TOWARD A PREHENSIVE MODEL OF SPACE
20/05/2014 20:28
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TOWARD A PREHENSIVE MODEL OF SPACE
Paul A. LaViolette
February 15, 1976
© Paul LaViolette, 2013
This unpublished paper presents a glimpse at the early formulation of the
subquantum kinetics methodology three years after its inception and 11 years
prior to its first journal publication. It presents a philosophical rationale for the
theory in the context of process philosopher Alfred North Whitehead's criticisms
of contemporary physics. The subquantum kinetics approach, which was
developed without knowledge of Whitehead's work, is shown here to provide a
viable reformulation of microphysics that is consistent with Whitehead's concept
of prehensive space. LaViolette also discusses the ether concept and at this stage
in the development of his theory he makes the bolder assertion of referring to his
proposed subquantum media as composing ether states in an inherently
"alchemic" ether.
In his book Science and the Modern World, the American philosopher Alfred North
Whitehead criticizes the modern foundations of physics stating:(1)
"It is the defect of the eighteenth century scientific scheme that it provides none of the
elements which psychological experiences of mankind. Nor does it provide any,
elementary trace of the organic unity of a whole, from which the organic unities of
electrons, protons, molecules, and living bodies can emerge."
Whitehead finds that the trouble lies with the doctrine of materialism which is tacitly
assumed. He traces this world view back to the Hellenistic Age:(2)
"The answer, therefore, which the seventeenth century gave to the ancient question of the
Ionian thinkers, 'What is the world made of?' was that the world is a succession of
instantaneous configurations of matter - or of material, if you wish to include stuff more
subtle than ordinary matter, the ether for example."
He defines matter, or material, as anything which has the property of simple location. This
concept of simple location includes certain minor characteristics that space can be divided
without dividing time and that time can be divided without dividing space. But, Whitehead's
definition of simple location also refers to the popular concept, held to be characteristic of both
space and time, that in expressing spatio-temporal relations of a bit of material "it is adequate to
state that it is where it is, in a definite region of space, and throughout a definite finite duration of
time, apart from any essential reference of the relations of that bit of matter to other regions of
space and to other durations of time."(3)
Whitehead notes that this view of concrete reality met with success, in the seventeenth
century when scientific interest was mainly concerned with mechanical phenomena. Forces such
as gravitation were supposed to be determined by the particular configurations of bodies, such as
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their mass:(4)
"Thus the configurations determined their own changes, so that the circle of scientific
thought was completely closed. This is the famous mechanistic theory of nature, which
has reigned supreme ever since the seventeenth century. It is the orthodox creed of
physical science. Furthermore, the creed justified itself by the pragmatic test. It worked."
This doctrine of simple location which was at the foundation of the seventeenth century
scheme of nature also formed that basis for the ether theory accepted up through the 19th
century. Space was assumed to be filled with a substance known as the "ether" and objects such
as physical bodies were assumed to be simply located in this substance much like stones in a sea
of water. Different portions of the ether would not have any affect on these simply located
bodies. A body located in this ether, it was supposed, would not be affected by the ether
substance itself but would require the impingement of light waves, gravitational waves, etc.
transmitted through the ether. Hence, the ether (or space) played the passive role of carrier of
matter and energy.
This view has been retained even in modern theories, since modern field theories are
essentially remnants of the 19n century ether theories. The field theory developed by Maxwell
achieved surprising success by conceptually unifying with a general set of equations, diverse
branches of physics such as optics and electromagnetics. However, this theory was originally
based on the ether model. Fields were conceived as mathematical representations of real waves in
a mechanical ether. However, with the critical experiments of Michaelson and Morely, which
demonstrated the speed of light to be constant regardless of the frame of reference, the ether
theory was abandoned. Although the notion of the ether as a concrete substance was disclaimed,
still its mathematical field representation was retained. Modern physics merely rejected the
conceptual model of "ether" while mathematically retaining most of its underlying assumptions.
