Quantum mechanical ideas have been agents in aiding Bohm's development toward the notions of unbroken wholeness, the implicate order, and the holomovement, all interrelated ideas which deny the presently dominant analysis of the world into separately and independently existent parts.[1] My intention in this chapter is to explain and develop these concepts (including the mathematical modeling of them), ideas which, according to F. A. M. Frescura and Basil Hiley, seem "to offer the possibility of an alternative framework in which to encompass quantum phenomena and relativity, while at the same time giving new insights into physical processes in general and into the structure of space-time in particular."[2]
The holographic model for reality is derived from the properties of a holographic image of an object; any portion of a holographic plate (the hologram), which captures as a record the interference pattern of the light present in its region of space, contains information on the whole object imaged (though with less detail). Bohm describes reality as implicate, any portion of it involved in any other portion, and any portion containing information on every other portion implicated within it. Opposed to this is the notion of the explicate order which images reality as comprising wholly independent entities which may interact with each other. The holographic model of an implicate order is organic in the sense presented in the Introduction.
The suggestion by the
There are two essential properties of the holomovement.
The first property of the holomovement has to do with the "movement" part of the word. In looking in general terms at the relationships between the explicate and the implicate orders, the Birkbeck School decided not to look for "a Euclidean system of order in terms of rigid local connections"; rather than something essentially static, they take activity to be its basic form.[4] "As the implicate order gives primary relevance to activity, let us. . .call this primitive activity the holomovement."[5] The major point about the hologram, according to Bohm, is not the photographic plate, "but that there is movement taking place all the time."[6]
Bohm refers to a variety of psychological and neurological research which tends to indicate that the notion of an object is in fact an abstraction we learn from early childhood. There is a more fundamental or primitive level of perception, that of movement, or change, a break in the regular orders of arrangement. Objects which we perceive to be relatively fixed or slowly moving are built from our relatively invariant abstractions from the ensemble of fundamental perceptions of movement.[7] Some of the most advanced developments in physics closely resemble this primitive perception; for instance, in relativity theory an object can be abstracted from movement invariants. Our common-sense descriptions, which are mirrored in classical physics, are abstractions we are conditioned to regard as fundamental.
Grammar also mirrors our conditioned metaphysics. The noun, for instance, the indicator of an object – obviously necessary in everyday life – has a fundamental role. But verbs, which call attention to action, are apportioned a secondary status. In ceasing to call primitive the "thing in itself," we give the basic role to the verb and relegate nouns to being abstractions from verbs. Movement and activity are thus emphasized and objects are taken to be relative invariants of them, even in our informal speaking. The idea that there are separate constituents of the world must be dropped because movements are able to flow and merge into each other.[8]
The word "holomovement" (utilizing the prefix "holo" from the Greek meaning "whole") is applied to the unbroken and undivided totality of movement from which we abstract such things as objects.
The second element of the holomovement is that of "undivided totality" or "unbroken wholeness," as can be seen in the prefix "holo."[9] A conceptual model for this property is the above-mentioned hologram (used as giving insight into the notion of undivided wholeness just as a lens was in classical physics into the particular nature of the world).[10] This creates an image on a photographic plate by capturing the interference pattern formed by the interaction of a beam of laser light and a portion of that beam reflected from an object, the hologrammed. The illumination of the plate by laser light will produce an image which is three-dimensional. But the plate itself has the interesting property which was described above: the whole image can be reproduced from any portion of the plate (with less detail).[11] Bohm writes that the order inherent in the hologram[12]
is in the movement of the light whose intensity is recorded. What is characteristic of this order is that a whole is enfolded in the movement in each region of space. This movement may appear at first sight to be more of less random, but evidently it has a complex order within it. This we call the implicate order.
