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-&Vs&g+''\&"\ Relativistic Whiteheadian Quantum Field Theory:
Serial Order and Creative Advance
Henry P. Stapp
Lawrence Berkeley Laboratory
University of California
Berkeley California 94720
(August 2008)
Abstract. Alfred North Whitehead in his book Process and Reality describes the history of the universe in terms of a process of creative advance into novelty. This advance is produced by a collection of happenings called actual occasions, or actual entities. Each actual entity has an associated actual world, and it arises from its own peculiar actual world. (PR 284). Two occasions are termed contemporary if neither lies in the actual world of the other. A key issue is whether the words in Process and Reality commit Whitehead to the relativity-theory idea that, at least in our present epoch, the creative advance into novelty is not serially ordered, or whether, alternatively, the logical developments in Part IV entail, at a deep metaphysical level, that the facts specified by two contemporary occasions become fixed and settled in some definite order. Irresolution on this basic question renders Whiteheads theory obscure and plagued with controversy. I argue, in opposition to another paper in this issue, that Whitehead endorses the relativistic viewpoint, and consistently adheres to it. This makes Whiteheads theory compatible with relativistic quantum theory. Combining Whiteheads relativistic process theory with relativistic quantum field theory is therefore possible, and it holds the promise of producing a rationally coherent understanding far richer than what is provided by either theory alone of the relationships between the physically described aspects of the universe and human knowledge and intentions.
1. Introduction.
At the beginning of Section III of Chapter III of Part I of Process and Reality Whitehead asserts:
There is a prevalent misconception that becoming involves the notion of a unique
seriality for its advance into novelty. This is the classic notion of time, which philosophy took over from common sense. Mankind made an unfortunate generalization
from its experience of enduring objects. Recently physics has abandoned this notion. Accordingly we should now purge cosmology of a point of view which it ought never to have adopted as an ultimate metaphysical principle. In these lectures the term creative
advance is not to be construed in the sense of a uniquely serial advance. (PR 35)
This statement seems to be an unequivocal rejection by Whitehead of the idea that his creative advance into novelty is a uniquely serial advance. Nevertheless, the complexity of Whiteheads prose has led some students of Whiteheadian thought to maintain that Whiteheads theory of the extensive continuum, as elaborated in Part IV of PR, does in fact provide, at a deep metaphysical level, a fundamental serial-inclusive ordering of all occasions and their regions.
These quoted words come from a paper by Michael Epperson(EPP) entitled Logical Causal Order in Whiteheads Theory of Extension: Relating the fundamental mereological order and the relativistic spatiotemporal order in modern physics. That paper presents Eppersons view of a rather lengthy correspondence (ES) between us, in which I was arguing, specifically, that Whiteheads words in Process and Reality, including in particular the words in Part IV, do not entail or suggest that the mereological structure developed in Part IV provides for a unique serial ordering of the occasions in the creative advance into novelty. I argued that Part IV elaborates upon the relativistic approach adopted in the earlier parts, and does not entail or suggest a serial ordering of the actual occasions that conspire to produce Whiteheads creative advance into novelty.
The resolution of the conflict between the classical-intuitive and the relativistic conceptions of the advance into novelty is, in a very deep sense, the core subject matter of Process and Reality. That resolution depends essentially upon the nature of the emergence of actuality from potentiality, and upon the logical and causal features of the connection between the experiential and physical aspects of the creative advance into novelty, whose structure Whitehead is attempting to describe. That 1929 relativistic solution ties beautifully into the precepts of relativistic quantum theory developed in the middle of the twentieth century by S,Tomonaga (TOM)and J. Schwinger (SCH).
