Dirac’s Vector Analysis Update.
Anyone who has ever stood up in front of a classroom to address his/her students will tell you that simplicity is a worthwhile pragmatic and theoretical virtue goal iff the expected and appropriate pedagogic results are aimed at the student and not the teacher, independent of the corresponding level of complexity to be communicated. There is a presumption that ‘selling/marketing’ an idea by a professor implies there must be a ‘buyer’ student for a pedagogical transaction to be completed. Unless, of course, the professor, consciously knowing (or not) is engaged in a self-serving soliloquy justified as primitive, ‘self-evident’ propositions and often expressed as either theology or probable/statistical science inspired radical extremist pronouncements. Yet, a complex and changing nature, in its dynamic evolutionary progression in our 4-d space time existential reality, opts to reveal its complexity to human narrators in the form of the simplest possible model-poems solution that are compatible with the narrators’ brain dynamics’ phenomenology and combinatorial limitations, as amply detailed in our other publications. We now expand on the justifications for our general poem on the evolution of complexity as discussed under “The Immanent Invariant and the Transcendental Transforming Horizons.” See Ch. 12, “Nurophilosophy of Consciousness.”, Vol. IV and Vol. V.
If we ever have expectations from our biopsychosocial (BPS) model poem of human brain dynamics ever evolving into a reliable theory of everything (TOE) it must satisfy some minimum requirements as detailed below. The most important requirement being that the model’s principles must be rationally/logically justified as a general/universal application to any aspect of human enquiry, whether its content is exclusively epistemological idealism or an exclusively pragmatic, methodological and empirical type. The model approach can also take the form of a hybrid combination of idealism and empiricism in nature like our own Epistemontological hybrid tracking this super-complex reality as it evolves in our 4-d space-time biosphere niche. We hope that our consciously free willed choice of simplified analytic mathematical elaboration is readable and reaches the curiosity of all informed readers in any discipline. In the search for an adequate universal mathematical formulation we had to justify the need for ‘a priori’ metaphysical elements (including philosophy, theosophy, mathematics, etc.) and the need for ‘a posteriori’ pragmatic/physical elements as emerging from scientific methodology measurements/observations of nature. It is due time to rationally integrate pragmatic empiricism and rational idealism as a functional unit whole in living human reality as justified by consistent, falsifiable and predictable results from quantum theory based probability theory and/or Bayesian conditional statistics including theosophically-justified speculations and conjectures as exemplified by the famous Leibniz Monadology or our own sub-model arguments for the probability of a ‘transactional reciprocal information transfer between the human pre-motor neo-cortex attractor phase space and unspecific space-time n-1 coordinates in transfinity as mediated by the human brain baryonic dark matter DNA/RNA receptor site.
Our central focus on the human biopsychosocial (BPS) existential reality equilibrium adapting our species to familiar (or new) contingencies presenting a potential threat to human survival has led us to seriously consider how may the human inferior adaptive limitations to a changing environmental landscape (compared to other evolved subhuman species) notwithstanding, the human species have survived across generations performing the wondrous evolutionary technological and societal transformations other species are innately incapable of? What keeps the human species at the helm of the Bergsonian evolution of complexity, above the mere BPS survival other evolved subhuman species also share?
Intuitively, the easy answer is to search for entities outside/beyond our immediate 4-d space-time earth biosphere environment that specifically/selectively influence the human species. The same intuition, always looking for simplicity, makes you posit the probability that before being the architect responsible for the wondrous transformation the human species has first to be alive, healthy and psychosocially adapted, in equilibrium with his immediate, individualized environment. It makes intuitive sense to suspect that such transfinite source should first be able to functionally equip humans with the resources to offset the inferior adaptive capabilities in the biosphere milieu and second ‘create’ the super symmetry transfinite conditions that minimizes the probability of disruptive transfinite radiation affecting our biosphere. Part of that radiation may exclusively reach the human premotor neocortex to anticipate damaging radiation events.
The careful reader may have noticed the posited existence of two unreachable infinities at play, the micro sub-Planckian manifold actively controlling the local events and the cosmological manifold controlling transfinity. We immediately wonder what resources may our poorly adapted human species to life on earth, with its known phenomenal and brain combinatorial limitations, may mobilize to stay alive and become the architect of this wondrous civilization?? Can anyone imagine better adapted subhuman species like Rhesus monkeys or ants, roaches, etc creating optogenetic and gene transplant technology controlling DNA/RNA transduction, the same way transfinite radiation does? How else may any human being explain, if not describe, the cosmological order being influenced by natural complex asymmetries evolving to become the super symmetries that minimize universal damaging radiation impacting the earth and facilitating the reciprocal information transfer mechanism between humans and transfinity sources. We need a model poem formula that operates both at the local mesoscopic biosphere and at the cosmological order level that is compatible with the structural/functional idiosyncrasies of a human brain.