Thus, the Euclidean or Cartesian order of the object is not mapped into the hologram by a one-to-one relation.[13]
One of the concepts employed by Bohm and Hiley to describe their notion of unbroken wholeness is that of a system.[14] Remember that the classical concepts advocate the study of each part of the universe in relative isolation; these parts then get added together to explain the whole. Now the relationships and basic qualities of an element are taken to be dependent on the state of the whole, even if approximated to being relatively independent in function (for instance, the role of the observer can be discounted in most experiments). Rather than the fundamental reality being independent elementary parts which are arranged into the various systems, "inseparable quantum interconnectedness of the whole universe is the fundamental reality and. . .relatively independent behaving parts are merely particular and contingent forms within this whole."[15]
The pair wish to use the abstraction of reality into supersystem, system and subsystem, but, of course, not falling into the classical mode of assuming that any system is explicable in terms of its subsystems, or that a system is independent of the supersystems into which it may be incorporated. Subsystems are generally intimately dependent on their encompassing systems, in turn dependent of supersystems, and so on up to the whole universe which is an unknown totality without sharp boundaries. This wholeness of form may allow a relatively independent physical system to be brought into relief, as it were, against a background perhaps including the observer, that in this instance is functionally or behaviorally unimportant.
One must always bear in mind too that this emphasis on wholeness of form does not mean that a complete description is ever possible, for one system is contained in a supersystem, which is contained in another supersystem, and so forth. This incompleteness of content for a theory is required by wholeness in form:[16]
A theory that is whole in form may be compared with a seed that can grow in an indefinite number of ways, according to the context in which it finds itself; but however it grows, it always produces a plant in harmony with the environment, so that together they constitute a whole. Clearly, this is possible only because the articulation of the plant is not predetermined in detail in the seed. On the other hand, any theory that claims completeness of content must close itself off from the unknown totality in which all ultimately merges, so that it will eventually give rise to fragmentation in form.
We have now been introduced to the concept of the holomovement and its two constituent, though inseparable emphases, those of wholeness and movement. In order to give more substance to this proposal I intend now to raise a few matters which develop and refine the fundamental insights. Then I shall return to some of the physical matters highlighted in the previous chapters in order to enquire how the holomovement conceptual base might help to explain them.
First of all, let us consider the distinction Bohm draws between the implicate and explicate orders. Returning to the hologram, I noted that the photographic plate captures as a record the interference pattern of the light present in its region of space – each region of space will similarly contain such a pattern and store of information – and is able to distinguish implicitly differences over the whole of the illuminated object. Generalizing this, Bohm suggests that each region of space and time contains implicit in it the total order of the universe, past, present and future. "In terms of the implicate order one may say that everything is enfolded into everything."[17] Bohm thus arrives at the notion of the implicate or enfolded order, the word "implicate" being based on the verb "to implicate," "to fold inward." We are asked, that is, to explore the idea that in some sense each region of space and time contains the total structure of the universe "enfolded" within it, that the order of the whole is in some sense contained in any region.[18]
This implicate order becomes explicated or "unfolded" into relatively autonomous parts,[19] although in most contexts probably the implicate order is irreducible to an explicate order. In general the laws of physics have up to now referred to the explicate order; a principal function of the Cartesian co-ordinate frames is to describe clearly and precisely the explicate order.[20] But the Cartesian order, Bohm suggests, is only a particular case of the implicate order, of the universal holomovement; "the old view is all appearance – a certain appearance within this new essence."[21] Moreover, there is nothing absolute about being folded or being unfolded; in Bohm's eyes what counts is the relationship between folding and unfolding: "We will not say that one order is the unfolded order and other the folded one; rather, one is folded in relation to the other."[22] Bohm wishes to reformulate the laws of physics so that their primary reference is to the implicate rather than to the explicate order, to the whole rather than to individual particles; in fact the implicate order is similar to that involved in quantum mechanics.[23]
The holomovement is the "totality of movement of enfoldment and unfoldment. . .what is is the holomovement." Moreover, "everything is to be explained in terms of forms derived from this holomovement."[24]
Just as with the hologram where the movement of light in each region of space enfolds or carries the order of a whole illuminate object, so Bohm defines the holomovement – an unbroken and undivided totality – to be that which carries an implicate order. All forms of the holomovement merge and are inseparable. Thus, in its totality, the holomovement is not limited in any specifiable way at all. It is not required to conform to any particular order, or to be bounded by any particular measure. It is Bohm's primitive concept, a metaphor to help point our minds in a particular direction. Thus, the holomovement is indefinable and immeasurable. Because the various forms of the holomovement in general are inseparable and merge, so the holomovement cannot be specifiably limited in its totality. It is unbounded by any measure and does not conform to any order.