The book Process and Reality represents in a deep sense a 500 page description of one complex idea. As a matter of historical fact this description has elicited in the minds of its careful readers a diverse spectrum of interpretations. This diversity has impacted extremely adversely upon the reception of Whiteheads theory by the academic community. The differences between Epperson and myself is a particular manifestation of this general fact. However, I believe that our particular differences can be resolved by a careful attention to Whiteheads words in Part IV, and that this resolution, taken together with the basically similar resolution of essentially the same problem by relativistic quantum field theory provides the foundation of a rationally coherent interpretation of the whole of Process and Reality that is in good accord with modern physics, and hence can be combined with it to give a way of understanding nature and our place within it that is richer and more coherent than what is provided by either theory alone.
2. The Extensive Continuum and Serial Order.
Chapter II of Part II of PR is entitled The Extensive Continuum. In section II Whitehead says:
Curiously enough, even at this early stage of metaphysical discussion, the influence of the relativity theory of modern physics is important. According to the uniquely serial view of time, two contemporary actual entities define the same actual world. According to the modern view no two actual entities define the same actual world. I shall always adopt the relativity view (PR 65-6)
The issue in contention pertains to the relationship between the ideas presented in the earlier chapters, and the content of Part IV, which is also entitled The Extensive Continuum. I believe the latter to be an elaboration of the former that in no way overrides or contradicts the former, particularly on the issue of the non-serial character of the creative advance into novelty. I believe that Whitehead adheres throughout PR to the relativity theory viewpoint adopted by modern physics, and that the mereological serial order discussed in part IV pertains to something else, and in no way entails or suggests a unique absolute serial order of the occurrence of the occasions that mark the creative advance into novelty. This advance consists of the becoming, or the coming into actual beinginess, of the physical and experiential facts that define, at each stage of the advance, the aspects of the unfolding history of the world that have become fixed and settled.
The quote in Eppersons paper from Jorge Nobo makes clear the issue that I was raising. Nobo said I doubt you can find a passage in Whitehead in which he explicitly and unequivocally endorses the idea of an absolute order for the becoming and being of occasions . It is certainly true that Whitehead develops in Part IV certain notions involving serial ordering. But these serial orderings do not entail, or suggest, or support the notion of unique, or absolute, or objective, ordering for the becoming and being of the occasions. The seriality considered in Part IV pertains, rather, to the deduction of certain continuum-like properties of Whiteheads extensive continuum from certain logical premises and assumptions.
Prompted by figures drawn on a piece of paper we are able to conceive regions in a two-dimensional space exemplified by the interiors of such figures. (cf. PR 295-6). Nobody has ever directly experienced a drawing with lines of infinitely thin width. Nevertheless, it is a fact of human experience that many of us can imagine such lines, along with the other elements of Euclidian geometry. And we can imagine these just-mentioned two-dimensional extensions without their infinitely thin boundaries. We can also contemplate infinite nested sequences of such two-dimensional open regions, with each region of the sequence completely contained within its predecessor in the way suggested by Figure (i) of Diagram I on page 295 of PR. Points and lines are not contained in this complex of two-dimensional boundary-free regions. But they can be defined essentially in terms of limits of certain nested sequences of these two-dimensional open regions. We can then consider the boundaries of these regions, as collections of points
In our imagination we can conceive of generalization of such structures to spaces of dimension greater than two. Whitehead specifies (PR Definition 24, page 300)
When a complete locus consists of all points situated in a region, it is called the volume of that region; when a complete locus consists of all points in the surface of a region, the locus itself is called the surface of that region; when a complete locus consists of all the points incident in a segment between two end-points it is called a linear stretch between those end-points.
Thus Whiteheads extensive continuum is given a certain pre-geometric continuum-like structure, which can include dimensionality. Whiteheads says:
In the application of this theory of extention to the existing physical world of our epoch, volumes are four-dimensional and surfaces are three-dimensional. But linear stretches are one-dimensional (PR 301)
Whitehead asserts that Actual entities atomize the extensive continuum. This continuum is itself merely the potentiality of division: an actual entity effects this division. For each process of concrescence a regional standpoint has been adopted. In the mere extensive continuum there is no principle to determine what regional quanta shall be atomized, so as to form the basic phase in the concrescence [coming into being] of an actual entity. (PR 67: Square brackets enclose my insertion)
In order to understand our capacity to perceive the physical aspects of world about us in an orderly geometry-based way Whitehead is particularly concerned in Part IV to define straight lines and flat loci. To this end, he introduces:
Assumption 1. In the extensive continuum of the present epoch there is at least one ovate class& . (PR 305).
