In a recent project designed to describe the 'flyby anomalies' via Self-Field Theory, Hans van Leunen put forward another view of structure within the cosmos http://vixra.org/pdf/1802.0086v4.pdf.
In Han's paper called " Structure in Physical Reality " he ends up with a method that is clearly based on a voltage and not on a field (as defined by electrical convention). Does this cause the problems with gauge and renormalization etc with QT?
Can we fix these problems via a true field formulation (e.g. SFT)? (Note that conventionally these potentials are so-called 'fields' and the theory is called 'field theory'.
Fields are simply linear symbolic continuum mathematics that are easy for highly trained mathematicians that have NO correspondence with reality from Maxwell's EM theory to Particle-Theory.
The 'continuum' of the 'set' of real numbers as well as the 'infinity' of the 'set' of natural numbers are mathematical artefacts. The fact that these artefacts are appropriate for setting up successful physical theories for mathematical description of macroscopic physical phenomenons does not mean inevitably that these mathematical concepts are appropriate for microscopic physical phenomenons, i.e. atomic and subatomic physical phenomenons. Tony's question is related to the question of how to overcome the mathematical artefact of the 'continuum'. The path integral approach to QM indicates that considerations which are based on discrete mathematical structures for setting up the notions of 'space' and 'time' might be more appropriate for setting up a final reasonable theory for microscopic physical phenomenons which does not require the notion of 'fields' based on the mathematical ideas and concepts of the 'continuum'.
Hi All, including Karl and Herb
Karl and Herb, you are both to some extent missing the true benefit of Self-Field Theory (SFT) compared with its forerunner the statistical based quantum theory, in particular the quantum mechanics (QM) that was invented in the mid 1920’s. The benefits are mainly numerical (mathematical) and this line of research was not realised in over 100 years of intense research by the best minds on the Globe. I recently came across the Compendium of Quantum Physics, Daniel Greenberger, Klaus Hentschel, Friedel Weinert Editors which is an excellent summary of this research 1900-2017.
SFT has a much shorter history from about 1996-2018 following my work in studying standing waves in systems of emitters (including the electrons and protons inside atoms) using a mathematics that was suggested by the work of Hertz in 1888 in determining that it was EM radiation that could be transmitted by wire antennas. This SFT formulation used Maxwell’s equations to determine the fields around both the electron and the proton. This is fundamentally different to the formulation used with statistical quantum theory where only the fields around the electron are examined. In SFT we make the assumption that the energy of both the electron and the proton balance one another. Although the two formulations are very different I prefer to describe SFT as another evolution of Quantum Theory, an evolution that is deterministic and not probabilistic
Numerical matters. It is implicit in self-field theory that it is a distinct method to the line of mathematics that flowed down through the last decades of the 19th century via Planck, Einstein, Heisenberg, Bohr, and a multitude of others.
It is staggering (to me at least, given the eminence of all who have been involved) that this work has come down to us as a single formulation that includes its roots within the statistical mechanics that was ‘initiated’ (can’t think of a better word) by Maxwell and Boltzmann and used by Planck to solve the Blackbody problem at the start of the 1900’s. We, the antecedents of this work have not investigated other possibilities in the 120 years since Planck’s solution; until SFT where a different way is found to pose the mathematical application.
So, SFT is about Maxwell’s first order partial differential equations, whereas QM uses second order partial differential equations!
I’ll leave it there for today, but think about the benefits of solving not second order partial differential equations but first order partial differential equations. Think in terms of gauge and other numerical necessities.
Kind regards Tony
Hi Tony:
My critique of "field" theories is not they cannot produce correlative predictions about numbers that agree with observations but the whole exercise is ONLY epistemology; it has NO foundational ONTOLOGY.
In other words, what aspects of reality do your field symbols have with Natural Reality?
PS You might guess that I am no longer impressed with math propaganda, especially those that make LINEAR approximations that can then be 'solved'.
Hi Herb
It's clear you are making the same mistake many before you have made about those QT terms 'fields' 'potentials' and 'field theory'. QT has misnamed what a field is and what a potential (or voltage) is. Until you see the truth of this you will continue to be 'blind' to what I'm saying.
You might find I'm the 'Cavalry' riding into battle with those propagandists you see around you, for now I'm going to let your question go through to the keeper; SFT will have a profound effect on the philosophy of science; but it is far too early to discuss these philosophical effects yet. But watch this space.
More importantly learn what I'm saying of SFT compared with current quantum theory before you think of it as more of the same old.
The question of second order vs first order partial differential equations is central to this new deterministic strain of quantum theory.
Think about what a ‘field’ is (a stream of photons) is and what a ‘potential’ (or voltage) is (it's an integral of the field), and then think about how SFT sees this and how QT (can’t, or struggles to) see this.
Hi Tony
Classical field theory (CFT) as well as (mathematically well defined) quantum field theories (QFT) rely on the assumption that the math. description of "space" and "time" by means of a "continuum" is reasonable. However, in the context of physical phenomenons on an atomic or subatomic 'sale' the origin of the notions of "space" and "time" or "event" are not well introduced by definitions which are independent from mathematical models. Instead, most physicists simply use the idea of the dense "continuum" and use math. theories which are involved with real numbers such as Euclidean geometry, theory of manifolds, etc., and arrive finally at a theory for (3+1)-dimensional space-time (special relativity). The situation is similar to Newtonian mechanics (NM) where the notions of "space" and "time" are not introduced by convincing pure physical arguments. This is one of the main lacks of NM as well as of CFT and QFT. Since there is no convincing pure physical argument which justfies the "continuum" idea for "space" and "time" on each 'scale', any kind of the idea or notion of a "field" considered as a "continuous object" in "traditional" "space-time" is highly questionable.
G'day Karl
Good to hear from you and hope you are well and thanks for your view.
Can I get you to read the following article about the fields inside SFT compared with QT.
Article Self-field theory-new photonic insights
You, like Herb, seem to be saying SFT is a 'continuous' method, a classical method. Not so, far from it; read again. The photons are discrete 'wave-particles' although they can be thought of as fields surrounding 'bigger particles'; but this is not the whole story.
We are in fact touching upon the fact that SFT sees the continuum (for instance what we see at macro level) is actually a discrete series of 'wave-particles' (actually each photon is TWO 'wave-particles'). In other words, a fractal series, that gets smaller and smaller as well as bigger and bigger, an iterative solution, just like a fractal; no-one has mentioned fractals . This is NOT an analogue of what Planck saw within his Black-body solution; it eventually gets to the point of suggesting an 'ether'-like 'vacuum'; all these fractal structures keep going and we end up with an infinite fractal.
So the ‘continuum’ turns out to be a fractal. (Do a search for ‘fractal’ in The Compendium Of Quantum Physics I referenced a day ago, you won’t find any hits in the whole compendium.
" Since there is no convincing pure physical argument which justfies the "continuum" idea for "space" and "time" on each'scale', any kind of the idea or notion of a "field" considered as a "continuous object" in "traditional" "space-time" is highly questionable."
Maybe the view of reality as an infinite fractal may appeal to you and Herb as a model for reality?
I see lots of quantum mechanics adherents get hung up on this idea of 'the field' and all the time they mean 'potential' (or voltage), so they have to treat the 2nd order maths via gauge theory and 'renormalization theory'; all this is avoidable by using actual magnetic, electric, and acoustic fields, rather than potentials.
Have you got a juicy reference or two of what you are both saying?? I'm always willing to learn another view of this quantum world; as I hope you and Herb are of SFT and its role in quantum theory.
Best regards Tony
PS Let me add a paper describing the way a fractal structure helps assist replication within the biological cell: Conference Paper A range of fields over the spectrum in a cell colony may con...
A range of EM and vibrational fields across the spectrum initiated by the dielectric response of biological tissues in a colony of cells may control the timing of its cell cycle. The basis of these fields in biological tissues is the energy slide across the spectrum of their permittivity. The main features of the various field mechanisms within the cell cycle are: (1) an initial charge alignment caused by the energy slide due to the tissue permittivity of the colony; (2) a collective feedback between the colony and the central cell; (3) a superposition of fields that can act simultaneously; (4) a speedup in this initial electrostatic field due to the energy slide; (5) a diffusion and self-organization of dipolar membrane proteins near the cell's polar caps; (6) various resonances across the spectrum including the whole cell; (7) the rounding and stiffening of the cell as metaphase is approached; this enables the various specialized fields required to locate the aster poles, the centrosomes, and the microtubules; (8) a possible resonance of the chromosomes (chromatids) acting as loop antennas when the cells begin communicating with each other via UV; (9) a magnetic field that may assist in replicating the chromatid.
"
So the photon is like an atom within which there are 'wave-particles' at the level of the sub-particle. Notice the photon is neutral in charge so there may be two equally charged 'wave-particles' in the photon's structure. But if there are two such wave-particles, then we have described a fractal structure: just like the atom, so too perhaps the photon, so too perhaps the 'wave-particles' making up the photon.
Similar in part like Planck's discovery of discrete frequencies, but inside a fractal structure, one that may keep on going ad infinitum.
Hi Karl, Herb
We have got here rather quickly but nevertheless have you got any comments?
I made the following comment at https://www.researchgate.net/post/If_humans_have_souls_when_and_how_is_the_soul_created?view=5aa0153340485432660e5d9d
" Dear All
We are having a discussion about the "physics of reality" athttps://www.researchgate.net/post/Should_Fields_or_Voltages_be_used_in_the_current_formulations_of_Quantum_Theory?view=5a9d90b6eeae39d57d7e155a
"So the photon is like an atom within which there are 'wave-particles' at the level of the sub-particle. Notice the photon is neutral in charge so there may be two equally charged 'wave-particles' in the photon's structure. But if there are two such wave-particles, then we have described a fractal structure: just like the atom, so too perhaps the photon, so too perhaps the 'wave-particles' making up the photon.
Similar in part like Planck's discovery of discrete frequencies, but inside a fractal structure, one that may keep on going ad infinitum."
My idea is that the photon is part of the fractal of creation including life.
I see the photon as an 'infinite fractal' in which our dreams our thoughts, our souls play a role.
When Jesus died on the Cross He gave up the Spirit; it was His last conscious act before death. After this He was dead on the Cross. He gave up His Spirit. We could interpret this as perhaps some very tiny part of His Being, His Soul."
Dear Tony:
I have moved beyond the Old Greek obsession with nouns and objects towards verbs and relationships: more like Whitehead. As such, although I build on the universality of electrons (UET) as the ultimate material (point) objects, I give them no other properties than INTERACTIONS with other electrons, allowing the eventual appearance of large stable structures, ultimately living matter (including ourselves) and our most positive form of relationships (i.e. LOVE). Thus, my physics is now inspired by organic reality; not timeless human abstractions like mathematics and logic. One deeper result is to simplify the "objects" of the world by eliminating our human simplifications of abstract pseudo-existents, like LIGHT, imagined to be either a wave (water analogy) or particle (pebble analogy), both of which have their own "mathematical" models.
