Home

 

This section lists (latest news first) those recent discoveries in general physics, theoretical and experimental particle physics that may have relevance to the remote-viewing of the subatomic world by the Theosophists Annie Besant and C.W. Leadbeater and to my interpretation of their observations. It also discusses other contemporary discoveries or developments that are relevant to my researches into sacred geometries and the mathematical nature of the seven musical scales.

 

News item #10 (June 28, 2013)

 

Fluid trefoil knots observed for the first time — their connection to quarks

In the 1860s, the physicist Lord Kelvin proposed that atoms are vortices in the Aether, atoms of different chemical elements being vortex knots of varying topologies. Although Kelvin’s vortex model never became part of atomic physics, scientists have long believed that it should be possible to create knotted vortices in liquids. They have, however, never had success. Recently, Justin Kleckner, a postdoctoral scientist at the University of Chicago’s James Franck Institute and William Irvine, assistant professor in physics, designed and fabricated various plastic airfoils, using a 3-d printer. Accelerating them at more than 100 g through water filled with microscopic bubbles, the latter were sucked into a knot-shaped vortex. Kleckner & Irvine imaged the trefoil knot-shaped flow of bubbles with lasers. This was the first time knots of bubbles in a fluid had been created and observed. The two physicists are now investigating whether they can create more complicated knots, as well as larger ones, which might be more stable. Read the original article: "Creation and dynamics of knotted vortices," Nature Physics (2013) at: http://dx.doi.org/10.1038/nphys2560. See also the article with videos of the formation of the trefoil knot vortex in water at: http://phys.org/news/2013-03-physics-duo-vortex-fluid-video.html.

 

 

 vortex knot

 trefoil knot

 

Hydrogen triplets are up and down quarks

                         Bubbles in water forming a trefoil knot.
                                     Credit:
 Robert Kozloff (University of Chicago).
 Trefoil knot.

                         Positive & negative hydrogen triplets are, respectively, up and
                                     down quarks (From: Occult Chemistry, 3rd ed. (1951).

 

Vortices (see here) are found in many areas of nature, e.g., smoke rings, whirlpools, winds surrounding hurricanes, tornadoes, water spouts & dust devils. Here is a video showing vortex rings in nature:

 

 

 

 

 

Generally, they are either cylindrical or toroidal. The discovery that they can exist as knots such as the trefoil knot (the simplest knot — see video below) has great significance for the string version of QCD. According to this theory, colour SU(3) quarks are magnetic monopole endpoints of strings, or flux tubes —quantised bundles of colour electric flux that are expelled by the Meissner Effect from the ambient, superconducting Higgs field and channelled along narrow vortices in this superfluid between quarks. Such

 

 

 

Nielsen-Olesen vortices (supercurrents of Higgs bosons) are the non-Abelian generalisation of the Abelian Abrikosov supercurrents found in type-II superconductors. String theorists have considered Y-shaped and circular configurations of three quark monopoles embedded in the Higgs vacuum as models of baryons:

 

String models of baryons and mesons compared with some groups of UPAs 

But little effort has been made to study vortex knots as realistic models of hadrons. As we now know that such knots can exist on the macroscopic scale at least for the simplest type, it seems to be time to study their microscopic counterparts, especially — as we shall shortly see — the century-old, micro-psi work of Besant & Leadbeater confirms that they do, indeed, exist!

 

If we discard the working (but unproven) assumption made by most particle physicists that quarks are fundamental particles and consider the possibility that they are bound states of N colour SU(N) monopoles, the string theory of QCD and its confining mechanism can be generalised and applied to composite quarks; it is not just applicable to baryons and mesons. This is what the author’s research into the Occult Chemistry work of Annie Besant & C.W. Leadbeater indicates beyond any reasonable doubt. Their book contains numerous diagrams of hundreds of groups of UPAs, which they depicted as bound together by string-like lines of force. The most ubiquitous of these groups are the "hydrogen triplets," so-called because the groups of three UPAs make up the two hydrogen triangles in the hydrogen MPA (see here). Two varieties of hydrogen triplets were noticed: a “positive” type and a “negative” type. The two investigators did not explain what made them differentiate between these two types. However, Besant & Leadbeater depicted the difference in diagrams showing all the component particles that make up each MPA by drawing a positive triplet with its three UPAs pointing outwards away from its centre and a negative triplet with its three UPAs pointing inwards towards its centre. Self-consistent analysis of the MPAs of 46 elements published in Occult Chemistry reveals (see author's book "ESP of quarks & superstrings") that hydrogen triplets are quarks, a positive hydrogen triplet being an up quark and a negative hydrogen triplet being a down quark. Besant & Leadbeater said little about the nature of the lines of force binding UPAs together. In his first three books (see here), the author has interpreted the lines of force inside a hydrogen triplet as SU(3) flux tubes generated by Nielsen-Olesen vortices in the ambient, Type-II superconductor Higgs field. This means that the Meissner Effect should be seen as confining not only quarks inside hadrons but also as yet undiscovered subquark UPAs inside quarks.

 

Evidence confirming that the lines of force depicted in Occult Chemistry are SU(N) flux tubes, where N = 3 when the bound state of UPAs is a hydrogen triplet, is provided by a few diagrams published in the first edition of this book. Most of them usually show UPAs as having lines of force both entering them at their depressed end and leaving them at their pointed end. Sometimes, however, they are shown as the endpoints of a single line of force. Compare this with how the String Model conceives quarks as the monopole endpoint of a flux tube in the Higgs vacuum (see diagram above; see also the third picture here). It does not make any difference that, according to the author's research, UPAs are not quarks but their constituents because the concepts behind the String Model can be generalised to hypercolour SU(N) monopoles, with colour singlet baryons consisting of N such monopoles and coloured quarks being bound states of three hypercoloured monopoles. In many hydrogen triplets, the lines of force enter and leave each UPA, forming closed loops that appear in the diagrams to converge towards a point at the geometric centre of the triplet. The similarity of their geometry to the trefoil knot vortices observed by Kleckner & Irvine is striking and cannot, plausibly, be dismissed as a coincidence. It suggests that the lines of force holding the UPAs together in a hydrogen triplet are SU(3) Nielsen-Olesen vortices with the topology of a trefoil knot. Besant & Leadbeater did not investigate whether the lines of force emanating from the three UPAs actually converged to a point, as the diagrams in Occult Chemistry portray. As these lines of force were flux tubes, the author proposes that they crossed over one another very near the geometrical centre so as to form a trefoil knot, the crossover region being so small relative to the average size of the hydrogen triplet that it escaped the notice of the two investigators, leading them to assume that the lines of force linking three UPAs in a hydrogen triplet converged to a single point in space. That this topology is consistent with the SU(3) gauge field equations needs to be proven mathematically. But the discovery that a vortex can exist in water as a simple trefoil knot makes it easier to believe that Nielsen-Olesen vortex trefoil knots channelling the “colour” electric flux between three SU(3) monopoles can similarly exist in the subatomic world.  This is, of course, not the SU(3) gauge invariance of the quark-confining colour force described by quantum chromodynamics. Rather, it is the mathematically similar, hypercolour SU(3) symmetry of a new, as yet undiscovered force that confines three UPAs with three "hypercolour" states within a quark as an SU(3) hypercolour singlet bound state, the same mechanism of confinement (Meissner Effect) operating as that which, according to the String Model, imprisons quarks inside hadrons, so that — as experiments have indicated — they never exist normally as free particles.

 

News item #9 (July 14, 2012)

Re-discovery of the Higgs boson?
Two research teams at CERN in Switzerland have at last reported their detection of a new particle with a mass of about 126 GeV/c2 that they strongly suspect is the Higgs boson — the so-called "God particle," which physicists believe gives subatomic particles their mass (see here). However, the real "God particle" has yet to be found by them, or, more accurately, re-discovered in a scientific way. It is:

THIS

It is, of course, not what physicists understand by this misleading, sensationalist label, taken from Leon M. Lederman's book on the topic. Nevertheless, the nomenclature is appropriate when it refers to the as yet undiscovered, fundamental constituent of matter that, as this website proves, conforms to the universal blueprint embodied in the sacred geometries of various religions .....

What is a Higgs boson?

