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Discussion of Bohm's
"Time, the Implicate Order, and Pre-Space"

"Time, the Implicate Order, and Pre-Space", by David Bohm, in "Physics and the Ultimate Significance of Time" (1986), edited by David R. Griffin.

[Bohm, p. 182]
The present *is* but it cannot be specified in words or in thoughts, without it slipping into the past. When a future moment comes, a similar situation will prevail. Therefore, from the past of the present we may be able to predict, at most, the past of the future. The actual immediate present is always the unknown.

"The actual immediate present" is an illusion, the basis for perception in the mode of presentational immediacy, but the present subject which recognizes its own impermanence and contingency and therefore undertakes the process of becoming an actual entity of nature is the *only* kind of thing that can be known or that can know, because it is the only kind of thing that actually exists, according to Whitehead. So, Bohm's analysis here seems to miss the whole point of Whitehead's analysis. Whitehead does specify that consciousness, thought, and sense-perception (in the mode of presentational immediacy) cannot be essential to process for the very reason Bohm gives here, but prehensions are the real activities that are not precluded but rather mandated by the analysis of the present subject.

[Bohm, p. 183]
Here I think that Whitehead's suggestion of starting with actual occasions having the possibility of a complex inner structure is relevant. But now we add that the relationships of these actual occasions have to have the kind of ambiguity that is characteristic of the quantum theory. I suggest that we use the term *moment* (referring to our actual experience of the moment "now" as never completely localizable in relationship to other moments). This notion of ambiguous (and overlapping) moments is illustrated in figure 13.4. The extension and duration of these moments is in general determined only in some broader context in which they are embedded.

What is ambiguous in the phenomenal flow of time is the past. The whole idea is that the present stands apart from the phenomenal nexus of past and future in order to become truly present, in an existential sense, i.e., in order to ex-ist. The past is then ambiguous, for on the one hand it exists only in relation to the future, but on the other hand it is made ambiguous by the real existence of the present which will necessitate the causal reinterpretation of the past, since it is providing another context for the meaning of the past.

The present moment has several very specific meanings. The first of these is a reality within the classical order, while the present subject is in essence the whole classical order or the observer. In other words, the present moment defines another flow of past, present, and future within the classical order, instead of within the quantum explicate or implicate order. Within the noumenal end of the quantum explicate order, the present moment refers to the fact that the actual entity of the real subjective present is a holomovement and hence defines the basis states for the momentum representation.

The overlapping and ambiguous character of extension in time and space is indeed Whitehead's method of extensive analysis. The essential thing to realize here is that extension is a top-down concept. It ultimately reaches the *abstraction* of the point particle, which Whitehead transforms relativistically into the point-instant and the event-particle, but these are abstractions and not actual things in nature. I don't at the moment see how Bohm's concept of the present moment assists or furthers Whitehead's analysis, but he may be right.

[Bohm, p. 186]
Evidently the notion of enfolding and unfolding is close to Whitehead's idea of the *concrescence* of actual occasions, along with their *transjection* into a set of *consequences* that tends to pervade what follows.

Prehensions of past concrescences have the character of an enfolding that looks like a *potential|actual event*, where the superject of the past concrescence is the potential and the actual event is in the mental pole of the present actual entity. Anticipatory prehensions of future, not yet existent, concrescences have the character of an unfolding that looks like a *state vector|substance*. This is the predictive character of the present with respect to the future.

[Bohm, p. 188]
Recently Stapp has further shown that from this overall implicate order one may abstract a particular explicate order, which forms a relatively independent and autonomous context. This explicate order is based on the part of the overall implicate order corresponding to low-energy photons. But with the aid of some reflection on this point, we can see that it is in fact just these low-frequency waves that actually permit both the establishment and the measurement of space-time relationships in the context of objects of ordinary size.

Yes, this is beautiful and profound for several reasons. First of all, the autonomous low-energy explicate order, spoken of here, corresponds to the stream of consciousness, while the implicate order involving the high-energy processes would then be the sea of the cosmic consciousness or pure phenomenologically reduced consciousness, which is what consciousness is in itself. That also can be experienced, although not objectively, since it is the non-dualistic essence of pure subjectivity.

Secondly, Bohm is pointing out the difference between the phenomenal conception of space and the noumenal conception. This leads to the definition of motion as the holomovement, which unfolds the noumenal from the phenomenal and then re-enfolds the noumenal, so that it can be compared with the phenomenal in the formula for motion, v = x_2 - x_1 / t_2 - t_1. This was discussed earlier by Bohm in "Wholeness and the Implicate Order" (1980), pp. 200-5. We then get the causal spacetime continuum, which is in essence phenomenal, by enfolding the duration t_2 in the extension x_2, thus spatializing time. However, the measuring rods and clocks are noumenal, as Bohm points out here, and that paradox has never been adequately treated, nor can it be without this kind of deep metaphysical analysis. Bohm is talking here about seeking deep and profound ontological definitions of noumenal space and time that can be regarded as emerging from pre-space, which is again the phenomenological essence of infinite space and infinite consciousness, aka, cosmic consciousness.