There is thus no fundamental theory to which all physical phenomena might be reduced; any theory can only abstract an aspect relevant in a limited context. There is no way in which the holomovement can be described or specified explicitly because it is undivided essentially and necessarily. It is only through particular manifestations that it can be known and then only implicitly.[25]
We have now arrived at a further component in the development of the idea of the holomovement. From the holomovement certain aspects are relevant in any given context while others are not. The word "to relevate" is employed by Bohm: in a perception certain aspects of the holomovement are relevated, lifted into attention, are brought into relief. From the implicate order, areas of relatively autonomous, independent reality form and which appear to us as the relatively stable, independent and enduring world of its components, that is, the explicate order.
The context itself plays an active role in "potentiating" the relevant aspects of the holomovement, the content of the perception. In turn the potentiated content is described as an "ensemblation," in which each constituent is related to the whole:[26]
This feature of an ensemble can be illustrated by considering a painting. The individual spots of paint can be said to ensemblate, to form a whole content, including trees, houses, etc. This whole content is evidently of a very different character from the individual spots of paint, whose only significant relation is that they form such a whole. Similarly, movements ensemblate to form wholes. Thus in perception, all the changes or breaks in movement ensemblate to give rise to relatively invariant objects.
An example from physics can also be given. Curves in a bubble chamber are ensemblations of discrete bubbles, but in being an ensemble they also form a smooth curve which is the track of some particle. In turn, a number of tracks ensemblate to form a whole picture mathematically described in terms of wave functions or quantum states.[27] Another metaphor from physics can also be used: just as "an experimental apparatus can relevate and potentiate a content," so "any arrangement of matter potentiates and relevates a certain content."[28]
The idea that everything cannot be manifested at once contrasts with the Cartesian view in which "some all-encompassing intelligence" is able in principle to embrace reality, the given, at any moment. According to the view of the implicate order, there may be a number of different orders contained implicitly within any given activity and which perhaps cannot be manifested together. What is manifested is determined by the relation between the "inner" activity and the activity of unfolding. The Birkbeck scholars regard the unfolding as the "field of manifestation."[29]
In more complex situations. . .the implicate order may contain a number of different independent explicate orders or, more realistically, a multiplex of orders. Each explicate order may only be realized by its own unique unfolding process. Indeed, it may not be possible to realize all the explicate orders simultaneously, since the unfolding processes themselves may well be incompatible. But of course this is just what is required for quantum mechanics.
If we turn our minds from ontological questions to the more mundane task of actually describing a situation, the concept of relevating plays a similar role. Description begins, according to Bohm, with the holomovement and then abstracts from it a totality of sufficient breadth to enable the description to be adequate. However, analysis into autonomous aspects is valid in some circumstances although these are limited by "holonomy" ("the law of the whole"), their being relevated aspects rather than being interacting disjoint and separate things.[30]
A further related matter which is important for Bohm in his theory is the relative degree of implication:[31]
For example, if we take our own order of perceptual experience as explicate, then the electron's order is implicate. But we might equally well take the electron's order as explicate, in which case our own experiential order will be implicate. In other words, the laws of nature will be invariant, in the sense that their content will be the same, regardless of which order is taken as explicate.
For Bohm this describes a way in which the explicate order is abstracted from the implicate, as its "having no independence or substantiality of existence." It implies for him that localization cannot be fundamental; something local in an order is, in another order, enfolded throughout all of time and space, and no one order is more fundamental than is any other.
