The Spindle Vortex Model for Gravity, Energy, Matter, Magnetism, Antimatter.
David Noel
<davidn@aoi.com.au>
Ben Franklin Centre for Theoretical Research
PO Box 27, Subiaco, WA 6008, Australia.
The Structure of Matter
Wondering about the nature of the substances which make up the physical world must have been a preoccupation of Man for as long as he was a conscious being. Nowadays, we class as "matter" all those solid, liquid, and gaseous things which we consider as having "mass" or weight.
If substances have mass, is this mass a continuous quantity, or is it made up of vast numbers of individual units? For at least 2000 years, the latter opinion has achieved informed acceptance -- matter is made up of assemblies of individual atoms.
The atom is defined as "the smallest particle of a chemical element that can exist", that is, breaking a substance down into finer and finer pieces, eventually arrives at a point where an individual unit cannot be broken down further and still retain the properties of the substance.
The Concept of the Atom -- the Lucretius Model
The first person to describe the modern concept of an atom was the Roman poet Lucretius, who lived in the first half of the century before Christ. Lucretius wrote extensively about the nature of the universe in a work comprising 6 parts. Here is an extract about him from [6].
Titus Lucretius Carus (died mid to late 50s BCE) was an Epicurean poet of the late Roman republican era. His six-book Latin hexameter poem "De rerum natura", variously translated "On the nature of things" and "On the nature of the universe", survives virtually intact, although it is disputed whether he lived to put the finishing touches to it.
Figure BS802-F1. Lucretius. From [6].
The opening exposition of book 2 descends into the details of atoms' behaviour and qualities. They are in perpetual motion at enormous speed, since in the void they get no resistance from the medium, and when they collide they can only be deflected, not halted. Their weight gives them an inherent tendency to move downwards, but collisions can divert those motions in other directions. The result is that, when in a cosmic arrangement, atoms build up complex and relatively stable patterns of motion, which at the macroscopic level appear to us as states of rest or relatively gentle motion [6].
Lucretius gives us enough of his ideas of the nature of atoms for his description to be classed as a scientific model, the Lucretius Model. A scientific model is not a theory, instead it is a self-consistent description of the structure and workings of some entity, put together to test and extrapolate on the properties of the entity. It need not be "true", as long as it can be used to derive useful outcomes.
Atoms as Vortexes -- the Kelvin Model
Lucretius described an atom as "in perpetual motion at enormous speed". The next major development in describing atoms was the concept that they existed as Vortexes -- similar to whirlpools known to feature in seas and other water bodies. In modern times, vortexes have been suggested as existing in astronomical structures such as neutron stars, quasars, black holes, and even the AGNs (Active Galactic Nuclei) which lie at the hearts of galaxies, as in UG101: Recycling the Universe: Neutron Stars, Black Holes, and the Science of Stuff [7]. Even a solar system has many of the attributes of a vortex.
The concept that atoms exist as vortexes has a long history. As far back as 1867, the pre-eminent British scientist of the day, Lord Kelvin, suggested this. While the concept of atoms dates back to Lucretius, it was only in the modern scientific age, beginning in the 1600s, that researchers began to again think about the nature of atoms.
Figure BS802-F2. Lord Kelvin. From [2].
Kelvin's name has been honoured in its adoption in the Kelvin Scale of temperature -- temperatures measured from Absolute Zero, the minimum temperature possible in the physical world.
Kelvin (known as Sir William Thomson before his elevation to the House of Lords) noted Helmholtz's discovery of the law of vortex motion in a perfect fluid, and said that "this discovery inevitably suggests the idea that Helmholtz's rings are the only true atoms" [1]. Hermann von Helmholtz was a German physician and physicist who made significant contributions to fluid dynamics and other scientific fields.
By the late 1840s, interest in the vortex model of atoms had become established, and diagrams and wire models had been created and shown to the Royal Society of Edinburgh [1]. According to the theory behind the Vortex Model, atom vortexes would be of infinite lifetime, essentially consisting of pure rotational energy.
Following is an illustration of a double vortex, as used by Kelvin in a presentation to the Royal Society of Edinburgh (published in Proceedings of the Royal Society of Edinburgh, Vol. VI, 1867, pp. 94-105 [1]).
Figure BS802-F3. Kelvin's atom vortexes. From [1].
Vortexes appear in some surprising places in nature, such as in the trails behind aircraft [8], as shown below.
