

"The neutron in our network, for example, can be seen as 'bound state' of the proton and the p- from which it arises, and also a bound state of the S- and the K+ into which it disintegrates." Hadrons are thus understood here as mutually "existing" or "implied" in each other, and this mutual implication is the structure of hadrons, bypassing the necessity of postulating any such hadronic constituents as quarks which in another way collectively "represent" the mutual transformation of hadrons into one another. "Thus a proton exists potentially as a neutron-pion pair, a kaon-lambda pair, and so on. The proton also has the potential of disintegrating into any of these particle combinations if enough energy is available. [Such potential, i.e. these] tendencies of a hadron to exist in various manifestations are expressed by the probabilities for the corresponding reactions [i.e. the probabilities associated with the mutual implications in hadrons of one another], all of which may be regarded as aspects of the hadron's internal structure" (p. 265-6).

This mutual containment or implication in hadrons of one another is what Capra refers to as the essentially dynamic nature of the hadronic structure given by the S-matrix. But underlying this mutual implication is the principle of conservation, or the eternally and necessarily conserved substrate measured as energy. "[T]he total energy has to remain constant in every reaction. This means that a certain combination of particles can emerge from a reaction only if the energy carried into the reaction is high enough to provide the required masses [of the group of particles emerging from the reaction]. Furthermore, the emerging group of particles must collectively carry exactly the same quantum numbers that have been carried into the reaction by the initial particles. For example, a proton and a p-, carrying the total electric charge of zero [ -- and this nothingness must eventually be extrapolated backward as ultimately the most primordial, most origin state of existence, i.e. non-existence -- ], may be dissolved in a collision and rearranged to emerge as a neutron plus a p0, but they cannot emerge as a neutron and a p+, as this pair would carry a total charge of + 1" (p. 267-8).

This is very different from how the quark model explains the mutual transformation of hadrons one into another. We recall that in the Standard model the creation of the fermionic pair of quark-lepton was repeated three times in the early phase of nucleosynthesis (the quark soup preceding the nucleosynthesis of protons and neutrons), with only the first generation actually found in ordinarily existing matter. C.f. the table of the Standard Model of elementary particles and their properties given by Drell:

To explain the hadronic structure quarks are posited as the constituents of hadrons just as hadronic baryons, like protons and neutrons, are constituents of atoms. But quarks are so posited with fractional charges, as seen above, like -1/3 or 2/3, which go against the grain of tradition and, when the model was first introduced, accounted for the resistance to it. Note that each quark has an anti-quark corresponding to it with the opposite charge. All the baryons (protons and neutrons, etc.) and mesons (pions, etc.) are thought to be composed of the up and down quarks (with their anti-quarks) of the first fermionic generation -- with baryon of 3 and meson of 2 quarks -- and derive their properties from the combination of these quarks. So proton is made up of 2 up- and 1 down-quark and so has charge of +1 (2/3 + 2/3 + (-1/3) = 1) and neutron of 2 down and 1 up, giving 0 charge (-1/3 + (-1/3) + 2/3 = 0). Pions are made up of quark(s)-anti-quark(s) pair: p+ = up (2/3) + anti-down (1/3) = +1; p- = down (-1/3) + anti-up (-2/3) = -1; p0 = up (2/3) + anti-up (-2/3) + down (-1/3) + anti-down (1/3) = 0. (John Gribbin, In Search of the Big Bang, p. 277- 283) The quarks of the second fermionic generation onward serve as the constituents of heavy unstable hadrons that only appear in super collision and not in ordinary nature; for example, "strange" quarks, carrying the property of "strangeness", "build up particles with strangeness number of -1, -2, or -3... the omega minus [baryon] has strangeness -3 because it is built from 3 strange quarks, and so on." (Gribbin, ibid., p. 279) In this way the interaction above, for example, between proton and anti-proton (proton passing off a neutron to anti-proton) to give rise to pion+ and pion- is explained through simple arithmetic: p (2/3 + 2/3 + [-1/3]) - n (-1/3 + [-1/3] + 2/3) = 2/3 + 2/3 - 1/3 + 1/3 + 1/3 - 2/3 = 2/3 + 1/3 = +1 = p+ and the other side, -p (-2/3 + [-2/3] + 1/3) + n (-1/3 + [-1/3] + 2/3) = -2/3 - 2/3 + 1/3 -1/3 - 1/3 + 2/3 = -2/3 - 1/3 = -1 = p-. Here there are therefore no "bound states", or the mutual existence of hadrons in one another, as neutron is the bound state of proton and pion-: in the quark model, this mutual transformation or existence is simply the addition and cancellation of all the hadronic constituent parts, so that the quarks of proton + quarks of pion- = quarks of neutron (2/3 + 2/3 - 1/3 -1/3 - 2/3 = 0). Conservation -- in this case, of charge -- and the hadronic symmetries associated with it are effects of the persistence of the underlying constituents which are rearranged and recombined just as protons and neutrons are in atoms. Note also that quarks are thought to be bound up in hadrons by gluons, which are taken to be the real representative of the strong force, "the so-called strong interaction of nuclear physics [being] actually a side effect of the glue force". (Gribbin, ibid., p. 282) For now, let us continue the journey with Capra, from S-matrix to bootstrapping, leaving aside the issue of the opposition in approach, in regard to hadronic transformational patterns, between this and the quark model of the Standard Model, both of which actually arising at about the same time (1960s or so).

"The hadron reactions, then, represent a flow of energy [the substrate] in which particles are created and dissolved, but the energy can only flow through certain 'channels' characterized by the quantum numbers conserved in the strong interactions. In a S-matrix theory, the concept of a reaction channel is more fundamental than that of a particle. It is defined as a set of quantum numbers which can be carried by various hadron combinations and often also by a single hadron [the self-transformation or decaying of a single hadron]. Which combination of hadrons flows through a particular channel is a matter of probability but depends, first of all, on the available energy." (p. 268-9) Thus reaction channel is the consequence of (1) the conservation of the substrate despite its self-transformation and (2) the requirement of a "reason" for this self-transformation of the substrate from one hadronic manifestation (a single or group of hadrons) to another: i.e. an imput of energy. A proton and a p- can collide to form a neutron (a channel of the self-transformation of the substrate), but with more energy the collision can result (be channeled) in a L-K0 pair, a S--K+ pair, and various other combinations (p. 269).


1. This is the relativity principle (Lorentz-invariance in the special case), which Einstein after his special and general theory of relativity has elevated to the status of "principle", together with the laws of thermodynamics, in contrast to the "constructive theories that make claims about the constitution of physical objects". See the chapter on relativity later on for the meaning of this.

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