We have climbed on the shoulders of Dirac and others to formulate probable approximations compatible with all disciplines created by the same human physical brain. What follows is a brief summary of the salient technical features still undergoing revisions with the joint ‘help’ of the good willed informed literati and the ill willed vicious trollers that plague some HiQ online listings. .
For details on these formulations see Blog site: https://angelldls.wordpress.com/; and http://delaSierra-Sheffer.net For the present needs of this brief article on the merits of a modified Dirac notation we only highlite the possible interactive correlations between the local and transfinite sources of information and the need for functional approximations requiring a minimization of relevant interacting variables at both extremes of the spectrum, the phenomenologically invisible levels of activity at both the subplanckian local level and the cosmological level. At the micro level our sub model requires the attainment of supersymmetry to posit the presence of monopoles and gravitons to facilitate the influence of low intensity transfinite cosmic radiation on the local genetic transduction process of the brain neuron target cell via a dark matter baryon receptor. The ongoing debate centers on what subatomic micro particle is involved in the information transfer, the neutrino, the axion, etc. and where does it originate? We concentrate on the measurable how and give a lower priority to the theosophical why.
The charge free ‘neutrino’ is the candidate of choice to penetrate un-opposed miles deep through geological barriers to reach the buried instrument receptors at CERN. Radioactive, stable hydrogen H1 (spin 1) atoms are known to spontaneously emit ½ spin electrons during their Beta decay process to a suitable acceptor of opposite-1/2 spin leaving the originally stable spin 1 source spin -½ deficient as measured. In our model this naturally decaying or radiation-induced hydrogen atom can be on either side of the reciprocal communication path, the human brain cell or a transfinity source of radiation. It is assumed that path direction is a function of need to insure the availability of an BPS survival adaptive response to challenging environmental contingencies. All experiments confirm the same fractional deficit attending radioactive degradation. If, as the result of nucleosynthesis activity immediately after the Big Bang, dark baryonic particle radiation found its way into cellular DNA/RNA is not as farfetched as it seems to arm chair idealist theorists who rather prefer the charming argument of the ‘massless’ physical particle to justify the deep penetration of the particulate matter. Somehow the ‘massless’ particle particle has to be charge-neutral and only micro gravitational forces in the form of magnetic monopoles will do to avoid the dipolar nature of electromagnetic (EM) induced fields. A ‘massless’ particulate matter inducing EM fields?
Enter gravitons and Dirac who questioned what good theoretical reason explains why the un-observed/undetected monopoles could not exist within a quantum theory framework? A mathematical logic explanation made more overall sense to posit the existence of monopoles than its absence. It is clear that a consistent, falsifiable observation or a physics-laboratory experiment should not necessarily be always considered as a check on the necessary and sufficient proof of its truth content. In our opinion the same incompleteness applies to the conceptual mathematical correctness of the symbolic or sentential representations of the current Dirac-equation solution. However, when both the physical empirical measurement of a consistent/falsifiable effect and a metaphysical logic are integrated, the confirmation of the electron particle physical mass, graviton or monopoles structure become a goal whose detection ability in the electron physics lab is still beyond reach, if ever, but at least its predictions on a probability basis is the next best option.
The best way to explain the temporal evolution of the multidimensional complexity of any quantum state in a linear scalar progression (like the way our brain linearizes sensory information input) is to update the Schrodinger and Hamiltonian space into a Hilbert space that may take into account any vector ray projection path direction. This mathematical combination allows for the differential representation of a multiple number of relevant variable paths interacting between themselves as one single resultant package. Each of the participating quantum states can be represented in the standard ‘Bracket’ notation consisting of a left part, called the bra and a right part, called the ket. The notation was invented by Paul Dirac. The effective use requires minimizing the number of relevant dependent variants by approximations as they affect the phenomenological perceptualization of an independent invariant unit dimensional physical particle or aggregations thereof. In a TOE model any conserved value, matter, momentum, etc. will do as the invariant. It should be remembered that the progression range of all of the N particles (positive integer; 0) individual 3-d x,y,z dependent variables inputs as they project into a Hilbert space of 6N real dimensions gets reduced to a single valued function output. Quantum theory integrates the 3-d configuration space plus the 6-d Hilbert space into a 9-d space may now ‘represent’ the classical brain phase space. This way each projective ray path projection represents a frame-independent Schrodinger wave function where the operator defines the appropriate frame of reference. If one path harmonic ray rotates, stretches, etc., they all do (at right angles to each other or orthogonal) except when several points cohabit and interact in same 2-d plane (not the x,y,z line axis!) where each point coordinates lies (each eigenvalue, momentum, position, spin, etc. defining its probability amplitude) may have conflicting physical existence. Not all possible observables can be simultaneously measured, eg., position and spin of particle, giving rise to Heisenberg’ uncertainty principle. At the sub-planckian scale (10-33 cm) quantum gravity space is a lattice and we can have an infinity of dimensions for an open ended forever-expanding universe. Each of these mutually perpendicular basic rays represents a particular potential behavior of a quantum system and the set of all basic rays for a given property constitute the relativistic frame of reference in Hilbert space. Orthogonality provides for potential activities that are classically distinct or mutually exclusive. Also, the number of dimensions needed in this abstract space corresponds to the number of choices available for the quantum system, and this, as we have just seen, can go to infinity. In such cases the product of their Hilbert spaces gives rise to the “entangled states” of the Einstein-Podolsky-Rosen (EPR) effect. In Hilbert space the ubiquitous electron can be in all possible places all the time. In this respect a Hilbert space concept is more than adequate to carry on the baton for the representation of the quotidian familiar everyday world.
