8 Oct 2005 @ 18:45, by Beto Hoisel
This Theory of Relational Consistency is the scientific post-quantum expression of the Vedic and Buddhist view on Totality, and the solution of the age-old problem of its subjective/objective double face.
The Theory is well developed and scientifically sound in spite of lacking of mathemathical formalization, yet to be provided.
THEORY OF RELATIONAL CONSISTENCY - as revised in May 2006
Beto Hoisel
SUBVERSION AND REACTION
One of the most daring standing points in the history of science was taken by Niels Bohr, when he announced his principle of complementarity which separated science from Aristotelian logic, as he proposed that wave and particle are two different – however complementary – aspects assumed by matter and electromagnetic radiation. Despite being logically incompatible, both are true and will appear in one or the other manner, according to the experiment done. The wave associated to a particle is the equation of mathematical possibilities that such a particle shall manifest itself in a considered point (Schrödinger's function) and this only occurs when it "collapses" due to a conscious observer's intervention, bringing forth that particle from a potential into an actual condition of existence.
On that occasion, Heisenberg established for the first time a definite limit to the scientists' pretensions to fathom "everything" about reality as deep as they wish. With his uncertainty principle, he has shown the impossibility to know, with any desirable precision, pairs of observables such as moment and position of a particle. The more precise is one of these measurements, the less trustworthy will be the other. And this is not due to any imperfections of the instruments or methods employed; rather it's an intrinsic characteristic of nature itself.
From these principles the so called Copenhagen interpretation established, profound philosophical implications on the knowledge of the sub-microscopic world were introduced. First of all, we have to acknowledge that quantum reality has a probabilistic nature, instead of a determinate one: Only one experiment on a quantum property of a particle doesn't yield a trustful result; or that experiment is made on many particles or it should be done many times on the same particle, in order to obtain the average. The second implication is that it doesn't make sense to say anything about the physical properties of a quantum object without specifying the experimental arrangement used to know it. Or, in other words: In some mysterious form quantum reality is created by the observation act, which causes Schrödinger's wave to collapse, turning actual something only potential.
At this time, Niels Bohr said that "it's a mistake to suppose that the object of physics is to discover what nature is. Physics occupies only with what we can say about nature." That statement opened the way to John Wheeler's declaration that "No elementary phenomenon is a real phenomenon until it is an observed phenomenon", and, more recently, N. David Mermin of Cornell University to utter his famous boutade: "We now know that the Moon is demonstrably not there when nobody looks."
While the quantum revolutionaries, armed with their equations and puzzling experiments, proceeded with the sweeping subversion of the objective reality concept, the rest of the scientific establishment in the universities of the world ignored, or pretended to ignore, what was happening.
However, not all of them closed their eyes to that. And the reaction in defense of the sacrosanct paradigm of realism came in 1935 led by the grand patriarch of science, Albert Einstein, who, with his allies Boris Podolsky and Nathan Rosen, conceived an imaginary experiment that, as they expected, would demonstrate the errors of quantum conceptions. That famous mental experiment, described in many books of scientific popularization, would show that if the quantum propositions were true 1) or things would move to a speed superior to the light, something not acceptable by the theory of the relativity, 2) or then reality could not exist independently of the observer. Ever since, a controversy that lasted for decades was settled on the EPR paradox, as it came to be known. And the result, already confirmed at the laboratory but not entirely digested by the scientific community, is unfavorable to Einstein and his two friends.
There are many different interpretations of the quantum theory proposed and discussed among scientists, but the one that seems less to correspond to the experimental facts and the theoretical formalism is exactly the realistic interpretation, that states the existence of an objective reality independent of whom observes. Now, at the forum of debates of physics, there live together other theories that extend and deepen the quantum proposals and, with varied metaphysical assumptions, try to adjust facts to equations. Some of those theories are based on solid mathematical formalism, and other didn't achieve that much yet, although their concepts seem respectable and convincing. Such theories aim to explain important segments of the individual/cosmic totality, which includes, according to the quantum vision, the mysterious objective/subjective interlacement of the world.
