Ontological concepts for quantum theory
Implicate order and explicate order are ontological concepts for quantum theory coined by theoretical physicist David Bohm during the early 1980s. They are used to describe two different frameworks for understanding the same phenomenon or aspect of reality. In particular, the concepts were developed in order to explain the bizarre behaviors of subatomic particles which quantum physics describes and predicts with elegant precision but struggles to explain.
In Bohm's "Wholeness and the Implicate Order", he used these notions to describe how the appearance of such phenomena might appear differently, or might be characterized by, varying principal factors, depending on contexts such as scales. The implicate (also referred to as the "enfolded") order is seen as a deeper and more fundamental order of reality. In contrast, the explicate or "unfolded" order includes the abstractions that humans normally perceive. As he wrote:
In the enfolded [or implicate] order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the "explicate" or "unfolded" order, which is a special and distinguished form contained within the general totality of all the implicate orders ().
Overview.
The notion of implicate and explicate orders emphasizes the primacy of structure and process over individual objects. The latter are seen as mere approximations of an underlying process. In this approach, quantum particles and other objects are understood to have only a limited degree of stability and autonomy.
Bohm believed that the weirdness of the behavior of quantum particles is caused by unobserved forces, maintaining that space and time might actually be derived from an even deeper level of objective reality. In the words of F. David Peat, Bohm considered that what we take for reality are "surface phenomena, explicate forms that have temporarily unfolded out of an underlying implicate order." That is, the implicate order is the ground from which reality emerges.
The implicate order as an algebra.
Bohm, his co-worker Basil Hiley, and other physicists of Birkbeck College worked toward a model of quantum physics in which the implicate order is represented in the form of an appropriate algebra or other pregeometry. They considered spacetime itself as part of an explicate order that is connected to an implicate order that they called "pre-space." The spacetime manifold and the properties of locality and nonlocality all arise from an order in such pre-space. A. M. Frescura and Hiley suggested that an implicate order could be carried by an algebra, with the explicate order being contained in the various representations of this algebra.
In analogy to Alfred North Whitehead's notion of "actual occasion," Bohm considered the notion of "moment" – a moment being a not entirely localizable event, with events being allowed to overlap  and being connected in an overall implicate order:
 ;templatestyles src="Template:Blockquote/styles.css" / ;I propose that each moment of time is a projection from the total implicate order. The term "projection" is a particularly happy choice here, not only because its common meaning is suitable for what is needed, but also because its mathematical meaning as a projection operation, "P", is just what is required for working out these notions in terms of the quantum theory.
Bohm emphasized the primary role of the implicate order's structure:
 ;templatestyles src="Template:Blockquote/styles.css" / ;My attitude is that the mathematics of the quantum theory deals "primarily" with the structure of the implicate pre-space and with how an explicate order of space and time emerges from it, rather than with movements of physical entities, such as particles and fields. (This is a kind of extension of what is done in general relativity, which deals primarily with geometry and only secondarily with the entities that are described within this geometry.)
The explicate order and quantum entanglement.
Central to Bohm's schema are correlations between observables of entities which seem separated by great distances in the explicate order (such as a particular electron here on Earth and an alpha particle in one of the stars in the Abell 1835 galaxy, then a possible candidate for farthest galaxy from Earth known to humans), manifestations of the implicate order. Within quantum theory, there is entanglement of such objects.
This view of order necessarily departs from any notion which entails signalling, and therefore causality. The correlation of observables does not imply a causal influence, and in Bohm's schema, the latter represents 'relatively' independent events in spacetime; and therefore explicate order.
A common grounding for consciousness and matter.
The implicate order represents the proposal of a general metaphysical concept in terms of which it is claimed that matter and consciousness might both be understood, in the sense that it is proposed that both matter and consciousness: (i) enfold the structure of the whole within each region, and (ii) involve continuous processes of enfoldment and unfoldment. For example, in the case of matter, entities such as atoms may represent continuous enfoldment and unfoldment which manifests as a relatively stable and autonomous entity that can be observed to follow a relatively well-defined path in spacetime. In the case of consciousness, Bohm pointed toward evidence presented by Karl Pribram that memories may be enfolded within every region of the brain rather than being localized (for example, in particular regions of the brain, cells, or atoms).
Bohm went on to say: As in our discussion of matter in general, it is now necessary to go into the question of how in consciousness the explicate order is what is manifest ... the manifest content of consciousness is based essentially on memory, which is what allows such content to be held in a fairly constant form. Of course, to make possible such constancy it is also necessary that this content be organized, not only through relatively fixed association but also with the aid of the rules of logic, and of our basic categories of space, time, causality, universality, etc. ... there will be a strong background of recurrent, stable, and separable features, against which the transitory and changing aspects of the unbroken flow of experience will be seen as fleeting impressions that tend to be arranged and ordered mainly in terms of the vast totality of the relatively static and fragmented content of [memories].