[Bohm, p. 188]
In a way, the explicate order and its counterpart as a "constituent" of the implicate order are like two views of one object. In the explicate order, all the essential relationships prevailing in the context to which this order applies are displayed in such a way that they stand out, sharply and clearly visible. In a domain in which the implicate context is relatively independent and autonomous, this display is clearly a correct representation of whatever is within this context. But in a broader domain, one has to bring in the dependence of the implicate counterpart on the entire implicate order, and in doing this we are, as it were, seeing the same context from two different views and interpreting them through a single and more comprehensive view.

This is a very important passage. First it shows the identity of the quantum explicate and implicate orders - whatever is in one is in the other, with the essential structure unaltered. It is only the point of view that is different, and these points of view belong to the classical observer. Who else could Bohm be referring to by "we" when he says "*we* are, as it were, seeing the same context from two different points of view"?

[Bohm, p. 189]
How, then, is actual physical time to be incorporated into the theory? Here it should be noted that in the standard quantum-mechanical treatment, this can be done properly only by bringing in an observer who is outside the quantum system under discussion. The time of the quantum system has meaning only in relationship to that of the observer. But what if we wish to include the observer as part of the cosmos? This cannot be done consistently in terms of the usual interpretation of quantum theory.

Ordinarily, the measuring rods and clocks would be regarded as extensions of the observer. It is not generally recognized that there is a huge gulf between the causal spacetime continuum, which is in essence phenomenal, and the measuring rods and clocks that are supposed to establish it. The latter are in essence noumenal. The notion that there are processes in nature that constitute an ontological meaning for noumenal space and time is being suggested here by Bohm. This is then juxtaposed to not just phenomenal space, but phenomenological space, which is pre-space. Moreover, Bohm is saying that the processes which define space and time suggest a way of defining in a similar way a noumenal observer. However, I would suggest that such a noumenal observer is *still* metaphysical, i.e., at least one world removed from the physical, and looking down into the physical. The process which defines this noumenal observer is indeed an enfolding into the *vertical* implicate order.

[Bohm, p. 190-2]
We now let PSI mathematically represent the state of the totality, which enfolds all space and time in the depths of the implicate order going beyond both of these. We then consider an operation T that transforms PSI so its elements (or at least some of them) will have a local meaning in an explicate order (i.e., they will be external to each other in this order). The explicate form of the moment is then represented by

Phi_n = P_n T_n PSI

where P_n satisfies the usual algebraic relationship of a projection operator

(P_n)^2 = P_n.

Let us then define another operation that "undoes" the operation T. We call it T^-1 and by definition

T^-1 T = 1.

We then consider PSI_n = T^-1 Psi_n.

This operation may be said to "reinject" the explicate form of the n^th moment back into the implicate order. This gives PSI_n, which is just an element in what we have been calling the implicate counterpart of the explicate order. Note that

P_n T PSI_n = Phi_n.

Houston, we have a problem. Although the basic ideas here are beautiful and profound, they are not formulated correctly. The Totality is not the implicate order at all, but rather the classical order, in its similarity to the quantum implicate order. The total state, PSI, must be the state of both the explicate order wave function, Phi, and the implicate order, as well as the Totality. So, in the total system there are really three sub-systems to be considered: the Observed, the Mind of the Observer, and the Observer. We thereby cut out the middle man (the mechanical measuring device) in our fundamental and organic approach.

Let us call the state of the Observed, Phi; the state of the Mind of the Observer, Chi; and the state of the Observer, Rho. Now Bohm defines a transformation operator, T, that unfolds the quantum implicate order, Chi, or an element thereof, n, into a quantum explicate order. Recognizing that the Observed, Phi, is the physical world component of a seven-world system, Bohm then defines a projection operator, P, that will project onto this physical world subspace of the total explicate order, thus producing Chi:

P_n T_n Chi = Phi_n or Phi_n = P_n T_n Chi.