 

 

Named after the British physicist Peter Higgs, the Higgs particle was first described 55 years ago — that is, about five years before Higgs and five other physicists proposed its existence — by the Theosophist and clairvoyant Geoffrey Hodson (1886-1983), who possessed the same yogic siddhi called "anima" that Besant & Leadbeater had claimed to use in order to observe UPAs and what they thought were atoms (see here). In investigations in 1959 with Dr D.D. Lyness, M.B., Ch.B., D.P.M., M.A.N.Z.C.P., a psychiatrist from New Zealand, Hodson examined a UPA with this paranormal faculty. On January 26, 1959, he remarked:

"The sight I have of these objects is, I think, improved from the earlier observations. They're surrounded by a field of spinning particles going round them. The one I've got hold of is like a spinning top — the old-fashioned spinning top, but imagine that with (spinning rapidly) a mist or field round it of at least half its own dimension, of particles spinning in the same direction much smaller than itself. The Anu is not only the heart-shaped corrugated form that I have described, it is the centre of a great deal of energy and activity and within it. Outside it, as I have said, there's this rushing flood of particles, the corrugations themselves are alive with energy and some of it is escaping — not all of it, but some of it, and this gives it a tremendously dynamic look. Inside, it's almost like a furnace, it is like a furnace (I don't mean in heat) of boiling activity — organised by the bye, yes, in some form of spiral fashion admittedly, but there's a great deal of activity of free, minuter particles."*

These particles much smaller than UPAs that Hodson described as forming a "mist or field" that circulated a UPA are Higgs bosons, whose collective, circular motion around magnetic monopoles constitutes the Nielsen-Olesen vortices, or strings, that link the three hypercolour SU(3) magnetic monopoles/UPAs making up each quark. For more details, see here and chapter 6 (particularly p. 97) of the author's book Extra-sensory Perception of Quarks (download a PDF version here). Indeed, the very word "vortex" appeared in a strikingly similar diagram of the UPA in a book called "The Principles of Light and Color: the Healing Power of Color," which was published in 1878 by Edwin Babbitt, an American pioneer of colour therapy! The picture below on the right depicts what Babbitt (wrongly) thought was an atom that he had observed with clairvoyance. Notice the word "vortex" under the words "negative end" at the top of the diagram. Notice also the word "torrent" below the words "positive end" at the bottom of Babbitt's picture. Compare it with the phrase "rushing flood of particles" used by Hodson in the quotation above. (He could, of course, have seen this image in Babbitt's book. But how likely is it that in the heat of a scientific experiment he remembered reading the word "torrent" (a feat requiring a photographic memory) and substituted this apt phrase? Does it not seem far more probable that he was in fact remote viewing exactly the same thing!).

The UPA, according to Babbitt, Besant & Leadbeater

The particle that Babbitt thought was an atom is, in fact, the UPA, shown on the left, re-observed 17 years later with the same yogic, remote viewing faculty by Annie Besant and C.W. Leadbeater and now identified by the author as the subquark state of the E8×E8 heterotic superstring. Here, therefore, is undeniable, unambiguous confirmation made 134 years ago of the vortex in the Higgs field surrounding the UPA that was noticed again by Hodson in 1959 as a rapidly spinning "mist or field" — five years before the Higgs boson was even proposed in any scientific research paper, let alone discovered by theoretical physicists to have vortical modes of motion in the vicinity of colour SU(3) monopoles! This Higgs field is believed by some physicists to act as a so-called "Type II superconductor," or "superfluid," that permeates all space. Vortices in this field channel in quantized amounts the colour flux that links magnetic monopoles, forming strings or flux tubes (see News item #1 and chapter 5 of Extra-sensory Perception of Quarks). The fact that these monopoles are not quarks (as string theorists currently conceive them), but constituents of quarks is not a problem because they have generalized the theory to N vortices linking colour SU(N) monopoles at their endpoints, so that the validity of the concepts is not contingent upon quarks being fundamental. This means that the existence of the Higgs field confirmed by the remote viewing of UPAs by Babbitt, Besant, Leadbeater and Hodson is not incompatible with their being interpreted as subquarks. The Standard Model of particle physics, in which quarks are fundamental, monopole sources of the eight gauge fields of colour SU(3), will be proved wrong when the energies available to the Large Hadron Collider at CERN are boosted to the point where clear signatures of quark compositeness begin to appear in the data that it generates. Gluons certainly exist, but they are a subset of the multiplet of color and hypercolour gauge fields that confine both quarks in hadrons and subquarks in quarks. Babbitt and Hodson had to be examining a UPA that was bound to the two other UPAs in a quark, so they really were noticing a hypercolour SU(3) Nielsen-Olesen vortex in the Higgs superfluid that surrounded the UPA under their observation.** Recent lattice QCD calculations of the flux density for a Y-shaped configuration of three colour SU(3) flux tubes terminating on quarks bear a remarkable similarity to drawings that appeared in the 1908 edition of Besant's & Leadbeater's book Occult Chemistry (see the diagram at the bottom of the page here). Closed as well as open strings with UPAs at their ends were recorded in this book:

Open and closed strings compared with bound groups of UPAs

The "lines of force" binding UPAs together, which they recorded in numerous drawings throughout Occult Chemistry, are flux tubes created by vortices in the Higgs field, which squeezes the flux lines together through the Meissner Effect, creating a confining force that grows stronger with increasing separation between UPA monopoles (see also here). This mechanism confines both quarks inside hadrons and subquarks inside quarks. Such an abundance of unambiguous evidence for the existence of the Higgs field and for the validity of the Higgs vortex/string model of quark confinement that was published by Besant & Leadbeater 56 years before physicists conceived of this particle is highly convincing. Scientists who dismiss this huge body of evidence out of hand are letting their ideological prejudice towards the paranormal cloud their dispassionate evaluation of the intrinsic merit of the two Theosophists' observations. A skeptic who wants to argue that Besant & Leadbeater could have influenced Hodson (he had, no doubt, read their book) is missing the crucial point. The word 'vortex' appears nowhere in Occult Chemistry in their account of the UPA, nor does the scenario of a conglomerate of smaller particles spinning around it. Hodson could not, therefore, have borrowed this feature from their book, so that there was nothing in it that could have influenced him to speak of a rapidly spinning mist or field of particles.

 

Geoffrey Hodson


A statement by Dr D.D. Lyness concerning Geoffrey Hodson:

"I, of course, would be happy to state unequivocally my belief that Geoffrey Hodson possesses powers of accurate clairvoyant research.

"During the years 1956 to 1959 I was fortunate enough to work with Geoffrey Hodson. My contribution was to record his observations on the clairvoyant appearance of subatomic matter; I now have some forty hours on cassette tape giving a verbatim account of the experiments we performed. There is no doubt whatsoever in my mind that Geoffrey possesses quite remarkable powers of extra-sensory perception and invariably used these faculties with meticulous regard for accuracy in both observation and description. He frequently stressed the selective nature of clairvoyant observation and was fully aware of the pitfalls associated with the translation of what can be called 'raw extra-sensory data' through the brain-mind into words capable of conveying useful meaning to his hearers. Throughout these sessions he was a model of scientific caution, taking every possible care not to make statements that might be misleading."

11 September, 1981 (from here)

Geoffrey Hodson


On April 8, 1957, whilst examining the diamond in a ring, Hodson said:

"My first sight inside the diamond is of the funnels only, like a cluster of funnels, two sets. It is possible to see the two pyramids as if slightly separated so that the base of an upper one can be envisaged, visualised, almost seen, though cohesion is apparent and all eight funnels are radiating from a common centre. Now, I want to record again the experience of the whole phenomenon being pervaded by countless myriads of minutest conceivable, physically inconceivably minute points of light which I take to be free anu and which for some reason are not caught up in the system of atoms at all but remain unmoved by it and pervade it. These are everywhere. They pervade everything, like ... Strangely unaffected by the tremendous forces at work in the atom and rushes of energy, and so forth, they don't seem to get caught up in those or be affected much by them. If at all. They remain as a virgin atmosphere in which the phenomenon is taking place."†

In 1980, Dr Lyness added the comment "Therefore not gluons" to Hodson's observation of "countless myriads of minutest conceivable, physically inconceivably minute points of light" that "remain as a virgin atmosphere". The following year, he added to Hodson's statement the query: "? Higgs particles." His conjecture has turned out to be correct. During the psychiatrist's investigations with Hodson, the latter frequently reported seeing clairvoyantly myriads of minute points of light pervading the space occupied by atoms that his vision had focussed upon, as well as everywhere around him, whether his eyes were open or shut. For example, Hodson said:

"I wonder if you or your colleagues would care to comment to me upon the commonest phenomenon that I see, all the time, unless I make an effort to shut it out, and now when I emerge from my clairvoyant investigation it fills the whole air, world and universe, and it consists of countless myriads of the smallest possible points you can imagine, the whole air is filled with it. It is all in extremely rapid movement. Sometimes it makes little lines of groups of them. Sometimes it is a kind of shimmer. But it is all granular. Whatever there is granular. Minutely granular, far inconceivably beyond anything, a pin's point would be enormously large in relationship to this, if one could see a pin's point. It's extremely minute. And they are everywhere. And they've always been, ever since etheric clairvoyance showed itself to me at all, always the world, the air, everything I look at is pervaded and surrounded by these countless myriads of minute points."††

These were not "free anu," as he assumed (he never checked whether they really were UPAs by magnifying individual points of light). Nor were they just molecules in the air, for he categorically asserted that they appeared to his vision to be many orders of magnitude smaller than UPAs, which, as subquark states of superstrings, would be much more minute than even atomic nuclei, let alone atoms and molecules. Instead, his faculty of remote viewing the subatomic world was revealing the sea of Higgs bosons that fill space. Far from the core of a vortex, the density of the Higgs field is constant and the Higgs vacuum state is superconducting. It varies rapidly towards zero in the region of the core, where the Higgs field becomes a normal conductor. This was the "mist or field" composed of much smaller particles that he noticed revolving around the UPA, namely, the string-like, vortical excitations of the ambient, superconducting Higgs field in the vicinity of magnetic monopole sources of the colour flux that is squeezed into and channelled along the normally conducting core of these vortices.