Hi Herb
" This is a collection of ideas that together form a new worldview opposed to .... Mechanical Metaphysics, which arose around 1700 in Europe with the modern Scientific Revolution. " Well we certainly agree there Herb. We need a return to the study of metaphysics.
I note that the object that fully represents the previous form of physics (during what I might call the 'late quantum era 1927-1996') was the electron orbital , a probabilistic object that gave the expectation of finding the electron in an atom; it is almost thoguht of as a 'solid' whereas it is probabilistic due to the method of solution. - Thought of this while I was doing some research on Whitehead: it is impossible, says Whitehead, to conceive of a simple spatial or temporal location. To think that we can do so involves what he called “The Fallacy of Misplaced Concreteness,” the error of mistaking the abstract for the concrete (1925, 64, 72). This is a very interesting time in regards quantum theory with its inherent uncertainty.
As to the view that reality is actually a fractal (in which we don’t have a full knowledge or God’s Eye View):
Notice that implicit in Maxwell's equations is a circular period of analytic differentiation that may be mirrored within creation. For instance the gravitational fractal structure we see is partially based on this analytic cycle. When we differentiate the terms within Maxwell's equations at the EM level we end up with a period of 2 over which the terms begin to reappear.
Dear Herb
I also find this at https://plato.stanford.edu/entries/whitehead/
"fixed scientific cosmology which presupposes the ultimate fact of an irreducible brute matter, or material, spread through space in a flux of configurations. In itself such a material is senseless, valueless, purposeless. It just does what it does do, following a fixed routine imposed by external relations which do not spring from the nature of its being. It is this assumption that I call ‘scientific materialism.’ Also it is an assumption which I shall challenge as being entirely unsuited to the scientific situation at which we have now arrived. (1925, 22)"
The current cosmological prediction is often given as either the "Big Freeze" or the "Big Crunch" one or the other, both hellish forecasts.
Note that in SFT the new mathematics that we are talking about as a 'modern deterministic quantum theory' we find that the mathematics can supply a 'cosmostasis' a dynamic equilibrium where the whole of the created Universe comes into a final state of balance, and where life can continue unabated. (see http://www.unifiedphysics.com/)
Tony,
Let me say that I personally tend to agree with Karl, in that the notion of field in physics is more of a model to represent a putative form of behavior of space than its very structure and activity. It is true that the notion of self-field of particles was indeed originally a classical construction before it became adopted by QFT. The interesting thing is that QFT fell into the same quagmire that undermined the classical development of particle field physics, which was exactly due to the idea of self-field and initial conditions of interaction. This line of thoughts and representation brings you directly to the trauma of Renormalization.
I think that a true discussion of the pertinence of the notion of field in physics is overdue. My approach to this question is thru the notion of scale or shell of matter. One must attempt to understand the physics that you are left with, when you eliminate all structures beyond the realm of elementary particles: neutrons, protons, electrons, muons (all fermions) and photons. In this visualization, the universe is still edge-less and bound-less. And every object exists against one another, whether you imagine them separate from one another or stacked with one another. One could call that cauldron the elementary shell of particles or the natural particle gauge group. The void that exists ontolologically within any of these objects is of the same tensorial nature as the void that exists between them. And if you consider that the void is ontological to every particle object then you will have to accept that no object is local or “localized” from the point of view of its space spread component. And that the ontological space spread of an object is both internal and external to the object. What is most important to understand is not the physical separation between objects in this context but the correlation that exists between the scalar and the spatial torsion of the void in the entire gauge group. It is an invariant that is foundational to the transformations that are necessarily taking place in the gauge group. It defines the very Symmetry conformal to the gauge group.
If you want to introduce a circumventing field to the particles in that group to explain motion, then you have ignored the important fact that the void of space is intrinsically dynamical, it creates the wavefunction that characterizes each particle and that motion is primarily a covariant result between the specific scalar and space spread (aka wavefunction) making up the particle. If you want fermions to have a classical circumventing field, then you must assign a field to the photon in the gauge group as well, simply because they exist on the same ontological plane (I call it a Quanto-Geometric spectrum). Yet the idea of a field of any nature to the photon is extremely problematic and difficult to sustain.
How does a free particle become a “bound” particle? If the field existed, it would have to create structure within the same gauge group by agglutination of particle objects at the very least. What we see instead is an extraordinary systematic between neutron/proton and electron resulting from a new form of spatial void. It is by explosion of the activity of the vacuum pertaining to the elementary gauge group that atomic void arises (orbital edifices). In other words, the Symmetry of the elementary vacuum breaks or explodes in order to conformally create the atomic void, vital component of a new gauge group. The vacuum within an atom is not of the same nature as the vacuum inside an elementary particle. Further, one ought to remain cognizant that it is because classical theoreticians were attempting to explain atomic phenomenology with the field notions in vogue in classical physics that they notably failed to understand and unravel the latter. And I will even add that it is because we are unduly still clinging to the classical notions of fields in quantum theory that we are unable to understand structure or true shell structure (and other elements of organization as well) at the nuclear level.
My personal view.
Cordially
Dear Tony
The idea of fractal structures for space-time or even for intrinsic particle dynamics is indeed a very interesting field of research activities, cf. for example some of the contributions of L.Nottale.
https://www.researchgate.net/profile/Laurent_Nottale
https://www.researchgate.net/publication/251916649_Theory_of_Electron_in_Scale_Relativity
It is tempting to believe that this idea might be a key to 'prove' that there exists something in 'physical realitiy' which embodies physically the mathematical idea of the infinity of the set of natural numbers (introduced mathematically by means of the Peano axioms or by similar logical constructs) and of the dense and (Cauchy-)complete set of real numbers.
On the other hand, one must be very carfeful in extrapolating the results of physical 'observations' or 'measurements', which in any case only refer to a finite number of systems and a finite number of processes and a finite number of results. As I already mentioned in a comment to https://www.researchgate.net/project/Unification-of-classical-mechanics-and-quantum-mechanics-into-one-particle-mechanics I think that it is also reasonable to concentrate on generalizations of the math. concept of real numbers which lead to an enlarged set of numbers which includes the real numbers as well as a particular kind of 'fuzzy' numbers as two disjoint subsets. This should offer the possibility to replace the idea and concept of a 'sharp continuum' of numbers by some kind of 'fuzzy discontinuum'. And a resulting mathematical theory ('fuzzy manifolds'??) might lead to a geometry which is much more appropriate for the physical phenomenons on the atomic and subatomic and subnuclear scales. If this would turn out to be convenient, then we would have the quasi-paradoxical situation that 'fuzzyfication' is the price which must be payed in order to continue in making use of 'sharp' real numbers for setting up convincing physical theories.
Thanks Joseph, Karl and Herb
Let me say I do respect ALL of you including Herb (although Herb, you're a bit Bolshy for my liking, although Jesus was a passive rebel, but I do share some if not many of of your ideas; I'd like to continue the discussion we have begun; we need to see each other’s points of view).
I'll have to think hard about what you're ALL saying as a choir back to me. So give me time to respond to what I understand of your comments. (I need to read your words and references carefully)
I maintain that SFT is a very different mathematics to what we have seen for the past 100 odd years’ mainly this is because in SFT we don't get the terminology of 'fields' mixed up with ‘potentials’ (voltages)-I think this is a result of doing electrical engineering in my undergraduate learning; fields are DIFFERENT to potentials yet not a peep from the three of you. None of you has even mentioned this as an aside which I find very strange; ALL of you are focused on something that I’m not understanding completely. Surely you can see the mathematics of what I’m saying about such things as gauge, and difficulty of working with actual potentials, or numbers of ‘wave-particles’ and its relationship between probabilistic quantum theory (PQT) and the different mathematics of using Two sets of Maxwell’s equation for the two particles in the simple model of the atom?? These are all great steps forward in the solution of the ‘physics of reality’ above probabilistic quantum theory which has now been pretty moribund for several decades; it is SFT that adds a complete knowledge of ‘binding energy' that is not seen fully in PQT (‘through a glass darkly’ http://www.dictionary.com/browse/through-a-glass-darkly because of its inherent errors and its basis that has been there since statistical mechanics days of Maxwell and Boltzmann)
And when I say 'infinite' fractal I am extrapolating from finite to infinite; perhaps I should be careful not to extrapolate without suitable caveats about our Universe which may contain only certain parts of the infinite fractal which could be described as a finite quantum physics depending on the initial forcing function (the Big Bang); perhaps there ARE universes within the multiverse that depend on the finite quantum physics available (the initial forcing function given each Universe - by God?). BUt this is ignoring 'life' including humankind which may be 'semi-infinite' rather than finite.
Our 'visible' view of 'reality' does see {partial) fractals within physics, biophysics, cosmology, metaphysics, consciousness (awake, subconsciousness including sleeping, hypnosis, near-death experiences etc). Now these are advances on what we see in PQT where what we see is 'material’ only whereas SFT now sees a more complete view of what we have always thought of as ‘life’ and ‘spirit’, and ‘soul’ from the many sources, prehistoric, ancient, and new, Holy, and secular, of the natural and metaphysical Universe around us.
In the meantime I lifted this from my website which I see as the main point of our discussion:
LIFE AS A PHOTON FRACTAL: BODY, MIND, SOUL
As a consequence of the composite photon within SFT (see above), and the fact that there is a recursive need for fields at each successive level below the sub-photonic level, the photon has an internal structure that resembles a fractal, both a single photon with many levels inside it, and a bosonic fractal structure involving many different bosons forming different levels (our universe). Note that the whole universe is potentially an infinite fractal including all life within it.
Thus all known physics is observed to be a fractal structure extending from the domain of the photon to the domain of the universe. Much of biology is known to involve many fractal structures. Life too may be based on the composite photon with its fractal structure at the small end of the size spectrum. Hence there are possibly fractal levels within life itself, as well as biology and the physical universe. Our memories, thoughts, loves, beliefs, etc may be able to be stored as information in these photon fractals. This may be one reason why life extends beyond death. Death of the mortal body via physical means cannot destroy this internal photon structure and its layers of stored information; it is outside the energy levels inherent within the Big Bang and ongoing expansion of the universe. Thus human life (perhaps all life) may have a reality beyond physical death as the Bible says.