Bohm also claimed that "as with consciousness, each moment has a certain explicate order, and in addition it enfolds all the others, though in its own way. So the relationship of each moment in the whole to all the others is implied by its total content: the way in which it 'holds' all the others enfolded within it." Bohm characterises consciousness as a process in which at each moment, content that was previously implicate is presently explicate, and content which was previously explicate has become implicate.
One may indeed say that our memory is a special case of the process described above, for all that is recorded is held enfolded within the brain cells and these are part of matter in general. The recurrence and stability of our own memory as a relatively independent sub-totality is thus brought about as part of the very same process that sustains the recurrence and stability in the manifest order of matter in general. It follows, then, that the explicate and manifest order of consciousness is not ultimately distinct from that of matter in general.
Analogies.
Ink droplet analogy.
Bohm also used the term "unfoldment" to characterise processes in which the explicate order becomes relevant (or "relevated"). Bohm likens unfoldment also to the decoding of a television signal to produce a sensible image on a screen. The signal, screen, and television electronics in this analogy represent the implicate order, while the image produced represents the explicate order. He also uses an example in which an ink droplet can be introduced into a highly viscous substance (such as glycerine), and the substance rotated very slowly, such that there is negligible diffusion of the substance. In this example, the droplet becomes a thread, which in turn eventually becomes invisible. However, by rotating the substance in the reverse direction, the droplet can essentially reform. When it is invisible, according to Bohm, the order of the ink droplet as a pattern can be said to be "implicate" within the substance.
In another analogy, Bohm asks us to consider a pattern produced by making small cuts in a folded piece of paper and then, literally, unfolding it. Widely separated elements of the pattern are, in actuality, produced by the same original cut in the folded piece of paper. Here, the cuts in the folded paper represent the implicate order, and the unfolded pattern represents the explicate order.
Holograms and implicate order.
Bohm employed the hologram as a means of characterising implicate order, noting that each region of a photographic plate in which a hologram is observable contains within it the whole three-dimensional image, which can be viewed from a range of perspectives. That is, each region contains a whole and undivided image. In Bohm's words:
 There is the germ of a new notion of order here. This order is not to be understood solely in terms of a regular arrangement of objects (e.g., in rows) or as a regular arrangement of events (e.g., in a series). Rather, a total order is contained, in some implicit sense, in each region of space and time. Now, the word 'implicit' is based on the verb 'to implicate'. This means 'to fold inward' ... so we may be led to explore the notion that in some sense each region contains a total structure 'enfolded' within it". 
Bohm noted that, although the hologram conveys undivided wholeness, it is nevertheless static.
In this view of order, laws represent invariant relationships between explicate entities and structures, and thus Bohm maintained that, in physics, the explicate order generally reveals itself within well-constructed experimental contexts as, for example, in the sensibly observable results of instruments. With respect to implicate order, however, Bohm asked us to consider the possibility instead "that physical law should refer primarily to an order of undivided wholeness of the content of description similar to that indicated by the hologram rather than to an order of analysis of such content into separate parts...".
Implicate order in art.
In the work "Science, Order, and Creativity" (Bohm and Peat, 1987), examples of implicate orders in science are laid out, as well as implicate orders which relate to painting, poetry and music.
Bohm and Peat emphasize the role of orders of varying complexity, which influence the perception of a work of art as a whole. They note that implicate orders are accessible to human experience. They refer, for instance, to earlier notes which reverberate when listening to music, or various resonances of words and images which are perceived when reading or hearing poetry.
Christopher Alexander discussed his work in person with Bohm, and pointed out connections among his work and Bohm's notion of an implicate order in "The Nature of Order".
Bohm features as a fictional character in the novel "The Wave" by British author Lochlan Bloom. The novel includes multiple narratives and explores many of the concepts of Bohm's work on implicate and explicate orders.
Challenges to some generally prevailing views.
In proposing this new notion of order, Bohm explicitly challenged a number of tenets that he believed are fundamental to much scientific work:
Bohm's proposals have at times been dismissed largely on the basis of such tenets.
His paradigm is generally opposed to reductionism, and some view it as a form of ontological holism. On this, Bohm noted of prevailing views among physicists that "the world is assumed to be constituted of a set of separately existent, indivisible, and unchangeable 'elementary particles', which are the fundamental 'building blocks' of the entire universe ... there seems to be an unshakable faith among physicists that either such particles, or some other kind yet to be discovered, will eventually make possible a complete and coherent explanation of everything" ().
In Bohm's conception of order, primacy is given to the undivided whole, and the implicate order inherent within the whole, rather than to parts of the whole, such as particles, quantum states, and continua. This whole encompasses all things, structures, abstractions, and processes, including processes that result in (relatively) stable structures as well as those