Here, therefore, is unambiguous evidence that a well-known clairvoyant was able to notice vortical motion around the basic units of matter of numerous, smaller particles filling all space as a "field" five years before physicists proposed this type of particle and decades before string theorists discovered vortex solutions in the Higgs field in their analysis of the confinement of quarks by the string model version of QCD. These vortices are the non-abelian counterparts of the magnetic flux vortices, or Abrikosov vortices, known to permeate Type II superconductors, forming a lattice (see here & here; vortex solutions to the abelian Higgs model are analyzed here). The key phrases used by Hodson, namely (referring to UPAs) "They're surrounded by a field of spinning particles going around them" and "mist or field round it of at least half its own dimension, of particles spinning in the same direction much smaller than itself" (italics mine), are beyond dispute. The word "spinning," of course, refers here not to any intrinsic spin of these particles (Higgs bosons are spinless) but to the "mist or field" of these particles circulating around UPAs in the same sense that the latter spin on their axes (notice that his words "spinning rapidly" appear in parentheses before this phrase in the first quotation, clearly indicating that Hodson was referring not to individual particles but to a conglomerate of particles, which he aptly described as a "mist or field" that revolved rapidly around a UPA in the same direction that it was spinning. Such collective, rotational excitations of the Higgs field were unknown to particle theorists in 1959 when this crucial observation was recorded by Dr Lyness. Indeed, the Higgs field had not even been proposed then! (A short history of the ideas that led to the formulation of the Higgs mechanism can be found here). So nothing in the scientific literature of the time could have influenced Hodson to make his observation, just as Babbitt could not have been influenced by Lord Kelvin's model of atoms as vortex rings in the aether, which was published 11 years earlier in 1867 (see here), for he described UPAs not as such rings but as having a vortex of particles circulating around it — something that is conceptually entirely different. It constitutes, therefore, irrefutable evidence that Hodson detected in a paranormal manner the Higgs particles pervading space years before they were postulated by physicists and 53 years before the Large Hadron Collider at CERN provided statistically significant data consistent with their existence, although not yet establishing it with certainty. Any alternative interpretation of the points of lights filling space that were visible to him "all the time" must be rejected as wrong because it cannot account for the way the particles change their motion in the vicinity of UPAs to a circulation around them indicative of vortices — a feature that only their identification as Higgs particles can explain in the context of the String Model.

Update

Peter Higgs & Francoise EnglertThe Royal Swedish Academy announced today (October 8, 2013) that the Nobel Prize in Physics this year has been awarded to Peter Higgs of the United Kingdom and Francoise Englert of Belgium for their prediction of the Higgs particle nearly 50 years ago. On such a day of recognition of their brilliant discovery, nothing should be said that lessens its importance and this update should not be construed as such. At the same time, however, as we honour these two people, let us note that, just as Besant & Leadbeater published their discovery of the neon-22 isotope about five years before the physicist J.J. Thomson separated neon into two fractions and 12 years before his assistant Francis Aston separated and measured the masses of the neon-20 and neon-22 isotopes, which helped him to win the Nobel prize in physics, so Geoffrey Hodson — with no understanding of what he was seeing — described the presence of what can only be Higgs particles all around him, as well as their spinning around a UPA in his field of micro-psi vision, five years before Higgs and Englert even conceived that their mathematical field generating masses for subatomic particles might be that of another, yet-to-be-discovered particle. Scientific academies, of course, will never recognise Hodson's priority in discovering the Higgs particle because paranormal abilities like micro-psi vision have not been proven in a scientific way to exist in human beings. Yet, Hodson left us statements of ostensible, paranormal observation that warrant no alternative interpretation. Does it, then, really matter that the investigations during which these statements were made lacked the sophistication and rigorous protocols expected of tests in a modern, parapsychological laboratory? Does that cast doubt on the reliability of this evidence? Given that no scientific information or clues were available to Hodson that might have led him to anticipate this particular discovery — like some latter-day Leonardo da Vinci conceiving scientific ideas many years before they became part of society — what difference would it have made if the experiments conducted by Dr Lyness had been more tightly controlled? None whatsoever! Just as it made no difference to the scientific value of the micro-psi investigations carried out by Besant & Leadbeater. That is why sceptics of the claims they made in their book Occult Chemistry (and now those of Hodson) have nothing to fall back on as an alternative explanation of how they managed to anticipate future discoveries in particle physics by describing the existence and behaviour of alleged subatomic particles in a way that was unknown to the science of their time.


* From an unpublished transcript of investigations by Dr. D.D. Lyness (available here). The passage quoted above comes from observations made on January 26, 1959, which are among a few pages of the transcript omitted from the linked web page. The original, complete transcript, entitled "Some recent clairvoyant research in New Zealand," is deposited in the National Library of Australia collection (see here).

** SU(3)/Z3 Nielsen-Olesen vortex, where Z3 is the centre of SU(3), to be more accurate.

† Ibid, April 8, 1957.

†† Ibid.

 

News item #8 (July 19, 2011)

Hunting the already seen
An article entitled "Hunting the unseen" appeared on July 15 at Physorg.com. It reported the work of a Japanese research team called the HAL QCD Collaboration. Physicists know that so-called "baryons," such as the proton and the neutron, are composed of three quarks. A stable form of two baryons has been known since 1931, when Harold Urey discovered heavy water, in which the two protons in its molecule are replaced by the deuteron — a bound state of a proton and a neutron. Physicists have wondered whether other kinds of these "dibaryons" might exist. To assist their experimental detection, the team studied the theoretical stability of the hypothetical H dibaryon, which is a bound state of two up quarks, two down quarks and two strange quarks. Although the lattermost are heavier than the former types of quarks, the team had to assume their masses are equal in their use of lattice quantum chromodynamics in order to simplify their calculation of the binding energy of the H dibaryon. This, however, did not undermine the validity of their conclusion that the particle was stable because previous calculations assuming equal masses for the three types of quarks had revealed that the total energy of the dibaryon is less than the combined energy of the two separate baryons.

Comparison of H dibaryon & Hydrogen MPAIn the picture opposite, the image on the left provided by the RIKEN scientific research institute in Japan depicts the six quarks making up the H dibaryon. The three coloured spheres denote the three colour states of a quark, labelled red, green & blue. I have rotated the diagram through 90° in order to portray more clearly its obvious similarity to the picture on the right appearing in the book Occult Chemistry, which was published in 1951. Originally observed in 1932, it depicts what Annie Besant and C.W. Leadbeater believed was the atom of hydrogen. In my books, I interpreted it as the deuteron (the nucleus of the stable isotope of hydrogen), created prior to observation by their micro-psi selection of a hydrogen molecule, which resulted in its two protons fusing together to form a deuteron after one of them changed into a neutron:

p + p →1D2 + π+.

The lower Hydrogen Triangle in the hydrogen MPA is a proton, the two positive hydrogen triplets with outward-pointing UPAs being positively charged up quarks and the negative hydrogen triplet with inward-pointing UPAs being a negatively charged down quark. The upper Hydrogen Triangle is a neutron, the two linear hydrogen triplets being d quarks and the positive hydrogen triplet being an up quark. The hydrogen MPA is discussed in more detail here. The representation of the quarks in the scientific picture by such relatively large spheres is purely artistic, just as the circles in the hydrogen MPA depicting what looked to Besant & Leadbeater to be hollow spheres enclosing three bound UPAs are shown much larger than they really were. Besant & Leadbeater reported in Occult Chemistry that the hydrogen MPA is stable — in agreement with its identification as a deuteron. The fact that the picture on the left depicts a bound state of two up quarks, two down quarks & two strange quarks, whereas the picture on the right depicts, according to my interpretation, the three up quarks and three down quarks in a deuteron is, of course, beside the point. As another bound state of two triangular arrays of quarks, the deuteron would be depicted like the H dibaryon. What counts here is that both diagrams depict dibaryons, with the implication of the Occult Chemistry diagram being that quarks are not indivisible particles but bound states of three more fundamental particles.

The Japanese research is summarized in this article at Physorg.com. 

News Update
Using Jülich's accelerator COSY, German researchers confirmed in 2011 the possibility of dibaryons by discovering strong evidence for the existence of a short-lived resonance composed of six quarks. See here.