NOTE: The terms 'fractal', 'domain', 'gauge', 'diffeomorph', etc all mean slightly different things to different scientists, but they are all talking about a set of self-similar structures; in mathematics the term 'non-linear infinite series' (e.g. geometric series) is also composed of self-similar entities. Fractal-like structures are seen throughout physics and biology.
http://www.unifiedphysics.com/)
kind regards Tony
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Joseph Jean-Claude
QG Psychophysics Lab
>>>I maintain that SFT is a very different mathematics to what we have seen for the past 100 odd years’ mainly this is because in SFT we don't get the terminology of 'fields' mixed up with ‘potentials’ (voltages)-I think this is a result of doing electrical engineering in my undergraduate learning; fields are DIFFERENT to potentials yet not a peep from the three of you
Tony, I fully understand from your interventions that the notion of field is central to your theory and that you have a refined proposition for its ontology. Although I have yet to see the details of this development, I will say that what we commonly understand to be a potential is intimately related to the existence of a background physical field. The potential being cast as a difference between two points of the field. Gauge Theory, as you know, is modeled after the voltage potentials of an “electrical space” whereby the laws of electricity remain invariant no matter where in that space you chose your potential difference.
From that perspective, in order to understand what a field is ontologically, we would need to understand what a single point of potential really means, because in the model the field is populated by points of potentials. Or the ensemble of points of potentials make up the field. If you want to make a step forward, you would have to explain the physics of a potential point, beyond the pure mathematical representation of a potential difference (which only has mathematical meaning).
This takes you into a form of representation of continuum. If the field is made up of points (points of potential or else), then it is quantized. However Maxwell fields as well as Relativistic fields are conceived to be zero-point fields. Relativistic fields (EFE’s) refer directly to the void of space and the way that the Theory characterizes it is principally via tensors. I believe that the tensorial representation for the continuum of space is more assertive over the point representation, which is what Quantum Gravity is nowadays trying to achieve.
It is up to you to give us a taste here of how SFT models space in its field representation.
By the way, I fully understand as well that the stake of your SFT Theory is to achieve an interpretation of not only dynamics systems but biota and behavior as well, which is by all accounts no less than commendable.
Cheers.
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Tony Fleming
biophotonics research institute
Hi Joseph
Can I suggest you read my paper attached herein and published in
Electromagnetic Self-Field Theory and Its Application to the Hydrogen Atom, Physics Essays, Vol 18, 3 2005.
You will see a totally different formulation to probabilistic quantum theory being posed via Maxwell's equations in conjunction with the Lorentz Equations.
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Karl G. Kreuzer
Tony,
I agree very much with most of the conceptual ideas of the "self-field" (SF) you mentioned in Electromagnetic Self-Field Theory and Its Application to the Hydrogen Atom, Physics Essays, Vol 18, 3 2005.
SF can be viewed as a candicdate for an underlying principle for the type of motion of electrons with respect to the nucleus inside an atom. The idea that a large number of 'bound photons' confined inside a stable atom perform some 'collective motion' and which thereby give rise to the notion of a "self-field" seems to be very natural. Following this idea the concept of the "self-field" (and more generally a "field") represents a way to reduce the system of 1 nucleus + Z electrons + N 'bound photons' to a system of (1+Z) particle-like objects + 1 "field"-like object. It would be great if such a system could be handled mathematically and numerically by classical electrodynamics and relativistic mechanics (which would require to guess and to assume some appropraite initial conditions and boundary conditions for the dynamical variables of the system).
However, it is also very natural to assume that in contrast and in addition to the 'collective motion' of 'bound photons' there is a kind of 'stochastic motion', and/or to imagine that the 'collective motion' is merely a (good or bad) approximation for such situations where the degree of disorder of the stochastic motion is very low. In the case of stochastic motion one can adopt the idea of path integrals in order to describe 'motion' of a particle-like object. What seems to be strange in the path integral concept is the fact that there is no unique path (with lowest action) for a particle to move from a position A to a position B in 'space', the latter considered as a continuum.
If 'space' is considered as a DISCONTINUUM, i.e. a GRID for example, then it is quite obvious that there are several ways to connect A and B with a path which has minimum length. This means that the requirement of length to be at minimum is not sufficient to distinguish a particular and unique path among a huge family of many other paths. Instead of using the length of a path (i.e. the trajectory of a particle), the same arguement can be applied to the integral of the action along the path. In the case of a discontinuum it turns out that the classical action principle is not sufficient to distinguish one particular and unique path among many others.
The path integral formalism offers one way (but not the only one) out of this dilemma by introducing a complex-valued "transition amplitude" and a "propagator" for each pair of points along a path and by specifying a particular path by requiring that the transition amplitude for a propagation from point A to point B along a path C is given by the complex-valued "phase" exp(iS(A,B;C)), which leads to an integration in a space of functions (path integral). Just by using the word "probability" for the square of the "transition amplitude" and by ignoring resulting physical-ontological problems and mathematical problems of path integrals one usually arrives at a formalism which looks like Schrödinger's wave mechanics or QM in the position representation. The question of whether or not this "probability" interpretation is necessary and reasonable seems to be one of the most suppressed problems in contemporary quantum physics.
However, it seems that the physical meaning of the path integral concept can be founded in a quite different manner which is related to (1) ideas involved with particle structure and non-emptiness of 'space', and (2) ideas involved with a discontinuum as a math. means describing non-empty 'space', and (3) a set of a new kind of 'numbers' which has something to do with a rigged Hilbert space and which serves to describe the situation that there is (for various principle reasons) a non-vanishing uncertainty whenever rational or real numbers are associated with dynamical properties of a physical system at atomic or subatomic scale. All these things are subjects of my projects which are listed in my RG profile.
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Tony Fleming
biophotonics research institute
Hi Hans
Pardon me for moving our discussion (initially it was you writing to me in another project about the flyby anomaly) to this separated project space because I thought it better placed than in a project designed to interrogate the reasons behind the flyby anomaly where self-field theory (SFT) does appear to be giving a possible solution via the binding fields (rather than the potentials) between gravitational bodies within gravitational theory. This possible solution to the flyby anomaly via SFT does appear to be associated with the knowledge of the binding energy within SFT, and this is only seen in PQT (probabilistic quantum theory) 'through a glass darkly' because of the errors associated with PQT (probabilistic quantum theory) for which only Feynman diagrams apply which are simplified versions of the actual binding energy seen more accurately in SFT.
Article Self-field theory, general relativity and quantum theory
Despite several comments I notice you all have still not addressed the mathematical difficulties associated with the problem of solving the atom by posing the problem via potentials and not fields; although Karl has now mentioned it at least I see. If there is any mash in mathematical physics it is the use of the term 'field' in PQT (probabilistic quantum theory) while using actual potentials (voltages); and this has been standard practice for over 100 years. Those 'fields' are voltages; simple. If you want to solve for potentials you have to do a hell of lot more work than the solving for the fields via Maxwell's equation. And in practice the numbers of unknowns for the actual fields (the photons) turn out to have only one variable in PQT whereas they have two if we pose the problem via SFT using Maxwell's equations directly.
Hi Karl I will address your comments in a separate reply.
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Tony Fleming
biophotonics research institute
Hi Karl
At last, someone is addressing the original question for which I thank you. Can we use SFT as a basis for a more 'sophisticated' version of quantum theory, one without probabilities, a 'modern' version of quantum theory, if you will. I should think about what your saying, so give me some time to think.
BUt let me reply about your complex valued phase, I think you're right; we may be able to handle the motions inside an integral equation approach in such a way.
I have always thought of the three most common types of numerical approach to modern engineering problems, finite difference method, finite element method and boundary element method.
More to come Karl on the rest of your comments
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Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
Counting is a real activity by real exemplars of reality (humans) of real (sensory) distinct, stable, identifiable objects. The results of this process are given the VERBAL label NUMBERS.
As such, like most thoughts, they are NOT real (epistemology .NE. ontology). This is the core of the CON-trick played by mathematicians for thousands of years.
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Tony Fleming
biophotonics research institute
Herb
How about the mathematical search to find out how earthquakes happen? There is reason to believe that galactic fields are based on nuclear fields in the same way that solar system fields may be based on electromagnetic fields. We may be able to pinpoint how magma plumes inside the Earth's Core are initiated via gravitation from the Black-hole at the centre of our own Galaxy. (This may be a reason behind global warming perhaps.)
Again this is an example of knowledge of the binding energy within the Milky Way. Surely these physical thoughts are directed to help us in our existential plight which is a real plight for millions if not billions of people around the Globe, therefore ontological.
BTW Karl still working on my reply to your interesting response
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Joseph Jean-Claude
QG Psychophysics Lab
Tony,
I read, and I have the following comment.
With SFT you are relitigating a classical approach to the Hydrogen atom. The stake is perhaps to do away with the uncertainties and interpretative deficits inherent to Quantum Mechanics. I can be sympathetic to the objective but not the means.
Here is the problem. The free electron is not the same object as the bound electron. Therefore the field attributes to explain the dynamic system in the simple H atom is an impertinent approach. In chemistry, while a molecule is made up of 2 atoms minimally, the properties of the new molecular object are completely different from those of the constituent atoms. The molecule as an object does not exist on the same scale as the atoms it consists of.
Thus far, the problem of a hierarchical scale perspective has traversed our entire physical science and is majorly responsible for a vast swat of problems in physics. Field dynamics relating to particles cannot explain the atomic edifice. The atomic edifice possesses new attributes and ontological properties that are completely different from and stranger to field dynamics between free particles. That is why the fundamental premises for an ontological explanation of structure inside the H atom completely ignores the nucleus by pre-supposing that the bound electron simply behaves like a closed standing wave in a box of its own. With the added presumption that the energy is distributed by a factor of h. When these conditions are properly mathematically formulated (even employing the classical time variable), it organically results in a complete obliteration of the classical perspective, while bringing about a string of powerful solutions insofar as the observed energy spectral lines of the edifice and most importantly a deep understanding of Atomic Elements based on energy shells, foundation of the entire science of Chemistry. Most modern physicists do not understand the momentous role played by the emergence of Quantum Chemistry science in the final acceptation of Quantum Mechanics, one major caveat of which is indeed the ignorance of the nature of wavefunction animating the bound standing wave associated with the electron shell.
It does not matter how unwittingly Planck came to the realization of h, and how immature his views about that constant was, there is no natural mixing of Maxwell with Planck’s h, because Maxwell’s electromagnetic perspective leaves no path to the emergence of h as the cornerstone of the quantum physics present in nature.
As a rule, photons do not exist in the atom at ground state. In other words, they are not first-order ontological components of the edifice. They only appear phenomenologically (as a result of interaction) or as an effect of constructive instability. Although the shell-transition photonics of the atom may be important to understand from a technological viewpoint, it is my view that photons are best studied and understood within the framework of their own scale or Shell of matter, from a fundamental theoretical perspective.
Cordially.
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Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
Tony:
Earthquakes are time-sensitive activity of a complex system.
Mathematics has made very little progress in representing complexity being gounded in simple arithmetic, simplified geometry and vague statistics.