Now, this is supposed to represent a "moment", or what I will call a "present moment". As I have mentioned above, the present moment, unanalyzable according to Bohm, is not the true present subject, which does have a real structure analyzable in terms of prehensions. It is rather the abstraction that accompanies such a present moment. It is in the first place a classical concept within the classical order, Rho. However, it can also be found in the emotional world of the quantum explicate order. Its correlate in the physical world is the point-instant, defined as Whitehead does. The point has no spatial extension but unlimited temporal extension, while the instant has no temporal extension but unlimited spatial extension. Associated with the point-instant is the event-particle. This means that the point is essentially a relativistic Bohm Point or trajectory, while the instant is essentially a superspatial of J. A. Wheeler.

However, the point-instant is an abstraction - it is not the real thing in nature, which is the actual entity. Although on the classical level, the present subject as the classical order are on different levels and hence disconnected, in the quantum explicate order the present moment can indeed become unified with the present subject outpictured and hence the subject-superject of the fully developed concrescence of the actual entity. The moment is then unified with the concept of the system, or, the system is the system of the moment, but the moment is the abstract scaffolding and the system is the real objective structure of the actual entity and its prehensions.

Now, what is interesting is that within the sub-world structure of the physical world, the point-instant is a causal level reality, above the astral and the physical and below the mental and the etheric. It is a von Neumann's II or measuring device. So, what we have is the rather extraordinary conclusion that the point-instant, not the brain, can be regarded as the measuring device in the ultimate von Neumann chain. The brain is then regarded as part of I, the actually observed system, and the point-instant is the connection between the "ego-sum" as the actual observer and the brain-world complex. The point-instant is like unto the Bohm Point, so the addition of the Bohm Point is now just the addition of the measuring device as an extraneous element, which is perfectly in accord with the Copenhagen Interpretation!

Moreover, an essential point is that we now have the roots of a new understanding of Everett-type sub-systems and relative states, where PSI can be expressed in a number of alternative "constituents" associated with present moments, Chi-Rho, *and* their relative states, Phi. This was indeed Whitehead's understanding of process - he states explicitly in the opening chapters of "Process and Reality" that process does NOT occur in a unique temporal sequence. Rather, all moments happen at once, so to speak, and constitute different universes in the multiverse. Each actual entity indeed has its own unique actual world, according to Whitehead, and there is no other type of world than the actual world of a momentary actual entity.

[Bohm, cont.]
So PSI_n has the same projection into the n^th moment as the timeless totality, PSI. However, PSI_n will be a vanishingly small "constituent" within this totality. It may be thought of as an enfoldment that is something like a hologram of Phi_n, which interpenetrates the entire totality while yet being almost infinitely "thin" and "tenuous" in relationship to this totality.

As has been indicated earlier, however, each moment must contain further projections of earlier moments, which constitute a kind of nested sequence of enfolded images of its past. These may take the form of memories. More generally, however, they may be enfolded "reverberations" of earlier moments within the moment in question (e.g., as in the case discussed previously of cinematic images enfolding into the brain and giving rise to a sense of flowing movement and becoming). Such projection is still to be thought of primarily as a kind of creativity, but here we are discussing *the creation of a moment that is related to its past in a definite way*.

The best way to implement this is with a unified field theory based on the Sine-Gordon Equation. Hence, grad^2 PSI = sin PSI = Psi + 1/3! Psi Phi Chi + 1/5! Psi Phi Psi Phi Chi + .... In each new term, Chi has unfolded into Psi Phi and re-enfolded back into Chi, so we replace Chi by Psi Phi Chi, but this re-enfolding is not by an inverse to the unfolding operation, as in T T^-1, but rather by a continuous re-enfolding across the oroboric abyss between the physical world and the meta-physical world. If we ignored the re-injection from the past, we would just have the generalized Ginzburg-Landau Equation: grad^2 PSI = Psi + Psi Phi Chi.

So, a sequence of past moments is imposed by the unified field equation and this provides our sense of continuity and hence identity. The mathematics here are rather new and unusual, in that they presume that the sub-systems Phi and Chi are both the same and different from each other, while PSI is both a total system comprised of Phi and Chi-Rho, and hence different from them, and also a participant with them in the unified field equation, and hence essentially the same as each of them. This is the profound doctrine of acintyabhedabheda, inconceivably the same and different. Of course, we must find a way to conceive of the inconceivable.

[Bohm, cont.]
To describe this structure mathematically in more detail, let us suppose that the implicate counterpart, PSI_n, of the n^th moment contains a projection of the (n-1)th counterpart, which in turn contains a projection of the (n-2)th counterpart, and so on. This is to say, the projection operator, P_n, as it operates on PSI, will necessarily operate on each "constituent" of PSI, including PSI_n-1, PSI_n-2, etc. In general, we may expect that the projection of the (n-1)th moment as it appears in the n^th moment will have "lost" a great deal of original content; when we consider the projection of a moment in the distant past of the n^th moment, the result will be extremely "tenuous" even in relationship to that projection which constitutes the essence of the n^th moment (as its characteristic, for example, of memories or reverberations of earlier moments of consciousness).