  

 News item #7 (July 3rd, 2011)

European Space Agency Observatory shows that any quantum graininess in space is at least 13 orders of magnitude smaller than the Planck scale!

IntegralIn his General Theory of Relativity, Albert Einstein assumed that space and time are continuous quantities that are infinitely divisible. With, however, the discovery by Max Planck that energy in the form of photons was emitted by atoms in discrete quantities and Einstein's explanation of the photo-electric effect, implying that the energy of photons did not vary continuously, followed by Werner Heisenburg's formulation in 1927 of his Uncertainty Principle, it eventually became the received wisdom amongst theoretical physicists that the General Theory breaks down at the so-called "Planck scale" of space-time (L0 ≈ 10−35 metres & T0 ≈ 10−43 seconds), when the quantum aspect of the space-time continuum becomes dominant. They have believed that space-time was like a kind of continuous fabric, deformable by gravitating objects, that looks smooth on the large-scale, where General Relativity rules, but which becomes granular as its scale diminishes towards the Planck scale, at which limit distance (indeed, geometry itself) can no longer be defined as a classical variable because of the Uncertainty Principle. This led to the unquestioned assumption (indeed, a dogma) among string theorists that superstrings have the size of the Planck scale L0 and that unification of nature's forces took place on the Planck energy scale (E0 ≈ 1019 Gev). The European Space Agency's Integral gamma ray observatory has now undermined these assumptions by showing that, if space has any graininess at all, the indivisible grains must be smaller than 10−48 metres, that is, space is continuous for at least 13 orders of magnitude smaller than what was believed up to now to be the smallest that is meaningful in terms of classical, continuous geometry! According to current ideas, the polarisation of photons is affected by this graininess and depends upon their energy, so Integral looked for differences between the polarisations of high and low-energy gamma rays emitted by GRB 041219A, a supernova that blew up on December 19, 2004. None was found, indicating that, if space is grainy, the grains are at least 13 orders of magnitude smaller than the Planck scale, which may not apply to the typical size of superstrings.

What is the significance of this remarkable discovery for the micro-psi observations of Besant & Leadbeater discussed in Occult Chemistry? Well, they claimed that the UPA — the smallest unit of physical matter — is composed of whorls that are made up of seven orders of spirillae wound around successively smaller circles (see here). If the author's identification of this particle as the subquark state of the E8×E8 heterotic superstring is correct, such sharp features would be inconsistent with the Uncertainty Principle if the assumption made by most physicists that superstrings are on the Planck scale were correct, for geometry itself becomes "fuzzy" on this scale. How, for example, could the 7th-order spirillae be much smaller than the whorls of the UPA (as their observations imply) if the latter is a superstring whose size in 4-dimensional space-time is about equal to L0? The problem disappears if the assumption is relaxed by proposing that the UPA (and superstrings in general) is larger than L0 by a few orders of magnitude. However, the Integral discovery renders this hypothesis redundant because it means that features with classical geometry can exist (and, therefore, be remote-viewed with clarity) in subatomic particles even though their size is far smaller than the Planck scale.

The discovery by the European Space Agency Observatory is reported here.  A news article released by ESA can be found here.

News update
In 2009, researchers using the NASA's orbiting Fermi Gamma-ray Space Telescope detected two gamma-ray photons originating in a burst of energy (designated GRB 090510) caused by the collision of two neutron stars. After travelling for 7.3 billion years, they arrrived at the detector within 9/10 seconds of each other (see here). To one part in 100 million billion, the two photons, one with a wavelength a million times smaller than that of the other, had travelled at the same speed. This contradicts recent theories of a frothy, foamy space-time that predicts the speed of light to be energy dependent, so that the more energetic photon should have travelled much more slowly. After studying three photons that had been received in May, 2009 by this telescope, a team at Michigan Technological University has confirmed (see here) the earlier conclusion that space-time does not exhibit towards light the "roughness" that would be expected if it became foamy at the Planck scale, as currently conceived by most theoretical physicsts. The space-time continuum seems to remain a classical continuum even at this scale — at least as far as light is concerned! Does classical physics (in particular, Einstein's General Relativity) really break down at this point, as has been the dogma taught to successive generations of postgraduate physics students? Astronomical observations seem to be saying loudly: No.

 

News item #6 (March 3rd, 2011)

Do the latest results from LHC's ATLAS detector cast doubt on supersymmetry (SUSY)?
(No, they don't! The lack of evidence so far for squarks is consistent with the view that quarks are not fundamental, in which case SUSY applies, instead, to their subquark constituents, so that squarks need not exist).

According to the Standard Model of particle physics, there are three generations of quarks and leptons: the three pairs of up & down quark, charm & strange quark and top and bottom quark, and the three pairs of neutrinos and their associated leptons (electron, muon & tau). Electromagnetic forces are transmitted by the photon (γ), strong forces by the eight gluons (g) and weak interactions are due to exchange of the Z boson (Z) & the W boson (W). There is also an as yet undiscovered spin-0 particle called the "Higgs

 u
up quark
c
charm quark
t
top quark 

γ
photon 

 d
down quark
s
strange quark 
 b
bottom quark
 g
gluon
 νe
electron neutrino
 νμ
muon neutrino
 ντ
tau neutrino
 Z
Z boson

e
electron

 μ
muon

 τ
tau lepton

 W
W boson


particle" whose coupling to particles is supposed to generate their masses. Quarks and leptons have spin-½ and the particles transmitting the strong and electroweak forces have spin-1. The mathematical symmetry called "supersymmetry" was conceived in the 1970s. It hypothesizes that every spin-½ fermion is associated with a superpartner called an "sfermion" that has spin-0 and that every spin-1 gauge particle, such as the photon, is associated with a spin-½ particle that is called by adding "-ino" to the end of its name. Hence, there should be a spin-0 up squark, a spin-0 selectron, a spin-½ photino, a spin-½ gluino, etc. If supersymmetry is correct, the spin-0 Higgs particle should have a spin-½ superpartner called the "Higgsino."

ATLASDespite all its theoretical appeal, particles accelerators have not detected any of the particles predicted by SUSY. The Tevatron at the Fermi National Accelerator Laboratory in Batavia, Illinois, for example, has found no evidence of supersymmetrical squarks at masses of up to 379 GeV. The ATLAS detector at the Large Hadron Collider (LHC) in CERN, Switzerland, has failed to find any superpartners of the particles in the Standard Model up to about 700 GeV, and will be able to reach 1000 GeV at the end of the year. This negative result so far is beginning to worry many theorists, who have devoted years of their academic careers publishing research papers that assume that SUSY is true. However, even if none of the supersymmetric partners of particles in the Standard Model are found in the next year, this does not necessarily mean that SUSY only exists in the mathematical imagination of theoretical physicists. A tacit assumption has been made in the search for evidence of squarks, namely, that quarks are fundamental. If they are not, then squarks do not exist and leptons and sleptons will belong to a supermultiplet that includes spin-½ subquarks and their supersymmetric spin-0 partners, not quarks and squarks. If it were a bound state of three subquarks, a spin-0 squark would be a bound state of three such spin-0 partners of subquarks. As a boson, its wave function has to be symmetric with respect to interchange of whatever quantum observables they possess. According to the observations by Annie Besant and C.W. Leadbeater of hydrogen tripets (identified by the author as up and down quarks), their constituent UPAs are bound by the same confinement mechanism as applied to quarks, namely, the QCD string model (see here). The implication of this is that subquarks possess three "hypercolour" states which confine them in groups of three. As quarks possess colour, not hypercolour, a quark must be a hypercolour singlet. This means that the hypercolour wave function of the three bound subquarks would be antisymmetric. As their supersymmetric partners would be bound by the same type of force, their hypercolour wave function would also be antisymmetric. However, the overal wave function has to be symmetric, so that the rest of the wave function of the three supersymmetric subquarks to be antisymmetric to interchange of whatever variables define the representation of the symmetry group to which they belong. One of them would be their coordinates. Intuitively, one would expect that the three spin-0 supersymmetric subquarks in up and down squarks — the least massive of any generation of squarks — would be in an S orbital state whose spatial wavefunction was spatially symmetric with respect to interchange of the coordinates of any two of them because it contributes zero orbital angular momentum. But, then, the remainder of the wave function would have to be antisymmetric, indicating that the squark is a singlet state of some internal symmetry group described by an antisymmetric wave function. This leaves the flavour properties of quarks unexplained, for these would be expected to be attributable to subquarks themselves. Hence, it seems unlikely that squarks as bound states of three supersymmetric subquarks could even exist. The same conclusion might, possibly, apply even if a squark were, instead, regarded as a bound state of two subquarks and the supersymmetric partner of a subquark.