Some of the most respected names of contemporary science, as Henry Pierce Stapp, Geoffrey Chew, and David Bohm risked their reputations as scientists when they acknowledged the evidence of the essential role of the observer of an experiment. Such a view implied to acknowledge consciousness, subjectivity and the spirit itself, that imaginary face of wholeness rejected by the old paradigm's naïve materialism. Following the same path, many other workers in Physics, Cosmology, Neurology, Ecology and other don't fear to mention the spirit as the central agent of consciousness as they acknowledge the imaginary face of wholeness as "the stone rejected by the builders, that later has shown to be the keystone".
Riding this new wave, which comes to wide open the doors of a new millennium, I’m proposing the outline for a new theory of wholeness – the theory of relational consistency.
BEYOND 4-DIMENSIONAL SPACE-TIME
Just like in Geoffrey Chew's bootstrap conception, no aspect of the theory of relational consistency can be considered basic; almost all are imported from other theories and they only subsist due to its interdependence in a coherent configuration, capable of elucidating enigmas that other approaches don't solve per se. This way, relational consistency is a bootstrap theory once it refuses the reductionist conception ingrained into the current paradigm that says the universe to be made of basic elementary constituents, such as particles, laws, constants etc. In the view of relational consistency both 1) the search for minimal elementary sub-particles and 2) the investigation of what happened in the minimum fraction of linear time after the big bang are illusory roads that ultimately will lead to nothing.
A point to be preliminarily considered is the dimensional framework where that part of totality accessible to human knowledge is inserted. It's presented in two slopes, two faces of a same coin made compatible due to an extension of Bohr's principle of complementarity: 1) the face said to be real or objective, manifested in the three dimensions of the space (Euclidean or non-Euclidean, depending on the considered scale or the investigator's option) and 2) the imaginary or subjective face, manifested in the three dimensions of time. This way, the cognoscible being has two opposite and complementary faces in its wholeness, classically known as matter and spirit, that are no more than our peculiar form of noticing what, without this resource, would remain rationally unrecognized. Let's remember Einstein's words: "time and space are not properties of the universe in itself, but just forms we use to notice it".
With respect to the specific subject of time, curious things have been happening as a consequence of the constraints imposed by the standard paradigm that acknowledges time as one-dimensional - the usual linear time. First, we notice a specific blindness in some of the most outstanding personalities of science to certain results of their own experiments. Then, a repeated refusal to acknowledge obvious interpretations of facts emerging from experiments, if the case requires a basic reformulation of some aspects of the standard paradigm.
First of all, let's see Albert Einstein's refusal to admit that time, being an imaginary value – as suggested in his special theory of relativity, and more clearly stated in Minkowsky's considerations – should be understood as something connected to the subjective world, something imaginary, which appears in the physical-spatial world as a projection of a geometric nature. Einstein "saw" time has to be imaginary, but he didn't realize its subjective, non-physical character, so he could not develop the unfolding of this remarkable finding. Through this particular point – which passed unnoticed as a consequence of the Newtonian-Cartesian materialistic paradigm – science could jump over the metaphysical wall which averts physics of accepting the imaginary, the spiritual, the vastness of our inner world that forces its presence in the recent paradoxical experiments of quantum inquiries.
Minkowsky, in his paper "Space and Time" – presented to the 80th Assembly of German Natural Scientists and Physicists, which has taken place in Koln, September 21st, 1908 – introduces imaginary time in his proposal:
"We can determine the ratio of the units of length and time beforehand in such a way that the natural limit of velocity becomes c=1. If we introduce, further, the square root of -1 times t equals to tau (t=tau) in place of t, the quadratic differential expression dtau2 = dx2 dy2 dz2 ds2 thus becomes perfectly symmetrical in x, y, z, s; and this symmetry is communicated to any law which does not contradict the world-postulate. Thus the essence of this postulate may be clothed mathematically in a very pregnant manner in the mystic formula: 3 times 100000 km = square root of -1 secs.
