Foundations of Physics

Foundations of Physics How Hilbert’s attempt to unify gravitation and electromagnetism failed completely, and a resolution based on Helmholtz’s electron vortex from Kolmogorov’s theory of turbulenc --Manuscript Draft-Manuscript Number: Full Title:

How Hilbert’s attempt to unify gravitation and electromagnetism failed completely, and a resolution based on Helmholtz’s electron vortex from Kolmogorov’s theory of turbulenc

Article Type:

Original Research

Keywords:

Helmholtz electron vortex, electron morphogenesis, Le Sage gravitation, unification theory, gravitation, receding moon, Kolmogorov theory of turbulence

Corresponding Author:

Victor Christianto, DDiv. Malang Institute of Agriculture Malang, INDONESIA

Corresponding Author Secondary Information: Corresponding Author's Institution:

Malang Institute of Agriculture

Corresponding Author's Secondary Institution: First Author:

Victor Christianto, DDiv.

First Author Secondary Information: Order of Authors:

Victor Christianto, DDiv. Florentin Smarandache Robert Neil Boyd, Dr

Order of Authors Secondary Information: Funding Information: Abstract:

In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness theorem, b) Newton’s aether stream model. And we will also present our calculation of receding Moon from Earth based on such a matter creation hypothesis. We also present an outline of a new electron model based on Helmholtz’s electron vortex and Kolmogorov’s theory of turbulence. More experiments and observations are called to verify this new hypothesis, albeit it is inspired from Newton’s theory himself

Suggested Reviewers:

Alex Vano-Vinuales, Dr. Research Associate Gravitational Physics Group, Cardiff University [email protected] he is in gravitational research group Vaibhav Tiwari, Dr Research Associate Gravitational Physics Group, Cardiff University [email protected] he is in gravitational research group Oliver David Lomax, Dr. Research Associate Astronomy Group, Cardiff University [email protected] he is in astronomy research group Walter Gear, Professor

Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation

Head of Astronomy Instrumentation Group, Cardiff University [email protected] he is expert in astronomy instrumentation Peter Hargrave, Professor Deputy Head of Astronomy Instrumentation Group, Cardiff University [email protected] he is expert in astronomy instrumentation John Barrow, Professor DAMTP, University of Cambridge [email protected] he is a renowned mathematical physics

Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation

Click here to access/download;Manuscript;alternativeunification_Helmtholtz_A Click here to view linked References 1 2 3 4 How Hilbert’s attempt to unify gravitation and electromagnetism failed 5 completely, and a resolution based on Helmholtz’s electron vortex from 6 7 Kolmogorov’s theory of turbulence 8 9 10 11 12 Victor Christianto*1 & Florentin Smarandache2 & Robert N. Boyd3 13 14 1 Malang Institute of Agriculture, Indonesia 15 2 Dept. Math. & Sci., Univ. of New Mexico, USA. Email: [email protected] 16 3 Consulting physicist for Princeton Biotechnology Corporation, Dept. 17 Information Physics Research. Email: [email protected] 18 19 20 *Email: [email protected]. URL: http://researchgate.net/profile/Victor_Christianto 21 22 23 Abstract 24 25 In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic 26 27 program to unify gravitation theory and electromagnetism failed completely. An outline of 28 plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness 29 theorem, b) Newton’s aether stream model. And we will also present our calculation of 30 31 receding Moon from Earth based on such a matter creation hypothesis. We also present an 32 outline of a new electron model based on Helmholtz’s electron vortex and Kolmogorov’s 33 theory of turbulence. More experiments and observations are called to verify this new 34 hypothesis, albeit it is inspired from Newton’s theory himself. 1 35 36 37 38 39 Panta rhei, "everything flows" Πάντα ῥεῖ - Heraclitus 40 41 42 43 44 Introduction 45 46 47 First of all, it is known that Hilbert and Einstein were in race at 1915 to develop a new 48 gravitation theory based on covariance principle.[1] While Einstein seemed to win the race at the 49 50 time, Hilbert produced two communications which show that he was ahead of Einstein in term of 51 52 unification of gravitation theory and electromagnetic theory. Hilbert started with Mie’s 53 54 55 56 *Correspondence: Victor Christianto, Independent Researcher. Email: [email protected] 57 58 1 This paper is a continuation to a preceding paper in Annales de la Fondation Louis de Broglie, Volume 31, no 1, 59 2006 31 On the origin of macroquantization in astrophysics and celestial motion V. CHRISTIANTO. Url: 60 aflb.ensmp.fr/AFLB-311/aflb311m370.pdf 61 62 1|P age 63 64 65

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

electromagnetic theory. However, as Mie theory became completely failed, so was the Hilbert’s axiomatic program to unify those two theories [1]. Einstein might be learning from such an early failure of Hilbert to unify those theories, and years later returned to Mie theory.[1] What we would say here is that Hilbert’s axiomatic failure can be explained by virtue of Gödel’s incompleteness theorem: which says essentially that any attempt to build a consistent theory based on axiomatic foundations can be shown to be inconsistent. Nonetheless only few physicists seem to grasp this result.

What can we learn from that story? First of all, it leads us back to Newton’s aether stream model as will be discussed in the following sections. Moreover, it may be not only that it is an elusive dream to unify gravitation and electromagnetic theories from pure thoughts, but it clearly shows that we ought to return to the old days of Maxwell and also Heaviside who have given hints on how to come up with a more realistic unification of gravitation and electromagnetic theories. To us, it also shows that we may need to re-read Maxwell’s original papers, perhaps we should find out how he thought about cogwheel, molecular vortices etc…and they may lead us to a correct theory of gravitation (and also how to connect it with classical electrodynamics). In the meantime, it is worth noting here that Tesla and other experimenters have tried to come up with a simpler version of such unification theories, although most of them were not as familiar to many physicists unlike General Relativity theory.