Figure BS802-F4. Double vortex left by airplane. From [8].
There is a vital point about double vortexes. Vortexes may contain large amounts of energy. In a fully-matched double vortex, with two vortexes rotating in opposite directions, the net rotational energy of the pair will be zero.
Atoms as miniature "solar systems" -- the Bohr Model
The next major step in developing models of the atom came in 1913, when Danish physicist Niels Bohr showed his model of the Hydrogen atom, for which he was later awarded a Nobel Prize.
Figure BS802-F5. Niels Bohr. From [9].
Bohr's model was the first to distinguish different parts of the atom. The simplest model was that of Hydrogen -- this consisted of a dense, positively-charged central nucleus (a proton) and a diffuse negatively-charged electron surrounding it. The electron was first imagined as orbiting the proton, like a planet orbiting the Sun, but this was later generalized to more of a cloud or of shells of concentric spheres.
Figure BS802-F6. The Bohr Model of the atom. From [11].
The Bohr model was developed to portray other atoms besides Hydrogen. As well as positively-charged protons, these other atoms had neutral particles called neutrons in their nuclei. In their free state, all atoms had equal numbers of protons in their nuclei and of electrons surrounding them, with a total net charge of zero.
With atoms larger than the simple hydrogen, the chemical identity of an atom was defined by the number of protons at its nucleus (its atomic number), while its atomic mass was defined by the number of its nucleons (protons plus neutrons). A given element had a particular number of protons, but the number of its neutrons could vary -- the different types being called isotopes.
The Electron Shell Model in Chemistry
The electrons surrounding a given nucleus were envisaged as contained within a number of shells, each of which could hold a given number of electrons -- the innermost shell could hold 2 electrons, the next shell out could hold 8.
Figure BS802-F7. Shell models of different atoms. From [12].
These shell models gave a satisfying picture of the nature of chemical bonds. In forming a chemical bond between two atoms, they were envisaged as one atom giving up an electron (and so becoming positively charged) to the other (which became negatively charged), as though an electron was taken out of the first atom's outermost shell and slotted in to the outermost shell of the second atom.
The Bohr model also explained why light emitted or absorbed from an atom occurred at specific wavelengths or energy levels. In the shell model, all electrons in a given shell had the same energy level. By jumping from an inner shell to an outer one (of lower energy), an electron had excess energy, which was given out as a photon with energy defined as the difference between the energy levels of the two shells involved.
The next model of the atom to undergo development was rather different, in that it looked inside an individual atom, to make out its parts. This field of study is called quantum dynamics, with particular branches called quantum chromodynamics and quantum electrodynamics.
Quantum mechanics led to the recognition of the parts making up the nuclei of atoms, and of the small particles, smaller than a proton, which can exist for brief intervals when an atomic nucleus is split apart. Examples of these are pi-mesons, and mu-mesons.
Figure BS802-F8. Structure within the Atom. From [13].
Quantum mechanics also recognizes entities called quarks, which have a variety of properties and are theoretical particles considered as parts of a nucleon (proton or neutron), with 3 quarks in each nucleon. Then there are forces which are considered to hold a nucleus together, these may themselves be considered as particles, called gluons.
The full table of all entities in quantum mechanics is called the Standard Model. The model also includes photons (light packets treated as particles), electrons, and neutrinos (tiny entities still of somewhat uncertain status). Following is a chart of the Standard Model. This is included, not with the usual explanatory role, but purely to show its complexity -- don't look at the details.
Figure BS802-F9. Standard Model of Fundamental Particles and Interactions. From [13].
Quantum mechanics is a field which has built up its own extensive jargon. The following paragraph, from Wikipedia [14], is an example of this jargon. Again, don't look for meaning within it, it certainly contains meaning, but only for those who have delved deep within the field.
"In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics."
Although an esoteric field, the development of the Standard Model has been a big advance in putting forward explanations of the nature and behaviour of sub-atomic particles.
Quantum mechanics has yielded Nobel Prizes for a number of researchers, including Murray Gell-Mann, Julian Schwinger, Shinichiro Tomonaga, and the brilliant and likeable Richard Feynman, known for his side interests of playing the bongo drums and opening safes.
Figure BS802-F10. Richard Feynman. From [15].