Hence, the doctrine of simple location, which was tacitly assumed in the ether theory, was
carried over to modern field theory. Mathematically, this assumption appears as the assumption
of linearity. The fact that an electromagnetic wave is represented mathematically by a linear
equation indicates the acceptance of the assumption of simple location. According to such a
representation, the field intensities of an electromagnetic wave establish themselves in successive
regions of space much in the same way that a moving object would occupy successive spatial
locations. This view suggests that space is inherently passive, or inert, fields becoming
impressed on space much the same way that magnetic impulses are impressed on the magnetic
tape of a recorder. The linear assumption allows two or more wave equations to be
superimposed on one another such that their respective values at each spatial coordinate are
simply additive. Hence, each equation behaves independently. According to this assumption, if
two light waves were to cross paths, i.e., occupy the same region of space during the same period
of time, they would not interact with each other, as in the case of two waves crossing paths on
the surface of a pool of water. Whether or not this is a legitimate claim cannot be easily
ascertained. The mass of a single photon of the kind easily produced in the laboratory is not
very great, while its speed of travel is significantly high. By contrast, starlight can be observed to
bend when passing near a massive body such as the Sun. But even under such circumstances, the
deflection is minor and requires several million miles of travel to be adequately observed.
It is understandable why physical science has retained this assumption; linear equations have
been successful in representing a substantial range of phenomena, and more importantly, they are
relatively easy to solve mathematically. The significance of this last point cannot be overly
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stressed. Mathematical physics has unconsciously oriented its concepts of reality and its choice
of areas for investigation to conform with its ability to achieve mathematical workability.
Moreover, since field theory deals with phenomena which are observationally far removed from
the human level, we can never hope to directly measure the behavior of fields like we can
chemical compounds. We can only hope to draw inferences from indirect observations.
The physical sciences (especially field theory) seem to be alone among the sciences where use
of the linearity assumption (simple location) leads to acceptable approximations of the observed
phenomena, where the use of a mechanistic model appears to be a somewhat successful choice.
In all other sciences (i.e. biology, psychology, sociology, etc.) it was discovered quite readily that
the linearity assumption was inadequate. In the field of economics, this is only now being
recognized. In all these fields of study, the mechanistic model failed and was replaced by the
concept of organism. Most phenomena in these natural sciences are more appropriately
described by nonlinear equations. The elements of natural systems are generally not independent
in their behavior, but interactive.
There are, however, several physical phenomena which are more appropriately described by
nonlinear mathematics. Most of these phenomena deal with nonequilibrium systems, i.e. flow
phenomena (physical translocation) such as convection, tornadoes, weather patterns, or
transmutational phenomena (physical transformation) such as biochemical or nuclear reactions.
One example in the field of chemistry is the Belousov-Zhabotinskii reaction system, which may
be classified as essentially a transmutational phenomenon.
For brevity this model will not be discussed here due to its complex nature. Instead a simpler
reaction scheme will be substituted, one known as the Tri-molecular model, or Brusselator; see
below.
A → X (a)
2X + Y → 3X (b)
B + X → Y + D (c)
X → E (d)
This chemical reaction model, which was first introduced by R. Lefever and further studied
by P. Glansdorff and I. Prigogine,(5) is not observed to occur in nature, however it serves to
illustrate some important aspects of nonlinear systems. Kinetic equations (a) - (d) depict a series
of chemical transformations which proceed irreversibly in the direction indicated by the arrows.
As long as input chemicals A and B are supplied, the system will remain in a nonequilibrium
condition with the overall reactions proceeding as A X E and B D. Chemicals D and E are
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constantly being removed from the system (i.e. their concentrations arc maintained vanishingly
small). Therefore, if chemicals A and B were no longer supplied to the system, eventually all the
chemicals of the system would become transformed and nothing would remain. Such a system,
an "open system" is inherently dynamic, its existence being dependent upon the maintenance of
the dynamic state.
One important feature of this reaction scheme is that it has a nonlinear reaction, equation (b).
This equation is nonlinear because its product X has the tendency to grow in abundance
exponentially with time. This happens because equation (b) is self-catalyzing with respect to X,
that is, as more X is produced as a product (right side) more X becomes available as a reactant
(left side) to convert Y to X. However, the quantity of X is not able to grow indefinitely. It is
kept in balance by equation (c) which converts X back into Y. These two equations taken
together constitute a self-closing reaction loop. That is, they are coupled by elements X and Y
which are common to both equations. Coupling marks a second important feature of our reaction
scheme because, in general, nonlinear coupled reactions have the ability to oscillate. That is, the
rate of production of the respective species X and Y may not be constant, but may vary with
time such that first X grows in predominance at the expense of Y followed by a period when Y
grows at the expense of X. The nature of this exchange between X and Y is illustrated clearly by
the principle of yin and yang, wherein the total amount of activity remains constant while
alternating between two poles. In scientific terminology this is known as a "limit cycle"; see the
diagram below.(6)
Thus, the phenomenon of periodicity, Whitehead's principle of reiteration or endurance,
arises naturally in dynamic systems (such as chemical reaction systems) provided that such
systems have processes that are coupled (i.e. that take account of one another, in Bacon's
terminology) and provided that at least one of these processes is nonlinear, has growth
characteristics.