However, human ego thinks it can solve anything and know everything.
Bah, humbug. Physics is stuck in two-body simple models, like the hydrogen atom.
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Tony Fleming
biophotonics research institute
Thanks Joseph and Herb for your thoughts; I'll answer Joseph in this reply and get back to you Herb in a separate reply.
Joseph wrote "Field dynamics relating to particles cannot explain the atomic edifice."
No, absolutely not, you miss the essential point of self-field theory (SFT) which I will elucidate herein. It can explain the edifice much more accurately than previously. This is the crux of SFT and how it is indeed an evolutionary step forward from PQT (probabilistic quantum theory) towards a deterministic quantum theory (DQT) where the fields are used and NOT the potentials.
The binding energy is seen as a number, a scalar, if we treat the problem via PQT; problems in general have been solved as only the energies or masses of particles. We lose all contact with the fields, their direction and their physics. We end up with probability densities because of the nature of the way the problem is posed (via 2nd order mathematics). If we use 1st order mathematics as per SFT we end up with ALL the physics of the binding energy, its actual motion within the atom, and an essential physics in how these binding energies work. It is easy to miss this essential point and want to do things as we have always done them via PQT, but it’s a road to nowhere, only by SFT can we progress in our understanding of the physics of the binding energy.
In SFT the physics of the binding fields (on which the binding energies are based) are motions that complement the motions of the electron and the proton.
What am I talking about? Well in electromagnetic binding fields there can only be ONE such binding field going FROM one particle and going TO another particle (in EM). Doesn’t look much but this is the corner stone of SFT; there’s only one stream of particles per field (two altogether in EM fields). In PQT there are infinitely many streams.
Maybe think about this before I spell out how this changes PQT fundamentally, and how it simplifies the problem from what PQT sees.
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Joseph Jean-Claude
QG Psychophysics Lab
Dear Tony,
I will not chastise any Theory that is able to cast true contributions in terms of verifiable results, even if it only qualifies as an alternative methodology towards producing otherwise known results. If one is able to produce assertive deterministic physics for the microscopic world, that may lead to the establishment of a direct connection with known physics for the cosmological realm, aka Relativity. The pertinence of such a development is because Unity in Physical Law qualifies as a must for contemporary physics. I may need to spend more time on SFT to identify the details of the claimed contributions.
Nevertheless I confess that I am still somewhat reticent about your development, not being a friend of time-driven formulation of any physics. You write: “If we use 1st order mathematics as per SFT we end up with ALL the physics of the binding energy, its actual motion within the atom, and an essential physics in how these binding energies work.” In the interest of accuracy, I have to say that Schrodinger’s QM did not start out with differential equations but with a first-order functional description of the wavefunction animating the electron shell of the H atom. Moreover, that function was a time-driven function! It is the mathematical constraints inherent to the formulation that called for the quantum Operator and its eigensolutions. (I am not an advocate of Dirac’s Lagrangian of the H atom despite its two virtues.) Allow me to point out here as well that it is possible to significantly augment the intelligibility of bound quantum systems thru a re-dimensioning of Probability Theory, as I have demonstrated in Chapter 7 of my publication.
Data Quanto-Geometry Vol I: Chapter 7 - Quantum Phenomena in the Macrocosm
My second point of objection is your apparent assumption that in order for the physics of the hydrogen atom to be intelligible, it must be deterministic, based on a time-driven mathematical formulation. As much as you assume that the field artifact must be of necessity a part of the dynamics as a physical property. These are all a-priori assumptions heavily influenced by the Maxwellian perspective of physics. For me the marriage between Maxwell and Planck in the Theory is no less than traumatic because I did not see a foundational discussion of discreteness and continuum as they relate to the ultra-structure of the field, despite the nuance between voltage and potential that you emphasize. Maybe you could stir the discussion here in that direction and bring more clarification.
It may be that QM can only explain the two-particle system represented in the H atom. However it should never be underestimated that the energy density eigensolutions contributed to the profound shell understanding of Atomic Elements per their distribution in the Mendeleev Periodic Table, a momentous achievement that stamped QM in the physics community in its time. This historic fact is all too often ignored in contemporary physics, and any alternative theory must accomplish that much in my estimation.
Cordially.
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Tony Fleming
biophotonics research institute
Joseph
Actually it was by showing that the results were identical to PQT that SFT is shown to be validated. But as shown by the many other projects and scientific papers on my RG page that SFT is shown to extend its range of application far further than PQT.
It is exactly that shell description of the atom that the new mathematics zeroes in on. It is the Pauli exclusion principle that pops out of the physics. If we have a single electron in an outer shell the only way we can get another one in the same shell is by having it in an 'asymmetric' motion, or equivalently 180 degrees out of phase with the first electron. Thus the shell physics is all there inside SFT. Thus there is only ONE pair of photons streams per electron/proton pair. We have TWO streams per shell. If these shells are applied to the substructure of the nuclear particles we find a shell structure of the proton inside the nucleus in analogy with the electron inside the outer shells.
BOSONS including photons have there own 'shells', but more later.
There is a physics of orthogonality for all other shells.
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Joseph Jean-Claude
QG Psychophysics Lab
Tony,
It sounds very promising. If indeed the claims verify true, SFT will constitute for sure one solid element in the arsenal that is needed in order to break thru the new physics, by helping elucidate such conundrums as the full structure of atomic nuclei, the nature of the electron shell wavefunction and particle wavefunction in general, and others…
I will take a deeper look as time permits.
Cheers.
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Joseph Jean-Claude
QG Psychophysics Lab
Herb,
You write: “As such, like most thoughts, they [Verbal Label Numbers] are NOT real (epistemology .NE. ontology).”
Why are human thoughts unreal, Herb? I do not believe that there may exist any (sensible) human experience whatsoever without human thoughts. So therefore thoughts must be real as intangible as they may be. Whether they are electrical currents in our biological brains, or “field” projections from our brains as Tony might say, they must be real.
There is also the possibility that mentation is a 4-space or 5-space meta-phenomenon beyond 3-space biology of the living. Should that be the case, human thoughts would be even more real than biota or biological identity. This is for certain what religion of all stripes around the globe is telling us in their own cryptic languages!
Cheers.
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Tony Fleming
biophotonics research institute
Actually Joseph there's a certain @JohnJupe who can tell us all about those 'field' projections of our perceptions
best regards Tony
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Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
Really, Jean-Claude:
There was no objective reality before talking hominids appeared on this planet? Is that hubris or ignorance?
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Gudlaugur Kristinn Ottarsson
Academy of Industry & Arts
Dear Tony, regarding your question about "fields" and "voltages = electric potentials" as mutually exclusive, they are indeed the same - as we can have fields of any physical quantity, such as velocity, temperature, current, etc...
However, Hans van Leunen "structure", was already embedded in Maxwell's equations back in the 1860's by using 4-currents and 4-potentials that 50 years later became fashionable - while many took it for an abandonment of our good old 3D space which still holds good, if not only for the fact that 3D space is the only space that you can tie knots = create particles.
All the best,
Gudlaugur
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Joseph Jean-Claude
QG Psychophysics Lab
Hello Herb.
I am not sure you understand my point. I am surely one who believes that reality is observer-independent, if your last answer is calling me to task on that.
But I don't believe that human thoughts are unreal. They are deeply and extensively structured. And they can be subject to keen analysis by mathematical categories, as I have demonstrated here:
Article Mathematical Foundation of Human Cognitive Categories of Aim...
So too much structure for something that is not real.
Their intangibility does not mean that they are unreal. Simply that they exist in a dimension that is beyond 3-space, possibly 4-space or 5-space.
Lastly, if you equate mentation to consciousness, then that can open a better window to visualize them as some form of tangible experience, as refined as it might be, (but not unreal). Don't you think?
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Kazuo Oie
Oie Clinic
＠Joseph and readers;
You wright
Mass and weight are different properties, which are defined in the field of physics. Mass is a measure of the amount of matter a body possesses while weight is a measure of the force that is caused on the body by the gravitational field.
End of quote
Am I right to consider the force on the body by the gravitational field, is generated with The energy that is released by E=MC square not with a measure of the amount of matter a body possesses? I FEEL (thank the existential experiment by Qigong), NOT THINK both are the origin of energy, is this a kind of confusion?
Sincerely Yours;
Kaz
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Joseph Jean-Claude
QG Psychophysics Lab
Dear Kazuo, you write: I FEEL (thank the existential experiment by Qigong), NOT THINK both are the origin of energy, is this a kind of confusion?
For more on the distinction between sensation (sentiment) and volition or motivation, I invite you to read the paper I mentioned above. An analysis of how human thoughts develop within the framework of a coordinate system that axially incarnates these variables. And according to a well defined Function.
As to energy, one pertinent approach to the nature of the same is that there is two different basis kinds of energy. One is discrete with an irreducible equal to h (Planck constant) and the other is thermodynamic temperature with an irreducible equal to the Stephan-Boltzmann constant (σ). The second tends to behave as a continuum while the first tends to behave in bumps or packets.
Now according to Einstein gravitation is the result of the structure of space-time which acquires geometric properties under the impulse or presence of Mass. It does not require that any of the involved masses be moving at c, so E = mc2 does not apply to that dynamic. Einstein tried to seminally explain gravitation while Newton simply described it. But I think that if you should prefer Einstein’s approach (whether by intuition or reason), you are more on the side of the internal geometry and activity of spacetime than kinetic energy acquired by mass. Kazuo, what is the sound cast by one hand applauding?
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Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
Dear Joseph Jean-Claude:
I was pointing out that human mental constructions are personal (subjective) so they necessarily simplified (abstracted). Coherence is another meta-linguistic requirement but this does not bring them to the same level of reality as our shared sensory inputs (empirical evidence).
MAPS are real objects (paper) but they are NOT the the Territory.
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Joseph Jean-Claude
QG Psychophysics Lab
Herb,
You write: “MAPS are real objects (paper) but they are NOT the the Territory.”
True. But I don’t think that analogy quite faithfully reflects the point of the argument. A theory or a mental construction is successful to the extent that it is conformal or homeomorphic to the aspect of physical reality it attempts to model. Obviously the mental construction is not in itself that particular aspect of physical reality, but that does not mean that the mental construction has no physical reality per se. Just like a miniature model of a large object, like a home to be built, is no less real than the built home.
The crux of the argument is to understand that you cannot or should not exclusively circumscribe physical reality to 3-dimensional reality or 3-space. It is by pursuing a theoretical explanation of mathematical-physics nature as to why our universe of inhabitation is 3-dim or 3-space that one is led to the firm conclusion (by way of derivation) that other nth-space must exist, in confirmation of the propositions from religious metaphysics of old. Obviously falsification in that case requires observation, as the final seal.