Some years later, Einstein repeated in his book Relativity, the Special and General Theory:
"...Minkowsky's discovery [...] must be found mainly in the fact of his acknowledgment that the four-dimensional continuum of relativity [...] shows a pronounced relationship with the 3-dimensional continuum of Euclidean space. However, to give the right importance to this relationship we should replace the usual coordinate t with an imaginary value =1ct proportional to it. In such conditions, natural laws that satisfy the special theory of relativity exigencies assume mathematical forms where the time coordinates act precisely in the same way as space coordinates."
However, in spite of the acknowledgment that t needs to assume its condition of imaginary value to satisfy its own theory propositions, this was not interpreted – either by Einstein or any of his successors – as a clear indication that time is an imaginary subjective dimension which insinuates in the physical world through a projection. This is an ancient proposal of philosophy, of poetry and of the thought known as "mystical", that for centuries hold their own views on this mysterious and basic field.
Another aspect of the nature of time also discerned by Minkowsky and Einstein but ignored by later science concerns to the linear flow, usually associated to a line, as Heraclitus' river - which he saw as a projection of a more complex dimensional set. It seems curious that physicists' sense of esthetic didn't react to such a painfully unattractive structure of a lattice which has three dimensions of space and only one of time.
A structure formed by three dimensions of space and three dimensions of time can account for all phenomena and possibilities contained in wholeness, at least until the horizons our intelligence, intuition and feeling permit us to reach.
The Theory of Relational Consistency proposes that Euclidean 3-dimensional space adjusts to the objective face of wholeness – that one we call real – the existential locus of matter and objects that physical science recognizes as such. On the other hand, time, which is also 3-dimensional, is the existential locus of the subjective contents – the subjects – that we identify to the imaginary face of being, whose center is inside each one of us.
Today, linear time has the tremendous force of an archetype and the sweeping power of a god. It's true that we are subject to many of its constraints but this is also valid for space. We cannot move without encumbrance along linear, or 2-dimensional nor 3-dimensional time. But the same happens to space: even if we acknowledge its broad 3-dimensionality which unfolds up to the clouds and interstellar space, we are not free to move in it as one pleases. We are constrained by physical limitations, bounded to the Earth's surface, to the size of our ship or to the bars of a jail. The prisoner sees the blue sky and the far away mountains through the rails of the window, but he can only move in the tiny world of his cell.
First, we need to know what 2 and 3-dimensional time really are, and then to study a way – and by which means – we could move in these realms. It seems clear that we can figure out what one-dimensional time is. But, what could be a 2-dimensional time? What should be the metaphor that could adjust to it, or what kind of mental picture can we make of it? Why doesn't 2-dimensional time appear in the instruments and observations of physicists?
To understand what 2-dimensional time is (and also 3-dimensional) it's necessary to accept its imaginary – hence subjective – character, as bounded to the imaginary face of wholeness, which discloses only through subjectivities: Spirits or sentient beings, human or other. It's necessary to become aware that time is something essentially subjective, which manifests in the space of physical things as a projection of geometrical nature. It's essential to understand that transformation, even when it occurs in physical things of space, doesn't imply time, and that time is transformation being perceived by some subjectivity.
Time is imaginary and subjective. The notion of 2-dimensional time emerges when we get aware that each subjectivity has its own proper time, its exclusive worldline, also defined by Minkowsky in that very paper almost a century old, where he has shown the imaginary character of time.
Surface-time can be conceived as the sideways move of an individual worldline through the subjectivities that crowd the universe, human or otherwise. But – it can be argued – aren't these entities known to be discrete, individual, and discontinuous? Certainly not! They are not separate. All subjectivities that aspire to the right of existing (whatever this may mean) are dots in a vast continuity, like the countless emerging peaks of a gigantic submersed mountain range of uncountable complex beings that pervade the entire cosmos embedded in its 6-dimensional lattice.