Having briefly reviewed some of the dynamic characteristics of the Trimolecular model, let us
now study its behavior distributed in space: Imagine a volume filled with a reacting medium of
this sort. The concentrations of chemicals A, B, D, and E would be expected to be
homogeneously distributed in space and constant over time since the reaction kinetics dictate
time invariance for these quantities. However, with respect to variables X and Y, three
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conditions may prevail:
1) the concentrations of X and Y may remain uniform throughout the volume, unchanging with
time (i.e., remain in a steady state condition). Such behavior usually occurs when the rate of
transmutation is relatively low (near equilibrium);
2) the concentrations of X and Y may become inhomogeneously distributed in space while
remaining invariant with respect to time; or
3) the concentrations of X and Y may vary both spatially and temporally, hence this behavior
would give the appearance of propagating waves, with X and Y mutually oscillating with
respect to one another.
These last two possible modes of behavior of dynamic systems, known respectively as space
ordering and space-time ordering, usually occur when the rate of transmutation in the system
exceeds a certain critical threshold (i.e. when the reaction system is operating far from
equilibrium).
It is interesting to note that the periodic wave of condition (3) may be modeled by the same
type of linear wave equation used to describe the propagation of an electromagnetic wave, for the
special case in which the chemical wave travels in a one-dimensional medium such as along the
length of a capillary tube. Such an equation might successfully model the overall sinusoidal
character of the X, Y concentrations as they appear at successive positions in the tube, however,
they tell nothing about the underlying dynamic processes which, in the space-time ordered state,
produce the observed traveling wave pattern. Thus, the linear wave equation provides only a
superficial description of the chemical wave phenomenon.
As in the case of observing electromagnetic wave phenomena, imagine that all we are capable
of detecting is the superficial character of the chemical wave itself. Under these conditions, it is
quite likely that we would model it with a linear equation, and possibly even make the mistake of
assuming that its existence was independent of any underlying continuum. Since the substance
through which the chemical wave was traveling would remain invisible to detection, we might go
so far as to suppose it inert, simply a mechanical carrier or a volume possessing certain
mathematical properties. However, the truth is that we do know the nature of this underlying
substance (as postulated in the original definition of our model) and we know that the proposed
linear wave equation would only be an approximation. A more accurate representation would
depict a series of reaction equations, one of which would be nonlinear.
In studying the relationship between different regions of the proposed reaction volume, it
would be discovered that regions separated in space are not isolated from one another, but are
interwoven into an organic whole. That is, the chemical concentrations observed within a given
volume of medium, dV, will depend both on the production within that volume due to internal
reactions, and on the net transport of chemical molecules to or from that volume due to diffusion.
Since any change in concentration (say in X or Y) communicated to dV from its environment will
interact nonlinearly with the chemical medium within dV and since the resulting concentration
will no longer be simply the sum of the impinging external contributions, adjacent volumes of
medium must be considered as an inseparable whole. Since what is true of volume dV is true of
all volumes of the medium, we may say that the entire volume must be treated in organic unity.
This is essentially what Whitehead has in mind when he speaks of "prehensive unification" of
things being "together in space, and together in time even if they be not contemporaneous." The
diffusion of chemicals from one region of space to another region of space and their interaction
with chemicals present in that region would constitute a prehensive event.
This prehension is seen to be the basis for the propagation chemical waves through the
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reaction medium. For example, consider a region dV whose concentrations of X and Y are in
mutual oscillation over time at a fixed frequency, see limit cycle diagram. Due to the mutual
interconnection between this region and surrounding regions, as a result of diffusion, the X,Y
oscillation in adjacent regions will be synchronized but slightly out of phase with the oscillation
in region dV.