Enter Arthur Eddington The modern era of cosmology began with the publication of Einstein’s general theory of relativity in 1915. The first experimental test of this theory was Eddington’s famous expedition to measure the bending of light at a total solar eclipse in 1919. So famous is this experiment, and 2|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

so dramatic was the impact on Einstein himself, that history tends not to recognize the controversy that surrounded the results at the time.[3] To tell Eddington’s role in observation regarding General Relativity, allow us to let Peter Coles spoke for that matter:[3] “The story of the 1919 expeditions revolves around an astronomer by the name of Arthur Stanley Eddington. His life and work is described by Douglas (1957) and Chandrasekhar (1983). Eddington was born in Cumbria in 1882, but moved with his mother to Somerset in 1884 when his father died. He was brought up as a devout Quaker, a fact that plays an important role in the story of the eclipse expedition. In 1912, aged only 30, he became the Plumian Professor of Astronomy and Experimental Philosophy at the University of Cambridge, the most prestigious astronomy chair in Britain, and two years later he became director of the Cambridge observatories. Eddington had led an expedition to Brazil in 1912 to observe an eclipse, so his credentials made him an ideal candidate to measure the predicted bending of light. Eddington was in England when Einstein presented the general theory of relativity to the Prussian Academy of Sciences in 1915. Since Britain and Germany were at war at that time, there was no direct communication of scientific results between the two countries. But Eddington was fortunate in his friendship with the astronomer Willem De Sitter, later to become one of the founders of modern cosmology, and who was in neutral Holland at the time. De Sitter received copies of Einstein’s papers, and wasted no time in passing them onto Eddington in 1916. Eddington was impressed by the beauty of Einstein’s work, and immediately began to promote it. In a report to the Royal Astronomical Society in early 1917, he particularly stressed the importance of testing the theory using measurements of light bending. A few weeks later, the Astronomer Royal, Sir Frank Watson Dyson, realised that the eclipse of 29 May 1919 was especially propitious for this task. Although the path of totality ran across the Atlantic ocean from Brazil to West Africa, the position of the Sun at the time would be right in front of a prominent grouping of stars known as the Hyades. When totality occurred, the sky behind the Sun would be glittering with bright stars whose positions could be measured. Dyson began immediately to investigate possible observing sites. It was decided to send not one, but two expeditions. One, led by Eddington, was to travel to the island of Principe off the coast of Spanish Guinea in West Africa, and the other, led by Andrew Crommelin (an astronomer at the Royal Greenwich Observatory), would travel to Sobral in northern Brazil. An application was made to the Government Grant Committee to fund the expeditions, £100 for instruments and £1000 for travel and other costs. Preparations began, but immediately ran into problems. Although Britain and Germany had been at war since 1914, conscription into the armed forces was not introduced in England until 1917. At the age of 34, Eddington was eligible for the draft, but as a Quaker he let it be known that he would refuse to serve. … A special joint meeting of the Royal Astronomical Society and the Royal Society of London was convened on 6 November 1919. Dyson presented the main results, and was followed by contributions from Crommelin and Eddington. The results from Sobral, with measurements of seven stars in good visibility, gave the deflection as 1.98±0.16 arc seconds. Principe was less convincing. Only five stars were included, and the conditions there led to a much larger error. Nevertheless, the value obtained by Eddington was 1.61±0.40. Both were within two standard 3|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

errors of the Einstein value of 1.74 and more than two standard errors away from either zero or the Newtonian value of 0.87. The reaction from scientists at this special meeting was ambivalent. Some questioned the reliability of statistical evidence from such a small number of stars. This skepticism seems in retrospect to be entirely justified. Although the results from Sobral were consistent with Einstein’s prediction, Eddington had been careful to remove from the analysis all measurements taken with the main equipment, the astrographic telescope and used only the results from the 4inch. As I have explained, there were good grounds for this because of problems with the focus of the larger instrument. On the other hand, these plates yielded a value for the deflection of 0.93 seconds of arc, very close to the Newtonian prediction. Some suspected Eddington of cooking the books by leaving these measurements out. Others, such as Ludwick Silberstein, admonished the audience. Silberstein pointed a finger at the portrait of Newton that hangs in the meeting room, and warned: ’We owe it to that great man to proceed very carefully in modifying or retouching his Law of Gravitation.’ On the other hand, the eminent Professor J.J. Thomson, discoverer of the electron and Chair of the meeting, was convinced, stating “This is the most important result obtained in connection with the theory of gravitation since Newton’s day.””[3]

We present this account of history by relying on Peter Coles’s paper, so readers will notice that perhaps what is displayed at “Einstein and Eddington” movie, which was publicly released on several TV channels, was not historically correct at least, or may be just plainly redacted.

Enter Gödel’s incompleteness theorem Gödel’s groundbreaking results were obtained against the backdrop of the foundational debate of the 1920s. In 1921, reacting in part to calls for a “revolution” in mathematics by the intuitionist L. E. J. Brouwer and his own student Hermann Weyl, Hilbert had proposed a program for a new foundation of mathematics. The program called for (i) a formalization of all of mathematics in an axiomatic systems followed by (ii) a demonstration that this formalization is consistent, i.e., that no contradiction can be derived from the axioms of mathematics. Partial progress had been made by Wilhelm Ackermann and John von Neumann, and Hilbert in 1928 claimed that consistency proofs had been established for first-order number theory. Gödel’s results would later show that this assessment was too optimistic; but he had himself set out to with the aim of contributing to this program.[5[ To tell Godel’s monumental result, allow us to quote from Devlin:[4] “In 1931, a young Austrian mathematician published a paper that sent shock waves through the mathematical community and forced mathematicians to take a fresh look at their discipline. The 4|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

mathematician was Kurt Gödel, and the result proved in his paper became known as the Gödel Incompleteness Theorem, or more simply Gödel’s Theorem—although it was by no means the only major theorem he proved during his highly successful career. He is also known as one of the inventors of the theory of recursive functions (which formed part of the foundation for computers). Both of these major discoveries involved axiomatic systems, and neither can be properly understood without an appreciation of what mathematicians means by the word “axiom” and the role axioms play in mathematics. A misunderstanding of the nature of axioms is what lies behind a significant amount of nonsense that has been written about Gödel’s Theorem over the years. Gödel’s Theorem says that in any axiomatic mathematical system that is sufficiently rich to do elementary arithmetic, there will be some statements that are true but cannot be proved (from the axioms). In technical terminology, the axiom system must be incomplete. At the time Gödel proved this theorem, it was widely believed that, with sufficient effort, mathematicians would eventually be able to formulate axioms to support all of mathematics. The Incompleteness Theorem flew in the face of this expectation, and many took it to imply that there is a limit to the mathematical knowledge we may acquire. Few mathematicians think that way now, however. The change in our conception of mathematical truth that Godel’s theorem brought about was so complete, that today most of us view the result itself as merely a technical observation about the limitations of axiom systems.” [4]