This way, 2-dimensional time is the fabric of countless subjectivities that pervade the universe, each one bearing its proper time, individual and linear. But – someone could ask – how can the time we see in clocks and calendars seem the same, common to everyone? Initially I reply this is not exact, as states quantum physics, as well as relativity. Then I add something new: I am convinced of the existence of a principle of consistency, which allows the compatibility of interacting subjectivities' individual times.
This new principle of science, which comes out to join others discovered in the beginnings of quantum physics, states that interacting subjectivities' individual times connect to each other in such a way a perfect illusion is created: clock time seems to be the same for all of them, as if they were sharing a common experience. But this can occur only among interacting subjectivities, only if they are in touch or, in a sense, communicating by physical means. Non-interacting subjectivities can be bounded to very different individual times. Or, in other words: to look for equivalence between individual times of non-interacting subjectivities doesn't make sense, once they are bounded to universes that actually are not communicating.
Three-dimensional time, however, remains beyond human skill for abstract thinking and imagination. Three-dimensional time is the realm of gods. But a glimpse of its structure can be attained by the same geometrical expedient we used to understand 2-dimensional time, and should be seen under the strict limits of a metaphor: 3-dimensional time can be generated by a dislocation of 2-dimensional surface-time – formed by the weaving of many subjectivities – in a direction perpendicular to that "surface". This way we create something similar to a "volume", an inconceivable imaginary volume, the absolute volume that engulfs the evolution of wholeness, which contains everything and has no limits nor outside.
Three-dimensional time is the most close equivalent we can conjecture of God's mind, as well as three-dimensional boundless space – the universe – could be a metaphor for the locus of His physical body.
This way, the dimensional frame that supports the cognizable wholeness comprehends the three "real" dimensions of space x, y and z plus the three "imaginary" dimensions of time t, u and v. Everything real and all the imaginary realm, all the "objective" world and also the "subjective" kingdom, all physical and mental phenomena – including those said to be paranormal – can fit in that six-dimensional framework.
In the perceptive system ordinarily adopted, the "real" contents of the universe – the physical universe delimited by physicists and cosmologists as their object of study – are said to EXIST. On the other hand, the contents of the psychological "imaginary" world, as well as the ideal creations of all subjectivities – either human or not – we propose to say they INIST. To speculate on other contents outside of that dimensional framework is pointless, once such contents would not be accessible to human knowledge. The mathematical formulations that describe anything unfit for that framework would exist only, or better, would inist only as an abstract mathematical entity linked to its specific ontological status of the imaginary slope of wholeness.
Observe that, as we admit time as being 3-dimensional and imaginary – the point Albert Einstein missed – the whole problem of the origins and evolution passes to be referred to a non-sequential understanding of the cosmic facts. This is the deepest and most wide-ranging revolution of our proposal. It subverts all the investigation forms related to one-dimensional and linear time, with its arrow inexorably harnessed to the big bang and the second law of thermodynamics.
This puts us in face of the Buddhist's conception of Being. D.T. Suzuki writes:
"Buddha (...) is not one more who lives in a world conceived in terms of time and space. His consciousness is not more the consciousness of a common mind, regulated in agreement with the senses and logic. (...) Buddha (...) lives in a spiritual world that possesses its own rules."
The entity that physicists and cosmologists recognize as being the universe, the cosmos whose secrets they study, in truth is neither unique nor objective, except under a strictly consensual perspective. Each subjectivity, each spirit, each observer, each scientist, each person of any social level or cultural background, each consciousness – be it human or not, be it terrestrial or not – carries around a private universe of beatitude or anguish, of ignorance or light, built throughout the eons of his or her existence. This sends us to the theory of the monads, of Leibniz, a sage who reveals a surprising contemporary view. He had a premonition of important aspects of several recent theories, particularly the holographic vision of the brain (Karl Pribram) and also of the universe (David Bohm).