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Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
Dear Joseph:
Your vocabulary betrays your pre-soaking in abstract mathematics.
The serious point here is that our one-dimensional symbolic scheme (based on linear speech) CANNOT adequately represent the reality of THREE dimensions of space and the mystery of time, especially in static models, like language, logic, mathematics that were deliberately castrated at birth.
So here's a challenge: give us all an adequate DEFINITION of existence.
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Joseph Jean-Claude
QG Psychophysics Lab
Herb,
Does the term “abstract mathematics” qualify as a tautology and reflect a pre-soaking level in the understanding (or epistemology) of Mathematical science, since all of mathematics is in fact a total abstraction. To remain respectful, I will just take it as a language hiatus and I am no one to chastise anyone for a hiatus.
I do not believe that there is a “mystery” with time. What I believe is that there is a problem with time because time is a human construction that does not exist physically. If you are looking for something unreal, TIME is ONE. Time is a dimension that humans we impute to physical reality and that is not part of it, because a natural unit of time, long sought, has never been found.
This brings us to the question you ask: can you give us all an adequate DEFINITION of existence.
The existentialist question of all time, at the beginning of all avenues of knowledge, isn’t it? My answer to this question is clear and concise, and interestingly this is exactly where I anchored the development of Quanto-Geometric Theory. Just so I don’t repeat myself, here is a copy and paste of what I have written elsewhere about the irreducible duet that makes up everything in existence: the scalar and the spatial void spread.
Identity Definition
The scalar is a packet of some-thing as much as the space tenet is a spread of no-thing or the void. The first is as tangible as the second is in-tangible. Therefore both tenets are normal or reciprocal to one another. This definition is formally expressed by the relation: Q x S =1 or Q = S-1 (1), where Q is the scalar and S the space spread.
Attributes
The scalar is: 1) dense, 2) a-morphous and 3) static. Whereas the void spread is by contrast: 1) extent or expansive, 2) morphic or morphogenic and 3) motional or dynamical.
Phenomenology or Universal Covariance
In the universe, dual ontology is absolute and exclusive. Hence, there is no pure scalar as much as no pure space spread. The basis topological state of the universe is ultimately that of coexistence between the scalar and the intangible void. Their only fate is to correlate with each other. This conservation constraint creates the most primal order of ontological covariance in the universe.
Objects’ Covariant Ultra-Structure
In the Quanto-Geometric canon, because there is no pure scalar and no other ontological basis tenet in existence than the duplet in question, the scalar must ontologically incorporate an affine degree of expansiveness, thus becoming a size-able or scaled packet at the very least and at most a density packet. For the very same reasons, now on the rubrique of space, the space spread must ontologically experience a pullback from infinite expansiveness which turns it into a condensed or tensive spread within its very fabric of void.
I suggest this other reading if you want to see the full mathematical development of these concepts.
https://www.researchgate.net/publication/313114545_QUANTO-GEOMETRIC_TENSORS_OPERATORS_ON_UNIFIED_QUANTUM-RELATIVISTIC_BACKGROUND
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Joseph Jean-Claude
QG Psychophysics Lab
Tony,
A few questions about SFT.
1.- What in the photonic interaction beam-like field makes the two-particle system a stable system energetically? Since they each spontaneously generate this beam continually. The report I read does not sufficiently address this issue.
2.- Is there any account of the fact that the beam-like field from the electron must overshoot the proton which is much smaller and result in a continued loss of energy?
3.- Since the interaction is mediated by this beam-like field between the two particles, what makes the system radially distributed from the proton as the radial origin and not a different point along the axis of interaction? Seems to me that the nucleus as the radial center is a must for SFT to be compatible with QM and duplicate its results.
Cordially.
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Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
Joseph:
You are simply a modern version of the ongoing Platonic Echo-chamber.
You bring nothing new to this discussion.
I shall henceforth ignore your postings as a waste of my time.
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Kazuo Oie
Oie Clinic
Dear Joseph and readers;
You said rightly “what is the sound cast by one hand applauding?”
To rather awake than master what Qigong is, you feel just it, although everyone is able to climb that level with proper training or warming up. An example clear and obvious to everyone is, the warmness and comfort felt at your forehead in sunbathe. Sunbeam is vibration with fine mass, and you feel nothing if without mass.
Kazuo
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Joseph Jean-Claude
QG Psychophysics Lab
As Tony rightly pointed out in his referred paper, the notion of field has traversed all of physics and plays a seminal role in the understanding of physical interaction within dynamic systems. This notion pertains to a family of representations to which the notions of material wavefunction and the very nature and structure of the vacuum are firmly attached.
I thought that anyone interested in physics would be positively interested in a discussion of such concepts because they are far from elucidated, as well as contribute to further their understanding in one way or another by sharing and discussing their views. In any case that is the reason why I participate. I have no desire for bitter polemics. A bon entendeur, salut.
Finally, it is my view that the seminal nature of the intangible represents the paradigm of our times, in philosophy, religion, science and culture. To me our advancement depends on its resolution.
Just my personal view.
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Gudlaugur Kristinn Ottarsson
Academy of Industry & Arts
Dear colleagues.
Perhaps we are all describing the same elephant - while from different perspective and from different scales, as by zooming both out and in, Newton, Maxwell & Einstein in fact totally agree, as elaborated and enunciated here:
Preprint March Update: Unified Horizons of Electricity and Gravity
All the best,
Gudlaugur Kristinn
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Tony Fleming
biophotonics research institute
Dear Joseph
In part you wrote
"1.- What in the photonic interaction beam-like field makes the two-particle system a stable system energetically? Since they each spontaneously generate this beam continually. The report I read does not sufficiently address this issue."
The rationale for this energy to continue, not 'continually' as in classical theory, but 'discretely' as in quantum theory is a series of elastic and coherent 'collisions between photon and electron and photon and proton. This is a 'cycle' of collisions which spells out a discrete electromagnetic interaction. This cycle of photon collisions 'continues' over time, by performing a discrete number of 'cycles' per revolution of the electron and the proton. It is estimated there are 54 of these photon 'cycles' per revolution of the atomic electron and proton.During these 54 'cycles' both the electron and the proton perform rotating periods made up of polygon-like sides (54 of them); these are NOT circular, but polygon-like a bit like Pythagorus’s ‘tessarae’ into which he thought space was carved into by ‘fundamental shapes’
It is therefore the momentum of each of the 54 collisions that defines Planck’s constant and it is this that gives us a mass for the photon.Article Analytic Estimate for the Mass of the Photon
Dear Gudlaugur
I am reading you update in a minute with much interest.
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Joseph Jean-Claude
QG Psychophysics Lab
Tony writes: “This cycle of photon collisions 'continues' over time, by performing a discrete number of 'cycles' per revolution of the electron and the proton.”
Therefore I assume that the system is rotating around a center point somewhere along the axis of photonic interaction. I further assume that the two bound particles are exchanging photons by elastic collision in order to remain bound to one another.
How does the angular momentum of the rotational system arise from collision of exchange photons with the bound particles? – I understand that there is a correlation between the collision frequency and the rotational period. But I need to see what causes the angular momentum of the system and why it remains constant.
Note that I have many other questions to come… if you don't mind.
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Tony Fleming
biophotonics research institute
Joseph
I have much to tell; hopefully I can explain all your questions. Do please continue. You are becoming acquainted with the theory by your 'fifth degree grilling' and hopefully the formulation will stand up to your inquiry. Remember I've been in the knowledge of this technique for some twenty odd years so I've learnt much but I'm sure there's a wealth of knowledge still tucked away.
I didn't start publishing before I could satisfy myself of what I was saying at each step. (I am hoping you Joseph might be able to write a review about the formulation in a special book about 'recent advances in mathematical physics', hopefully a positive review but an honest review nevertheless. As well you might like to contribute a paper on your own work?)
It must be a coherent series of elastic collisions. So while the photons basically bounce 'back and forth', the electron and the proton move 'around' in a polygonal like motion. The photon is like a small atom spinning around and around in a spherical like motion (an s orbital if you like). The electron and proton must also be a composite structure which allows them to recoil 'around' a polygonal path with 54 elastic and coherent collisions. I like to think of this all as a 'finite difference technique' but one that is not 'classical' but discrete, where these motions can be calculated in a time evolution. We might have to use predetermined speeds such as the photons (speed of light) electron, and proton and assume these collisions are 'perfectly coherent' to get a result that shows what we would suspect. Note that at the moment I have used a simple linear approximation to estimate the 54 photon collisions per cycle, but the actual problem appears to actually be parabolic splines around the polygon.
Your idea of 'bound' particles needs to be fleshed out.
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Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
The spread of the Field concept across physics reflects Group-Think and the power of the professoriat to determine the thinking of the next generation of academics. Physics is NOT a popularity contest: Nature Rules, while BS fools.
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Joseph Jean-Claude
QG Psychophysics Lab
Tony,
I appreciate the two invitations. But as you know time is never on our side. I will let you know in due course via internal messaging whether or not I can commit.
A few more questions on SFT.
In order for the two-particle system to have a chance to be stable, photonic collisions at both ends have to occur simultaneously. That means that the photonic field must be of bosonic nature (the interaction photons must be transparent to one another). However if the photons must behave like fermions, that is interact with external entities thru mass (since you have them collide with the bound particles and you even compute their masses), they cannot be transparent to one another. While we know that the photon has dual ontological nature (particle and wave), we don’t know that it can experience interaction based on these two tenets at the same time. Note that an explicit mass for the photon is a bold assumption because its momentum is not a function of mass per De Broglie, but of its wave function.
Secondly, not all photons should be allowed to mediate the interaction but photons of specific wavelengths, in catering to the fact of the observed spectral lines resulting from the spectroscopy of the H atom. How does the theory account for this necessary restriction? I have not quite understood the quantization basis of the system. You seem to attribute the quantization of the system to the number of collisions (54) per rotation of the entire system. That would set the basis of a different form of quantization not associated with h.
What am I missing?
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Tony Fleming
biophotonics research institute
Joseph
What you have looked at so far is nudging up against a fundamental limit within SF; maybe this next discussion will help you modify your viewpoint.
I don’t think it is necessary for the timings to be so exact that the ‘collisions’ HAVE to occur simultaneously but it’s an interesting point of view, maybe it comes from a strict view of ‘action at a distance’ which as we know disturbed Isaac Newton gtreatly’ I think he would smile at what I’m about to say since he was the original thinker about light being composed of ‘tiny cannonballs’ or ‘corpuscles’. His ‘cannonballs’ helped him in his gerdanken about gravity and a cannonball fired horizontally but falling towards Earth on the way to finding his gravitational formula between masses
Two elements in my reply:
(1) I think we have to have a system that enables a certain level of ‘imbalance’ in the overall system; things are not ‘perfect’ in the timing, nor is the physics. So that ‘bound’ electron for instance has to be able to flee from being ‘bound’ (still not sure about this, can you give me your thoughts on ‘bound’ electrons and if I’m seeing what you mean) when e.g. the conditions are suitable for ionization of atoms. Also for fissile material the instability of the whole atomic system has to be able to allow bound nuclear electrons (and neutrinos) to escape the binding.