About Scientific Models
In looking at ideas about the atom, we have so far mentioned the Lucretius Model, the Kelvin Model, the Bohr Model, and the Standard Model -- and there are further variations on these.
The question might well be raised, as to which of these models is correct, which best describes the real world? The answer is, that all may be regarded as correct, all may be useful in describing one or more features of the real world. Scientific models are not true or false, right or wrong, just differing in their ability to explain different experimental results and data.
We'll go on soon to look at yet another model of the atom, the Spindle-Vortex or Gemma Model, but before doing so it might be useful to consider a basic part of physics, the nature of energy and mass.
Energy and Mass
It is now generally acknowledged that Energy and Mass can be converted, one into the other, and back. The formula involved is the well-known Einstein equation, E=Mc2, which says the amount of energy E which can be derived from a mass M is found by multiplying M by the square of the velocity of light, c.
There is a limitation on this -- the Law of Conservation of Mass/Energy. This says that while energy and mass can be inter-converted, their total, expressed in the proper units, remains the same.
Figure BS802-F11. Mass and energy. From [18].
The Einstein equation works both ways -- it also tells you how much energy you would need to create a given amount of mass. This is not as familiar an area to most people. However, it does appear that energy is being routinely recycled into mass in the AGNs, the Supermassive Black Holes, which lie at the hearts of galaxies. For more on this, see UG101: Recycling the Universe --Neutron Stars, Black Holes, and the Science of Stuff [7].
The same article [7] also gives a new classification of energy and mass into types of "Stuff". Briefly, Stuff1 is electromagnetic radiation and other forms of energy; Stuff2 is ordinary matter, atoms and the like; Stuff3 is the material in neutron stars, essentially atomic nucleons; and Stuff4 is the material in black holes, which is much denser than that in neutron stars.
The EQUIVALENCE of Energy and Mass
We need to push on slightly for a better understanding of the matters involved. As mentioned, it's generally accepted that mass and energy can be inter-converted. The small step forward is acceptance of the idea that mass and energy are equivalent. That is, that "mass" and "energy" are just alternative aspects of looking at the same situation.
We already have a sort of de-facto acceptance of this idea in quantum mechanics, where forces within the nucleus, called gluons, are treated as particles. Similarly when we are dealing with light, which can be regarded as photon packets (particles) or as electromagnetic waves (energy). Newton and his contemporaries argued as to whether the particle or the wave model of light was correct. Today we accept both, as describing different aspects of the same situation.
Those interested in this topic may like to look at The Photon Hoop Model for light, where half-wavelength pieces of light are treated as "photon hoops", each hoop essentially a packet. This model for light thus combines both wave and particle aspects.
Already mentioned is that energy and mass can be placed into 4 categories of "Stuff" [7]. These categories represent vastly different degrees of energy/mass density. Stuff1, such as visible light, has low density. This is apparent by considering the enormous amount of light and other energy created by the conversion of a few grams of matter in a hydrogen bomb.
Ordinary matter, Stuff2, is what we are most familiar with, with densities of around 1 kg per cubic metre for gases, around 1 tonne per cubic metre for solids. When we move on to Stuff3, the material inside neutron stars, we are dealing with something orders of magnitude denser than ordinary matter. Stuff3 is essentially atomic nuclei, without the vast electron clouds which swell out ordinary atoms.
When we get to Stuff4, the material inside Supermassive Black Holes, we are looking at orders of magnitude greater density again. A feel for the situation can be gained by considering how big the Earth would be, if made from the different stuffs.
The diameter of our Earth, mostly Stuff2, ordinary matter, is about 12,700 kilometres. If the Earth was made entirely from Stuff3, compressed neutrons, its diameter would be about 330 metres. And if it was made of Stuff4, black-hole substance, its diameter would be about 3 centimetres [7].
Black holes are essentially giant vortexes, of enormous mass, rotating incredibly rapidly. They contain truly gigantic amounts of energy in their rotating material. It seems very possible that what is perceived as their mass is just a reflection of the energy in this rotation.
The Spindle Vortex Model of atoms
We move on now to the main topic of this article, the idea that an atom can be represented as a type of vortex, with specific properties. In some senses, the model is a development of the Kelvin Model.
Here this model is called a Spindle Vortex. It can be represented as a rapidly spinning ball, with a defined axis and direction of rotation.
Figure BS802-F12. A Spindle Vortex.