In conclusion, the micro-psi studies of subatomic particles carried out over a century ago by Annie Besant and C.W. Leadbeater proved beyond any reasonable doubt that quarks are not fundamental, contradicting the working assumption of the Standard Model. The implication of this is that it is not legitimate to speak of the supersymmetric partner of a quark, as SUSY would apply to the constituents of quarks if they really exist, as my analysis of these studies confirms that they do. Bose-Einstein statistics may not allow squarks to exist as bound states of three spin-0, supersymmetric partners of spin-½ subquarks, thereby possibly explaining why LHC has not detected them to date. A summary in Nature of what the ATLAS detector has found (or, rather, has not discovered!) can be read here. Links to Arxiv preprints of the research by various teams at LHC appear at the end of the Nature article. See also this article at Physorg.com.

 

News item #5 (July 8, 2010)

The proton has shrunk!

A study reported in Nature suggests that the radius of the proton is four per cent smaller than previously thought.

The size rp of the proton has a well-defined meaning in particle physics. The proton may be imagined as a cloud-like distribution of electric charge due to the orbital motion of its two positively charged up quarks and its negatively charged down quark. rp2 is the average value of the square of the magnitude of the position vector r occupiedLines of force in hydrogen MPA by its electric charge, weighted according to the density of the latter in 3-dimensional space. Electron-proton scattering experiments have determined rp with an accuracy of about two per cent. Its present, most accurate value is 0.8768(69) fm, where 1 fm = 10-15 metre. The atom of muonic hydrogen (a proton orbited by a negatively charged muon) is much smaller than the hydrogen atom because the muon is more than 200 times heavier than the electron. The properties of this atom are more sensitive to the size of the proton because the muon interacts more strongly with the latter in a much smaller orbit. By measuring the Lamb shift* in muonic hydrogen, a team of 32 international scientists has now calculated rp to be 0.84184(67) fm, which differs by 5.0 standard deviations from the most accurate value accepted up till now! This is very surprising — even shocking. The new experiment was at least 10 times more accurate than any performed to date. They conclude that either quantum electrodynamics (QED) does not accurately calculate effects in atomic hydrogen or muonic hydrogen atoms or the size of the Rydberg constant** used for decades to calculate properties of atoms is inaccurate.

For more details, see the article "Honey, I shrunk the proton" at Physorg.com and the synopsis of the research team's letter to Nature here (full access requires subscription). Read the editor's summary here.

An assumption made in calculating the value of rp is that electrons interact electromagnetically with charged quarks that — like themselves — are point-like. Could it be, however, that, instead of the Rydberg constant having the wrong value or something being wrong with QED — two unlikely possibilities that physicists would be loath to consider because of their implications — this discrepancy indicates that quarks are not point-like particles but objects that are extended in space because they are bound states of several fundamental particles? This is precisely what is indicated by the micro-psi observations of the hydrogen MPA by Annie Besant and C.W. Leadbeater. The diagram of this MPA shown opposite is taken from the first edition of Occult Chemistry, which was published in 1908. It depicts the various stages of break-up of the MPA, starting from what the two Theosophists wrongly thought was the gaseous state of hydrogen. The two spheres released at the first (E4) stage are the proton (lower) and the neutron (upper). Neither picture is to scale, of course, because the large differences in size between UPAs, hydrogen triplets and hydrogen triangles that Besant & Leadbeater reported would have been impractical to depict accurately in a book. The neutron originated in the deuteron formed from the nuclear fusion, prior to observation, of the two protons in a hydrogen molecule:

p + p →1D2 + π+.

(for more details, see Occult Chemistry).


* The Lamb shift is a small difference in energy between the two energy levels 2S1/2 and 2P1/2 in the hydrogen atom. It arises because zero-point oscillations in the electromagnetic field cause a small, oscillatory perturbation in the position of the electron, which alters its Coulomb energy e2/r and its energy level predicted by the Bohr model of the atom, which should be the same for these two orbitals.

** The Rydberg constant for an atom consisting of a positively charged nucleus of mass M and electric charge +Ze, around which a particle of mass m and negative electric charge −e orbits, is given by

 R =      R0Z2(1+m/M) R0 = 2π2me4/h3

where h is Planck's constant.

 

News item #4 (July 5, 2010)

A critique of Dr Kennedy's discovery of musical structure in Plato's writings

It has been recently reported that Dr Jay Kennedy, a science historian at the University of Manchester, has claimed that he has deciphered the so-called "Plato code" in the ancient philosopher's writings. By analyzing the text in Plato's books with a special computer program, Kennedy discovered correlations between clusters of words related to music and the positions of the text where they appeared, i.e., after 1/12th, 2/12th, 3/12th, etc of the total length of the text. Words signifying consonant notes that the human ear regards as harmonious occurred at sections marked by the numbers 2, 3, 4, 6, 8 & 9 when the whole text was divided into 12 sections. Here, Plato described sounds associated with love or laughter in passages about virtue, the Platonic forms, beauty, etc. Dissonant notes marked with screeching sounds or war or death occurred at sections marked by the numbers 1, 5, 7, 10 & 11. The ancient Greeks knew that, when these numbers represented lengths of string, the sounds created by plucking them were consonant or dissonant with respect to a sound created by a string 12 units long. Because this pattern manifests in many of Plato's books, Kennedy concludes that the philosopher had encoded his writings with a cryptic, musical code, as though he meant his books to be a kind of musical composition.

Links to Dr Kennedy's papers and files can be found here.

The problem with this claim is that there is really nothing musical about most of the numbers demarcating these hidden patterns. Kennedy talks glibly about the existence of a "12-note scale" (actually, it would be a 13-note scale when the tonic is included) because he needs to explain the association that he finds between the integers 1-12 and the musical contexts secretly marked by the various clusters of words appearing at multiples of one-twelfth throughout the various texts. However, neither the followers of Pythagoras nor the ancient Greeks regarded the musical scale as made up of 12 notes. Certainly, Plato would have been aware of the 12-tone, so-called "Pythagorean chromatic scale":

C-C#-D-D#-E-F-F#-G-G#-A-A#-B-C.

generated from the 8-note Pythagorean scale with the pattern of seven successive intervals:

T-T-L-T-T-T-L

by splitting up its five tone intervals (T) into leimmas (L), or Pythagorean semitones, where T = 9/8 and L = 256/243. But this creates a musical scale that is impractical for various reasons, e.g., it has two types of semitones — the chromatic semitone T/L and the leimma, their ratio T/L2 ≈ 1.0136... being known as the notorious "Pythagorean comma." This problem was well-known to musicians during Plato's time, so the Pythagorean chromatic scale was not some great secret that he might have wanted his books to encrypt. What later came to be called the "church modes"  were, originally, different musical scales, although whether any of them was synonymous with what the ancient Greeks called the "Phrygian mode," the "Dorian mode," etc remains a controversial issue amongst musicologists (see Article 14). For various historical reasons, the eight-note scale was eventually replaced by the modern equal-tempered scale, in which the octave is divided into 13 notes separated by 12 equal semitones. According to Kennedy: "This leads naturally to the idea of a scale of twelve notes produced by strings with lengths corresponding to the integers from one to twelve. In theSymposium, symbolic passages are located at each twelfth of the dialogue, and these will be associated here with the integers 1 to 12." (see here). It may seem natural now to him, but the idea is merely a modern conceit without historical support. First of all, a set of sounds that are either consonant or dissonant per se does not constitute a musical scale. Secondly, in ancient Greece, the eight-note musical scale was based upon the tetrachord of four notes. No doubt Plato was, indeed, aware that musical sounds created by vibrating strings were consonant or dissonant, depending upon whether their lengths were these numbers, and he might have encoded his writings to reflect this fact, although sceptics may ask why he ever bothered to do this, given that it was common knowledge amongst musicians. But, please, do not ask us to regard all these specific sounds as being the notes of an actual musical scale, let alone one that was known to learned ancient Greeks like Plato but which had to be kept secret! They are nothing of the kind. These numbers are just a bunch of integers which divide into two families that happen to have significance vis-à-vis the human ear. Certainly, by his time, musicians had moved beyond the limitations of the eight-note diatonic scale. However, a mathematical philosopher like Plato would have known the huge difference between the ideal character of this scale and the various more complex, artificial scales concocted by musical theorists. Nor was he trying to turn his writings into a series of movements of a classical musical composition (how many people at the time would have noticed that?!). Plato was no doubt encrypting them mathematically in order to hide certain musical facts that he regarded too sacred to be discussed openly. Like the good Pythagorean that he was, Plato was merely following the traditions of this esoteric brotherhood. Alchemists in the Middle Ages, too, wrote in cryptic ways in order to guard their secrets. Dare one say it, even Sir Isaac Newton, the father of classical physics, did so because he was a fervent alchemist! The question is: what arcane, musical (and perhaps more universal) truth was so precious to Plato that he went to the considerable effort of designing the structure of his books in order to encrypt it?