The concept of a quantum potential raised previously appears to suggest the need for a more radical and deeper change in our basic outlook than merely the providing of an alternative description of quantum phenomena; "what seems to be suggested is that the particle itself should be regarded as an abstraction from something deeper [the holomovement] rather than being taken as some primary, a priori substantive form." While the Birkbeck School's more recent ideas were implicit to some extent in Bohm's earlier work, they were not brought out, and now with the addition of further insights can be pursued into new directions.[32]
In the Cartesian scheme a substantive object is taken to pass through all the points of its trajectory, and change is due to the rearrangement of a set of basic and also substantive particles. "What is suggested instead is its replacement by what we will call the continuity of form."[33] The quantum potential irreducibly combines the properties of all the elements participating, for instance in a quantum interference, and also implies that space cannot be considered a "neutral back cloth" in the quantum domain because it constrains by its structure the processes embedded in it. "More surprisingly still," explain C. Philippidis, C. Dewdney, and Hiley, "this structure arises out of the very objects on which it acts and the minutest change in any one of the properties of the contributing objects may result in dramatic changes in the quantum potential." This may have implications perhaps for matter's geometrical and topological configurations.
A "different conceptual framework," that centered on the holomovement, is required for the assimilation of the quantum potential concept, with its "globalness and homogeneity in the sense of not being separable into well-defined source and field points."[34] Frescura and Hiley continue:[35]
structure will not be composed of static forms but will be simply structured activity. The activity itself is to be taken as a basic form from which all else arises and it is not to be regarded as the movement of things. Indeed all the properties of a real thing can never be given completely, because its inner structure is forever unfolding in an infinitely continuing process constrained only by its total environment, so that permanence, which is demanded by the Cartesian view, is actually an illusion.
The pair also point out that the idea of continuity of substance has long been denied by the relative ease by which substance, particles for instance, can be created and annihilated in transformation into and from electromagnetic energy. "Continuity of form" is what is suggested as a replacement. Anything from a particle upwards in complexity "appears as a semiautonomous, quasi-stable structured movement within the whole process."[36]
The early work by the Birkbeck School on electrodynamic potentials and localizability imputes to space-time a structural and topological "graininess" in the relationships between its points, which is the forerunner to the current ideas of this school in regard to the mathematical structure of reality.[37] The latter theories proposed by the Birkbeck team for the structure of reality which see wholeness and not disjunction as the essential form, also provide it with a natural graininess or discreteness. Present Cartesian-based theories assume a continuous space-time backcloth and other classical concepts for a particle, mass, charge, etc. "The result is that there are endless arguments about 'quantum jumps' and the type of questions raised by the Einstein-Podolosky-Rosen paradox."[38] The new theories are said to alleviate such concerns.
Let us look at the way the holomovement hypothesis treats the questions of nonlocality and the quantum principle (the participation of the observer and observing apparatus in the observed).
In relation to the holomovement and nonlocality Hiley writes:[39]
The basic relationships or "connections" as we prefer to call them are neither local nor nonlocal. They will be neutral or a-local. It is this neutrality that will enable us to include the macroscopic connection that occurs in the EPR situation and appears in that context to be nonlocal. Hence this type of connection is to be regarded as a macroscopic manifestation of the basic underlying a-local connection. With such connections there is no question of "the passing of information or energy with speeds greater than those of light." The measurement simply breaks the connection and produces a spontaneous localization. No energy transfer is involved.
Thus, unlike the older order, locality is no longer taken to be an absolute, but rather is in essence a relationship between the manifesting field and the manifest. It is as in the hologram: the local features observed in the object are not locally related in the hologram but can be found in every portion of it. Locality is stored nonlocally and can be recovered using laser light, the appropriate manifesting field.[40]
It is instructive to read in a paper by Bohm and Hiley how the quantum potential is suggested to act so as to elicit nonlocality without an "action at a distance" or the superluminal transfer of signals of information. Thus they think that there is no violation of relativity theory in their scheme. The entire quantum field of some configuration can be nonlocally connected in such a way "that instantaneous effects may be carried from one point to another that is quite distant." One has to rid from one's mind the image of a collection of individual particles; rather a quantized field "is a dynamic structure, organized by the quantum information potential, so that it may give rise to discrete results, though the process itself is not discrete."[41]
The second question of the quantum principle, in which not all aspects of reality can be manifest together, receives this treatment from Hiley:[42]
To make any one aspect of the holomovement manifest we need some activity, some form of manifesting field, in which we can make a thing manifest. In other words, we must always relevate one aspect of the holomovement against another. In this domain there is no ding-an-sich with all its properties manifest together and displayed independently of the process of manifestation. There exists a kind of immutable relationship. . .between that which is being manifested and that which is being manifested against.
