The issue here is whether Whitehead’s theory of nature, particularly as described in Process and Reality (PR), entails the existence of a universal/absolute/objective linear ordering in which all occasions (or at least their initiation and termination “dates”) can be placed. Nobo’s theory contains such an ordering (supersessional time), and one question is whether the existence of such an ordering is entailed by Whitehead’s actual words.

This issue has been the subject of a discussion involving Mike Epperson, Jorge Nobo, and myself. These exchanges have served to define the issues, and our respective understanding of W’s scheme. Mike’s position has been that W’s full scheme does entail an absolute serial order. My position is that W’s words do not entail such an absolute serial order of the coming into being of the occasions (or of their initiation and termination “dates”), and implicity that Nobo’s supersessional ordering involves adding essential content to what W said (at least in PR). Whitehead’s words permit, I believe, a “relativistic” notion of coming into beingness in which the ordering of the parts of occasions whose standpoints are wholly spacelike is not ontologically or metaphysically or logically significant.

This present message takes of from the communication of Nobe to Epperson of July 31 (2008), in which Nobe says to Mike: “After skimming your exchanges with Henry, I am beginning to think that Henry is right and Whitehead cannot provide for an absolute order of occasions. This makes my differences with Whitehead all the more important.”

To simplify the discussion, I am considering a special case of our own epoch in which each actual occasion has a “standpoint” in a 4-d spacetime continuum.

Whitehead (W) describes the process of creative advance in terms of the coming into being of actual occasions, each of which has its own actual word (its causal past). The full set of eventually completed actual occasions are classified, relative to an occasion X, as belonging to X’s causal past, its causal future, or its causal elsewhere, the later set of occasions being its “contemporaries”.

It is tempting at this point to identify an occasion’s past, future, and contemporary occasions by means of the relative locations of their standpoints (or some particular “physical point of causation” within each standpoint) with respect to lightcone conditions. I do not think what Whitehead’s word definitely preclude this possibility. The way he says things seem to me to be constructed so as to not rule out this possibility. If this possibility is not definitely ruled out by W’s actual words, then if one is proposing a conception that differs from this simple “relativistic” construal, one must say how it differs from this relativistic construal. Doing so will add to what is implied by W’s own words themselves.

W says (PR 21) “The many become one and are increased by one”. The context in which these words appear seem clearly to be talking about the coming into being of an occasion, in relationship to the many occasions in its own causal past. This is compatible with a “relativistic” construal in which there is no absolute serial ordering of the ‘dates” of contemporary occasions with standpoints that are completely spacelike separated. The assertion (PR 35) “In these lectures the term ‘creative advance’ is not to be construed in the sense of a uniquely serial advance.” reinforces to idea that W intended to accommodate the “relativistic” possibility that the order of coming into being of occasions whose standpoints are completely space-like-separated is not specified. This intent seems so clear and unequivocal at this point (PR 35) that one is justified, in cases where possible ambiguities may exist, in interpreting all other statements to be compatible with it. Later (PR 65) W says: “Curiously enough, even at the early stage of metaphysical discussion the influence of the ‘relativity theory’ of modern physics is important. According to the classical ‘uniquely serial’ view of time ” W is here reinforcing the idea that he intends to accommodate a lack of any absolute serial order for the coming into being of contemporaries.

The faster-than-light aspects of nature entailed by quantum theory came to be widely appreciated only in the 1960’s, long after PR was written. Nobo is attempting to accommodate this new development, which contravenes certain ideas of relativity theory. To do so, Nobo (or anyone else who wants to accommodate violations of normal relativity) must add ideas that go beyond Whitehead’s apparent intentions to accommodate “relativity”, in the sense not ascribing to contemporaries any absolute serial order of coming into being.

The way that “relativity”and faster-than-light (FTL) transfer of information are consistently accommodated in Relativistic Quantum Field Theory (RQFT) instructive.

The quantum state of the universe—which one can conceptualize as a collection of (very large dimensional square) matrices, one for each tiny cell in a cellularization of the 3-d spatial continuum, can be thought of as one giant matrix of an infinite number of dimentions. It evolves via a repetitive sequence of a sequence of three different processes.

Process One divides the cellularized 3-d space into a set of non overlapping regions, each containing a set of cells. The collection of matrices associated with the cells in each region can be represented as a giant matrix. A local process associated with each region “poses a Yes/No question”. This action is represented by an operation that reorganizes this matrix and divides the rows (and, correspondingly, the columns) into two disjoint part, labeled “Yes” and “No” respectively. It is important that this Process One leaves unchanged the “Traces” of all matrices, where a Trace of a matrix M is the sum of the “diagonal” elements of M. Process Two can be visualized as a local deterministic process that advances a spacelike surface “Now” , divided unto regions by Process One, a short distance into the future, but keeping all boundaries of regions fixed (in space-time). Process Three then collapses the state associated with the new temporally advances spacelike surface by choosing for each region either the Yes/Yes or the No/No part of the associated matrix. This Process Three is supposed to conform “statistically” to rules specified by quantum theory. This is what gives QM its predictive power.

Because of the Trace condition mentioned above no prediction in one region can depend directly on which questions were asked in space-like-separated regions: there is no possibility of sending a message chosen by an agent in one region to a witness in a space-like-separated region. This is in accord with the classical idea of “relativity”.

However, the way in which Process Three choices of outcomes made in two space-like-separated regions are correlated entail that the Process Three must in some cases be able to access the information inputted in spacelike separated regions. The Process Three acts like a global witness/agent in which witnesses and acts over the space-like “Now” described earlier. Process one acts like a set of independent question posers, but Process Three BEHAVES like a global answerer. The Process Three response, as represented by the behavior of quantum state of the universe, is the collapse behavior appropriate for a representation of the collective state of knowledge of all the local probers. Heisenberg calls it “our knowledge”.

“The many become one, and are increased by one” acquires new meaning with respect to the global process. At each stage there is “One” new global state at a new global space-like surface “Now”, which is then decomposed into many specific possibilities by the actions of the many local question-posers, who act independently on the basis of local conditions. These “Many” are then converted by The Process into a new “One”.

This way of combining QM with W is a variation of the one given in Chapter 13 of Mindful Universe. There each step was connected to a local advance of the surface “Now”: here each such advance is global, but with local inputs from local IGUSes.

(cf. Gell-Mann)