On Bohmian Re‐versation and Re‐Ordination

DavidBohm-WholenessAndTheImplicateOrder.pdf

This device consisted of two concentric glass cylinders, with a highly viscous fluid such as glycerine between them, which is arranged in such a way that the outer cylinder can be turned very slowly, so that there is negligible diffusion of the viscous fluid. A droplet of insoluble ink is placed in the fluid, and the outer cylinder is then turned, with the result that the droplet is drawn out into a fine thread-like form that eventually becomes invisible. When the cylinder is turned in the opposite direction the thread-form draws back and suddenly becomes visible as a droplet essentially the same as the one that was there originally.

It is worth while to reflect carefully on what is actually the enfolding-unfolding universe and consciousness happening in the process described above. First, let us consider an element of fluid. The parts at larger radii will move faster than those at smaller radii. Such an element will therefore be deformed, and this explains why it is eventually drawn out into a long thread. Now, the ink droplet consists of an aggregate of carbon particles that are initially suspended in such an element of fluid. As the element is drawn out the ink particles will be carried with it. The set of particles will thus spread out over such a large volume that their density falls below the minimum threshold that is visible. When the movement is reversed, then (as is known from the physical laws governing viscous media) each part of the fluid retraces its path, so that eventually the thread-like fluid element draws back to its original form. As it does so, it carries the ink particles with it, so that eventually they, too, draw together and become dense enough to pass the threshold of perceptibility, so emerging once again as visible droplets.

When the ink particles have been drawn out into a long thread, one can say that they have been enfolded into the glycerine, as it might be said that an egg can be folded into a cake. Of course, the difference is that the droplet can be unfolded by reversing the motion of the fluid, while there is no way to unfold the egg (this is because the material here undergoes irreversible diffusive mixing).

The ink particles in each droplet will of course be carried along by the fluid motions, but with each particle remaining in its own thread of fluid. Eventually, however, in any region that was large enough to be visible to the eye, red particles from the one droplet and blue particles from the other will be seen to intermingle, apparently at random.

When the fluid motions are reversed, however, each thread-like element of fluid will draw back into itself until eventually the two gather into clearly separated regions once again. If one were able to watch what is happening more closely (e.g., with a microscope) one would see red and blue particles that were close to each other beginning to separate, while particles of a given colour that were far from each other would begin to come together. It is almost as if distant particles of a given colour had ‘known’ that they had a common destiny, separate from that of particles of the other colour, to which they were close..

In the case of this device, the overall necessity operates mechanically as the movement of fluid, according to certain well-known laws of hydrodynamics.

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As indicated earlier, however, we will eventually drop this mechanical analogy and go on to consider the holomovement. In the holomovement, there is still an overall necessity (which in chapter 6 we called ‘holonomy’) but its laws are no longer mechanical.

...as pointed out in section 2 of this chapter, its laws will be in a first approximation those of the quantum theory, while more accurately they will go beyond even these, in ways that are at present only vaguely discernible.

...ensembles of elements which intermingle or inter-penetrate in space can nevertheless be distinguished, but only in the context of certain total situations in which the members of each ensemble are related through the force of an overall necessity, inherent in these situations, that can bring them together in a specifiable way

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Now that we have established a new kind of distinction of ensembles that are enfolded together in space, we can go on to put these distinctions into an order. The simplest notion of order is that of a sequence or succession. We shall start with such a simple idea and develop it later to much more complex and subtle notions of order.

chapter 5, the essence of a simple, sequential order is in the series of relationships among distinct elements:

A : B :: B : C :: C : D ....

For example, if A represents one segment of a line, B the succeeding one, etc., the sequentiality of segments of the line follows from the above set of relationships

Let us now return to our ink-in-fluid analogy, and suppose that we have inserted into the fluid a large number of droplets, set close to each other and arranged in a line (this time we do not suppose different colours). These we label as A, B, C, D ....

...We then turn the outer cylinder many times, so that each of the droplets gives rise to an ensemble of ink particles, enfolded in so large a region of space that particles from all the droplets intermingle. We label the successive ensembles A′, B′, C′, D′....

It is clear that, in some sense, an entire linear order has been enfolded into the fluid. This order may be expressed through the relationships

A′ : B′ :: B′ : C′ :: C′ : D′ ....