To summarize: “Gödel’s Incompleteness Theorem changed the concept of mathematical truth and showed the limitations of axiom-based systems.” In other words, Godel effectively put Hilbert’s axiomatic program into ruins. And so was Hilbert’s approach to unify gravitation and electromagnetic theory. Now the hard question: is it possible to find a way out from such a Godel’s spider web? One of us (RNB) has an interpretation of Godel theorm in theoretical and mathematical physics: “Without observations, experiences, and explorations and experiments, our mathematics and physics start to become non-physical fictions, fantasies, or lies. Physics concepts without physical evidence to support them, do not function well, in the engineering sense. In the sense of Godel, we can never know everything there is to know, intellectually. But we can experience everything, directly. That is the way out of Godel's Law. Then, a new kind of intellect develops, based on direct experiences and observations, in the moment. Experiential intellect is superior to the analytical intellect, because it is based on the physical facts, the way things actually are, now, rather than abstractions based on the past. Nature functions based on experiential understandings, not abstractions. Summarizing: The way out of Godel's Law is Direct Experience, which is keeping the attention only in the senses and sensitivities, without thinking. This is a form of meditation.” 5|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

A plausible resolution of the above problems a. Why do we need a new approach? Karl Popper’s epistemology suggests that when the theory is refuted by observation, then it is time to look for a set of new approaches. Now, it is clear that Hilbert’s axiomatic program has failed not only by experiment (Mie theory does not agree with experiment) but also in terms of logic (Godel’s theorem). Therefore we set out a new approach, starting from an old theory of Isaac Newton.

b. Recalling Newton’s aether stream model Newton brought up his aether stream model in a letter to Robert Boyle, 1678. For interested readers, complete letter of Isaac Newton to Boyle can be found in Appendix section. Comments on Newton aether stream model by DeMeo go as follows: “The letter clearly shows the young Newton, who wrote this in 1679 when he was 37 years old, had a firm belief and working grasp of the ether of space as a thing of substance and "ponderability", something which participated in the movement and ordering of the planets and universe, as a working force in optics, chemistry and gravitation. In this, Newton was continuing the conceptual ideas of Galileo, which had been such an irritant to the Vatican Bishops, who would tolerate no possibility of a motional force in nature other than God. The idea that ether and god might be identical descriptions for the "prime-mover" was equally intolerable, as while one could scientifically know and measure the ether, one could not by definition measure or know "the divine". The young Newton was not bothered by such conceptual difficulties as which bothered the Bishops of Rome, however, but the older Newton increasingly became preoccupied with theological matters, to the point that nearly all his biographers would agree he had become as much of a theologian as scientist in his last decades. Even only 20 years after penning this Letter to Boyle, he writes in the last query of his Optics, the following: "Now by the help of these principles, all material things seem to have been composed of the hard and solid particles, above-mentioned, variously associated in the first creation by the counsel of an intelligent agent. For it became him who created them to set them in order. And if he did so, it's unphilosophical to seek for any other origin of the world, or to pretend that it might arise out of a chaos by the mere laws of nature; though being once formed, it may continue by those laws for many ages..." (quoted in Sullivan, p.125-126) During those later periods, Newton would drop ideas such as a ponderable and moving cosmic ether in favor of more abstract concepts, such as the divine "prime mover" or deified "absolute space", which was foundational for most later astrophysical investigations into the nature of the cosmos. The most obvious result of this shift was, that in the original Michelson-Morley experiment for testing of ether-drift, everyone anticipated a very large ether-drift effect, based upon the assumption the Earth was racing through an intangible and substance-less static and 6|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

immobile cosmic ether at very high speeds. No such intangible static ether has ever been demonstrated, nor could it be. But a material and substantive entrained ether, moving more slowly at lower altitudes and close to the speed of the earth itself, something quite similar to that proposed by the young Isaac Newton, was detected repeatedly..”[6]

c. Remark on Aether stream by RNB (consistent to Le Sage/Laplace theory) The higher the energy, the higher the velocity of the aether entities in the given place and time, and the lower the density. The phase states can exhibit turbulence, which is more marked at the higher densities, the way I am looking at this right now. The Kolmogorov Limit of 10e -58 meters plays a part here. Entities smaller than that will not exhibit much turbulence, primarily because they tend to be superluminal, so any turbulence will be hard to see. The following figure is on Mishin’s Aether phase states:

Figure 1. Aether phase states (Mishin), after R.N. Boyd

7|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

There is an illustration of the process of aether particles being slowed by existing matter and eventually forming electron vortices as the local aether density and turbulence increases, while the energy drops due to interactions with existing matter, or aether in a denser phase state. Moreover, for years, one of us (RNB) developed a novel theory of gravity based on an old theory of Le Sage/Laplace (it is known as Le Sage gravitation theory). An interesting remark on impetus to Le Sage gravitation theory can be found in article by the late Prof. Halton Arp on his work with Narlikar: “Nevertheless the ball had started rolling down hill so to speak and in 1991, with Narlikar's help, I outlined in Apeiron the way in which particle masses growing with time would account for the array of accumulated extragalactic paradoxes. Later Narlikar and Arp (1993) published in the Astrophysical Journal Narlikar's original, 1977 solution of the basic dynamical equations along with the Apeiron applications to the quasar/galaxy observations. … The first insight came when I realized that the Friedmann solution of 1922 was based on the assumption that the masses of elementary particles were always and forever constant, m = const. He had made an approximation in a differential equation and then solved it. This is an error in mathematical procedure. What Narlikar had done was solve the equations for m = f(x,t). This a more general solution, what Tom Phipps calls a covering theory. … But Narlikar had overwhelmed me with the beauty of the variable mass solution by showing how the local dynamics could be recovered by the simple conformal transformation from t time (universal) to what we called τ time (our galaxy) time. The advertisement here was that our solution inherited all the physics triumphs much heralded in general relativity but also accounted for the non-local phenomena like quasar and extragalactic redshifts.”[35]

Summarizing, it is very significant to consider matter creation process in nature. For instance, one can begin by considering the correct presentation of Newton’s third law is not F=ma, but F=d(mv)/dt=v(dm/dt) + m(dv/dt). In other words, it remains possible to think of matter creation (dm/dt) in the Newtonian framework, and this hypothesis seems quite consistent with Narlikar’s work. We will explore this effect in receding Moon from Earth, in calculations in subsequent section.