In general terms the Dirac notation below satisfies the identities inside the *brackets where is the complex conjugate. By mathematical logic transformations the general terms can be further transformed into operational functional representations allowing a ‘visualization’ of the temporal course of evolution of any unit dimensional invariant particle aggregates as they project their evolutionary progression into the multidimensional Hilbert space allowing for predictable warnings about probable future happenings in our biosphere of interest.
Summary and Conclusions.
If the objective reader still considers recorded history as at least a reliable guide as to how complexity has evolved from memorable Aristotelian times to our convulsive 21th. Century, it should be obvious that each historical period had the task to reconcile the immanent/pragmatic, phenomenological ‘seen’ and the transcendental, relevant epistemological ‘unseen’. We can summarily mention Aristotle’s analytical guide in his ‘ceteris paribus’ strategy to minimize the number of postulates or hypotheses to make your model poem more credible. Even St. Thomas Aquinos recognized in the Middle Ages how natural laws of simplicity adequately guide the course of universal evolution. Likewise Kant—in the Critique of Pure Reason—supports the idea of minimizing the number of non-phenomenological assumptions/principles contained in ‘Pure Reason’-based arguments underlying scientists’ theorizing about nature. If true and sufficient, as consistently verified by all human observers, whether philosophers, experimentalists, and/or practitioners, why muddle the truth content goal with the claim of exclusivity based on pronouncements about subjective radical sensory or extrasensory individualized experiences? Why not heed today the pragmatic, universal suggestions from 14th. Century Occam’s Razor, Galileo or Newton’s Principia Mathematica? Why settle for the self serving pomp and circumstance of superfluous causalities as defended by the radicalized arm chair physicalist theorists or the experimentalists, practitioners and philosophers? On the other radical extreme, why should anyone accept as the exclusive truth the metaphysical, subjective, individualized content of a physical human brain’s theosophy-inspired cosmogony experiences? Three centuries ago the chemist Lavoisier ridiculed the hypothetical metaphysical ‘phlogiston’ as the exclusive explanation of phenomenological chemical reactions observed, a rejection based exclusively on mathematical logic principles that minimizes the arbitrariness of non phenomenal brainstorms. Again, mesoscopic existential reality demands the easiest and simplest explanations to explain the realities a healthy physical human brain experiences. To guaranty the maximum probability of truth content we need to integrate the maximum number of empirical consistent, falsifiable human measurements/observations resting on logical deductions and a bare minimum of axiomatic-based model poems. This is true of all disciplines created and narrated by the exclusive, individualized human brain dynamic activity whether we like it or not. The polarization we witness between the hands-on physical ontologists and the armchair metaphysical epistemologists in current 21st. century debate on ‘consciousness’ seem to rely exclusively on the burden of proof summoned in defense of one’s point of view, thanks to the magic experimental results coming from modern technology, especially when they score high in the predictive value. All things being hopefully considered, the undersigned author still believes that providing credible arguments rooted on solid consistent measured/observed empirical facts refuting competing theories is more important as a starting point in the debate as to the probable truth content of our conscious model choice. A case in point is the un-necessary causality debate on probable truth content between the undeniable linguistic elegance of armchair mathematics theorists and the hands-on cold probable/statistical laboratory facts reports of real time-space practitioners. Considering the evolving super complexity of both the physical human brain structure/function and that of the universe how dare either extreme version proclaim the exclusivity of their domain of discourse at the exclusion of the rival unknown other? Why do materialist physicists knowingly posit the existence of two coexisting but different ontologies in the mind-brain dualist interpretation of the human brain dynamics when they should know that etymologically ontology belongs to the phenomenological domain whereas mind is an epistemological denotation? Why not share and learn from each other including the justifiable arguments of each other in a current but evolving hybrid Epistemontological synthesis as we have proposed and have exhaustingly analyzed in our BPS model of brain **dynamics.
The reason we briefly discussed the Dirac methodology is because we also believe that if our model aspirations of becoming an universal theory of everything (TOE) we should justify the BPS model poem of brain dynamics as applicable to any area of human enquiry regardless of being formulated as an epistemology or methodology principle. Because we consider both principles as two coexisting, inseparable aspects of the same mesoscopic existential reality in our human species biosphere.
Dr. Angell O. de la Sierra, Esq. Deltona, Florida Spring, 2013-04-27.