Quantum Quandries - Part 6
There seems
to be a very strong tendency in modern thought (a tendency which is rooted historically in
a variety of traditions in mathematics and science) to suppose that dimensionality
necessarily involves some sort of surface, or plane or space. Consequently,
almost unconsciously (although, perhaps, tacitly would be a better way of stating it),
even if the real and complex number systems are used to give representational expression
to the idea of a non-spatial dimension, the points of such number systems often are
intuitively construed in a spatial sense even while it is simultaneously maintained that
the 'space' being described is an abstract one.
One could
conjecture, perhaps, that one of the reasons why investigators traditionally have been
frustrated in their attempts to grasp the character and origins of time is precisely
because it does not appear to be readily reducible, if at all, to some combination of
surfaces, planes, spaces or number systems. Of course, surfaces, planes, spaces and number
systems are all used to represent the temporal dimension, and this has led to the
spatialization of time. However, the spatialization of time has, in turn, led to a variety
of distortions in our understanding of the character of time since we are inclined to
confuse our methodologies, mathematical or otherwise, with the temporal aspects of
ontology which the methodologies purport to describe, represent or model.
The real and
complex number systems, of course, do not necessarily entail, in and of themselves,
spatial dimensions. After all, both number systems permit a wide variety of operations,
transformations, mappings and so on, which need not involve curvature or a metric, or the
like. Nonetheless, questions arise, concerning the meaning or significance of the point
sets of the real and complex number systems when applied to the idea of, say, non-spatial
manifolds or dimensionality.
A common
assumption seems to be that irrespective of the structural character of a given manifold
or intersection of dimensions, the real and complex number systems are legitimate ways of
representing or interpreting such manifolds or dimensional systems. Yet, we lack real
insight into the structural character of the non-spatial dimensions alleged to lie hidden
beneath, or outside of, the so-called 4-space world in which we live day-to-day.
Therefore,
we have difficulty constructing a solid foundation on which to base a non-spatial
interpretation of, or assign a non-spatial significance to, the real or complex n-tuples
and the operations which are applied to these sorts of manifolds or systems of dimensions.
In addition, although mathematics may be able to offer tremendous precision and rigor when
dealing with the issue of non-spatial dimensionality, nevertheless, one is not always
clear about what it is that one is enjoying such rigor and precision.
The
traditional mathematical manner of talking about or describing dimensionality proves quite
elusive and unsatisfactory as far as enabling one to get a handle on what constitutes the
nature of dimensionality in and of itself. To say that a dimension can be represented by a
given axis in a coordinate system or that a dimension can be represented by one of the
components of a given n-tuple in an algebraic system, does not really say what a dimension
is, not even if the dimension being represented is a spatial one.
Such modes
of description or representation permit one, to some extent, to map out the constraints
and degrees of freedom of a dimension. Such modes of representation also permit one to
characterize a dimension in different ways.
However,
none of these modes of description or representation necessarily tells one what, say,
space is. They tend, instead, to be ways of: engaging dimensionality, sampling it,
operating on it, interacting with it, operationalizing it, and/or reflecting on its
various properties.
Nonetheless,
when one needs to establish a definition or characterization that captures the essence of
a given dimension, mathematics appears to be just as helpless as philosophy is in this
regard. Somehow, the essence of dimensionality always seems to slip through our conceptual
grasp.
In other
words, dimensionality seems to have a sort of interstitial status. As such, the ontology
of various kinds of dimensionality continues to fall into the holes surrounding and
permeating the conceptual edifices that have been built by human beings down through the
ages.
In view of
the interstitial character of dimensionality, there would seem to be considerable 'space',
if not need, for seeking new approaches to the problem of dimensionality. Ideally, these
new approaches would prove to be of much greater heuristic value, across a more diverse
set of topics, than is the case with prevailing perspectives concerning the issue of
dimensionality which have been heavily influenced and shaped by the spatialization of
dimensionality that is, and has been, quite pervasive in science, as well as mathematics.