The observer and the observation apparatus become participators which in manifesting certain attributes of the manifesting field or holomovement relevate certain other aspects. The wholeness metaphysic means for the quantum situation, that "terms like 'observed object,' 'observing instrument,' 'experimental conditions' and 'experimental results' are just aspects of a single overall 'pattern' that are, in effect, abstracted and 'pointed out' or 'made relevant' by our mode of discourse. Thus, it has no meaning to say, for example, that there is an 'observed object' that interacts with the 'observing instrument.'"[43]
The distinction or sharp separation between the apparatus and the system under observation is avoided when an experiment is not considered to be a procedure investigating a property of something existing separately.[44] They are inseparable and constitute a whole which makes irrelevant analysis into parts. "This whole flows and merges into the totality of the universe, including the human observer."[45]
In quantum theory and elsewhere, however, it is apparent that one state may obtain sometimes only to the exclusion of others (the principle of complementarity describes such a thing in the usual quantum physics). That is, the theory which Bohm proposes must take cognizance of the fact that different states have the potential of being realized in different systems, arrangements or situations.
The Birkbeck School is able to rebuild a quantum theory from their informal language of the holomovement, utilizing the notions of discreteness, potentiation, and ensemblation. It is interesting to note that in it no fundamental relevance needs to be accorded to the uncertainty principle or to the principle of complementarity; the new metaphysical model has no need of such recourse.[46] In fact, the holographic image is claimed to be an altogether more adequate picturing or model for the reality quantum theory describes than that of classical metaphysics. Frescura and Hiley write:[47]
while Cartesian order gives primary relevance to local objects following well-defined trajectories. . .quantum mechanics seems to give primary relevance to the holographic image. Here time evolution involves a change of the total order in which the old order is "enfolded" into each region, giving rise to a new total order. It is this total order that is called the implicate order and it is this order that we should take as basic.
Bohm wants the holomovement ideas to be precisely expressed mathematically in order to provide a new description of the implicate order as coherent and systematic as can be given in classical physics using Cartesian co-ordinates. He is after a mathematical form to replace the calculus which is the description of the Cartesian order. And then using this mathematical theory he aims "to understand the overall situation in physics in a way that is free of current contradictions and confusions (e.g., the infinities of quantum field theory)."[48]
The first discussions about mathematicizing the ideas of an implicate-explicate order appeared early in the 1970's, for Bohm in particular in a 1973 article in which he suggested the algebra as the most appropriate mathematical tool. He makes this particular choice because he believes that the algebra does not assume a continuum and is what is at root in quantum mechanics. Take as an example the motion of an elementary particle. Hiley notes that the classical approach is to describe the motion "using one-parameter groups and we imagine this as a mapping of one mathematical object into another at neighboring points of a trajectory. This corresponds to a motion that Bergson calls 'les images du caractère cinématographique.'"[49] In comparison, motion described in the new holomovement approach is a continual unfolding and enfolding process, giving rise to a kind of natural recurrent process. All that is manifested is a trace of dots in a bubble chamber. No object is seen to pass from one point to another by passing through all the intermediate points. The manifestation of dots can equally be regarded as a continuous unfolding or restructuring under the influence of the manifesting field.
Here we have the algebraic form hypothesized because it allows for two different operations: succession of events is described using the multiplicative properties of the algebra, and the interaction between them using its additive properties. Taken together they make an algebra.[50] Perhaps this could be rephrased by saying that holo + movement = algebra. Thus the attention of Bohm, Hiley, and their colleagues in the Birkbeck School is towards finding an appropriate algebra with which to describe reality and its holomovement.[51]
The metaphysical ideas have come first; the mathematics second. But it is not a matter of mathematicizing a set of fixed ideas, but rather a two-way process is involved. The mathematics and the physics, in Bohm's view, are only aspects of a single whole:[52]
In order that the general language and its mathematicization shall be able to work together coherently and harmoniously, these two aspects have to be similar to each other in certain key ways, though they will, of course, be different in other ways (notably in that the mathematical aspect has greater possibilities for precision of inferences). Through a consideration of these similarities and difference, there can arise what may be called a sort of "dialogue" in which new meanings common to both aspects are created. It is in this "dialogue" that the wholeness of the general language and its mathematics is to be seen.