The overall effect will be to give the appearance of a wave being propagated through the
medium at a fixed velocity, its propagation velocity and wavelength being related to this diffusion
dependent phase difference and to the oscillation frequency. Thus, a wave is, in effect, a phase
pattern fleeting through a medium of underlying dynamic activity. At any given instant this
pattern will incorporate an internal reality and an external reality. Such a model seems to fit the
description of Whitehead:(7)
"Accordingly, a non-materialistic philosophy of nature will identify a primary organism as
being the emergence of some particular pattern as grasped in other events, whereby those
other events receive a modification, or partial determination. There is thus an intrinsic and an
extrinsic reality of an event, namely, the event as in its own prehension, and the event as in
the prehension of other events. The concept of an organism includes, therefore, the concept
of the interaction of organisms."
In the remainder of this paper I would like, to propose the idea that the above nonlinear
reaction model, or something similar to it, be proposed as a new concept of space. Such a model
would embody the essential features that Whitehead stressed. One might envision the following
reaction scheme, where A, B, G, X, Y, D, and Ω represent different media filling space:
A → G (a)
G → X (b)
(--) 2X + Y → 3X (c)
B + X → Y + D (d)
X → Ω . (e)
Media A, B, D, and Ω would remain homogeneously distributed in space and in time, hence
they would be physically undetectable, while media G, X, and Y would be free to acquire spacetime
dependence. A gradient in the G medium would indicate a gravitational field while a gradient
in the X and Y media would indicate the presence of an electrostatic field (magnetic field affects
arise from the X,Y media gradients when observed from a different frame of reference). These
various media might be thought of as different states of an all embracing ether whose inherent
nature is not passive, but dynamically active, being in a continual state of transformation. The
physical universe would be a manifestation of oscillations in the X, Y, and G variables while the
global reactions A → G → X → Ω and B → D could be conceived as being a portion of a hyper7
dimensional "primal flow" or prana. Time becomes viewed now as this 4th spatial dimension of
the ether which is inherently dynamic. Our perception of time, or of change, arises because our
physical universe has evolved from a stationary point in this primal flow (the X, Y cycle).
This view of the underlying character of the universe would conform with Shelly's conception
of nature. According to Whitehead:(8)
"Shelly thinks of nature as changing, dissolving, transforming as it were at a fairy's touch.
The leaves fly before the West Wind 'Like ghosts from an enchanter fleeing.' In his poem
The Cloud it is the transformations of water which excite his imagination. The subject of
the poem is the endless, eternal, elusive change of things: 'I change, but I cannot die.'"
Whitehead also emphasizes the importance of endurance and eternality:(9)
"Every scheme for the analysis of nature has to face these two facts, change and
endurance. There is yet a third fact to be placed by it, eternality, I will call it. The
mountain endures. But when after ages it has become worn away, it has gone. If a replica
arises, it is yet a new mountain. A color is eternal. It haunts time like a spirit."
One might say that the respective ether states, or media, are eternal in their nature, that in the
presence of this ethereal transformation, these unique states persist. Also, the pathways of
transmutation and the self-closing X,Y cycle could be said to be eternal.
What was described earlier with regards to the Trimolecular model could be applied to this
spatial ether, which may be referred to as the alchemic ether to distinguish it from the
conventional materialistic concepts of ether prevalent in the 18th and 19th centuries. Light
waves according to this theory would not be impressed upon space like waves on the surface of
water, but would emerge in space as temporal modulations, or limit cycles in the ever present
transmutation (i.e., X → Y, Y → X) going on in all regions of space.
We arrive, therefore, at a new concept of space, of space being active and organic. This view
abandons the traditional notion of simple location, for as Whitehead says:(10)
"In a certain sense, everything is everywhere at all times. For every location involves an
aspect of itself in every other location. Thus every spatio-temporal standpoint mirrors
the world."
In summary, we see that the reaction-diffusion ether concept proposed here offers a viable model
for realizing Whitehead's prehensive, organic view of space.
References
1) Whitehead, A. N. Science and the Modern World, New York, Macmillan, 1925, p. 73.
https://evankozierachi.com/uploads/Whitehead_-_Science_and_the_Modern_World.pdf
2) Ibid., p. 50.
3) Ibid., p. 58.
4) Ibid., p. 50.
5) Glansdorff, P., and Prigogine, I. Thermodynamic Theory of Structure, Stability, and Fluctuations,
New York: Wiley, 1971.
6) Ibid., p. 241.
7) Whitehead., p. 103.
8) Ibid., p. 86.
9) Ibid., pp. 86-87.
10) Ibid., p. 91.
