IntroductionIssues of duality, non-duality and multiplicity are central to any serious
discussion of the relationship between science and religion. Non-western
thinkers have long been aware of the dual nature of consciousness, i.e.
consciousness with respect to objects and objectless consciousness.
Objectless consciousness eludes talk for the simple reason that objectless
consciousness is 'languageless' consciousness. One 'does' or experiences
objectless consciousness. One does not (cannot) talk about it. Language is
constructed on the framework of duality (logic). It lives and breathes
multiplicity. Without multiplicity there is no language and there are no
concepts. Western thinkers have produced thousands upon thousands of
volumes talking about the former (consciousness with respect to objects)
while being unable to say much about the latter (objectless consciousness).
In this article, I will outline a topology based approach to address the
relationship of non-duality to multiplicity and objectless consciousness to
language based and concept based consciousness. Additionally, one real world
example will be presented to illustrate how a similar approach might be
useful in particle physics.
Consciousness
The first question to ask is "What does consciousness do to get from one
state to the other?" Using simple mathematics as a metaphor, "What type of
a surface (topology) would permit the smooth transition between multiplicity
and non multiplicity?"
There exists just one non-multiplicity in the number line, namely the number
'one.' 1.0001 is a multiplicity as is .9999. We can extend these decimals
indefinitely, so as far as the number line is concerned, as such these
multiplicities are "infinitely distant" from the non-multiplicity. Since
zero does not count due to its signifying non-existence as opposed to
non-multiplicity, the closest mathematical distance from multiplicity to
non-multiplicity is the immediate integral step from one to two. Two is
multiplicity one is not.
If one wants to create a multiplicity from non-multiplicity, it is not
enough to say that you begin with "one" and add another "one." If there is
only "one," where did the other "one" come from? Adding one and one is
clearly question begging.
As a metaphor then consciousness must go smoothly and unnoticeably from one
to two. Notice that here it is not being claimed that consciousness of any
variety can be mathematically defined. However the number line and some
simple topology are good mathematical metaphors for consciousness' smooth
journey from multiplicity to non- multiplicity and back again. How can we
exploit this concept?
Duality and Non-duality in Particle Physics
In particle physics there is a close relationship between particles and
anti-particles, namely, particles have all of their charges opposite, except
mass which is identical. Even when discrete symmetries are broken, this
correspondence comes from the PCT theorem. [1] Dirac suggested that the
positron is really a hole in an infinite negative energy sea.[2] Feynman
carried it one step further by interpreting anti-particles as particles
moving backward in time.[3] Here, yet another connection is made which
additionally goes to suggest a possible explanation for the cosmological
missing mass. That connection being that particle and anti-particle share a
Mobius topology and, therefore, an identity in a dimension one above our
phenomenological four dimensions, (x,y,z,t). This explains the differing
analyses of Dirac and Feynman, as well as predicts a warp phenomenon,
measurable in the laboratory.
The Mobius strip, is the simplest non-orientable surface. Specifically, it
is proposed to model a space-time warp by a Mobius string-like strip
topology that is twisted in a dimension higher than four.
The definition of a generalized Mobius strip is a geometric form of
unspecified length, a smaller unspecified width, and an unspecified metric,
having a differential thickness and the following topology:
The extreme ends are raised into a higher dimension (outside its
differential thickness), and twisted in the higher dimension so as to be
joined with a 180 degree relative rotation.
This connects one side with the other such that a path taken along the
length wherever initiated must connect to both sides and eventually (after
4() the starting point. In 4 dimensions the strip seems to have 2 sides.
In 5 dimensions the sides of the strip are identical (i.e. they share the
same topology). What is proposed to be analogous is the existence of events
which appear to influence one another instantaneously in a four dimensional
space where cause and effect cannot be simultaneous.[4]
An additional venture is added to the analogy by proposing that matter and
anti-matter can be interpreted as the four space manifestations,
cross-sections (or intersections) of a Mobius strip-like string of five
dimensions. Specifically it is suggested that in a higher dimension the
topologies of particle and anti-particle are indistinguishable. Any time
the state of a particle is altered in a particular way, so too is the state
of the anti-particle at the same time. This topology should be evident for
any entangled particles that occupy different physical spaces but identical
momentum spaces.
Consider a simple closed string, and rotate it around the circumference, if
this string is five dimensional it will pierce four dimensions in two places
(except for the case where the string just touches the four dimensional
plane). One could use these two locations as the locations of intersections
of string with plane, resulting in a four dimensional view that these places
are point particles. If we now rotate the circumference through these
locations notice that any change involved in location of intersection on the
topology is accompanied by a simultaneous change of location at the other
intersection. This means that if something were to affect the topology so
as to move it in this fashion at one location, the topology would change in
an equal and opposite fashion at the other location in four-space at the
same time. In order to do this we only need to ascribe to the surface the
property of "semi-rigidity."
The semi-rigid Mobius "string like strip" would have this same property. The
semi-rigid Mobius topology can be used to explain the non-local causality
which is asserted to occur in the particular gedanken experiment in which
the measured helicities of particle and anti-particle seem to be connected
instantaneously. Here it is proposed that it is the reality that particle
and anti-particle share the same topology. This allows the causal
connection in four dimensions to be instantaneous or near-instantaneous.
The appearance of the "point particles" in four dimensions cannot sever the
simultaneous connection of those "particles" in five dimensions.
The possibility of non-local causation, contrary to the theory of
relativity, has entered quantum physics through the observed violations of
Bell's inequalities and associated Einstein-Podolsky paradoxes.
The Aspect Experiments of the "1980s" suggest that when matter and
anti-matter are separated, there is an instantaneous communication of
information between particles and anti-particles. This could not be the
case in a four dimensional space where cause and effect propagate at the
speed of light. This problem can be addressed by assigning a semi-rigid
Mobius topology to matter and anti-matter. This shape also allows for both
Dirac and Feynman analyses in four dimensions and additionally predicts a
warp in local space-time due to the twisted and dual nature of the topology.
As it turns out light should be lensed maximally on the order of 10^-23
degrees for every electron/positron pair. The amount of lensing is directly
proportional to the size of the particles of concern. Given enough
particles, this lensing should be able to be brought to measurable levels.
Among other places, this mathematics was presented on October 18-19 in a
seminar given by the author at the Atominstitut in Vienna, Austria. Methods
are now being discussed on how to affect this space-time warp in the
laboratory. This is done under the general rubric of "quantum
teleportation."
This has been a brief excursion into the power of the conceptual or
otherwise bridge between the polar concepts of "duality" and "non-duality."
It is the hope of the author to sew a delicate thread of duality from
consciousness to the actual objects of consciousness themselves, showing
that duality exists conceptually (two types of consciousness) and
empirically (matter and anti-matter.) Furthermore the Mobius shape has
interesting applications for both, in that it contains the path to duality
from non-duality which seems to be important to both the understanding of
consciousness and it's objects.
Notes:
1. Bogolubov, N.N., Logunov, A.A., Todorov, I.T., Introduction to Axiomatic
Quantum Field Theory, translation by Fulling, S.A., and Popova, L.G.; edited
by Fulling, S.A., W.A. Benjamin, Advanced Book Program, 1975.
2. Dirac, P.A.M., The Principles of Quantum Mechanics, Oxford at the
Clarendon Press, 1958.
3. Feynman, R.P., Weinberg, S., Elementary Particles and the Laws of Physics
(Dirac Memorial Lectures), Cambridge.
4. Aspect, A., Granger, P., Roger, G., Experimental Tests of realistic local
theories via Bell's Theorem, Physical Review Letters, vol. 47,7, pages
208-215, 1981.
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