8|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

d. Introducing a renewed version of Helmholtz’s electron vortex model There are various models of electron which have been suggested, for instance see Chekh et al. [10] But we seek a more realistic electron model which is able to describe to experiments conducted by Bostick et al. [9]. In our attempt to explain such experiments of electron creation in plasma, allow us to come up with a new model of electron, based on Helmholtz’s electron vortex theory. In turn, we will discuss a plausible model of electron capture event inside Earth (matter creation), which in turn can serve a basis to explain Le Sage/Laplace’s push gravity. We will discuss its implications along with receding Moon effect in two forthcoming papers. The Helmholtz vortex model of the electron as illustrated in the photo of a Helmholtz vortex (Fig. 2), is a toroid made of nested concentric toroidal flows of smaller particles, perhaps the inertons of Krasnoholovets, or aggregate particles made from Bhutatmas. (The "Bhutatma" infinitesimal particle of Vedic lore is the ultimate building block of everything, being the smallest unit of matter, and at the same time, the smallest unit of Consciousness. Lines of constant flow are given by r = a sin Ώ = a sin Ώt, where a is a constant. The velocity components are dr/dt = a Ώ cosine Ώ t and r dθ/dt = a Ώ sin Ώ t The Ώt implies that a characteristic wave function is associated with the vortex, but we haven't worked on it yet. This may be an indication of origin of the de Broglie’s wave of the electron, or it may have something to do with the Compton radius of the electron, or both. The constant a may represent the outer limit of the vortex-particle, if the internal circulation velocity of smaller particles does not exceed light speed. If the circulation velocity is larger than c, at the outer shells of the nested vortex, there may be a species of sub-particles which is always being removed from the nested toroidal form, which must be replenished to the vortex which is living in an "atmosphere" made larger circulations of sub-particles. This is due to considering the electron as having a fixed mass, a fixed extent, and a fixed charge (which may not be the case for all time and in all circumstances). 9|P age

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

There should be some set of equations which shows vortex sub-particle replacement activities from the ambient aether, but we haven't worked on it either. The first equation is a circle tangent to the z axis at the origin, with a center located in the X Y plane at the distance a/2 = p where p is the potential of the electron, and is independent of the orientation of the electron vortex. Then the electron can be viewed as a toroid, with a volume V = 2 π r times π r ^2 = 2 π^2 r^3 Three potentials are indicated here: Static potential, Spin potential, and a Dipole potential. Since the electron vortex has mass (which may change from its present value, according to the parameters of the ambient aether in the vicinity of the electron at the given place and time), a total of six potentials are implied.

Figure 2. electron vortex capture event – Helmholtz electron vortex is nearly indestructible (after R.N. Boyd)

10 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Figure 3. electron vortex capture event (after R.N. Boyd)

Figure 4. llustration on how matter creation can take place in inner core of Earth (Source: https://www.dreamstime.com/royalty-free-stock-photography-earth-core-image1890727)

11 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

This illustration (Fig. 4) shows stellar and interstellar aether flows interacting with electron vortices. In some cases the stellar flux is diverted by the electron vortex. In other cases, the flux entity misses entirely, similar to a neutrino. In some unusual cases the flux is captured by an electron vortex and participates in it for a while. The illustrations were produced to show (electron) capture events of individual infinitesimals from the omni-directional aether fluxes which comprise, and cause, gravitation in the LeSageLaPlace paradigm, to show how individual infinitesimals can be intercepted by electron vortices. The process of electron formation happens most often, due to vortex "street" events due to existing electron spheres, intersected by parallel aether flows, which can event-sourced, on occasion, or omni-directional, most of the time. So, although infinitesimal capture events are relevant, it seems at this moment, that the primary electron-positron pair creation events are due to von Karman streets of vortices of alternating directions, which will form vortex rings, when a directional aether flow (a sustained gust of aether wind) is impeded by an existing electron KH vortex sphere.

And, the most salient part of the KH electron vortex form, at its outermost margins, is almost spherical, as well as toroidal, as can be seen from the diagrams and the photograph of KH vortices. Thus, due to laminar flows intersecting with existing spheres, vortex streets are caused to form into KH vortex rings, which are rotating in alternating opposite directions. Electrons and positrons also have equal and opposite "charge" and are considered to be "anti-matter" in relation to one another.

But at this point, readers may ask: what is "anti-matter" really, other than opposite directions of rotation of similar particles? And what is "charge" really, in terms of aether behaviors?

So, essentially, electron-positron pair formation is properly described and justified for the first time in the history of particle physics, as both electrons and positrons are KH vortices, rotating in opposite directions. Electron-positron pairs are, at least temporarily, linked by bridges of the same material particles which the e-p particle pairs are being formed in.

12 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

This view may be related to Falaco Soliton vortex pairs as described and discussed by the late R.M. Kiehn [11][12][13], but it is not clear yet if this is actually a correct model when describing KH electron-positron pair formations.2 See Figure 5.

Figure 5. Photon bi-vortex in SQ Aether media (Falaco soliton model) (After: RN Boyd)

Pairs of electrons and positrons are required to make the larger particles, such as the proton, which is an agglomeration of an exact number of electrons and positrons, with one positron excess, to account for the positive charge produced by the proton. What needs to be discovered here is: what property of the aether determines the exact numbers of electron-positron pairs, required to form protons and neutrons? Does this have to do with "packing" limitations, imposed by the media? Is this to do with the phi ratio inherent in the media?