Definition 1. One such ovate class will be denoted by : all definitions will be made relatively to this selected ovate class. (PR 305)
The physical extensive continuum with which we are concerned in this cosmic epoch
is four dimensional. (PR 305)
The members of any ovate class have whole-part relationships that resemble, by definition, those of ovals in a positive-metric space. In particular, they have whole-part relationships analogous to those that follow from the fact that the boundary surfaces of ovals are everywhere non-concave. This leads to the possibility of defining, relative to that particular ovate class, flat loci and straight lines by the intersections of the surfaces of regions that are externally connected, in the sense illustrated by figures (v) and (vi) of Diagram I (PR 295). This passage from regions to points, lines, surfaces, and volumes rests on the seriality of the infinite nested sets of non-tangentially internally connected regions.
It will be noticed that each abstractive set is to be conceived with its members in serial order, determined by the relationship of inclusion. The region starts with a region of any finite size, and converges indefinitely towards smaller and smaller regions, without any limiting region. (PR 298)
It is this seriality that is the focus of Part IV, and that is used to construct the continuum properties of the extensive continuum. These continuum properties underlie in a deep sense, the description of the process of creative advance. But this seriality of the nested sets that is used to deduce the continuum properties of the extensive continuum does not entail a serial ordering of the becoming of the occasions in the creative advance into novelty. These two applications of the notion of seriality are, logically, profoundly different. One pertains to an infinite succession of ever smaller inclusively arranged regions that is used to construct the pre-geometric continuum aspects of the extensive continuum, while the other pertains to the ordering in which the experiential and physical facts specified by the occasions that are associated with non-overlapping finite regions, that are called their standpoints, become fixed and settled. No retreat from, or negation of, the commitment to relativity theory made so forcefully in Parts I and II is entailed or suggested by the seriality of nested sets considered in Part IV.
The difference between these two applications of the notion of seriality is connected to the difference between external and internal connection.
In part IV Chapter III Section IV Whitehead begins with the words
The importance of external connection requires further discussion. (PR 307)
He then emphasizes the importance of external connection to the defining of straight lines. This refers to his use of the convexity (non concavity) properties of externally connected ovals to define flat loci of various kinds.
He then notes that:
the concept of actual occasions, adopted in the philosophy of organism allows the following explanation of physical transmission.
Let two occasions be termed contiguous when their standpoints are externally connected. Then by reason of the absence of intermediate actual occasions, the objectification of the antecedent occasion in the later occasion is particularly complete. Thus the notion of continuous transmission in science must be replaced by the notion of immediate transmission through a route of successive quanta of extensiveness. These quanta of extensiveness are the basic regions of successive contiguous occasions. (PR 307)
This discussion of causal relationships between occasions and the placement of their standpoints in the extensive continuum refers to external connection, which is illustrated by figures (v) and (vi) of Diagrams I (PR 295). On the other hand, the unique serial properties that Whitehead refers to in Part IV pertained to non-tangential internal connections of the kind illustrated by figure (i) of Diagram I. It is those latter properties that were used by Whitehead to allow the concept of points and surfaces and volumes of the extensive continuum to be deduced from logical assumptions.