Kennedy makes a lot (in fact, too much) out of the fact that the pattern of numbers 6:8:9:12 generating tone ratios of some of the notes of the Pythagorean scale could have led to Plato dividing up some of his books into 12 sections. This is because these four numbers well-known to students of music belong to a tetractys array of ten numbers as large as 27 (see the diagram below), two sides of which, known as the "lambda," Plato referred to in his cosmological treatise called Timaeus, and there is no written evidence that he (nor, indeed, Pythagoreans before him) ever gave any fundamental, musical significance to the number 12. Indeed, the numbers 6, 8, 9 & 12 are actually members of a tetrahedral array of twenty numbers — see Article 11 & Article 12). However, my research (see The seven musical scales) has shown that 12 types of notes between their tonic and octave make up the seven diatonic, 8-note, musical scales that became seven of the eight musical modes used for centuries by the Roman Catholic Church, the eighth mode (Hypomixolydian) being merely a repetition of the notes in the first one (Dorian). The tone ratios of these 12 notes are:

256/243

9/8

32/27

81/64

4/3

1024/729

729/512

3/2

128/81

27/16

16/9

243/128

But only two of them, namely, the perfect fourth with tone ratio 4/3 = 12/9 and the perfect fifth with tone ratio 3/2 = 12/8, are defined by numbers belonging to the set of integers 1-12. Therefore, only these two sounds (both consonant) are actual notes of some of the seven diatonic, musical scales. Only these scales can be regarded as 'natural' and embodying Plato's divine Ideal because they constitute a seven-fold whole whose properties are found in sacred geometries, as Articles 11, 12, 14, 26, 31 & 42 indicate. All other scales known to musicologists are artificial in the sense that they have been fabricated by humans for whatever practical, musical advantages they possess, in particular, the addition of new tones to increase the range of emotions that can be expressed by musical instruments. Unlike the seven diatonic scales, these concocted scales do not reflect the seven-fold nature of the cosmic spiritual order. This means that it is hardly likely that Plato would have divided his books into twelve sections that mirrored some man-made, 12-note scale existing during his time, for his writings were devoted to the Ideal and he would never have devised a hidden structure in them that referred to anything less than the divine perfection of the Ideal. Plato would never have regarded the imperfect, mathematical structures of his contemporary music as sacred or important enough to receive such elaborate, literary encryption. So why the division into twelve parts? Perhaps because he understood that the seven diatonic, musical scales are the musical manifestation of the seven-fold nature of the divine order (see my slideshow "The Divine Nature of Music"), and he wanted to mark out the text of his books so as to reflect the existence of the 12 different types of notes between the tonic and octave. That, perhaps, was the real, mathematical secret that was worth encrypting. If it was, it was very effective. How many musicologists even today know that the seven diatonic scales contain 12 types of notes? However, Plato was trying to achieve more than just encryption of  a great secret — and certainly nothing as banal as a 12-note scale! He wanted the very composition of his books to reflect their discussion of the ideal in nature and society. This ideal in music was the set of 12 notes dividing the octave in the seven musical scales.

Here is evidence to support such an interpretation: Article 16 analyzed the numbers of Pythagorean and non-Pythagorean intervals between the notes in the seven musical scales. By identifying in a scale the subset of intervals belonging to the set of 14 basic notes that appear at least once amongst the intervals, it is possible to determine how many Pythagorean intervals in each scale are repetitions of this subset. Their numbers are:

Hypolydian

Mixolydian

Lydian

Dorian

Hypodorian

Phrygian

Hypophrygian

13

11

12

12

11

13

12

There are 84 repetitions of Pythagorean intervals, where 84 = 12 + 32 + 52 + 72. They comprise the first five notes after the tonic in the Pythagorean scale (see p. 21 in Article 16). As the octave appears only once in the intervals between the notes in each scale, these repetitions are those of the 12 notes listed above. The average number of repetitions of the basic intervals per scale, which total 46 (the number of chromosomes in the human cell) for all seven scales, is 84/7 = 12. Here is that number 12 again! On average, 12 of the repeated intervals in the seven scales are Pythagorean. In fact, the four authentic modes (Dorian, Phrygian, Lydian & Mixolydian), have, on average, 12 repeated, Pythagorean intervals, as do the three distinct plagal modes (Hypodorian, Hypophrygian & Hypolydian).

The holistic character of this pattern of 84 repetitions is demonstrated by the following correspondences: there are 84 yods up to the top of the 1-tree (the lowest of any set of overlapping Trees of Life), when its 19 triangles are turned into tetractyses. They comprise 48 red yods up to Chesed and 36 black yods above it. They are the counterpart of the 48 red & green corners of the third & fourth sets of triangles in the 3-dimensional Sri Yantra and the 36 blue & violet yods in the first & second sets of triangles. The

Equivalence of 1-tree, 3-d Sri Yantra, 2nd-order tetractys & Lambda tetractys

former are also the counterpart of the 48 brown hexagonal yods in the seven 1st-order tetractyses corresponding to the seven Sephiroth of Construction that surround the centre of the 2nd-order tetractys. The latter are the counterpart of the 36 green yods either in the tetractyses at corners of the 2nd-order tetractys or at corners of 1st-order tetractyses. Their counterpart in Plato's Lambda tetractys is the sum (48) of the integers 2, 3, 4, 9, 12 & 18 at the corners of a hexagon and the sum (36) of the integers 1, 8 & 27 at the corners of the Lambda tetractys. The integer 6 at its centre denotes the six Pythagorean notes that belong to the basic set of 12 notes and the sum (84) of the nine integers surrounding it denotes the number of their repetitions in the intervals between notes in the seven diatonic scales.

What is the musical meaning of this 48:36 division? The four authentic musical modes (Lydian, Mixolydian, Dorian & Phrygian) have 48 repeated Pythagorean intervals and the three plagal modes (Hypolydian, Hypodorian & Hypophrygian) have 36 repeated Pythagorean intervals. Other combinations of modes generate the same two numbers, but this is beside the point. What is remarkable is that this fundamental division manifested in sacred geometries should reappear in the simple distinction between authentic and plagal modes! Moreover, the four authentic modes have 26 Pythagorean intervals that have these 48 repetitions, showing how they are prescribed by YAHWEH, the Godname of Chokmah in the Tree of Life with gematria number value 26 (see Sacred geometry/Tree of Life, p. 7).

The holistic parameter 84 manifests also in the disdyakis triacontahedron — the outer form of the polyhedral Tree of Life. When its axis passes through two diametrically opposite A vertices as north and south pole, there are 12 vertices in its equatorial plane (see here). The 90 vertices in each half of the polyhedron correspond to the sum (90) of the integers in the Lambda tetractys. They comprise 6 vertices in one half of the central, 12-sided polygon and 84 vertices in its upper half. They correspond to the six ascending,

Correspondence between disdyakis triacontahedron and Pythagorean intervals of 7 diatonic scales  

Pythagorean intervals that belong to the basic set of 12 notes and to their 84 repetitions in the intervals between the notes of the seven musical scales. The six vertices in the other half of the central polygon and the 84 vertices in the lower half correspond to the six descending, Pythagorean intervals and to their 84 repetitions. As the polyhedral manifestation of holistic systems, the edges of the disdyakis triacontahedron express the basic, Pythagorean intervals in the seven diatonic scales and their 168 repetitions, each mirror-image half of the polyhedron corresponding to the distinction between rising and falling intervals.

The 84 repeated, Pythagorean intervals comprise five types of notes with the following numbers of repetitions:

 D E F G
 28 11 23 17

There are 28 D, 28 (E & G) and 28 (F & A). The fact that the 84 intervals divide up naturally into three unique sets of 28 is highly significant because the 84 edges in the disdyakis triacontahedron with A, B & C vertices that either above or below its equatorial plane comprise 28 AB edges, 28 BC edges & 28 AC edges. These three sets of edges correspond to the three sets of repeated, Pythagorean intervals that belong to the seven diatonic scales.