Our model for the relational consistency is sustained on the shoulders of those precursors.
SUBJECTIVITY AS FOCUS
As to the interpretations of the quantum paradoxes, we emphatically endorse the discovery (we see it as a discovery) that consciousness creates reality, when it triggers the collapse of Schrödinger's function, turning actual (real) what was only a potential existence (imaginary). That process, countlessly repeated in all observational actions, turns actual worlds potentially hidden in quantum possibilities, as it builds his or her parallel universe around that observing subjectivity.
Thus, we link ourselves also to the interpretation of the multiple universes, of Hugh Everett III, as we acknowledge the universe as, actually, a multiverse: An inexhaustible unfolding of universes that can portray small – or much accentuated – differences among themselves.
However, we distinguish our interpretation from Everett's. He admits that all countless versions of universes in some way would "exist", superposed in a hyper-space of endless simultaneous realities as we, collectively, would only have consciousness of one. In our view, conversely, each of these multiple versions can exist only when centralized around a subjectivity that functions as its existential nucleus: Each subjectivity is the center of his or her own parallel universe. We consider as evident that something not perceived cannot be real, as observed John Wheeler. Therefore, universes not provided of a conscious subjectivity as its perceptive nucleus, cannot exist.
Our proposition, however, doesn't mean that each subjectivity is confined in only one parallel universe that, for him or her, would exist "forever" as a single private universe, according to the classic conception. It is nothing like this. In our view, each consciousness is a pole of ever unfolding universes that each subjectivity brings about according to the myriad quantum options embedded in their decisions – conscious or not – that we would call observations, equivalent to what, in formal quantum experiments, is characterized as a measurement.
This way, each subjectivity is a focus of unfolding parallel universes, as predicted by calculations and admitted in Everett's interpretation. However, each one of these parallel universes has a size restricted to the limits of that subjectivity's range of perception. I remark the fundamental difference that, while in Everett's interpretation only one unfolding system exists, actualizing a single hypothetical reality where all of us would cohabit, in our proposal that old reality – independent of observers and common to all – stops having autonomous existence and turns into an existence of consensual nature. Which, for its time, is not unique: There are countless consensual realities, however compatible and consistent with the subjectivities inside them. Consensual realities which are not under interaction can be very different; but if they don't interact there's no problem.
Synthetically, we propose that the thing we call reality passes to be understood as a vast inter-subjective network that interlaces consensual realities shared among groups of interacting subjectivities.
The generation of the phenomena shared by multiple subjectivities happens according to processes of holographic nature, each part containing information on the entire interacting group. This view synthesizes the theories of Pribram and Bohm in only one conception and suggests a dimensional locus – 3-dimensional time – where can comfortably be inserted the implicit order of Bohm; the domain of frequencies of Pribram; the morphogenetic fields of Sheldrake; the said paranormal phenomena; the archetypes of Plato and Jung etc.
We live in a consensual universe mathematically built by our consciousness according to the Fourier's transformation, as it interprets patterns of electromagnetic frequencies originated from other subjectivities as geometric projections of the superior dimensions of space-time. Consciousness is a hologram that reproduces "one" holographic universe in perpetual mutation – a holomovement, according to Bohm – due to the continuous motion of interacting subjectivities. The most present physical processes in the forming of that consensual world are interference and resonance of the entire spectrum of electromagnetic waves – mostly of them unsuspected, however present.
I emphatically agree with the Scandinavian scientist Hannes Alfvén, when he says that "our cosmos is more an electromagnetic than gravitational being".
THE PRINCIPLE OF CONSISTENCY
It remains, now, another problem to be examined. To consolidate those propositions it seems indispensable to provide a formulation of the principle that allows the compatibility of the many universes in their updating process. Around each conscious pole (we call it a subjectivity) the illusion of a single reality seems solid and convincing in the way ordinarily verified. If each subjectivity unfolds his or her own universes, how is it possible that this is not perceived and the suggestion of a single unique reality seems so obvious?