It will be recalled that Descartes created analytic geometry, with its idea of representing geometric structures by equations that impose restrictions upon the sets of points constituting a uniform background continuum. This mathematics became an essential tool for Newton, who in the Scholium in his Principia sets forth as the basic foundation of his work the ideas of a three-dimensional uniform continuum, space, and one-dimensional uniform continuum, time. But Whitehead wants to go deeper, and root these geometric ideas in logic. In the preface Whitehead mentions the foundational character of this work when he says, in reference to the geometric underpinnings of Descartes and Newtons work:
But in Part IV, this question is treated from the point of view of developing the detailed method in which the philosophy of organism establishes the theory of this problem. (PR xii)
In contrast to this project of providing a logical foundation for the continuum properties of the extensive continuum, the issue in contention here pertains to the order in which the various entire occasions become. The causal physical transmission from occasion to occasions pertains to the external connections of standpoints in the extensive continuum. The process of becoming thus depends in a certain basic way upon the underlying continuum structure of the extensive continuum, simply because the standpoints of the actual occasions are located in this continuum, and physical causation acts through them. But the serial ordering of the abstractive sets associated with non-tangential inclusion used to introduce the points of the extensive continuum does not logically entail or suggest the logically very different property of a uniquely serial order in which the experiential and physical facts created by occasions associated with finite non-overlapping regions of this continuum become fixed and settled. This point is the source of my difference with Epperson pertaining to Whiteheads stance on the issue of whether the order in which occasions come into being is uniquely serially ordered.
3. Durations and Unison of Becoming.
Quite apart from the questions stemming from Whiteheads use of a notion of serial order in Part IV there is another feature of Process and Reality that might seem to suggest his acceptance of the notion of an absolute order in which contemporary occasions occur. This is his use of the phrase unison in becoming in connection with the collection of occasions that constitute a duration:
The term duration will be used for a locus of unison of becoming . (PR 128)
According to Whitehead,
A duration is a locus of actual occasions, such that () any two members of the locus are contemporaries, and () that any actual occasion, not belonging to the duration is in the causal past or the causal future of some members of the duration.
A duration is a complete loci of actual occasions in unison of becoming or in concrescent unison. It is the old fashioned present state of the world. (PR 320)
By its definition, a duration which contains an occasion M must lie within the locus of contemporaries of M. According to the classical pre-relativistic notions of time there would be only one duration including M, and it would contain all Ms contemporaries. According to the modern relativistic view, we must admit that there are many durations including M---in fact an infinite number, so that no one of them contains all Ms contemporaries.
Thus the past of a duration D includes the whole past of any actual occasion belonging to D, such as M for example, and it also includes some of Ms contemporaries. Also future of duration D includes the whole future of M, and also includes some of Ms contemporaries. . The paradox that has been introduced by the modern theory of relativity is two-fold. First, the actual occasion M does not, as a general character of all occasions, define a unique duration; and secondly, such a unique duration, if defined, does not include all contemporaries of M. (PR 320)
These characteristics of durations make the association of duration with unison of becoming untenable, insofar as unison of becoming has the normal intuitive meaning of coming into actual being together with, as applied to a stage of the creative advance into novelty. This is because the conditions on durations allow an occasion A to lie in a duration that includes an occasion B that lies in a duration that includes an occasion C that lies in the future of A. But the normal notion of coming into actual being together with is transitive. Yet Whiteheads theory certainly does not allow one to say that an occasion C that lies in the future of A is in unison of becoming with A.
I believe that Whitehead means to resolve the paradox by rejecting the pre-relativity idea that everything in a duration that includes M comes into actual being together with M
4. Comparison of Relativistic Process Theory to Relativistic Quantum Field Theory.
Quantum mechanics rests upon a mathematical foundation provided by classical mechanics. The latter rests upon the idea of particles and fields. A particle is supposed to have, at each instant of time, a position and a velocity in three-dimensional space. A field is supposed to have, at each instant of time and each location in three-dimensional space, a value, specified by a real number. The field variables are connected to the particle variables in way that allows one to compute the forces upon---and hence acceleration of---each particle due to the presence and the motion of the other particles.
Newton conjectured the existence of repulsive forces that prevent particles from coming too close to each other. This condition combined with his other laws appears to entail causal closure of the physical: the description of the physical aspects of the state of the universe at one single time, or perhaps over some short interval of time, determines the physical aspects of the state of the universe for all times.
