Bohmian Holonomy
http://www.gci.org.uk/Documents/DavidBohm-WholenessAndTheImplicateOrder.pdf
To generalize so as to emphasize undivided wholeness, we shall say that what ‘carries’ an implicate order is the holomovement, which is an unbroken and undivided totality. In certain cases, we can abstract particular aspects of the holomovement (e.g., light, electrons, sound, etc.), but more generally, 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. Thus, the holomovement is undefinable and immeasurable.
To give primary significance to the undefinable and immeasurable holomovement implies that it has no meaning to talk of a fundamental theory, on which all of physics could find a permanent basis, or to which all the phenomena of physics could ultimately be reduced. Rather, each theory will abstract a certain aspect that is relevant only in some limited context, which is indicated by some appropriate measure.
To illustrate what it means to relevate certain aspects of the implicate order in the holomovement, it is useful to consider once again the example of the mechanical device for stirring a viscous fluid, as described in the previous section. Suppose that we first put in a droplet of dye and turn the stirring mechanism n times. We could then place another droplet of dye nearby and stir once again through n turns.
Suppose, then, that after thus ‘enfolding’ a large number of droplets, we turn the stirring device in a reverse direction, but so rapidly that the individual droplets are not resolved in perception. Then we will see what appears to be a ‘solid’ object (e.g. a particle) moving continuously through space. This form of a moving object appears in immediate perception primarily because the eye is not sensitive to concentrations of dye lower than a certain minimum, so that one does not directly see the ‘whole movement’ of the dye. Rather, such perception relevates a certain aspect. That is to say, it makes this aspect stand out ‘in relief’ while the rest of the fluid is seen only as a ‘grey background’ within which the related ‘object’ seems to be moving.
Such a description has to start by conceptually relevating certain broader orders of movement, going beyond any that are similar to those relevated in immediate perception. In doing this, one always begins with the holomovement, and then one abstracts special aspects which involve a totality broad enough for a proper description in the context under discussion. In the present example, this totality should include the whole movement of the fluid and the dye as determined by the mechanical stirring device, and the movement of the light, which enables us visually to perceive what is happening, along with the movement of the eye and nervous system, which determines the distinctions that can be perceived in the movement of light.
To specify this movement in more detail, it is useful here to introduce a new measure, i.e., an ‘implication parameter’, denoted by T. In the fluid, this would be the number of turns needed to bring a given droplet of dye into explicate form. The total structure of dye present at any moment can then be regarded as an ordered series of substructures, each corresponding to a single droplet N with its implication parameter TN.
Evidently, we have here a new notion of structure, for we no longer build structures solely as ordered and measured arrangements on which we join separate things, all of which are explicate together. Rather, we can now consider structures in which aspects of different degrees of implication (as measured by T) can be arranged in a certain order.
Such aspects can be quite complex. For example, we could implicate a ‘whole picture’ by turning the stirring device n times. We could then implicate a slightly different picture, and so on indefinitely. If the stirring device were turned rapidly in the reverse direction, we could see a ‘three-dimensional scene’ apparently consisting of a ‘whole system’ of objects in continuous movement and interaction.
In this movement, the ‘picture’ present at any given moment would consist only of aspects that can be explicated together (i.e., aspects corresponding to a certain value of the implication parameter T). As events happening at the same time are said to be synchronous, so aspects that can be explicated together can be called synordinate, while those that cannot be explicated together may then be called asynordinate. Evidently, the new notions of structure under discussion here involve asynordinate aspects, whereas previous notions involve only synordinate aspects.
It has to be emphasized here that the order of implication, as measured by the parameter T, has no necessary relationship to the order of time (as measured by another parameter, t). These two parameters are only related in a contingent manner (in this case by the rate of turning of the stirring device). It is the T parameter that is directly relevant to the description of the implicate structure, and not the t parameter.
When a structure is asynordinate (that is, constituted of aspects with different degrees of implication), then evidently the time order is not in general the primary one that is pertinent for the expression of law
Rather, as one can see by considering the previous examples, the whole implicate order is present at any moment, in such a way that the entire structure growing out of this implicate order can be described without giving any primary role to time
The law of the structure will then just be a law relating aspects with various degrees of implication. Such a law will, of course, not be deterministic in time. But, as has been indicated in chapter 5 determinism in time is not the only form of ratio or reason; and as long as we can find ratio or reason in the orders that are primarily relevant, this is all that is needed for law
...the wave-particle properties of matter show that the overall movement depends on the total experimental arrangement in a way that is not consistent with the idea of autonomous motion of localized particles; and, of course, the discussion of the Heisenberg microscope experiment indicates the relevance of a new order of undivided wholeness in which it has no meaning to talk about an observed object as if it were separate from the entire experimental situation in which observation takes place. So the use of the descriptive term ‘particle’ in this ‘quantum’ context is very misleading.