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Bohmian Re-Ordination

This order is not present to the senses. Yet its reality may be demonstrated by reversing the motion of the fluid, so that the ensembles, A′, B′, C′, D′ . . ., will unfold to give rise to the original linearly arranged series of droplets, A, B, C, D ....

In the above, we have taken a pre-existent explicate order, consisting of ensembles of ink particles arranged along a line, and transformed it into an order of enfolded ensembles, which is in some key way similar

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We shall next consider a more subtle kind of order, not derivable from such a transformation.

Suppose now that we insert an ink droplet, A, and turn the outer cylinder n times. We then insert a second ink droplet, B, at the same place, and again turn the cylinder n times. We keep up this procedure with further droplets, C, D, E . . . .

The resulting ensembles of ink particles, a, b, c, d, e, . . ., will now differ in a new way, for, when the motion of the fluid is reversed, the ensembles will successively come together to form droplets in an order opposite to the one in which they were put in

For example, at a certain stage the particles of ensemble d will come together (after which they will be drawn out into a thread again).

This will happen to those of c, then to b, etc. It is clear from this that ensemble d is related to c as c is to b, and so on. So these ensembles form a certain sequential order.

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Intrinsically Implicate Order

However, this is in no sense a transformation of a linear order in space (as was that of the sequence A′, B′, C′, D′ . . ., that we considered earlier), for in general only one of these ensembles will unfold at a time; when any one is unfolded, the rest are still enfolded.

...we have an order which cannot all be made explicate at once and which is nevertheless real, as may be revealed when successive droplets become visible as the cylinder is turned.

We call this an intrinsically implicate order, to distinguish it from an order that may be enfolded but which can unfold all at once into a single explicate order. So we have here an example of how, as stated in section 2, an explicate order is a particular case of a more general set of implicate orders.

On the Re-Solution of A single Explicate Order and Intrinsically Implicate Order

Let us now go on to combine both of the above-described types of order.

We first insert a droplet, A, in a certain position and turn the cylinder n times. We then insert a droplet, B, in a slightly different position and turn the cylinder n more times (so that A has been enfolded by 2n turns).

We then insert C further along the line AB and turn n more times, so that A has been enfolded by 3n turns, B 2n turns, and C by n turns.

We proceed in this way to enfold a large number of droplets.

We then move the cylinder fairly rapidly in the reverse direction.

If the rate of emergence of droplets is faster than the minimum time of resolution of the human eye, what we will see is apparently a particle moving continuously and crossing the space.

Enfoldment and Unfoldment With Respect to Implicate Order

Such enfoldment and unfoldment in the implicate order may evidently provide a new model of, for example, an electron, which is quite different from that provided by the current mechanistic notion of a particle that exists at each moment only in a small region of space and that changes its position continuously with time.

What is essential to this new model is that the electron is instead to be understood through a total set of enfolded ensembles, which are generally not localized in space.

At any given moment one of these may be unfolded and therefore localized, but in the next moment, this one enfolds to be replaced by the one that follows.

The notion of continuity of existence is approximated by that of very rapid recurrence of similar forms, changing in a simple and regular way (rather as a rapidly spinning bicycle wheel gives the impression of a solid disc, rather than of a sequence of rotating spokes)

Of course, more fundamentally, the particle is only an abstraction that is manifest to our senses. What is is always a totality of ensembles, all present together, in an orderly series of stages of enfoldment and unfoldment, which intermingle and inter-penetrate each other in principle throughout the whole of space.

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It is further evident that we could have enfolded any number of such ‘electrons’, whose forms would have intermingled and inter-penetrated in the implicate order.

Nevertheless, as these forms unfolded and became manifest to our senses, they would have come out as a set of ‘particles’ clearly separated from each other.

The arrangement of ensembles could have been such that these particle-like manifestations came out ‘moving’ independently in straight lines, or equally well, along curved paths that were mutually related and dependent, as if there had been a force of interaction between them.

Since classical physics traditionally aims to explain everything in terms of interacting systems of particles, it is clear that in principle one could equally well treat the entire domain that is correctly covered by such classical concepts in terms of our model of ordered sequences of enfolding and unfolding ensembles.