The hermeneutics of dimensionality and hidden variable theories
The
hermeneutics of dimensionality may also play a central role in providing a way out of, or
around, some of the problems discussed earlier in relation to issues such as: von
Neumann's supposedly incontrovertible proof against hidden variable theories, Bohm's pilot
wave idea, Bell's interconnectedness theorem, and Einstein's restrictions on the rate at
which signals may be transmitted. More specifically, a promising avenue to pursue may
involve gaining a proper understanding of the process of dimensional dialectics,
especially in relation to the role of the temporal dimension with respect to such
dialectics.
Einstein's
special theory of relativity places a restriction on signaling with respect to physical
transmissions across spatial distances. However, his theory says nothing about the
possibility of transmitting signals or information by means of phase relationships.
The temporal
dimension appears to have 'contact', of some sort, with space everywhere, but there is no
evidence to indicate the temporal dimension is contained by, or in, space anywhere. In
other words, there is no evidence requiring one to suppose that time either occupies
space, or that time involves spatial distance.
The
Minkowski marriage of space and time into space-time is a mathematical convenience which
allows one to describe certain aspects of the way time and space dialectically interact.
Yet, this convenience says absolutely nothing about the ontology of time.
Let us
suppose, for the sake of argument, that Bohm's pilot wave were an expression of the
order-field. Let us further suppose that the pilot wave 'communicates' with, or signals
to, various particles by means of the phase relationships which are generated through the
dimensional dialectics set in motion by the order-field. Finally, let us suppose there is
no spatial distance involved in such signaling or communication. Given the foregoing
suppositions, transmission of information concerning the state of different particles at
different places in the universe could take place instantaneously without violating the
restrictions which had been introduced in Einstein's special theory of relativity.
In other
words, on a level of scale involving spatial relationships, the capacity of objects to
influence one another without any apparent mediation, and despite being separated by
spatial distances, may appear to be violating the locality assumption. Nevertheless, on
another level of scale involving phase relationships, there can be instantaneous
transmission of information concerning various kinds of influences since no spatial
distances are involved in the transmission.
Therefore,
the process of influence or interaction can be seen as a purely local phenomenon, but one
which involves other non-physical or non-material dimensions. One still could advocate a
locality position, but it would be quite different from the usual sense of locality which
is restricted to a spatial and material context.
Whether or
not a given signal or piece of information will be transmitted depends entirely on whether
or not, for whatever reason, there are barriers which seal off a given phase relationship
from, or makes it insensitive or resistant to, the presence of other phase relationships.
Thus, transmission is a matter of the receptivity, sensitivity or openness of one phase
relationship, or a set of such relationships, to other phase relationships. When that
receptivity or sensitivity is there, transmission is instantaneous.
The
foregoing discussion seems to leave open the possibility of, in principle at least, a mode
of time travel. For instance, by becoming sensitive to, or open to, the right aspect of
phase relationships, one apparently could gain access to other time frames.
There are
several reasons why the foregoing possibility is unlikely. First, and foremost, are the
problems of: (a) determining the precise character of the phase relationships being given
expression through a particular time-space-material-energy (to name just a few dimensional
components) dialectic for a specified event, state, condition or process; (b) determining
how one is to render oneself sensitive or open to such a set of phase relationships in
order to gain access to a given event, etc..
Quite
conceivably, there are intrinsic barriers capable of preventing one from realizing (b)
even if one could establish (a). Furthermore, figuring out the proper character of (a)
would seem to be fraught with methodological difficulties.
However,
having said the foregoing, quite possibly, the reason why some people have photographic
memories or eidetic imagery memories is because they are capable of tapping into certain
aspects of phase relationships. On the other hand, these sort of individuals cannot
recreate the whole complex set of phase relationships which would permit the individual
complete access to the original ontological dialectic. People with this kind of memory
have access to only a portion of the original set of phase relationships - namely, those
that permit the individual to recreate, in a limited sense, scenes in which one
participated.
There is
another application of the foregoing approach to the dialectic of dimensions which also
involves, albeit in a different way, issues of locality and action-at-a-distance. More
specifically, consider the saltation process of the action potential in myelinated
axon fibers. In the saltation process, the action potential leaps from
node of Ranvier to node of Ranvier, apparently without being mediated by any intervening
medium between one node and the next.