The notes in the seven scales comprise 12 different types of ascending intervals below the octave and 12 different types of descending intervals with tone ratios that are the reciprocals of the tone ratios of the former — a total of 24 intervals. Hence, there are 84 ascending, Pythagorean intervals and 84 descending Pythagorean intervals, totalling 168 such intervals. The factorisation 168 = 7×24, where 24 = 12 + 12, appears in holistic systems such as the seven diatonic scales (other examples are the 168 automorphisms of the Klein quartic, whose Riemann sheet is tessellated into 24 heptagons — see p. 25 in Article 15 — and the 84 permutations of pairs and triplets of octonions ei (i = 1-7) in the seven 3-tuples (ei, ei+1, ei+3) and the 84 permutations of pairs and triplets of their inverses ei-1 = -ei). The geometrical counterpart in the inner Tree of Life of this 84:84 division is the 84 yods that line the sides of each set of the first six enfolded polygons and the 168 yods needed to turn the sectors of the dodecagon — the seventh of the polygons — into Type A triangles, there being 84 red yods either on sides of sectors or at centres of tetractyses and 84 blue yods on other internal sides of tetractyses:

 

(84+84) yods on sides of first (6+6) enfolded polygons

24 sets of 7 yods in dodecagon

 

The 12 corners of the dodecagon (six corners and their six opposite corners) symbolize the six ascending and six descending Pythagorean intervals in the basic set of 12 types of notes that make up the seven diatonic musical scales. The physical realisation in the microscopic world of this 84:84 division is the 84 circularly polarized oscillations made in each whorl of the UPA (the subquark state of the E8×E8 heterotic superstring that was first described by Besant & Leadbeater in 1895) as it winds through an angle of 90° around the axis of spin of the particle. Each oscillation can be thought of as the equivalent of a repetition of a Pythagorean musical interval, the ten sets of 168 oscillations in a whorl corresponding to ten octaves of the 168 repetitions of the rising and falling Pythagorean intervals in the seven musical scales, the 840 rising intervals corresponding to the 840 helical turns in the outer half of each whorl and the 840 falling intervals corresponding to the 840 turns in its inner half. The five types of notes that they contain correspond to the five revolutions of each whorl and the basic set of 24 types of ascending and descending intervals (12 ascending and 12 descending) that make up the seven diatonic scales correspond to the 24 gauge bosons of E8 whose gauge charges are spread around each whorl, 12 in its outer half and 12 in the half that winds in a narrower spiral around the core of the UPA. Superstrings are the physical manifestation of a mathematical pattern manifesting in sacred geometries that is also inherent in the seven diatonic musical scales! Article 51 pointed out that their 42 notes between tonic and octave contain 26 Pythagorean notes, where 26 is the number value of YAHWEH. According to bosonic string theory, 26 is the dimensionality of space-time, in which the string-like whorls of the UPA are embedded. This is not a coincidence. Instead, the same mathematical archetype embodied in this Godname expresses itself as a parameter of a holistic system.

In conclusion, Dr Kennedy has uncovered a significant example of how Plato used his writings to veil his mathematical teachings about facts of nature, just as the medieval alchemists wrote books with several levels of meaning to their text and symbols. There is, however, a danger that this important discovery will be misunderstood and dismissed because of unwarranted and inaccurate hyperbole surrounding it (partly journalistic reporting and partly instigated by Kennedy himself). Claims that contradict long-established views amongst scholars need careful formulation. What Kennedy has revealed is the existence of a kind of musical structure in Plato's books. However, contrary to what he wildly claims, he has not uncovered the existence of a hitherto secret, 12-note musical scale, and that is definitely not what Plato was secretly emulating in the 12-fold structure of his books. More likely, Plato was encrypting the arcane, mathematical fact that the seven musical scales, which hundreds of years later became known as the 'church modes,' contain 12 types of notes between their tonic and octave. He meant the correlation between text section numbers and the consonance or dissonance of sounds made by vibrating strings with these numbers as their lengths to be the musical clue that pointed to their existence. It was a subtle way of indicating that the number 12 had a sacred, musical connotation. In other words, the 12-fold division in Plato's books referred to a similar pattern not in one particular musical scale but in all the seven possible diatonic scales — truly, an expression of their mathematical completeness and perfection that would be worth emulating in literary works. The evidence for this is the fact that between these 12 types of notes are 84 rising and 84 falling Pythagorean intervals that are repetitions of the six Pythagorean notes that they contain, i.e., they display a (84+84=168) pattern that many of my research articles have proven is a fundamental property of holistic systems embodying the divine Ideal, as represented in space by sacred geometries. Plato could have designed the structure of his books so as to reflect this fundamental 12-fold division in holistic systems like the seven diatonic scales. In terms of the inner Tree of Life, this division appears in the two sets of the first six enfolded regular polygons (see diagram above). Article 4 shows that they constitute a holistic subset of polygons prescribed by the Godnames. Many other articles of mine available on this website demonstrate how these 12 polygons embody the parameters that are characteristic of holistic systems. The same pattern manifests in the 1-tree as the set of 12 yods in each of the seven triangles associated with each half that make up its branches, i.e., 168 = 12×7 + 12×7= 12×14 (see here). In terms of a single regular polygon, this holistic pattern is revealed by the construction of the 12-sided dodecagon from tetractyses, with 14 yods per sector, as pointed out above. I propose that Plato divided the structure of his books in analogy to the 12 sectors of this regular polygon — the last of the regular polygons making up the inner Tree of Life. As a Pythagorean, he would have realized that this polygon has ideal significance because it is the tenth type of regular polygon and is, therefore, singled out by the Decad, which represents perfection symbolized by the tetractys because it closes the sequence of integers 1-10 that can be used to express all other integers. Using numbers that express consonance and dissonance was merely intended to be a clue that Plato had embodied a musical ideal in the design of his writings. This implies that he must have known that the seven types of musical scales are composed of 12 types of notes between the tonic and octave. It is something which would certainly not have been beyond Plato's mathematical skills to ascertain. He never intended the 12-fold division to allude to something as banal as some 12-note musical scale unknown even to musicians of his day. The secret that his writings encrypted was far more important and sacred than that! They were encrypting a mathematical ideal of God — one which this website demonstrates is embodied in sacred geometries. They include the five Platonic solids because, when their faces are constructed from tetractyses, the tetrahedron with 12 tetractyses has 12 hexagonal yods at their centres and the other four solids with 168 tetractyses in their faces have 168 hexagonal yods at their centres (84 in their upper halves and 84 in their lower halves). This is the regular polyhedral counterpart of the 12 types of notes and the 84 ascending and 84 descending repetitions of their Pythagorean intervals discussed above, as symbolized by the 12 corners of the Type B dodecagon and its 168 other yods, consisting of 84 red yods & 84 blue yods (or, alternatively, 84 yods in each half). The 12 types of notes making up the seven musical scales comprise three Pythagorean notes, three non-Pythagorean notes and the inversions of these six notes. They are symbolized, respectively, by the three hexagonal yods at the centres of the tetractyses in one face of the tetrahedron, the three hexagonal yods at the centres of the tetractyses in another face and the two sets of three similar hexagonal yods in the remaining two faces. Their counterparts in the 12 sides of the 12-gon in the equatorial plane of the disdyakis triacontahedron discussed above are the generic set of three types of edges: AB, BC & CA, their repetitions and the mirror images of these six sides on the opposite side of the 12-gon. Truly, holistic systems exhibit a 12-foldness, and it explains why Plato should design his books according to this archetypal structure.

 

News item #3 (June 15, 2010)

More trouble for the Standard Model?

According to the Standard Model, neutrinos and antineutrinos have zero mass, whatever their flavour. The now well-established phenomenon of 'neutrino oscillations' implies that this is untrue. As yet unmeasured differences of mass allow actual neutrinos to be mixtures of the three known types of neutrinos. However, the latest measurements from Fermilab's MINOS experiment suggest that the differences between the masses of neutrinos deviate significantly from the masses of antineutrinos. Neutrino oscillations depend on two parameters: the square of the neutrino mass difference, Δm2, and the mixing angle, sin22θ. MINOS has yielded the most precise value to date of Δm2, namely, Δm2 = 0.0024 ± 0.0001 eV2. For antineutrinos, however, MINOS found that Δm2 = 0.0034 ± 0.0004 eV2. Theorists expected these two values to be the same. Instead, Δm2 is smaller for neutrinos by about 40%, which is statistically significant, although there is still a 5% probability that they are the same. The mixing between antineutrinos seems to differ significantly from that between neutrinos. Should improved data confirm this discrepancy beyond doubt, it will indicate not merely that the Standard Model is wrong (as if that were any surprise) but perhaps that CPT symmetry itself (on which so much of particle physics is based) is incorrect, that is, in the case of neutrinos, that the masses of particles and their antimatter counterparts are not the same. As shown in 2002 by Greenberg,* this would indicate that Lorentz invariance (which the CPT theorem assumes) breaks down! Neutrino and antineutrino fields would be non-local, e.g., they would no longer anticommute at space-like separations, whilst their observables would no longer commute at such separations. Current evidence for such a possibility is summarized here. A less drastic (and more plausible) alternative could be that the discrepancy is either a statistical fluctuation based upon insufficient data or merely the result of ignoring more complex oscillations between more than three types of neutrinos, tentative evidence for which has been provided by DZero, one of Tevatron's detectors at Fermilab (see News item # 2). Improving the accuracy of the antineutrino data will help resolve this issue.

For more details, see "Neutrinos and Antineutrinos Differ in Key Property, Experiment Suggests" at ScienceDaily.com, the article entitled "Unexpected antineutrino masses a puzzler for Standard Model" at Ars Technica and the article "Scientists see evidence that rules of particle physics may need a rewrite" at Physorg.com.

Update
A release of new information on August 25, 2011 from the MINOS research team has quelled concern about the seeming disparity between the masses of neutrinos and antineutrinos that it reported last June. At the International Symposium on Lepton Photon Interactions at High Energies in Mumbai, India, the team announced that, by almost doubling the size of its data set, it had established that the discrepancy, which left only a 2 per cent chance that the neutrino and antineutrino masses were identical, was most likely have been simply a statistical fluctuation that has now lessened. The oustanding difference is expected to be reduced further when an upgraded muon neutrino beam comes into operation in 2013. Details of the update can be found here.