So this small degree of imbalance means the whole system has ‘limits’ within which the quantum physics ‘still works’ but is heading in the direction for instability. (This leads to another quantum number where the electric and magnetic fields play a role in determining the overall stability. e.g. Zeeman and Stark effects)
(2) The whole mathematics is ‘fractal’ or ‘iterative’. For example I just assumed a linear-sided polygon (made from straight lines) but it should be something iterative, so we need to add in the ‘field-particles’ and the ‘mass-particles’ within the photon itself but then THIS is iterative too, etc, etc, each sub-particle needs a field at a lower level of ‘fracticality’. I used the g-lande factor for the electron but this is the limit of PQT whereas SFT is possibly infinite
So the Universe after this SFT finding sees no bottom of the size spectrum; in the same way as we didn’t see any upper limit until we discovered the Big Bang. Even now we imagine there’s a ‘multiverse’. At this point we don’t see any reason for an upper level at the ‘small’ end of the size spectrum and this is all within the photon, currently our smallest known ‘wave-particle’.
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Joseph Jean-Claude
QG Psychophysics Lab
Tony,
I am afraid you may have misread my comments. Part of what I am saying is this:
1.- your proton-electron system has the particles locked or bound to one another via photonic exchange. (I am using the term “bound” in analogy to the same term used in QM to describe behavior of the electron in the H atom with respect to the proton nucleus.)
2.- the photon emissions at both ends of your proton-electron pair must be in phase with one another for the system to have any chance at stability as a rotational system (I gather that the system is in rotation), and even if the system is not quite in rotation.
3.- if you assume the photons to be massive, then they must collide with each before they can reach the end particles (they are travelling in diametrically opposed directions). You can’t have the photons behave both as fermions and bosons. The only known particle with this ability is the neutrino.
4.- the closest known effect to your construction involving an elastic photon collision with a particle is the Compton Effect. In that exercise, each particle goes their own merry way after the collision. What I am saying is that you have not sufficiently explained what keeps the two particles in your construction together as a permanently bound or closed system.
5.- this is all before we can get to the polygonal geometry of the shell formed by your particle pair in quasi 3-dim rotation (as I understand).
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Tony Fleming
biophotonics research institute
Joseph
Go and have another look at the Physics Essays paper again; I think you may be talking at cross purposes to what I'm saying. Your view seems always to hark back to the paradigm of quantum mechanics where there are definitely errors in the formulation, firstly but not only with the number of variables for the binding energy, in this PQT case the photons are treated as 'scalars' a one dimensional wave-particles (a rather strange object that is both a wave and a particle simultaneously); if you've understood the SFT formulation to this point you will see that in SFT these bosons (in this case photons) have TWO wave-particles, so they are different entities (in fact similar to atoms) to what we see in PQT (probabilistic quantum theory).
There is a stage in the mathematics where you can put the electron or the proton on one side of the equations, while the photons are on the other side; in other words the particles are being balanced by the fields in the mathematics (using Maxwell's equations and the Lorentz equations. So we find photons are small versions of atoms
2.- the photon emissions at both ends of your proton-electron pair must be in phase with one another for the system to have any chance at stability as a rotational system (I gather that the system is in rotation), and even if the system is not quite in rotation.
No not so, there is a 'wriggle room' for the atom to be not quite as 'perfect' as you say; in SFT you actually have another 2 quantum numbers, besides the normal 4 quantum numbers known to PQT, that allow the fields to vary while in equilibrium, so there's a range of fields that allow the atom to remain in balance.
3.- if you assume the photons to be massive, then they must collide with each before they can reach the end particles (they are travelling in diametrically opposed directions). You can’t have the photons behave both as fermions and bosons. The only known particle with this ability is the neutrino.
There is another part of all this that you may not have woken up to yet and this is that the photon, like the atom, is a particle with a composite structure; it has a structure that has sub-particles, like the hydrogen atom has an electron and a proton 'bound' to each other by sub-fields. The photon is not a tiny '1-D dot' particle; it has two sub-particles (I call them the ephectron and the phroton) and they possess charge just like the atom has a negatively charged electron, and a positively charged proton. Also the photon has a ‘volume’ similar to the volume of the hydrogen atom is a sphere-like with a radius known as the Bohr Radius. Same with the electron and the proton, they too have structures that have volumes in space. So it is the case that like the Earth-Sun gravitational system the photons do not collide with each other, although things can get complicated if the atom is in a strong field environment such as inside the Sun or the Earth where the fields are not those of free-space.
Presentation Self-field theory: Analytic spectroscopy of the photon - Presentation
Ponder this while more to come, this is what you are missing, I suspect.
kind regards Tony
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Joseph Jean-Claude
QG Psychophysics Lab
Tony,
You must realize that most everyone reviewing SFT as a proposal for the organization of the H atom, will be doing it against the backdrop of QM. That is why a detailed explanation of the motivation for the Theory is very important, no less than a discussion on the referred “errors of QM” .
Having yet to see a detailed graphical representation of the model, I have been picturing it in my mind from what I gather from the formulation. If you present a model of two particles, a proton and an electron, in a field-driven interaction, to be the origin of the construction, you are picking the problem from where classical physics (and even Bohr’s model) left it before Schrodinger took over. Those models had been superseded because they could not quite result in a stable atom. That is what motivated E. Schrodinger to visualize a different model for the system that is based on a stranding wave trapped in a virtual box for the dynamics of the electron, yes the “bound” electron. Bound because it is not in free travel and it is constrained to behave as restrained within a virtual box.
To fail to understand the above is to fail to understand an important part of QM. In other words, the energy density orbital is not the model, but physical reality. The model being the particle endowed with a material standing wave. To be extreme one could say that the model did not even need the proton nucleus (that is why we still don’t know how the hell this nucleus is organized). And so the energy density orbital is the real empirical system as it results as an eigensolution to the root standing wave operator, the quantum Hamiltonian Operator.
It is my assessment that many modern-day physicists fail to understand the departure from the vision of a free classical electron to that of the electron as a shell. Because they don’t understand the seminal transformation that takes place to make the electron shell possible and the role played by the vacuum in that transformation. The atom does not emerge as an object because a proton and an electron are chasing each other from a Newtonian perspective, but because the internal symmetry of the vacuum breaks or explodes from one tensored level to another. That is why both the bound electron and the bound proton are shell objects, eventually the neutron as well as part of the nucleus in the following atoms of the suite.
And so Tony, if you want your model to be a polygonal shell at the outset (with two different particles), which gives us the configuration of the atom at once, it becomes incumbent on the model to keenly show why the polygonal shell is in itself stable or what are the underlying physical laws of interaction that make it stable. It would be good if SFT fields were more conventional constructs that could naturally support the representation. If they are new constructs, then they must obey accepted representations, in particular the Representation Theory of particle topologies. As I have explained in my previous interventions, they do not.
I will say this, a full graphical representation of the model aiding to visualize it I have not seen in the presentation thus far and remains a due. If you have not attempted that full pictorial representation, perhaps it will help you pinpoint the weaknesses of the proposal, in particular the field model based on a massive photon. Although I agree that the photon must have sub-structures, it is clear that photons obey the Bose-Einstein statistics which extol the fact that in topology they are totally transparent to one another. But if you make them massive, they MUST obey the Fermi-Dirac statistics which gathers the fact that massive or fermionic particles cannot exist in transposition or superposition with one another but only in juxtaposition.
These are my first impressions of the proposal. But I will keep reading reiteratively in order to further my grasp of it and further identify the contributions.
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Tony Fleming
biophotonics research institute
Joseph
It seems you write from what you see as the 'castle' of PQT (probabilistic quantum theory, what you want to call QM) as if it has all the 'runs on the board' and anything else is not worthy of its 'wondrousness', its ‘correctness’ and its completeness, that everything else pales into nothingness in comparison; well I'm not going to make you have any faith in SFT; you can continue to believe that PQT is the ‘one true mathematical framework for all our physics’. But don't say I didn't tell you otherwise; you're not the first and you won’t be the last.
Before criticizing your comments let me say we have only got into the EM component of SFT; but there's a lot more that delves into the nuclear equations that can be treated in a very similar way, via a modified system of Maxwell-Lorentz equations. The same physics of resonance cycles in the nucleus with respect to THREE fields, not two as in EM physics give us similar ways to see our way into nuclear energy in a new way, in comparison to EMSFT.
" To fail to understand the above is to fail to understand an important part of QM. In other words, the energy density orbital is not the model, but physical reality. Really? But that is one of the first problems with QM!! Those wave functions are said to extend out to infinity, the so-called raison d’être for radioactivity (Not true).The model being the particle endowed with a material standing wave. To be extreme one could say that the model did not even need the proton nucleus (that is why we still don’t know how the hell this nucleus is organized). And so the energy density orbital is the real empirical system as it results as an eigensolution to the root standing wave operator, the quantum Hamiltonian Operator. " I think you would be shocked if I told you the QM commutators (pq-qp)., the well-known bra-ket products, look pretty much like a version of the Curl function straight out of Maxwell’s equations or at least you should be shocked. Maybe this is the reason for the single inequality eqn known as Heisenberg’s INEQUALITY Principle in PQT unlike SFT which has instead two EQUALITY equations that provide the same deterministic solution without all the probabilities.
I think before you cast judgement on SFT you should realize first of all that it is early days in the SFT formulation; second, you need to address my criticisms of PQT. We get the deterministic solutions to QM by using Maxwell-Lorentz equations, and not via a set of early (2nd order) equations that to any sensible view can be shown to be incomplete, incorrect numerically and that require probability analysis. Don't forget SFT has NO numerical problems, because it finds deterministic solutions.
And lets joust about this too if you wish That 'complementarity' in physics that is thought of as a 'principle' is incorrect because of the QM errors in the mathematics of its formulation..
Kind regards Tony
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Joseph Jean-Claude
QG Psychophysics Lab
Tony,
I want to make it clear that what I am doing here is not a formal peer review of SFT but an exchange of views over the Theory. Reason why my comments should not be construed as “casting judgement” on the Theory, and that is also why I allow myself to advance personal views about QM and the quantum Theory in general in these comments, which should not be part of a peer review.
