Editing Implicate and explicate order (section)

=== The implicate order as an algebra ===
Bohm, his colleague [[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 (physics)|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 [[Principle of locality|locality]] and [[Nonlocal Aharonov–Bohm effect|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 [[Algebra representation|representations]] of this algebra.<ref>F. A. M. Frescura, B. J. Hiley: [http://www.bbk.ac.uk/tpru/BasilHiley/P12FrescandHiley3.pdf Algebras, quantum theory and pre-space], pp.&nbsp;3–4 (published in Revista Brasileira de Fisica, Volume Especial, Julho 1984, Os 70 anos de Mario Schonberg, pp. 49–86)</ref><ref>See also: [[Basil Hiley#Implicate orders, pre-space and algebraic structures|Work by Bohm and Hiley on implicate orders, pre-space and algebraic structures]]</ref>

In analogy to [[Alfred North Whitehead]]'s notion of  "actual occasion,"<ref>A. N. Whitehead, ''Process and Reality'', Corrected Edition, ed. D. Griffin and D. Sherburne (New York: Macmillan, 1978), pp. 18 ff.</ref> Bohm considered the notion of ''moment'' – a moment being a not entirely localizable event, with events being allowed to overlap&nbsp;<ref>David Bohm: ''Time, the implicate order, and pre-space,'' In: David R. Griffin: ''Physics and the Ultimate Significance of Time'', State University of New York Press, 1986, {{ISBN|0-88706-113-3}}, pp.&nbsp;177–208, [https://books.google.com/books?id=hXWKzPFgv_wC&pg=PA183 p. 183]</ref> and being connected in an overall implicate order:<ref>David Bohm: ''Time, the implicate order, and pre-space'', In: David R. Griffin: ''Physics and the Ultimate Significance of Time'', State University of New York Press, 1986, {{ISBN|0-88706-113-3}}, pp.&nbsp;177–208, [https://books.google.com/books?id=hXWKzPFgv_wC&pg=PA189 p. 189]</ref>

{{Blockquote| 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:<ref>David Bohm: ''Time, the implicate order, and pre-space'', In: David R. Griffin: ''Physics and the Ultimate Significance of Time'', State University of New York Press, 1986, {{ISBN|0-88706-113-3}}, pp.&nbsp;177–208, [https://books.google.com/books?id=hXWKzPFgv_wC&pg=PA192 pp. 192–193]</ref>

{{Blockquote| 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.) }}