...we have here to deal with something that is similar in certain important ways to the example of stirring a dye into a viscous fluid.
In both cases, there appears in immediate perception an explicate order that cannot consistently be regarded as autonomous.
In the example of the dye, the explicate order is determined as an intersection of the implicate order of ‘the whole movement’ of the fluid and an implicate order of distinctions of density of dye that are relevated in sense perception.
In the ‘quantum’ context, there similarly will be an intersection of an implicate order of some ‘whole movement’ corresponding to what we have called, for example, ‘the electron’, and another implicate order of distinctions that are relevated (and recorded) by our instruments.
...the word ‘electron’ should be regarded as no more than a name by which we call attention to a certain aspect of the holomovement, an aspect that can be discussed only by taking into account the entire experimental situation and that cannot be specified in terms of localized objects moving autonomously through space
...of course, every kind of ‘particle’ which in current physics is said to be a basic constituent of matter will have to be discussed in the same sort of terms (so that such ‘particles’ are no longer considered as autonomous and separately existent).
Formalization of A New General Physical Description In Which 'Everything Implicates Everything' In An Order of Undivided Wholeness
Thus, we come to a new general physical description in which ‘everything implicates everything’ in an order of undivided wholeness. A mathematical discussion of how the ‘quantum’ context can be assimilated in terms of the sort of implicate order discussed above is given in the appendix to this chapter.
We have seen that in the ‘quantum’ context, the order in every immediately perceptible aspect of the world is to be regarded as coming out of a more comprehensive implicate order, in which all aspects ultimately merge in the undefinable and immeasurable holomovement. How, then, are we to understand the fact that descriptions involving the analysis of the world into autonomous components do actually work, at least in certain contexts (e.g., those in which classical physics is valid)?
To answer the question, we first note that the word ‘autonomy’ is based on two Greek words: ‘auto’, meaning ‘self’, and ‘nomos’ meaning ‘law’. So, to be autonomous is to be self-ruling.>
Evidently, nothing is ‘a law unto itself’. At most, something may behave with a relative and limited degree of autonomy, under certain conditions and in certain degrees of approximation. Indeed, at the very least, each relatively autonomous thing (e.g., a particle) is limited by other such relatively autonomous things. Such a limitation is currently described in terms of interaction. However, we shall introduce here the word ‘heteronomy’ to call attention to a law in which many relatively autonomous things are related in this way, i.e., externally and more or less mechanically.
Now, what is characteristic of heteronomy is the applicability of analytic descriptions. (As pointed out in chapter 5, the root of the word ‘analysis’ is the Greek ‘lysis’ meaning ‘to dissolve’ or ‘to loosen’. Since the prefix ‘ana’ means ‘above’, it may be said that ‘to analyse’ is to ‘loosen from above’, i.e., to obtain a broad view as if from a great height in terms of components that are regarded as autonomous and separately evident though in mutual interaction.)
As has been seen, however, in sufficiently broad contexts such analytic descriptions cease to be adequate. What is then called for is holonomy, i.e., the law of the whole. Holonomy does not totally deny the relevance of analysis in the sense discussed above. Indeed, ‘the law of the whole’ will generally include the possibility of describing the ‘loosening’ of aspects from each other, so that they will be relatively autonomous in limited contexts (as well as the possibility of describing the interactions of these aspects in a system of heteronomy). However, any form of relative autonomy (and heteronomy) is ultimately limited by holonomy, so that in a broad enough context such forms are seen to be merely aspects, relevated in the holomovement, rather than disjoint and separately existent things in interaction.
Scientific investigations have generally tended to begin by relevating apparently autonomous aspects of the totality. The study of the laws of these aspects has generally been emphasized at first, but as a rule this kind of study has led gradually to an awareness that such aspects are related to others originally thought to have no significant bearing on the subject of primary interest.
From time to time, a wide range of aspects has been comprehended within a ‘new whole’. But of course the general tendency until now has been to fix on this ‘new whole’ as a finally valid general order that is henceforth to be adapted (in the manner discussed in section 1) to fit any further facts that may be observed or discovered.
It is implied here, however, that even such a ‘new whole’ will itself be revealed as an aspect in yet another new whole. Thus, holonomy is not to be regarded as a fixed and final goal of scientific research, but rather as a movement in which ‘new wholes’ are continually emerging. And of course this further implies that the total law of the undefinable and immeasurable holomovement could never be known or specified or put into words. Rather, such a law has necessarily to be regarded as implicit.
The general question of the assimilation of the overall fact in physics in such a notion of law will now be discussed.