You are right that some of my comments reflect my own understanding of QM, but it is also fair to say that there is a minimum feature set that most everyone agrees on. It is also true that every physicist bears their own particular understanding of the quantum Theory, in my view because mass has never been ontologically defined in physical science, neither has the material wavefunction ever been clearly understood, not even Energy. This creates a gray space for a very flourished set of personal interpretation (sometimes in a vacuous exotic wording, I might add. No allusion to you).
QM is a 100-year old established science, with solid and prolific technological extensions, not the least of which is the computer we are using to exchange these views. The traditional quantum perspective has resulted in the techniques of doped semiconductor layers with quantum activity at the junctions that have set the grounds for the entire engineering technology of both Electronics and Photonics to which our Culture owe so much. Context in physics and physical applications today is very different from what they were in the 1920’s when the atom was a mystery to be solved. That is why I must submit to you that the presentation of the Theory will find better ears if it is exposed against what you view as the drawbacks and insufficiencies of QM and how SFT cures them, instead of a re-start from the electron-proton particle system as the problem. I am not talking about a re-cast of the formulation itself but a recast of the presentation, because in that way you may be able to build support for the Theory incrementally.
I fully understand what this means as an editorial enterprise in light of the several decades that it took for you to achieve this construction. You have to consider however that every physicist or scientist here has their own construction, perhaps much less thorough, but dear to them and for which they are looking for (exclusive) prominence. This climate forces one to be as compelling as might be to capture attention. Furthermore, one cannot totally blame orthodoxy and the QM “castle” from which they view the world, because knowledge in culture requires institutionalization for the purpose of its development and dissemination, and you equally ought to consider that if SFT becomes one day official science, it will require that much as well. That said, I will certainly agree with anyone that the current climate in the community is emaciated and profoundly distorted to say the least.
Kind regards.
Joseph
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Tony Fleming
biophotonics research institute
Dear Joseph
Yes true; if it were a formal peer review I would NOT be allowed to criticize the basis of quantum mechanics.
So I thankfully acknowledge your earnest and brave attempt to provide a non-formal peer review of SFT and I agree with many of your sentiments, e.g whatever might replace probabilistic quantum theory might become eulogized as 'perfect in every way' while other perhaps more worthy candidates might be overlooked by the next generation of peer reviewers.
Which is not what you or I want to achieve over the next decades. I think we are in agreement with what we are both trying to achieve; let’s hope we have a true scientific platform (with a 'level playing field') in which critical review might be balanced by an open and far sighted vision of scientific progress.
I've thought about whether this should be a new version of 'Red October Revolution in the Winter Palace in St Petersburg in 1917', or whether we might achieve a milder 'evolution' by seeing the common threads between current quantum theory (what I call PQT) and self-field theory (SFT). I think we have a lot to be grateful for including the internet by which we can all get about the business of scientific progress in a timely manner. I notice that even Darwinism is evolving towards a larger truth that sees a level of determinism within evolution.
Best regards Tony
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[1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1]T
⊗
[1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1]
You finally obtain the 1D quantum transition matrix,
489^(1/32)/489 2*489^(1/32)/489 489^(1/32)/163 4*489^(1/32)/489 5*489^(1/32)/489 2*489^(1/32)/163 7*489^(1/32)/489 8*489^(1/32)/489 3*489^(1/32)/163 8*489^(1/32)/489 7*489^(1/32)/489 2*489^(1/32)/163 5*489^(1/32)/489 4*489^(1/32)/489 489^(1/32)/163 2*489^(1/32)/489 489^(1/32)/489
2*489^(1/32)/489 4*489^(1/32)/489 2*489^(1/32)/163 8*489^(1/32)/489 10*489^(1/32)/489 4*489^(1/32)/163 14*489^(1/32)/489 16*489^(1/32)/489 6*489^(1/32)/163 16*489^(1/32)/489 14*489^(1/32)/489 4*489^(1/32)/163 10*489^(1/32)/489 8*489^(1/32)/489 2*489^(1/32)/163 4*489^(1/32)/489 2*489^(1/32)/489
489^(1/32)/163 2*489^(1/32)/163 3*489^(1/32)/163 4*489^(1/32)/163 5*489^(1/32)/163 6*489^(1/32)/163 7*489^(1/32)/163 8*489^(1/32)/163 9*489^(1/32)/163 8*489^(1/32)/163 7*489^(1/32)/163 6*489^(1/32)/163 5*489^(1/32)/163 4*489^(1/32)/163 3*489^(1/32)/163 2*489^(1/32)/163 489^(1/32)/163
4*489^(1/32)/489 8*489^(1/32)/489 4*489^(1/32)/163 16*489^(1/32)/489 20*489^(1/32)/489 8*489^(1/32)/163 28*489^(1/32)/489 32*489^(1/32)/489 12*489^(1/32)/163 32*489^(1/32)/489 28*489^(1/32)/489 8*489^(1/32)/163 20*489^(1/32)/489 16*489^(1/32)/489 4*489^(1/32)/163 8*489^(1/32)/489 4*489^(1/32)/489
5*489^(1/32)/489 10*489^(1/32)/489 5*489^(1/32)/163 20*489^(1/32)/489 25*489^(1/32)/489 10*489^(1/32)/163 35*489^(1/32)/489 40*489^(1/32)/489 15*489^(1/32)/163 40*489^(1/32)/489 35*489^(1/32)/489 10*489^(1/32)/163 25*489^(1/32)/489 20*489^(1/32)/489 5*489^(1/32)/163 10*489^(1/32)/489 5*489^(1/32)/489
2*489^(1/32)/163 4*489^(1/32)/163 6*489^(1/32)/163 8*489^(1/32)/163 10*489^(1/32)/163 12*489^(1/32)/163 14*489^(1/32)/163 16*489^(1/32)/163 18*489^(1/32)/163 16*489^(1/32)/163 14*489^(1/32)/163 12*489^(1/32)/163 10*489^(1/32)/163 8*489^(1/32)/163 6*489^(1/32)/163 4*489^(1/32)/163 2*489^(1/32)/163
7*489^(1/32)/489 14*489^(1/32)/489 7*489^(1/32)/163 28*489^(1/32)/489 35*489^(1/32)/489 14*489^(1/32)/163 49*489^(1/32)/489 56*489^(1/32)/489 21*489^(1/32)/163 56*489^(1/32)/489 49*489^(1/32)/489 14*489^(1/32)/163 35*489^(1/32)/489 28*489^(1/32)/489 7*489^(1/32)/163 14*489^(1/32)/489 7*489^(1/32)/489
8*489^(1/32)/489 16*489^(1/32)/489 8*489^(1/32)/163 32*489^(1/32)/489 40*489^(1/32)/489 16*489^(1/32)/163 56*489^(1/32)/489 64*489^(1/32)/489 24*489^(1/32)/163 64*489^(1/32)/489 56*489^(1/32)/489 16*489^(1/32)/163 40*489^(1/32)/489 32*489^(1/32)/489 8*489^(1/32)/163 16*489^(1/32)/489 8*489^(1/32)/489
3*489^(1/32)/163 6*489^(1/32)/163 9*489^(1/32)/163 12*489^(1/32)/163 15*489^(1/32)/163 18*489^(1/32)/163 21*489^(1/32)/163 24*489^(1/32)/163 27*489^(1/32)/163 24*489^(1/32)/163 21*489^(1/32)/163 18*489^(1/32)/163 15*489^(1/32)/163 12*489^(1/32)/163 9*489^(1/32)/163 6*489^(1/32)/163 3*489^(1/32)/163
8*489^(1/32)/489 16*489^(1/32)/489 8*489^(1/32)/163 32*489^(1/32)/489 40*489^(1/32)/489 16*489^(1/32)/163 56*489^(1/32)/489 64*489^(1/32)/489 24*489^(1/32)/163 64*489^(1/32)/489 56*489^(1/32)/489 16*489^(1/32)/163 40*489^(1/32)/489 32*489^(1/32)/489 8*489^(1/32)/163 16*489^(1/32)/489 8*489^(1/32)/489
7*489^(1/32)/489 14*489^(1/32)/489 7*489^(1/32)/163 28*489^(1/32)/489 35*489^(1/32)/489 14*489^(1/32)/163 49*489^(1/32)/489 56*489^(1/32)/489 21*489^(1/32)/163 56*489^(1/32)/489 49*489^(1/32)/489 14*489^(1/32)/163 35*489^(1/32)/489 28*489^(1/32)/489 7*489^(1/32)/163 14*489^(1/32)/489 7*489^(1/32)/489
2*489^(1/32)/163 4*489^(1/32)/163 6*489^(1/32)/163 8*489^(1/32)/163 10*489^(1/32)/163 12*489^(1/32)/163 14*489^(1/32)/163 16*489^(1/32)/163 18*489^(1/32)/163 16*489^(1/32)/163 14*489^(1/32)/163 12*489^(1/32)/163 10*489^(1/32)/163 8*489^(1/32)/163 6*489^(1/32)/163 4*489^(1/32)/163 2*489^(1/32)/163
5*489^(1/32)/489 10*489^(1/32)/489 5*489^(1/32)/163 20*489^(1/32)/489 25*489^(1/32)/489 10*489^(1/32)/163 35*489^(1/32)/489 40*489^(1/32)/489 15*489^(1/32)/163 40*489^(1/32)/489 35*489^(1/32)/489 10*489^(1/32)/163 25*489^(1/32)/489 20*489^(1/32)/489 5*489^(1/32)/163 10*489^(1/32)/489 5*489^(1/32)/489
4*489^(1/32)/489 8*489^(1/32)/489 4*489^(1/32)/163 16*489^(1/32)/489 20*489^(1/32)/489 8*489^(1/32)/163 28*489^(1/32)/489 32*489^(1/32)/489 12*489^(1/32)/163 32*489^(1/32)/489 28*489^(1/32)/489 8*489^(1/32)/163 20*489^(1/32)/489 16*489^(1/32)/489 4*489^(1/32)/163 8*489^(1/32)/489 4*489^(1/32)/489
489^(1/32)/163 2*489^(1/32)/163 3*489^(1/32)/163 4*489^(1/32)/163 5*489^(1/32)/163 6*489^(1/32)/163 7*489^(1/32)/163 8*489^(1/32)/163 9*489^(1/32)/163 8*489^(1/32)/163 7*489^(1/32)/163 6*489^(1/32)/163 5*489^(1/32)/163 4*489^(1/32)/163 3*489^(1/32)/163 2*489^(1/32)/163 489^(1/32)/163
2*489^(1/32)/489 4*489^(1/32)/489 2*489^(1/32)/163 8*489^(1/32)/489 10*489^(1/32)/489 4*489^(1/32)/163 14*489^(1/32)/489 16*489^(1/32)/489 6*489^(1/32)/163 16*489^(1/32)/489 14*489^(1/32)/489 4*489^(1/32)/163 10*489^(1/32)/489 8*489^(1/32)/489 2*489^(1/32)/163 4*489^(1/32)/489 2*489^(1/32)/489
489^(1/32)/489 2*489^(1/32)/489 489^(1/32)/163 4*489^(1/32)/489 5*489^(1/32)/489 2*489^(1/32)/163 7*489^(1/32)/489 8*489^(1/32)/489 3*489^(1/32)/163 8*489^(1/32)/489 7*489^(1/32)/489 2*489^(1/32)/163 5*489^(1/32)/489 4*489^(1/32)/489 489^(1/32)/163 2*489^(1/32)/489 489^(1/32)/489
Whose eigenstate vector is,
[1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1]T
-------
Similarly, for 9 free 2D QM nodes, start with the sawtooth form of the outer product of:
[1 2 1 2 3 2 1 2 1] T
⊗
[1 2 1 2 3 2 1 2 1]
You finally obtain the 2D quantum transition matrix:
29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 3*29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29
2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 6*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29
29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 3*29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29
2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 6*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29
3*29^(1/8)/29 6*29^(1/8)/29 3*29^(1/8)/29 6*29^(1/8)/29 9*29^(1/8)/29 6*29^(1/8)/29 3*29^(1/8)/29 6*29^(1/8)/29 3*29^(1/8)/29
2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 6*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29
29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 3*29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29
2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 6*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29 4*29^(1/8)/29 2*29^(1/8)/29
29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 3*29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29 2*29^(1/8)/29 29^(1/8)/29
Whose eigenstate vector is:
[1 2 1 2 3 2 1 2 1] T
--------------------
Once again, for 27 free 3D QM nodes, let's start with the sawtooth form of the outer product of:
[1 2 1 2 3 2 1 2 1 2 3 2 3 4 3 2 3 2 1 2 1 2 3 2 1 2 1
] T
⊗
{1 2 1 2 3 2 1 2 1 2 3 2 3 4 3 2 3 2 1 2 1 2 3 2 1 2 1]
We finally obtain the 3D quantum transition matrix:
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 2*3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 2*3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 2*3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42
2*3^0.5*14^(1/4)/63 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/21 8*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 4*3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 2*3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 2*3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 2*3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/14 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/21 3^0.5*14^(1/4)/42
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 4*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/21 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/63
3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 2*3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/42 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126 3^0.5*14^(1/4)/63 3^0.5*14^(1/4)/126
Whose eigenstate vector is:
[1 2 1 2 3 2 1 2 1 2 3 2 3 4 3 2 3 2 1 2 1 2 3 2 1 2 1] T
Note that all the above numeric values are expressed as dimensionless arithmetic numeric values.