2

Note by RNB: I brought it up with Kiehn, many years ago that electron-positron pairs might be Falaco Soliton pairs. He gave no response to that suggestion, which is not quite a good sign. But I tried to develop further his ideas.

13 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Each electron which already exists, acts as a large rock in a moving stream, causing deflections of the normal aether flow, slowing down the flow-rate, and producing eddy currents and turbulence in the ambient aether near the given electron. When the turbulence becomes large enough, additional electrons form in the media, which act to choke off the interstellar aether flow even more and impede its normally unencumbered motion. This is similar to adding more and more rocks into the channel of a stream of water, so that the flow rate of the water slows down, as more and more rocks are added. This process was discovered by Nikola Tesla during his experiments at his Colorado Springs laboratory. It is a good thing this happens, or aether avalanches produced by Tesla's 100,000,000 volt explosive electrical discharge events could have burned away the very air we live in. Tesla was relieved to find out the discharges were choked off, accompanied by vast numbers of newly created electrons. Tesla found the excess electricity resulting from the excess electrons to be a nuisance to his other experiments, so he dumped the excess electrical power into the earth's crust.

e. More proof: Calculating matter creation in Earth and its effect to receding Moon One of us have made a calculation to show that the observed receding Moon from Earth, should be properly attributed to increasing size of the Earth. The latter phenomenon could be attributed to “matter creation” as effect of aether stream (vortex). In this section we start with some basic equations that will be used throughout the present article. It is assumed that the solar nebula is disc-shaped and is in hydrostatic equilibrium in the vertical direction. Let suppose that the disk has approximately Keplerian rotation, ; then the halfthickness of the disk is given by [15d; p.4-5]:

d  cs / 

(1)

cs  kT / m

(1a)

and

14 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

where d and cs represents half-thickness of the disk and sound velocity, respectively. In order to find the spherical kinetic dynamics contribution to Lense-Thirring effect, we begin with the spinning dynamics of solid sphere with mass M. Using the known expression [16; p.6, p.8]:

Ekinetic   I zz 2 / 2

(2)

I sphere  2MR 2 / 5

(2a)

where Izz, , M, R represents angular momentum, angular velocity, spinning mass of the spherical body, and radius of the spherical body, respectively. Inserting equation (2a) into (2) yields:

Ekinetic   MR 2 2 / 5

(3)

This known equation is normally interpreted as the amount of energy required by a spherical body to do its axial rotation. But if instead we conjecture that ‘galaxies get their angular momentum from the global rotation of the Universe due to the conservation of the angular momentum’ [17], and likewise the solar system rotates because of the corresponding galaxy rotates, then this equation implies that the rotation itself exhibits extra kinetic energy. Furthermore, it has been argued that the global rotation gives a natural explanation of the empirical relation between the angular momentum and mass of galaxies: J  M 5 / 3 [18]. This conjecture is also relevant in the context of Cartan torsion description of the Universe [19]. For reference purpose, it is worthnoting in this regard that sometime ago R. Forward has used an argument of non-Newtonian gravitation force of this kind, though in the framework of GTR (Amer. J. Phys. 31 No. 3, 166, 1963). Let suppose this kind of extra kinetic energy could be transformed into mass using a known expression in condensed-matter physics [19b; p.4], with exception that cs is used here instead of v to represent the sound velocity:

Ekinetic (n, p)  cs . p  ms .cs

2

(4)

where the sound velocity obeying [19b; p.4]:

cs (n)  (n / m)(d 2  / dn 2 ) 2

(4a)

Physical mechanism of this kind of mass-energy transformation is beyond the scope of the present article, albeit there are some recent articles suggesting that such a condensed-matter radiation is permitted [20]. Now inserting this equation (4) into (3), and by dividing both sides of equation (3) by

t , then we get the incremental mass-energy equivalent relation of the spinning mass: 15 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

ms / t   .( / t ).MR 2 /(5.cs ) 2

(5)

By denoting    / t , then this equation (5) can be rewritten as:

M / t   .MR 2 /(5.cs ) 2

(5a)

For   0 the equation (5a) shall equal to zero, therefore this equation (5a) essentially says that a linear change of angular velocity observed at the surface of the spinning mass corresponds to mass flux, albeit this effect is almost negligible in daily experience. But for celestial mechanics, this effect could be measurable. If, for instance, we use the observed anomalous decceleration rate [21] of angular velocity of the Earth as noted by Kip Thorne [2]:

 /   6 x1011 years

(6)

And using values as described in Table 1 for other parameters: Table 1. Parameter values to compute kinetic expansion of the Earth Parameter Value Unit Re 6.38x106 m Me 5.98x1024 kg Te 2.07x106 sec 3.04x10-6 rad/s e cs 0.14112 m/s

It is perhaps worth noting that the only free parameter here is cs =0.14112 m/sec. This value is approximately within the range of Barcelo et al.’s estimate of sound velocity (at the order of cm/sec) for gravitational Bose-Einstein condensate [23], provided the Earth could be regarded as a spinning Bose-Einstein condensate. Alternatively, the sound velocity could be calculated using equation (1a), but this obviously introduces another kind of uncertainty in the form of determining temperature (T) inside the center of the Earth; therefore this method is not used here. Then inserting these values from equation (6) and Table 1 into equation (5a) yields:

M / t  3.76x1016 kg / year

(7)

Perhaps this effect could be attributed to a recent Earth bulging data, which phenomenon lacks a coherent explanation thus far [24].3

3

One of us (RNB) remarked that he once found a data from NASA showing that the observed value of increasing mass of Earth is at the order of 10^13 tons/yr. But he forgot the source of that particular report. It would be tremendous significance to find out new data on this issue.