As in the rest of this presentation of the ideas of the Birkbeck School, the mathematical details of the algebraic model for the holomovement will not be provided. Rather I will be describing some of its consequences, assumptions and developments linguistically.
The first attempt of the Birkbeck School to mathematicize the holomovement ideas for a pregeometric structure used the language of homology and cohomology theory.[53] This was in 1970, and partly drew its inspiration from Wheeler's earlier work.[54] Bohm, Hiley, and Allan Stuart's "Abstract" for their 1970 announcement of this innovation contains the following:[55]
This new informal language [such as is involved in the holomovement hypothesis as mooted above] leads to a mathematical formalism which employs the descriptive terms of a cohomology theory with values in the integers. Thus our theory is not based on the use of a space-time description, continuous or otherwise. In the appropriate limit, the mathematical formalism contains certain features similar to those of classical field theories. It is therefore suggested that all the field equations of physics can be re-expressed in terms of our theory in a way that is independent of their space-time description. The point is illustrated by Maxwell's equations, which are understood in terms of cohomology on a discrete complex. In this description, the electromagnetic four-vector potential and the four-current can be discussed in terms of an "ensemblation" of discontinuous hypersurfaces or varieties. Since the cohomology is defined on the integers the charge is naturally discrete.
Bohm relates the development of some of these mathematical concepts:[56]
it is necessary first to develop a way of describing mathematically the set of relationships. . .which define each moment in relation to its past and its elsewhere. It turns out that such a set of relationships can be expressed in a very natural way in terms of certain kinds of matrices, having the property that each matrix is a member of a certain kind of sequence, such that it can be obtained from the previous one, by a characteristic matrix operation. . . .[These] matrices enable each moment to be located in relation to the total process. The next requirement grows out of the study of how a space can be discrete and yet have a kind of homogeneity that we usually associate with the notion of continuity. We shall, in fact, regard the space as built of a discrete set of structures called "simplices," consisting of points, lines, planes, pyramids, etc. We require, naturally, that these simplices generally fit together, boundary against boundary. The places where such a failure of perfect fitting occur. . .would then correspond to matter, while homogeneous fitting would correspond to "empty" space.
The homology groups of topology are concerned with the fitting of boundaries of regions. Also,
the notion of the homogeneity of space also contains implicitly the notion of congruence of one region with another. The transformations between regions that express this relation of congruence, correspond to another group (the so-called Lie group) which is, in fact, very deeply related to the homology groups describing boundary relationships.
It is suggested that the mathematical description which is appropriate for making activity and wholeness the primary reality rather than the object itself being so, "should use the descriptive terms of homology and cohomology theory (e.g., simplexes, complexes, chains, cochains, etc.) that is, the basic description should be cellular."[57] In a later paper the mathematical formalism using the theory of homology and cohomology – originating with the intuitive idea of division into cells[58] – is related to attempts of some others to understand elementary particle phenomena.[59] The use of a cohomology theory is a natural attempt at formalizing the informal holomovement idea, and is a development from the usual classical quantum-mechanical formalisms such as the notion of a Hilbert Space and unitary transformations which are interpreted in terms of probabilities. New forms of mathematics can be introduced which go "outside the limits of theories that can be interpreted in terms of 'classical' informal description."[60]
Hiley relates their progress with regard to quantum theory:[61]
Here we represented the structures by abstract simplical complexes so that the simplexes themselves provided a description of the outward manifestations of the inner process of becoming. In such a scheme the quantum fluctuations could be considered as the creation and annihilation of distinctive relationships and it is this structure that can be statistically ordered into a coherent whole. While the basic relationships do undergo change, this change does not take place in space and time. Rather space and time are themselves relationships which are to be ultimately abstracted from the underlying structure, thus giving rise to what we may call a statistical geometry.