Most recent update
Scientists from the MINOS experiment have now (June, 2012) announced that their results, which amount to the most accurate ever measurements of the mass difference between neutrinos and antineutrinos, confirm that they have the same mass. See here.

New upper limit for all neutrino masses
Using the largest ever 3-dimensional map of galaxies, called Mega Z, which covers over 700,000 galaxies recorded by the Sloan Digital Sky Survey, cosmologists at University College, London have recently calculated an upper limit of 0.28 eV for the rest mass of all neutrino species. This is the most accurate measurement to date of the mass of the neutrino. Read the UCL report here. The BBC reported their research here.


* Greenberg, O.W. (2002). "CPT Violation Implies Violation of Lorentz Invariance". Physical Review Letters 89: 231602; arxiv PDF.

 

News item #2 (May 18, 2010)

A fourth generation of quarks?

According to the Standard Model of particle physics, there are three types (or "generations") of basic particles. Each consists of two types of strongly interacting particles (hadrons) called "quarks," namely, the up (u), charm (c) & top (t) quarks and their associated partners, the down (d), strange (s) & bottom (b) quarks, and two types of weakly interacting particles ("leptons"), namely, the electron (e-), its associated neutrino (νe) and their heavier versions, the muon (μ-) and its associated neutrino (νμ) and the tau (τ-) and its associated neutrino (ντ):

 1st generation

 2nd generation

 3rd generation

 u

 d

 νe

 νμ

 ντ

 e-

 μ-

 τ-


For two decades, it has been the received wisdom amongst physicists that only three generations of quarks exist. For example, in August, 1989, the Stanford Linear Collider at the University of California at Stanford was able to put a limit on the number of generations at 3.0 ± 0.9, which excluded four families of quarks with a confidence level of about 70%. By September, the large Electron-Positron Collider (LEP) at CERN established a better limit of 2.7 ± 0.7, excluding four generations with a confidence level of 96%. Nevertheless, physicists have speculated about the existence of a fourth generation of quarks ever since the discovery of the top quark was announced in March, 1995 (see here). Indeed, some physicists had predicted its existence. For example, the author had predicted the existence of five generations of quarks sixteen years earlier in his research paper unifying the strong and electro-weak forces between hadrons and leptons! But his theory was ignored because the prediction was based upon the still heretical notion that quarks are not fundamental particles but composite bound states of three more basic objects (see "Composite quarks and hadron-lepton unification," Physics Letters, Vol. 84B, June, 1979; the author's paper is reproduced in his first book, entitled "Extra-sensory Perception of Quarks," which was published in 1980; free download here). Now hints of a fourth generation of quark have turned up in experiments at the Tevatron particle accelerator in Batavia, Illinois. This machine smashes together protons and antiprotons and examines the debris created by their collisions. Researchers at the CDF detector at the Tevatron were examining all the data accumulated between March 2002 and March 2009 in a search for evidence of a fourth-generation quark. Instead of finding two muon decay events predicted by calculations based upon three generations of quarks, the CDF team saw eight events, hinting that a fourth-generation quark created by the annihilation of protons and antiprotons had decayed as well as the first three generations of quarks. The difference was not large enough to be statistically significant but large enough to interest many researchers and to create debate. More evidence from DZero, Tevatron's other main detector, hints of a fourth generation that is harder to ignore. The decay products were found to consist of slightly more muons than antimuons, their antimatter counterparts (see here). The standard model predicts a difference between the numbers of matter and antimatter particles that is about 1/40th of what DZero encountered. This time, the difference was statistically significant — about 3.2 standard deviations from the standard model prediction. It could indicate the creation of a fourth-generation quark that was interfering with the decay of the B mesons containing the bottom quark created by the proton-antiproton collisions. However, the existence of such a quark is not the only explanation for the observed asymmetry between matter and antimatter. Alternative ways of explaining these anomalous results are higher dimensions of space and supersymmetry, in which each particle in the three known generations of matter, as well as those that transmit forces, is accompanied by a heavier partner with different spin angular momentum. The only definitive proof of the existence of this spin-0 quark (the so-called "squark") will come from creating and directly detecting particles that contain it. That will require the energies provided by the Large Hadron Collider at CERN. [update: so far (April, 2011), squarks with masses less than 870 Gev have been excluded by the data accumulated by the ATLAS detector at LHC (see here)].

For more details, see "Matter: the next generation," News Scientist, 29 May, 2010 and the article at Physorg.com entitled "Scientists discover evidence for significant matter-antimatter asymmetry."

 

News item #1 (May 3, 2010)

According to the recent results of a research group led by Cornell physics professor G. Peter Lepage (Physical Review Letters (Vol. 104:13), the mass of the up quark has been calculated with an uncertainty of a few percent to be about 2 MeV (about four times the mass of an electron), whilst the mass of the down quark is about 4.8 MeV. For more details, see PhysOrg.com.

Annie Besant and C.W. Leadbeater started in 1895 to remote-view the up and down quarks in atomic nuclei, athough, of course, they had no notion at that time that nuclei even exist. Below is a typical picture of these particles, which they called, respectively, 'positive hydrogen triplets' & 'negative hydrogen triplets,' as observed in the free state (at least according to what they believed):

remote viewed up and down quarks

Their book Occult Chemistry published in 1908 contains hundreds of these pictures (even more in its third edition). This, of course, is to be expected, given that quarks are constituents of the scores of protons and neutrons inside many atomic nuclei! Their book also contains many diagrams of multi-UPA bound states that do not exist in atomic nuclei and whose detection can be understood only if what they assumed were atoms were created prior to observation by some of the quarks in pairs of nuclei breaking up into their constituent UPAs and then recombining into many types of exotic bound states that were stable under the local physical conditions of their micro-psi observation. It may be objected that, according to quantum chromodynamics, which is the current theory of the strong force, quarks cannot exist on their own (as Besant & Leadbeater claimed for some hydrogen triplets) because the colour force between quarks increases with distance, permanently confining them in groups of three or as quark-antiquark bound states. According to the string version of this theory, confirmed beyond all doubt by Occult Chemistry, the strings, or colour flux tubes between the coloured quarks, exist because of the Meissner Effect, which expels the flux from the ambient Higgs vacuum because the latter is a type 2 superconductor, squeezing it into a vortex in the Higgs field whose ends are the quarks or antiquarks. This vortex motion was first noticed in 1959 when Geoffrey Hodson, the Theosophical writer and clairvoyant, remote-viewed a UPA (see News item #9). But what would happen if a region of the superconducting Higgs field were heated above its critical temperature in some psychokinetic way (not deliberately, of course) by the person exercizing micro-psi so that it temporarily became a normal conductor? The vortical excitations in the Higgs field that channel the colour flux between the UPAs in quarks would then cease to exist when the Meissner Effect no longer operated. The colour force in turn would cease to confine the quarks as the flux tubes disappeared. In the real world revealed by the remote viewing of Besant & Leadbeater, the colour force acts between the subquarks making up different quarks. An analogous mechanism traps them, according to the plethora of pictures in Occult Chemistry of the string-like forces binding UPAs together. However, although the confining mechanism would be turned off for quarks, it would not cease to operate for subquarks as well. A different phase of the Higgs field wih a different critical temperature traps the latter, and this would remain in a superconducting state, with the internal string bonds between subquarks intact. Of course, the quarks would not be free in the strict sense understood by particle physicists because, although not bound by strings, they would still interact with one another by strong forces; the difference is that these forces would no longer permanently confine them. What, therefore, we see depicted above and throughout the pages of Occult Chemistry are not free quarks but unconfined quarks immersed in heated-up domains of the Higgs vacuum that are in a normal state where vortices/strings linking quarks do not exist; altrhough not bound by string forces, they are still bound by residual strong forces. Micro-psi atoms (MPAs) are complex aggregates of multi-quark and multi-subquark bound states embedded in 'bubbles,' or domains, of different phases of the Higgs field. MPAs are rather like what are known in nuclear physics as 'compound nuclei,' which are formed by the fusion of two nuclei colliding at high speed. However, they differ fundamentally in that the nucleons from the two parent nuclei have broken up into many exotic, multi-quark and multi-subquark bound states with variable colour valencies, although some of the nucleons in the nuclei that came under observation survive as such in the case of the MPAs of a few elements, such as nitrogen, chlorine and — most spectacularly — arsenic (see my book ESP of Quarks and Superstrings, pp. 189-191; see also here). The analysis in Remote viewing of atoms of the elements in the Periodic Table up to calcium (together with the element gold) provides overwhelming evidence in support of this interpretation of what Besant & Leadbeater described when they focussed their micro-psi vision on the atoms of these elements.

 

Home