In the tradition of the founding fathers of the quantum quest, whenever a crucial aspect on the conception of reality and the means and limits we have to apprehend it was reached, something emerged as a principle, a basic parameter that establishes a pattern and delimits the cognitive process. This way appeared Bohr's principle of complementarity; Heisenberg's principle of indetermination; Pauli's principle of exclusion and several others. This feature seems to be an intrinsic characteristic of wholeness or, at least, of our process of apprehension of its deeper aspects.
In the same way I glimpsed what can be called a principle of consistency, which makes compatible the many worlds generated by interacting subjectivities, so that the consensual fabric comes out without flaws or fractures. That principle, as general and including as the others we have mentioned, is a key condition that allows the contents of a non-linear time – a 2 and 3-dimensional lattice – to be geometrically projected in our perceptible space-time and interact in its realm.
According to the principle of consistency, the arrow of time comes out from no conflicting sequential collapses of quantum waves (Schrödinger's function). This starts with the endless conscious interventions in the super-hologram, triggered by the individual holograms of each subjectivity. This process forms the super-holomovement we see as reality, or "the world". Therefore, consensual reality is shaped in the linear time by the successive accumulation of myriad quantum collapses in the super-hologram common to the interacting subjectivities. That sequences – which exist only in the linear time of the each subjectivity – spread common views of a reality updated in a growing consensual field, as a growing fractal that continuously incorporates new subjectivities, without contradictions or inconsistencies.
As can be inferred from the propositions above, the now called consensual reality – that to our view replaces the old concept of an objective reality – is formed together with lineal time as auto-consistent patches that grow according to mathematical auto-correlation functions of fractal characteristics, dispersing from different generation centers. As our perspective is holographic (non-local), we admit that such patches exchange information, even if they are not spatially close to each other, preventing they fit together without any cracks when they enter in further contact.
However, that compatibility is not always perfect. Sometimes those processes present flaws that can be detected, if they are not yet healed and adjusted. The more distant in the perceptible space-time and less interacting among themselves, more probable it will be the occurrence of compatibility fissures among different patches of consensual realities in their process of formation.
An interesting example is the case of the neutrinos. For many years in the researches realized in Western laboratories neutrinos didn't accuse any mass, but in Russia invariably they appeared as bearers of very small, but measurable mass. That crack in the pot of reality was healed in January of 1995 when finally the American experiments have found mass in the neutrino.
This consensual conception of reality and the cosmos rests on epistemological foundations rather different from the one that sustained science until the end of 20th century. It also stands largely far from the Western cultural inheritance of Greek roots. Now we need to review countless remaining crucial aspects in many sciences and research methods.
More than a revolution, what is configured now in the relationship between the individual soul and the cosmos is a sweeping subversion of many things supposed to be known in Cosmology, in Physics, in Anthropology, in History, in Psychology. From now on, it will be essential that, with courage and humility – we don't see them as incompatible – all of us became willing to acknowledge and assume the paradoxes and marvels offered to human knowledge and fruition on the verge of this new millennium.
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NOTE: 1: This paper is part of the book The Annals of an Imaginary Symposium, by Beto Hoisel, which is available only in its original Portuguese version as published by Palas Athena Association – São Paulo, Brasil, 1998 (English language publisher is welcome). However, six of the twelve chapters (or lectures) are translated into English and can be read and print from our site Journey Across the Cosmos - of knowledge and wisdom. (site address: [link] ) This paper is at the end of the Lecture #6 – The New Reality, signed by a fictitious scientist christened Sir Philip Quarks F.R.S.
2: The real & imaginary author of this paper, Beto Hoisel (beto@hoisel.com.br) is very interested in making contact with someone skillful in high mathematics to join him and help to create a mathematical formalization to this Theory of Relational Consistency.
Beto Hoisel – October 2005 / May 2006
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