3+1 structure of of Universe
Discussion
4 replies
- Sergey Bondarenko
How we know about the dimensions given in sensations? At the level of our feelings three dimensions are not more than orientation of body in respect to the local gravitational field. Take off the gravity the dimensions will disappear in our feelings, so that is not good source of knowledge about the world's dimensions. Then, as always, will turn to the physics experiments. From there we know that any quantum field (perhaps except scalar which we have no in a stable form in reality) are built in a way to respect the symmetry of the 3+1 dimensional world and does depend on the 4 coordinates (which are in general is simply human way to mark a point, there are no any coordinate as physical quantities in reality). Nevertheless, we need 4 coordinates for fields of 4 dimensional world and that works absolutely perfect in any physical experiment description. Now let's speculate. Let's assume that there is no such thing as spatial dimensions (will not talk about the time arrow right now) and the dimensions are simply a human way to handle a position of our bodies in an external gravitational fields. How it can work? First of all, what about the fields, why they respect a symmetries of 3+1 world? The answer can be simple in fact. These fields do respect the symmetry 0f 3+1 world but they are do not request an existence of 3+1 dimensions of Universe as a unique and only option. In some extend we talk about the 3+1 dimensions of whole Universe simply because the fields we explore have this structure. Namely, take a world without the gravity, make experiments, make conclusions about the structure of the world. The simplest conclusion will be that we can handle and feel only that kind of fields and corresponding matter, but the conclusion that the whole Universe has that 3+1 structure is a kind of not necessary logical jump. We simply made of and observe that kind of matter that respect the symmetries of 3+1 physical bubble but nothing more. Now will consider a gravity field. First of all, classical gravity field has a form of metric of 3+1 manifold, so it must be a proof 3+1 world's structure for the first sight. But, quantum gravity is not a geometry as it seems right now. So, if we will consider a metric simply as a spin 2 quantum field it will not be related to a geometry at all. We can replace all physical geometrical notions by the notions of interplay of quantum fields without introducing spatial dimensions, instead the dimensions we will have a number of components of the spin 2 field. In this picture is assumed, we can imagine that we live in big something where each physical event we can observe is defined by particular matter fields and their mutual interactions. Namely, the law of physics we have are dictated by the fact that we and the world we explore are made of the same matter and we can feel, observe and handle only that particular reality made from the particular particles and fields. Of course, two questions remain then, what is time dimension and why we so perfectly isolated from other possible phenomena of possibly more complicated general Universe. I do not like an anthropic principle as an answer.
"How do we understand special relativity?"
Discussion
4 replies
- Abbas Kashani
"How do we understand special relativity?"
The Quantum FFF Model differences: What are the main differences of Q-FFFTheory with the standard model? 1, A Fermion repelling- and producing electric dark matter black hole. 2, An electric dark matter black hole splitting Big Bang with a 12x distant symmetric instant entangled raspberry multiverse result, each with copy Lyman Alpha forests. 3, Fermions are real propeller shaped rigid convertible strings with dual spin and also instant multiverse entanglement ( Charge Parity symmetric) . 4, The vacuum is a dense tetrahedral shaped lattice with dual oscillating massless Higgs particles ( dark energy). 5, All particles have consciousness by their instant entanglement relation between 12 copy universes, however, humans have about 500 m.sec retardation to veto an act. ( Benjamin Libet) It was Abdus Salam who proposed that quarks and leptons should have a sub-quantum level structure, and that they are compound hardrock particles with a specific non-zero sized form. Jean Paul Vigier postulated that quarks and leptons are "pushed around" by an energetic sea of vacuum particles. 6 David Bohm suggested in contrast with The "Copenhagen interpretation", that reality is not created by the eye of the human observer, and second: elementary particles should be "guided by a pilot wave". John Bell argued that the motion of mass related to the surrounding vacuum reference frame, should originate real "Lorentz-transformations", and also real relativistic measurable contraction. Richard Feynman postulated the idea of an all pervading energetic quantum vacuum. He rejected it, because it should originate resistance for every mass in motion, relative to the reference frame of the quantum vacuum. However, I postulate the strange and counter intuitive possibility, that this resistance for mass in motion, can be compensated, if we combine the ideas of Vigier, Bell, Bohm and Salam, and a new dual universal Bohmian "pilot wave", which is interpreted as the EPR correlation (or Big Bang entanglement) between individual elementary anti-mirror particles, living in dual universes.
Fred-Rick Schermer added a reply
Wolfgang Konle
That is incorrect, Wolfgang. You are not paying attention.
When there is an omelet, then we know that there was an egg. That is NOT a miracle. Is the egg still around? No, that is the entire point of what the omelet shows us.
The results tell us something about the origin. It is NOT a miracle that there was an origin. It is too bad that we cannot know more about the origin other than it producing the results, but the results do present us a clear storyline how the results came about.
I'd like you to go back to the basics of science and rethink the conclusion you came to.
The following question is truly the first step:
Is the material universe somehow based on a unifying principle, or is the material universe somehow based on the lack of a unifying principle?
Both positions are good scientific positions to start out from. We have the omelet, and we want to understand how the omelet came about. We are not investigating where the egg came from or what the egg tells us. Only the omelet is doing the talking.
Know that I do not mind if you do not agree with the proposal. I have no problem there. Yet your declaring it is a miracle is not based in good science. I must urge you to find your scientific footing.
Wolfgang Konle added a reply
Fred-Rick Schermer "Here the quarks aligned themselves immediately into neutrons and protons."
According to everything we currently know, this would be a miracle, which drastically violates charge neutrality.
"That is incorrect, Wolfgang. You are not paying attention. When there is an omelet, then we know that there was an egg. That is NOT a miracle. Is the egg still around? No, that is the entire point of what the omelet shows us."
No, you are not paying attention. A process which just generates neutrons and protons violates charge parity. According to the number of generated protons an equal amount of electrons also must be generated.
Cosmin Visan added a reply
Santa Claus.
Fred-Rick Schermer added a reply
Wolfgang Konle
We do have the exact same amount of positively charged protons and negatively charged electrons.
There is no miracle. Yet the protons are indeed part of the energy that got changed during the Big Bang process, from being immaterial energy at first to becoming damaged energy: the quarks. The quarks are self-based energy, incapable of returning to their original format.
Meanwhile, the electrons are pulled from the very large remainder of (unchanged) energy; the large remainder was not damaged. The electrons are not self-based in outcome; they are proton-focused, neutralizing the positive charge of the protons. In effect, the protons manifest the electrons from the energized field. The electrons do not annihilate the charge because they cannot undo the damage of the quarks. They are there only to neutralize the charge and yet they cannot undo the charge at the subatomic level.
There are therefore two realities for matter:
Original (undamaged) energy, some say this could be as much as 96% of all energy there is in the universe.
Damaged energy, the quarks.
Matter is said by some to be about 4% of all energy there is. This includes then the electrons since they got pulled into the material realm, yet do not contribute anything close to what the quarks contribute in material energy.
--
There is no miracle here, Wolfgang. It is all about the mechanics of what went wrong during the materialization process.
Wolfgang Konle added a reply
Fred-Rick Schermer "Yet the protons are part of the energy that got changed during the Big Bang process, from being immaterial energy at first to becoming damaged energy: the quarks. The quarks are self-based energy, incapable of returning to their original format.
...
There are therefore two realities for matter:
Original (undamaged) energy, some say this could be as much as 96% of all energy there is in the universe. Damaged energy, the quarks."
You are telling absurd stories without any foundation. This is unacceptable.
Fred-Rick Schermer added a reply
Wolfgang Konle
I am actually staying fully within the scientific realm, Wolfgang.
Let's start at the beginning once more.
A/ The material universe is either based on a single foundation, or
B/ The material universe is based on the lack of a single foundation.
That is a real good scientific question, and the data that we have can therefore be organized in two different manners, either via A or via B.
The Lambda-CDM model follows A.
The Big Whisper model, named for Penzias and Wilson who discovered the whisper of the materialization process, follows B.
The Lambda-CDM model is mechanically incomplete, question marks abound.
The Big Whisper model is mechanically complete. The question how matter could have come about is answered fully. It does require to accept that Energy is already a given.
Both A and B represent scientific approaches, both fully within the scientific realm.
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