The members of the Birkbeck School were able with this approach to unearth, they felt, "very suggestive ideas" which related neatly to parts of physical theory, and by it were also able "to give partial mathematical expression to the idea of the inseparability of the manifest and the manifesting field." It even introduced the wholeness feature and the notion of discreteness. But they felt that they only had a remote hope of realizing their objective of a statistical geometry, and they also felt the inability of this mathematicization to capture "the active ingredient" that they felt "to be so essential."[62]
Since discarding combinatorial topology as the vehicle with which to express the algebraic holomovement structure of reality and in particular of quantum theoretic reality, members of the Birkbeck School have turned their attention to the structures underlying the Clifford and simplictic algebras in their attempt to mathematicize the implicate order.[63] Hiley has briefly outlined the significance and consequences of their newfound approach with respect to quantum theory:[64]
the importance of these particular algebras is related to the fact that the Clifford algebra carries the rotation group, while the simplictic algebra is related closely to the group of canonical transformations and its quantum analogue, the Heisenberg algebra. In the case of the Clifford algebra we have the additional advantage in that the algebra itself carries the spinor structure in a natural way and it is the spinor that plays such a predominant role in quantum mechanics.
Having explored the spinor nature of the algebraic formalism (in a sense the spinor can be said to describe an implicate order),[65] Frescura and Hiley proceed to ask themselves whether the quantum formalism can be put completely in the algebraic form such that the distinctions between the observer and the observed are removed, thus making possible an understanding of quantum theory in terms of the implicate order. They conclude that it is possible to express completely the content of quantum mechanics in terms of a purely algebraic structure, and that it thus offers scope for discussing a pregeometry based on process.[66] They are able to approach the relationship between classical and quantum theories in a way which permits both of them to be expressed in the same mathematical language, making clear at the same time the essential differences and similarities between the two theories. Moreover, there appears to be a close relationship, they believe, between this work and that of the group headed by I. Prigogine.[67]
This new approach they feel offers exciting possibilities in terms of mathematicizing the implicate order for the quantum realm. It remains to be seen whether the program can be carried through thoroughly, let alone be accepted by the community of physicists.
[1]. Bohm and Hiley 1975: 96; Bohm 1980a; 1978a; Sharpe 1983 (part of which is included in Chapter 4 below).
[2]. Frescura and Hiley 1980a: 7. With regard to the relativity-quantum mechanical reconciliation within this new wholeness approach, see, for example, Bohm and Hiley 1975: 106-8.
[3]. Bohm 1978a: 37-8; see also Bohm 1966: 256-86.
[4]. Hiley 1980: 94.
[5]. Frescura and Hiley 1980a: 12.
[6]. Bohm 1978b: 91.
[7]. Bohm, Hiley, and Stuart 1970: 175. Detailed in the Appendix to Bohm 1965.
[8]. Bohm, Hiley, and Stuart 1970: 175-6. See also Mary Daly 1973 on the change of language and grammar that the feminist perspective would encourage.
[9]. Hiley 1980: 78.
[10]. Bohm 1973: 143-6; 1978a: 38; 1978b: 90. In the development of medicine and in the development of science in general, machines often provide models, constraints and inspiration for theory; see Gregory 1981.
[11]. Bohm 1973: 144-5; Bohm 1978b: 90-1. Frescura and Hiley 1980a: 9. Bohm 1971d is one reference which discusses the mathematics of the hologram. Another model often cited as a description of the holomovement or implicate order is that of droplets of dye dropped onto glycerol and enfolded by being stirred; e.g., see Frescura and Hiley 1980a: 10-1; Bohm 1978a: 39; 1978b: 91-2.
[12]. Bohm 1978a: 39; original emphases removed.
[13]. Hiley 1980: 94.
[14]. Bohm and Hiley 1975: 101-6.
[15]. Ibid., p. 102; see also Davies 1984: 219-21.
[16]. Bohm and Hiley 1975: 105.