This closure feature allows the evolving state of the universe to be pictured as block physical universe; namely by a collection of infinitely thin wires running through the space-time, in the direction of increasing time, and in a way that is uniquely determined for all times by this physical structure at any single instant of time. (The fields should also be represented, but the pictorial image is slightly more complicated.) No representation of experience, or knowledge, or experienced intent need be added, That is why this imagined property is called causal closure of the physical.
The transition from classical mechanics to quantum mechanics brought human knowledge and experience into the theoretical framework. The reason, basically, is this: the way the mathematical/physical description enters into practical applications is closely analogous to the way that the mathematical/physical description enters into classical statistical mechanics; and classical statistical mechanics is, in regard to its practical applications, closely tied to human knowledge: A sudden change in our knowledge causes, in classical statistical mechanics, a sudden change in the mathematical/physical representation of our knowledge.
A key feature of quantum mechanics is the Heisenberg Uncertainty Principle. The effect of this principle is, essentially, to convert each wire of the block universe picture into a smear of possibilities. More precisely, for a many-particle universe, it is to replace the one single classical many-particle universe by the collection of all such (weighted) possibilities compatible with the present state of our knowledge. Because of the sensitive dependence of macroscopic degrees of freedom upon microscopic initial conditions, the diversity of this population of possibilities tends to increase with the passage of time. But from time to time we gain, via our (sense) experiences, new knowledge. Just as in the case of classical statistical mechanics, this new knowledge will usually exclude some of the possibilities that were mathematically generated by the equations of motion acting upon the mathematical representation of our prior knowledge. Thus the sudden gain in knowledge will be coordinated to a sudden collapse of the mathematical representation of our state of knowledge just before the gain in knowledge to the collapsed state just after this gain in knowledge. The physically described collapse is thus a logical consequence of our increased knowledge.
There is nothing mysterious about such collapses in classical statistical mechanics, and the collapses that occurs in quantum mechanics are, at the level of actual scientific practice, analogous to it: the mathematical representation of our knowledge changes abruptly when our knowledge changes abruptly.
But there is a conceptual problem: the different classically conceived possibilities interfere with each other in a way that they cannot do in classical statistical mechanics, but that would be understandable if the mathematical representation of our knowledge described an objectively real structure, instead of just an idea about a set of classically conceivable possibilities.
The resolution of this conceptual problem is to interpret the mathematically described state of the universe as a representation not of possibilities but rather of potentialities: i.e., as a representation of objective tendencies, created by past psychophysical events, for the occurrence of future psychophysical events. This interpretation is essentially implicit in orthodox quantum mechanics, and it is what Whitehead sought to express in a rationally coherent way. This understanding places our knowledge in a much more central, and indeed, in a much more dynamical, position than what it was in classical mechanics.
Of course, science has always been about our knowledge in a certain ultimate way. It is about what we can know, and how we can use what we know to affect what we will experience in the future. However, the effect of Newtons monumental work was to push questions about knowledge and our acquisition of knowledge, out of science. Yet the conversion of the physically represented information of classical physics to the causally efficacious knowledge of quantum physics constitutes a radical break with Newtons model of the relationship between mind and matter.
The main idea in quantum physics is that each acquisition of knowledge occurs discretely in conjunction with a collapses of the quantum state to a new form that incorporates the effect of adding the conditions logically imposed by the increase in knowledge. This tight logical linkage of an experientially recognized change in a state of knowledge to the corresponding mathematically represented change in the physical state of the universe is what Whitehead represents as a concrescence of an actual occasion. The new psychophysical state represents also a new set of potentialities for future concrescences.
In non-relativistic quantum mechanics the quantum state of the universe at time t is represented as an evolving density matrix (t). Each increment of knowledge occurs at some particular time t=tn . At that instant t=tn a sudden collapse to a new state (tn) occurs. This sudden change consists of sudden changes in potentialities---for future concrescences---that extend in principle over all of space at that instant of time. This idea of a sudden change occurring over the entire universe at an instant of time is not in line with ideas arising from the theory of relativity. And it is hard to reconcile with common sense.