Bohm's Proposal

What we are proposing here is that in the quantum domain this model is a great deal better than is the classical notion of an interacting set of particles. Thus, although successive localized manifestations of an electron, for example, may be very close to each other, so that they approximate a continuous track, this need not always be so. In principle, discontinuities may be allowed in the manifest tracks – and these may, of course, provide the basis of an explanation of how, as stated in section 2, an electron can go from one state to another without passing through states in between. This is possible, of course, because the ‘particle’ is only an abstraction of a much greater totality of structure. This abstraction is what is manifest to our senses (or instruments) but evidently there is no reason why it has to have continuous movement (or indeed continuous existence).

On Bohmian Re-Formation of Bohiam Process

Next, if the total context of the process is changed, entirely new modes of manifestation may arise. Thus, returning to the ink-in-fluid analogy, if the cylinders are changed, or if obstacles are placed in the fluid, the form and order of manifestation will be different. Such a dependence – the dependence of what manifests to observation on the total situation – has a close parallel to a feature which we have also mentioned in section 2, i.e., that according to the quantum theory electrons may show properties resembling either those of particles or those of waves (or of something in between) in accordance with the total situation involved in which they exist and in which they may be observed experimentally.

Summary

What has been said thus far indicates that the implicate order gives generally a much more coherent account of the quantum properties of matter than does the traditional mechanistic order. What we are proposing here is that the implicate order therefore be taken as fundamental. To understand this proposal fully, however, it is necessary to contrast it carefully with what is implied in a mechanistic approach based on the explicate order; for, even in terms of this latter approach, it may of course be admitted that in a certain sense at least, enfoldment and unfoldment can take place in various specific situations (e.g., such as that which happens with the ink droplet).

However, this sort of situation is not regarded as having a fundamental kind of significance. All that is primary, independently existent, and universal is thought to be expressible in an explicate order, in terms of elements that are externally related (and these are usually thought to be particles, or fields, or some combination of the two). Whenever enfoldment and unfoldment are found actually to take place, it is therefore assumed that these can ultimately be explained in terms of an underlying explicate order through a deeper mechanical analysis (as, indeed, does happen with the ink-droplet device).

Our proposal to start with the implicate order as basic, then, means that what is primary, independently existent, and universal has to be expressed in terms of the implicate order. So we are suggesting that it is the implicate order that is autonomously active while, as indicated earlier, the explicate order flows out of a law of the implicate order, so that it is secondary, derivative, and appropriate only in certain limited contexts. Or, to put it another way, the relationships constituting the fundamental law are between the enfolded structures that interweave and interpenetrate each other, throughout the whole of space, rather than between the abstracted and separated forms that are manifest to the senses (and to our instruments).

Holonomy

What, then, is the meaning of the appearance of the apparently independent and self-existent ‘manifest world’ in the explicate order? The answer to this question is indicated by the root of the word ‘manifest’, which comes from the Latin ‘manus’, meaning ‘hand’. Essentially, what is manifest is what can be held with the hand – something solid, tangible and visibly stable. The implicate order has its ground in the holomovement which is, as we have seen, vast, rich, and in a state of unending flux of enfoldment and unfoldment, with laws most of which are only vaguely known, and which may even be ultimately unknowable in their totality. Thus it cannot be grasped as something solid, tangible and stable to the senses (or to our instruments). Nevertheless, as has been indicated earlier, the overall law (holonomy) may be assumed to be such that in a certain sub-order, within the whole set of implicate order, there is a totality of forms that have an approximate kind of recurrence, stability and separability. Evidently, these forms are capable of appearing as the relatively solid, tangible, and stable elements that make up our ‘manifest world’. The special distinguished sub-order indicated above, which is the basis of the possibility of this manifest world, is then, in effect, what is meant by the explicate order.

Vidation of Explicate Order

We can, for convenience, always picture the explicate order, or imagine it, or represent it to ourselves, as the order present to the senses. The fact that this order is actually more or less the one appearing to our senses must, however, be explained. This can be done only when we bring consciousness into our ‘universe of discourse’ and show that matter in general and consciousness in particular may, at least in a certain sense, have this explicate (manifest) order in common. This question will be explored further when we discuss consciousness in sections 7 and 8.