Guest guest Posted July 16, 2007 Report Share Posted July 16, 2007 Duality in Life, the Universe, & Everything By Mark MacDowell Introduction Issues 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. and gratitude also to: Metanexus:Forum on Religion and Science ..b b.b. Quote Link to comment Share on other sites More sharing options...
Guest guest Posted July 16, 2007 Report Share Posted July 16, 2007 " I wonder who, exactly, he expects will be reading these posts. I can't expect anyone to be reading mine. But this is good journaling, for me. Surely he knows that all this stuff is accessible elsewhere. Nis, I believe, is rather for inter personal sharing, not impersonal publishing. " Nisargadatta , " .b bobji baba " <Roberibus111 wrote: > > Duality in Life, the Universe, & Everything > By Mark MacDowell > > Introduction > > Issues 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. > > and gratitude also to: > > Metanexus:Forum on Religion and Science > > .b b.b. > Quote Link to comment Share on other sites More sharing options...
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