[17]. Bohm 1980b: 177; see also Bohm 1978b: 94-5; and Bohm and Weber 1978: 45-7 for a discussion on time.
[18]. Bohm 1973: 146-7; 1978b: 91.
[19]. Bohm 1978b: 93.
[20]. Bohm 1978a: 39.
[21]. Bohm 1978b: 91-2.
[22]. Bohm 1978b: 94.
[23]. Bohm 1973: 148; and 1978b: 92.
[24]. Bohm 1980b: 178.
[25]. Bohm 1973: 149; 1978a: 40; and 1978b: 93.
[26]. Bohm, Hiley, and Stuart 1970: 176.
[27]. Ibid., pp. 176-7. See also Bohm 1962b: 311; and 1973: 152-3.
[28]. Bohm, Hiley, and Stuart 1970: 176.
[29]. Frescura and Hiley 1980a: 11-2.
[30]. Bohm 1973: 149-54; 1978a: 40; 1978b: 93; Bohm and Hiley 1975: 99.
[31]. Bohm 1978a: 40.
[32]. Bohm and Hiley 1975: 95.
[33]. Frescura and Hiley 1980a: 10. See also Bohm and Hiley 1975: 96-101; and 1976a for re-examinations of this "novel potential" raised earlier by Bohm.
[34]. Philippidis, Dewdney, and Hiley 1979: 27-8.
[35]. Frescura and Hiley 1980a: 11.
[36]. Frescura and Hiley 1980b: 705.
[37]. Aharonov and Bohm 1963: 1629. See also de Broglie, Bohm, Hillion, Halbwachs, Takabayasi, and Vigier 1963.
[38]. Hiley 1971: 183.
[39]. Hiley 1980: 93.
[40]. See also Baracca, Bohm, Hiley, and Stuart 1975; and Bohm 1978b: 93.
[41]. Bohm and Hiley 1984: 271. The authors continue (pp. 272-4) by demonstrating the relativistic covariance within their theory, but that it implies the existence of some sort of ether which is a special frame of reference. The existence of the frame implies that there is a level at which quantum theory breaks down.
[42]. Hiley 1980: 80.
[43]. Bohm 1971b: 38.
[44]. Bohm, Hiley, and Stuart 1970: 171.
[45]. Ibid., p. 172.
[46]. Ibid., p. 173.
[47]. Frescura and Hiley 1980a: 9.
[48]. Bohm 1978a: 40; 1978b: 94.
[49]. Hiley 1980: 89.
[50]. Frescura and Hiley 1980a: 13-20; 1981: 27-30. Bohm 1973: 156-7 provides a simple mathematical building towards the algebraic structure.
[51]. There is an historical precedent for using algebras to describe movement, as well as to describe aspects of quantum behavior.
[52]. Bohm 1973: 155.
[53]. Hiley 1971: 187-9; Atkin 1971; Bohm, Hiley, and Stuart 1970: 177-83; Bohm 1962b: 311-4.
[54]. See Bohm, Hiley, and Stuart 1970: 173-4; Hiley 1971: 188; and the discussion above on Wheeler and pregeometry.
[55]. Bohm, Hiley, and Stuart 1970: 171.
[56]. Bohm 1962b: 312-3.
[57]. Hiley and Stuart 1971: 247-8.
[58]. Hiley 1971: 181, 185-9.
[59]. Hiley and Stuart 1971.
[60]. Bohm, Hiley, and Stuart 1970: 177.
[61]. Hiley 1980: 93.
[62]. Ibid., pp. 94, 98; Bohm, Hiley, and Stuart 1970: 177. See also Frescura and Hiley 1980a: 13.
[63]. Frescura and Hiley 1980a: 13-30.
[64]. Hiley 1980: 94.
[65]. See also Frescura and Hiley 1980a: 21-9; and 1981.
[66]. Frescura and Hiley 1980a: 20-1; and 1980b: esp. pp. 706, 718-9.
[67]. Bohm and Hiley 1981a; see also Bohm and Hiley 1983.
© Copyright by KOI TRUST, 1987
© Copyright by Kevin Sharpe, 2000
To view the next section of this work, click on Chapter 4.