16 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65



Calculation of the receding Moon

Now let suppose this predicted value (7) is fully conserved to become inertial mass, and then we could rewrite Nottale’s method of celestial quantization [25]. Alternatively, we could begin with the known Bohr-Sommerfeld quantization rule [27]:

 p .dq j

j

 n j .2 .e 2 /  e .c 

(8a)

Then, supposing that the following substitution is plausible [27]:

e 2 /  e  GMm /  g

(8b)

where e,e,g represents electron charge, Sommerfeld’s fine structure constant, and gravitationalanalogue of fine structure constant, respectively. This corresponds to Nottale’s basic equations

vn   g .c / n  vo / n and vo=144 km/sec [25]. And by introducing the gravitational potential energy [16]:





 

r ,   GM / r. 1  J 2 .(a / r )2 . 3 cos2   1 / 2

(8c)

where  is the polar angle (collatude) in spherical coordinate, M the total mass, and a the equatorial radius of the solid. Neglecting higher order effects of the gravitational quadrupole moment J2, then we get the known Newtonian gravitational potential:

  GM / r

(8d)

Then it follows that the semi-major axes of the celestial orbits are given by [25][27]:

rn  GMn 2 / vo

2

(8e)

where n=1,2,….is the principal quantum number. It could be shown, that equation (8a) also corresponds to the conjecture of quantization of circulation [28b]. By re-expressing equation (8e) for mass flux effect (5) by defining M n1  M n  M n / tn , then the total equation of motion becomes:

( M  M / t )  (r  r / t ).v0 /(G.n 2 ) 2

(8f)

For   0 , equation (8f) can be rewritten as: dM / dt   .dr / dt  M  r.  0

where 17 | P a g e

(8g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

  v0 2 /(G.n 2 )

(8h)

Now inserting (5a) into equation (8g), and dividing both sides by , yields:

dr / dt  M /   r   .MR 2 /(  5.cs )  0 2

(8i)

This equation (8i) can be rewritten in the form: r  r    0

(8j)

by denoting r  dr / dt and

   M /  .[1   .R 2 /(5.cs 2 )]

(8k)

if we suppose a linear decceleration at the surface of the spinning mass. Equation (8j) and (8k) is obviously a first-order linear ODE equation [30], which admits exponential solution. In effect, this implies that the revised equation for celestial quantization is likely to take the form of spiralling motion. This could also be interpreted as a plausible solution of diffusion equation in dissipative medium [31], which perhaps may also correspond to the origin of spiral galaxies formation [32]. To this author’s knowledge these equations (8j) and (8k) have not been presented before elsewhere, at least in the context of celestial quantization. Inserting result in equation (7) into (8e) by using n=3 and vo=23.71 km/sec for the Moon [26] yields a receding orbit radius of the Moon as large as 0.0401 m/year, which is very near to the observed value ~ 0.04 m/year [33]. The quantum number and specific velocity here are also free parameters, but they have less effect because these could be replaced by the actual Moon orbital velocity using vn  v0 / n [25]. While this kind of receding Moon observation could be described alternatively using oscillation of gravitational potential [34], it seems the kinetic expansion explanation is more preferable particularly with regard to a known phenomenon of continental drift [29], and also perhaps a known periodic geological layering described by Alvarez et al. Furthermore, using this kind of approach it seems that we could also offer a plausible explanation for the kinetic origin of volcanoes eruption. Apparently, none of these effects could be explained using oscillation of gravitational field argument, because they are relentless effects.

f. More proof: Dayton Miller’s experiment DeMeo remark on Dayton Miller’s experiment: 18 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

“The history of science records the 1887 ether-drift experiment of Albert Michelson and Edward Morley as a pivotal turning point, where the energetic ether of space was discarded by mainstream physics. Thereafter, the postulate of "empty space" was embraced, along with related concepts which demanded constancy in light-speed, such as Albert Einstein's relativity theory. The now famous Michelson-Morley experiment is widely cited, in nearly every physics textbook, for its claimed "null" or "negative" results. Less known, however, is the far more significant and detailed work of Dayton Miller. Dayton Miller's 1933 paper in Reviews of Modern Physics details the positive results from over 20 years of experimental research into the question of ether-drift, and remains the most definitive body of work on the subject of light-beam interferometry. Other positive ether-detection experiments have been undertaken, such as the work of Sagnac (1913) and Michelson and Gale (1925), documenting the existence in lightspeed variations (c+v > c-v), but these were not adequately constructed for detection of a larger cosmological ether-drift, of the Earth and Solar System moving through the background of space. Dayton Miller's work on ether-drift was so constructed, however, and yielded consistently positive results. Miller's work, which ran from 1906 through the mid-1930s, most strongly supports the idea of an etherdrift, of the Earth moving through a cosmological medium, with calculations made of the actual direction and magnitude of drift. By 1933, Miller concluded that the Earth was drifting at a speed of 208 km/sec. towards an apex in the Southern Celestial Hemisphere, towards Dorado, the swordfish, right ascension 4 hrs 54 min., declination of -70° 33', in the middle of the Great Magellanic Cloud and 7° from the southern pole of the ecliptic. (Miller 1933, p.234)”[8]

Figure 6. Dayton Miller's light-beam interferometer, at 4.3 meters across, was the largest and most sensitive of this type of apparatus ever constructed, with a mirror-reflected round-trip light-beam path of 64 meters. It was used in a definitive set of ether-drift experiments on Mt. Wilson, 1925-1926. Protective insulation is removed in this photograph, and windows were present all around the shelter at the level of the interferometer light-path. [8]

19 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

The followings are quotes from Miller and Einstein as mentioned in DeMeo’s article:[8] "The effect [of ether-drift] has persisted throughout. After considering all the possible sources of error, there always remained a positive effect." — Dayton Miller (1928, p.399) "My opinion about Miller's experiments is the following. ... Should the positive result be confirmed, then the special theory of relativity and with it the general theory of relativity, in its current form, would be invalid. Experimentum summus judex. Only the equivalence of inertia and gravitation would remain, however, they would have to lead to a significantly different theory." — Albert Einstein, in a letter to Edwin E. Slosson, 8 July 1925 (from copy in Hebrew University Archive, Jerusalem.) See citations below for Silberstein 1925 and Einstein 1926. "I believe that I have really found the relationship between gravitation and electricity, assuming that the Miller experiments are based on a fundamental error. Otherwise, the whole relativity theory collapses like a house of cards." — Albert Einstein, in a letter to Robert Millikan, June 1921 (in Clark 1971, p.328) "You imagine that I look back on my life's work with calm satisfaction. But from nearby it looks quite different. There is not a single concept of which I am convinced that it will stand firm, and I feel uncertain whether I am in general on the right track." — Albert Einstein, on his 70th birthday, in a letter to Maurice Solovine, 28 March 1949 (in B. Hoffman Albert Einstein: Creator and Rebel 1972, p.328)