Of course, all these projections into any given moment will have the past of the entire universe as their potential content, which is thus enfolded into the moment in question. In fact, however, moments that are distant in time and space from the one under discussion will generally enfold very weakly (with the result that, as already indicated, each moment can be understood, at least up to a point, in its own relatively independent context).

Let us now consider further how different moments are to be related. Such relationships could, for example, determine general laws that held in broad contexts. These would permit prediction (usually approximate and statistical) of the qualities of later moments in terms of those of earlier moments. But here we recall that knowledge is in the past in any given moment, and from the past in an earlier moment all that we can predict is the past in a later moment. So laws will take the form of generally valid relationships between the nested sets of projections of its past enfolded in one moment and the corresponding set enfolded in another moment. The special creative quality of each moment cannot, however, be predicted in this way.

Of course, all these relationships have to be understood primarily as being between the implicate "counterparts" of the explicate moments. That is to say, we no longer suppose that space-time is primarily an arena and that the laws describe necessary relationships in the development of events as they succeed each other in this arena. Rather, each law *is* a structure that interpenetrates and pervades the totality of the implicate order. To formulate such a law is more like painting a "whole picture" than it is like trying to find a set of dynamical equations for determining how one event follows another. Such dynamical equations will appear only as approximations and limiting cases valid in explicate contexts. Fundamentally, the principles from which the law flows will involve qualities like harmony, order, symmetry, beauty, etc. It has to be kept in mind, however, that breaks in the form of disharmonies, asymmetries, etc., can provide the ground for achieving these qualities anew in a richer way and at a higher level. Perhaps this general feature of the universal order is the reason that the search for symmetries that are later "broken" has been proving to be fruitful in the development of modern quantum-mechanical field theories.

[Bohm, 193-4]
...The fundamental laws of the current quantum-mechanical field theory can be expressed in terms of mathematical structures called "algebras". These algebras contain relationships such as addition and multiplication, which enables new terms to be derived from combinations of terms that are already given. For example, one may write

A = BC + D.

The key point for our purpose here is that any term, K, in the algebra can be transformed into another term, K', by means of a transformation,

K' = TKT^-1,

*where T itself is part of the algebra*. What is particularly significant, then, is that in general this transformation enfolds each term into an implicate order. (That is, K' is a kind of "hologram" of K.) Nevertheless, the relationships between the transformed terms are the same as those between the original terms; or, in the example given above,

A' = B'C' + D'.

In other words, algebraic relationships are invariant to transformation into an implicate order.

The next step is to connect these algebraic relationships to geometric properties. ...the Clifford algebra (in principle combined with the Bosonic algebra) is able to faithfully portray essentially all the basic geometric properties of relativistic space-time. These include, for example, direction, length, space and time displacements, structures such as lines and their intersections, light cones, triangles, tetrahedra, etc., along with their locations and orientations. This range is wide enough to show that the basic geometric properties of explicate space-time can be mapped into algebraic relationships.

Even more important, however, is the fact that all these relationships can now be put into the implicate order. Or, to put it differently, we can say that an algebraic relationship, such as A = BC + D, corresponding to some explicate geometric features, has an implicate counterpart, A' = B'C' + D', corresponding to the same feature in the implicate order. Although these implicate counterparts all overlap and interpenetrate in the implicate order, their distinctness and their interrelationships are still preserved in an invariant algebraic structure that is characteristic of the quantum-mechanical domain.

With the aid of such algebraic structures, the properties of the explicate order can clearly be related to those of pre-space. For instance, one may at first sight wonder how it will be possible to explain the persistence of location and form of an explicate object, which is constantly being created and annihilated in a very rapid succession of projection operations. The answer is very simple. The permanence and constancy of location and form is already being expressed in current physical treatments in terms of standard types of field theories by the requirement that these characteristics (i.e., location and form) be invariant to an *explicate* time displacement D.

But this is an algebraic operation, and so there is another similar operation, D' = TDT^-1, which is the implicate order. If the implicate counterpart of a geometric property is invariant under the operation D', its explicate form will be invariant under D. Thus, by a natural generalization of the mathematical methods ordinarily used to establish constancy of location and form in the explicate order, we can instead ground these in enfolded relationships in the pre-space.

When this is done the way is opened to go much further, for the ordinary explicate order will now come out only as a relatively invariant context in a much vaster implicate order, containing new features that go beyond those of current space-time and geometrical structures in a radical way.

Peter Joseph Mutnick 1949 - 2000