This difficulty is resolved by the work of Tomonaga(TOM) and Schwinger(SCH).They show, within the framework of relativistic quantum field theory, that the density matrix (t) gets replaced by (), where designates a spacelike surface. Such a surface is obtained from a constant t surface by pushing the points forward or backward in a continuous way keeping every point space-like separated from every other one.
In this relativistic quantum field theory the sequence of constant time surfaces t=tn , with n the set of integers, gets replaced by the sequence of space-like surfaces n, where no point of n lies in the open backward light-cone of any point of n-1. This sequence of space-like surfaces define a corresponding sequence of regions Rn, where Rn is the region between n and its predecessor n-1.
These regions can atomize the space-time continuum: for any bounded region R of the space-time continuum we can assume that there is some n such that that the union of closures of the set of possible standpoints Rm with md"n cover R.
This sequence of possible standpoints Rn is ordered by the integer n that label the two surfaces n-1 and n between which it lies. This ordering of standpoints can be imagined to define the definite order in which the occasions corresponding to these standpoints come into being. However, many different orderings of the same set of surfaces n can define the same set of standpoints, differently ordered. Given some n and two space-like separated standpoints that lie adjacent to it, and in its future, the rules of relativistic quantum field theory are such that no prediction depends on which of the two collapses occurs first, or whether the two occur together as one single collapse. Thus even though one can elect to do the computations with some particular idea in mind of what is globally and absolutely fixed and settled at each stage n of the process of creative advance---namely the aspects determined by the occasions whose standpoints lie in the past of the surface n ---there seems to be no empirical, or even logical, basis for claiming that the order in which two occasions associated with space-like separated standpoints comes into being has any absolute or objective meaning. This practical irrelevance of the order of occurrence of contemporary happenings is the property whereby relativistic quantum field theory justifies its claim to be relativistic.
Although Whitehead does not spell out the mathematics of this field theoretic resolution of the problem of reconciling with relativity theory the quantum theoretic idea of the conversion, via collapses, of potentialities into actualities, he does take great pains to incorporate into his theory the relativity-theory-based avoidance of the idea of some essential absolute order for the becoming of the facts fixed and settled by the concrescences of space-like separated actual occasions. On the other hand, relativistic quantum field theory does allow us, for computational purposes, and for ease of human comprehension, to allow the process of the unfolding of actuality to be viewed as a serially ordered sequence of abrupt changes occurring along a serially ordered sequence of space-like surfaces n that advance into the future by the sequentially increasing union of the closures of the disjoint space-time regions that are the standpoints for an associated serially ordered sequence of actual occasions.
Whitehead s relativistic process theory seems therefore to be in satisfactory accord with relativistic quantum field theory. But his theory goes far beyond field theory in its effort to provide a rationally coherent understanding the interplay between the experientially described and the physically described aspects of the universe. The following section elaborates upon this point.
5. Relativistic Whiteheadian Quantum Field Theory.
Combining Whiteheads relativistic process theory with relativistic quantum field theory holds the promise of producing a rationally coherent understanding far richer than what is provided by either theory alone of the relationships between the physically described aspects of the universe and human knowledge and intentions. A key question is how the discrete regions that are the standpoints for the actual occasions are determined. In this connection, Whitehead says:
The question, as to how the extensive continuum is in fact atomized by the actual entities, is relevant to the determination of the loci [of entities in unison of becoming].