That Dayton Miller’s experiment seems quite consistent with other experiments such as Michelson-Morley non-null result, which indicates solar system in motion. [40-41].

g. More proof: preferred direction and Milky Way moving to The Great Attractor Another type of observations seems to suggest that there is preferred direction in the Universe at large scale, and especially that the Milky Way is moving at large speed toward the Great Attractor.[37-39] While this effect may be not detected in the Miller’s days, two things are for sure: (a) no general relativity based theories can explain this effect, and (b) it makes Copernican Principle on question. This effect is seemingly consistent with Tifft’s finding of rest background frame.[36]

20 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Figure 7. The Great Attractor from Southern Hemisphere

Figure 8. Shapley Supercluster

21 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Figure 9. Shapley Supercluster

Concluding remarks We begin with Hilbert’s axiomatic program to unify electromagnetic and gravitation theory, and we remark that Godel finding effectively put Hilbert program into ruins. We also mentioned Eddington's observation, because this month is centenary celebration of that eclipse observation by Eddington in November 1918. Summarizing, it is very significant to consider matter creation process in nature. For instance, one can begin by considering the correct presentation of Newton’s third law is not F=ma, but F=d(mv)/dt=v(dm/dt) + m(dv/dt). In other words, it is possible of matter creation (dm/dt), and this is consistent with Narlikar’s work. This seems to be the essence of Le Sage gravity theory. We also presented a calculation of receding Moon from Earth. All of these stuffs, if they are near to the observed facts, may offer hints that time has come to reconsider not only the relativity

22 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

theory but also Copernican principle. But of course, first of all we need to look to these observations and check for better measurement methods.

Acknowledgement One of us (VC) would extend sincere gratitude to Prof. Akira Kanda, Arno Gorgels, Volodymyr Krasnoholovets, and last but not least: to Prof. Thee Houw Liong for suggesting VC to look to J. Narlikar’s works.

References: [1] K.A. Brading, T.A. Ryckman / Studies in History and Philosophy of Modern Physics 39 (2008) 102– 153 103 [2] George Shpenkov. Some words about fundamental problems of physics. www.shpenkov.com [3] Peter Coles. Einstein, Eddington and the 1919 Eclipse. ASP conf. series (unknown date) [4] Keith Devlin. Kurt Gödel—Separating Truth from Proof in Mathematics. Science’s Compass. [5] Richard Zach. Kurt Gödel, ‘¨Uber formal unentscheidbare S¨atze der Principia mathematica und verwandter Systeme I’ (1931). First publication: Monatshefte fur Mathematik und Physik, 37, 173–198. Reprints: S. Feferman et al., eds., Kurt Godel. Collected Works. Volume I: Publications 1929–1936. New York: Oxford University Press, 1986, pp. 116–195. [6] J. DeMeo. Isaac Newton's Letter to Robert Boyle, on the Cosmic Ether of Space – 1679, url: http://www.newtonproject.ox.ac.uk/view/texts/normalized/NATP00275 [7] Dublin: A. Ewing and W. Smith, 1745. 1st Edition. FIRST EDITION, FIRST PRINTING OF A RARE 18th c. WORK INCLUSIVE OF NEWTON’S WRITINGS ON THE AETHER, A LETTER FROM NEWTON TO BOYLE ON THE SUBJECT, & ROBINSON’S OWN WRITINGS TRYING TO ACCOUNT FOR ANIMAL MOTIONS BY NEWTON’S PRINCIPLES. url: https://www.atticusrarebooks.com/pages/books/727/isaac-newton-bryan-robinson/sir-isaac-newton-saccount-of-the-aether-aether-ether-with-some-additions-by-way-of-appendix-dublin-g [8] J. DeMeo. Dayton Miller’s ether drift experiment: a fresh look. Earlier version presented to meetings of the Natural Philosophy Alliance, Berkeley, California and Storrs, Connecticut, May and June 2000, 23 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

and later published in Infinite Energy Magazine #35, Summer 2001, and in Pulse of the Planet #5, 2002. url: http://www.orgonelab.org/miller.htm