This
saltation phenomenon may be an example of how dimensions dialectically interact to produce
phenomena which cannot be explained in terms of, or reduced to, mediated interactions
within the confines of the conventional notion of 3-space, construed as spatial
dimensions. In other words, the phenomenon of saltation has characteristics which might be
explicable in terms of an interaction involving, besides the action potential, one or more
non-spatial and non-material dimensions linked to the spatial/material realm by means of
various phase relationships. Once the interaction takes place, some of the phase
relationships ensuing from that interaction may manifest themselves as a continuation of
the action potential being transmitted from the previous node via the unseen dimensional
dialectic.
Once again,
Rucker's drawings, together with his explanation, in his book The Fourth Dimension,
are suggestive here. More specifically, he has indicated that when a being or object of a
higher dimension intrudes into the world of a lower dimension, the higher dimension being
or object will manifest characteristics which seem extraordinary by the standards of the
lower dimensional world. For example, the higher dimensional being or object could seem to
dip into the lower dimensional world and, then, inexplicably (as far as the lower
dimensional beings are concerned) disappear, only to show up at some other portion of the
lower dimensional world.
Rucker's
account, when translated into the context of the notion of a dimensional dialectic, seems
quite compatible or consistent with many of the characteristics of the saltation mode of
transmission of the action potential in myelinated axons. In fact, there are some very
intriguing possibilities emerging out of this combination of ideas that may have a great
deal of heuristic value.
For example,
one possibility is that information concerning sensory and bodily processes could be
transmitted to other non-spatial or non-material dimensions. Similarly, the dimensional
dialectic could provide a means of accounting, at least in general terms, for how
non-spatial and non-material influences might be transmitted to brain functioning.
Moreover,
the possibility that the saltation process associated with the action potential involves a
dialectic of dimensions, not all of which are spatial or material in character, also
potentially provides another sort of explanation. For example, consider cases in which
various kinds of intellectual functioning are impaired or disappear when certain kinds of
damage is done to the brain through disease, lesions, or some other form of trauma.
Essentially,
one might contend the trauma to the brain interrupts the latter's dialectic with other
dimensions providing critical phase information for brain functioning. Such disruption
could occur by either shutting down the saltation process or interfering with processes
leading to, or subsequent to, the saltation process. In either case, the critical
dimensional dialectic never occurs or its information is not transmitted or the nature of
the transmission is distorted or garbled in some fashion.
Even if, at
some future time, someone discovers that the saltation process is rooted entirely in a
physical/material process which is not currently detectable, the general principle being
suggested in the foregoing should not be ruled out automatically. All that such a
discovery would have shown is that the saltation process is not the agency through which
inter-dimensional communications are transmitted.
Given the
present state of out understanding, however, the saltation process is very useful as an
illustration of how such non-material/non-spatial transmission might occur. Furthermore,
it might even turn out to be an actual exemplar of the principle which is being
illustrated.
Nothing
which is being proposed in this essay violates any of the laws of physics. What the
proposals do is induce one to re-think a variety of basic concepts which may be distorting
the character of our current approach to, and understanding of, the way things work in the
universe.
What is
being suggested in this essay is capable of offering solutions to a variety of problems
which have plagued physics for many years. Moreover, what is being proposed here leaves
the methods of calculating mathematical solutions completely intact.
The only
things which have to change are: (1) one's interpretation of the significance of the
aforementioned sorts of calculation, as well as: (2) the meaning of certain concepts
central to the methodological theory which stands behind such calculations. Without these
kinds of changes, one has difficulty understanding how quantum physicists intend to
resolve a variety of diseases that have infested the theoretical roots of the modern
quantum perspective.
These
diseases include: (a) the arbitrary and unfalsifiable character of the randomness
postulate; (b) the problem of self-energy; (c) the difficulties surrounding the treatment
of fundamental particles as being like mathematical points; (d) the rather ad hoc
character of the manner in which re-normalization theory attempts to rid theory of
infinities; (e) the tendency to project (implicitly if not, at times, quite explicitly)
the structural character of quantum methodology (especially in relation to its
mathematical techniques and processes) onto ontology, confusing the former for the latter
(e.g., Heisenberg's uncertainty principle); (f) the tendency to interpret dimensionality
in an almost exclusively spatial manner; and (g) the rather implausible (and Herbert
himself admits as much in his book) ideas that have worked their way into the
interpretation of quantum theory.
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