The factor of temporal endurance selected for any one actuality will depend upon its initial subjective aim. The categoreal conditions which govern the subjective aim are discussed later in Part III. They consist generally in satisfying some condition of a maximum, to be obtained by the transmission of inherited types of order. This is the foundation of the stationary conditions in terms of which the ultimate formulations of physical science can be mathematically expressed. (PR 128)
This description emphasizes the point that the choice of temporal endurance, which is the temporal span of the standpoint of the occasion, is controlled in part by a subjective aim to propagate a certain type of order. This conception ties perfectly into recent suggestions (STA) that the intent-controlled choices of the timings of von Neumanns Process 1 quantum probing actions allows human intent to influence human actions by holding in place locally, by means of the quantum Zeno effect, certain types of order.
As regards the spatial extension of the standpoint, this choice also should be driven by aims associated with the locally defined potentialities for a transmission of order. These considerations provide the basis for closing a huge causal gap in orthodox quantum theory, namely gap caused by the absence in orthodox quantum theory of any rules for fixing, even in a statistical sense, the choice of the logically essential Process 1 probing action. It is important in this connection that the Process 1 probing action leave the trace of unchanged. This implies that the mere choice of the Process 1 action in one region can have no effect on any quantum prediction pertaining to any observable appearances in any region space-like separated from the firs
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lmuv$a$gdb$a$gdF-zt region. no signal can be transmitted faster than light. The choice of the Process 1 probing action that must precede any knowledge increasing feedback from nature can therefore be regarded as a local process controlled by local realities. But natures feedback, which answers the Yes-No query posed by the associated Process 1 probing action, is, under certain conditions, necessarily connected to feedbacks in faraway regions in ways that demand faster-than-light transfers away from a region R of the information about which Process 1 action was chosen in region R. Thus whereas we localized combinations of occasions can be conceived to act
locally, the feedback process must be conceived to be in some way a global process, to which we can however contribute in causally efficacious ways by posing proper questions.
The field theoretic condition entail that the quantum mechanical state, which represents the potentialities, will propagate through the standpoint region in accordance with the field theoretic counterpart of the Schroedinger equation of simpler quantum theories. The Process 1 collapse and the further collapse directly associated with natures feedback to that query are both confined to the leading-in-time surface of that standpoint region Rn. But correlations created in the past can entail that the collapse associated with natures feedback will be accompanied by correlated changes in n. This latter change accounts for the faster-than-light effects mentioned earlier.
As just mentioned, the physical description, represented by the evolving quantum state of the universe, propagates through the stand point region Rn in accordance with the Schroedinger equation, and hence in a way that does not show the internal workings of the process of the concrescence of the actual equation associated with this standpoint. This agrees with Whiteheads insistence that this internal process not be mapped into space-time. One can introduce another time, called process time, to accommodate this internal process of becoming. It is this internal process that brings into the process of becoming the experiential aspects of reality.
These consequences of combining of Whiteheads theory with relativistic quantum field theory bring in only the grossest aspects of Whiteheads rich and complex writings. But having an overview securely tied to modern physics paves the way to a useful interpretation of the complex whole
References.
PR: Alfred North Whitehead, Process and Reality (1929) (Corrected Edition, 1978, Eds. D.R. Griffin and D.W. Sherburne, Free Press, New York)
EPP: Michael Epperson, Logical Causal Order in Whiteheads Theory of Extension: Relating the fundamental mereological order and the relativistic spatiotemporal order in modern physics. 8/13/08
ES: Michael Epperson and Henry Stapp, http://c-p-n-s.org/discussion Logical Causality in Quantum Mechanics
TOM: S. Tomonaga, On a relativistically invariant formulation of the quantum theory of wave fields, Progress in Theoretical Physics, Vol. 1, p. 27 (1946)
SCH: J. Schwinger, The theory of quantized fields I, Physical Review, Vol. 82, p. 914-927.
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hKIh"hF-zhb hkqH*hkqhG hGH*:STA: J. Schwartz, H. Stapp, and M. Beauregard, Quantum Theory in neuroscience and psychology: a neurophysical model of the mind/brain connection. Phil. Trans, Royal Society, B 360(1458) 1309-27 92005);
H. Stapp, www-physics.lbl.gov/~stapp/stappfiles.html
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