[9] Winston H. Bostick. What Laboratory-Produced Plasma Structures Can Contribute to the Understanding of Cosmic Structures Both Large and Small. IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-14, NO. 6, DECEMBER 1986; [9a] W.H. Bostick. The Morphology of the Electron. International Journal of Fusion Energy, Vol. 3, no. 1, 1985 [10] Yu. N. Chekh, A. A. Goncharov, and I. M. Protsenko. Large-Scale Electron Vortex Structure Formation in a Plasma Lens. 1063-7850, Technical Physics Letters, 2006, Vol. 32, No. 1, pp. 51–54. © Pleiades Publishing, Inc., 2006. [11] R.M. Kiehn. Falaco Solitons — Cosmic strings in a swimming pool. url: https://pdfs.semanticscholar.org/3a68/7d3f839f6596888cbac989346233529b1846.pdf [12] R.M. Kiehn. Falaco Soliton. url: http://coll.pair.com/csdc/pdf/fal10305.pdf [13] RM. Kiehn. Experimental Evidence for Maximal Surfaces in a 3 Dimensional Minkowski Space. Url: http://math.mit.edu/~dunkel/Teach/18.354_2014S/2005Kiehn_Falaco.pdf [14] C.K. Thornhill. Real or imaginary space-time? Reality or Relativity? Hadronic Journal Suppl. 11, 3, (1996) 209-224 [15] Lineweaver, C. et al., Scientific Frontiers in Research on Extrasolar Planets, ASP Conf. Series Vol. 28, Deming et al. (eds), (2003) preprint at arXiv:astro-ph/0209382 [16] Essen, H., “The physics of rotational flattening and the point core model,“ arXiv:astro-ph/0403328 (2004). [17] Li, L-X., arXiv:astro-ph/9703082 (1997) p.7. [18] de Andrade, L.G., arXiv:astro-ph/0011477 (2000); also gr-qc/0405062 (2004) [19] Volovik, G., “Superfluid analogies of cosmological phenomena,” arXiv:gr-qc/0005091 (2000a); [19b] Volovik, G., “Links between gravity and dynamics of quantum liquids,” Int. Conf. “Cosmology. Relativistic Astrophysics. Cosmoparticle Physics” (COSMION-99) (2000b) preprint at gr-qc/0004049; [19c] Volovik, G., gr-qc/0104046 (2001); [19d] Nozieres, P., & D. Pines, The theory of quantum liquids: Superfluid Bose Liquid. Wesley Publ. Inc., 116-124 (1990). [20] Kovrizhin, D., & L.A. Maksimov, arXiv:cond-mat/0109236 (2001). [21] Khokhlov, D., arXiv:physics/0309099 (2003). [22] Thorne, K., “Vorticity”, Chapter 13. Url; http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/1214.1.K.pdf [23] Barcelo, C., S. Liberati, & M. Visser, “Analogue gravity from Bose-Einstein condensate,” Class. Quantum Grav. 18, 1137-1156 (2001). Also Barcelo, et al., “Analogue gravity from field theory normal modes,” Class. Quantum Grav. 18, 3595-3610 (2001); M. Visser, arXiv:gr-qc/0204062. [24] Sciforums, “Satellites reveal a mystery of large change in earth's gravity field,” Sciforums.com, August 01 (2002). Also in Science, August 02, 2002. [25] Nottale, L., G. Schumacher, & E.T. Levefre, Astron. Astrophys. 361, 379-387 (2000); also Nottale, L., “Nondifferentiable space-time and scale relativity,” in Proc. of Inter. Colloquium Géométrie au XXè siècle, Paris, 2429 Sept. 2001, Ed. D. Flament (2002); Nottale, L., Astron. Astrophys. 327, 867-889 (1997); Nottale, L., et al., Astron. Astrophys. 322, 1018 (1997); preprint at http://www.daec.obspm.fr/users/nottale [26] Rubcic, A., & J. Rubcic, “The quantization of solar-like gravitational systems,” Fizika B 7 Vol. 1, 1-13 (1998).

24 | P a g e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

[27] Agnese, A.G., & R. Festa, Proc. Workshop on Modern Modified Theories of Gravitation and Cosmology 1997, preprint at arXiv:astro-ph/9807186 (1998). Also Agnese, A.G., astro-ph/9910534; Neto, M., et al., astroph/0205379 (Oct. 2002); C. Costa, quant-ph/0402200 (2004). [28] Chechelnitsky, A., “Hot points of the Wave Universe concept,” in JINR, Dubna, Aug. 22-26, 2000; preprint at arXiv:physics/0102036 (2001); [28b] Chechelnitsky., A., “Epoch of quantization and Wave Universe,” (1995) http://web.ccr.jussieu.fr; [28c] Coles, P., astro-ph/0209576 (2002); [28d] Chavanis, P., astro-ph/9912087 (1999); [28e] Van Holten, J., “Particles, fluids, and vortices,” gr-qc/0107041 (2001). [29] Oudet, X., “The quantum state and the doublets,” Annales de la Fondation Louis de Broglie Vol. 25 No.1, 24p (2000). For derivation of Bohr-Sommerfeld quantization rules from a slightly-generalized Maxwell electrodynamics, see V.M. Simulik & I.Krivsky, Annales de la Fondation Louis de Broglie Vol. 27 No.2 (special), 303-329 (2002), preprint at arXiv:hep-th/0201160; also Annales de la Fondation Louis de Broglie Vol. 27 No.3, 523-527 (2002). [30] Lan, Y., & P. Cvitanovic, “Variational methods for finding periodic orbits in a general flow,” arXiv: nlin.CD/0308008 (2003). [31] Tornkvist, K., & E. Schroder, “Vortex dynamics in dissipative systems,” Phys. Rev. Lett.Vol. 78, No. 10 (1997). Also Anile, A.M., et al., gr-qc/9810014; Castro, C., J. Mahecha, & B. Rodriguez, arXiv:quant-ph/0202026v1 (2002). [32] Roscoe, D., arXiv;astro-ph/0306228 (2003); L. Smolin, astro-ph/9612033. [33] Khokhlov, D., arXiv:physics/0309099 (2003). [34] Myers, L.S., “Our planet is expanding by internal core expansion,” http://www.expanding-earth.org (2002).

[35] Halton Arp. The observational impetus for Le Sage Gravity. url: http://www.haltonarp.com/articles/the_observational_impetus_for_le_sage_gravity [36] W. G. Tifft. Redshift Quantization in the Cosmic Background Rest Frame. J. Astrophys. Astr. (1997) 18, 415 [37] M.B. Bell and S.P. Comeau. Further Evidence for Quantized Intrinsic Redshifts in Galaxies: Is the Great Attractor a Myth?, arXiv: astro-ph/0305112 (2003) [38] Krzysztof Bolejko and Charles Hellaby. The Great Attractor and the Shapley Concentration. arXiv: astro-ph/060402 (2006) [39] Consoli, Constanzo, Palmisano. Motion toward the Great Attractor from an ether-drift experiment. arXiv: astro-ph/0601420 [40] M. Consoli and E. Costanzo. The motion of the Solar System and the Michelson-Morley experiment. arXiv: astro-ph/0311576 (2003) [41] M. Consoli. Relativistic analysis of Michelson-Morley experiments and Miller’s cosmic solution for the Earth’s motion. arXiv: astro-ph/0311053 (2003)

Document history: Version 1.0: 25/11/2018, pk. 21:38 VC, FS, RNB 25 | P a g e