The axle of the spindle is represented as a black-and-grey tube with a barber-pole pattern. It is not thought of here as an actual structure, the pattern is merely to give a visual expression of the rate of rotation of the atom.
The bulk of the atom is represented as a gas-like ball of somewhat spherical shape, with arrows on the surface of the ball inserted to again give a visual sense of its motion. The ends of the axle have red and green caps added to represent the North and South poles of the vortex, and again are purely for visual effect -- though the poles do exist as defining the direction of rotation of the atoms.
Any given atom vortex has a rate of rotation, here referred to as its Vortex Rotation Number (VRN). The hydrogen atom is assigned a VRN of 1. All other atoms will have higher VRNs, which may be fractional. For example, the heaviest atom found is nature is believed to be Uranium-238, which we will see has a VRN of about 15.4. All other atoms will have a VRN between 1 and 15.4.
What is the physical implication of the VRN? In the new model, an atom's VRN is its rate of rotation, relative to Hydrogen, so a Uranium-238 atom is rotating 15.4 times as fast as a Hydrogen atom.
We now come a fundamental basis of our model. This assumes that the mass of an atom is directly proportional to its rotational energy. That is to say, we perceive the atom's Energy as Mass.
Proposition BS802-P1.
Compared to the Periodic Table and the Standard Model of the atom, this is a fundamentally new way of looking at the magnitude of a given atom. The Periodic Table will list the magnitude of an atom by its Atomic Number (for Uranium, AN=92) and by its Atomic Weight (for Uranium-238, AW=238). The Atomic Number is the number of protons the nucleus contains, and the Atomic Weight is the number of nucleons (protons plus neutrons) in the nucleus.
In a way, the traditional picture says the number of protons in a nucleus defines the chemical nature of an atom, while its neutrons are just a sort of packing, and the number of these can vary. So the most common form of Uranium is Uranium-235, which has the same number of protons as Uranium-238, but 3 fewer neutrons.
In the Spindle Vortex Model, the magnitude of an atom is defined by its rotational energy, given by its Vortex Rotation Number or VRN. With this model, the VRN of Uranium is about 15.4. Uranium-235 and Uranium-238 will have slightly different VRNs; the former has VRN=15.3297, the latter has VRN=15.4272.
Proposition BS802-P2.
The question is, how are these Vortex Rotation Numbers derived? They are simply the square roots of the conventionally-known masses of the atoms. This is because the rotational energy in a spinning object varies as the square of its rate of rotation.
This may be made clearer by some examples. A Hydrogen atom has a nucleus containing a single proton with no neutrons. Its mass is defined as equal to 1, its AN (Atomic Number = number of protons) is 1, and its AW (Atomic Weight), the same as its number of nucleons (protons plus neutrons), is also 1. With the new model, Hydrogen's VRN (Vortex Rotation Number) is by definition also 1. Its SEV (Spindle Energy Value) is the square of its VRN, which is still 1.
Now move on to the 8th element in the Periodic Table, which is Oxygen (for an example of the Periodic Table, see [20] ). A standard Oxygen atom has a nucleus containing 8 protons and 8 neutrons. So its AN (Atomic Number) is 8, and its AW (Atomic Weight) is 16. In the new model, Oxygen's VRN (Vortex Rotation Number) is 4, and its SEV (Spindle Energy Value) is the square of 4, that is 16, the same as its Atomic Weight.
The interpretation of these figures in the Standard Model is that the Oxygen atom nucleus contains 16 nucleons, each of similar mass to a proton or hydrogen nucleus, so its mass is 16. In the Spindle Vortex Model, the Oxygen spindle is rotating 4 times as fast as a Hydrogen spindle (VRN=4), so its rotational energy is 4-squared or 16, the same number as its mass.
A rather more massive/faster atom is Copper, which has an AN of 29 and an AW of 64. Standard Model says its nucleus has 29 protons and 35 neutrons, adding up to a mass of 64. Spindle Vortex Model says the Copper spindle has a VRN of 8, hence a SEV of 64. (Some of the numbers in the above are not exact whole numbers. This is because most elements are a mixture of isotopes of slightly different masses).
So the two models lead to similar conclusions, and, as with all scientific models, may each be of value in interpreting what's going on in a given situation. The Standard Model, with its assemblies of tiny proton and neutron balls, is probably the most intuitive in explaining mass. But we will go on to show that the Spindle Vortex Model has definite advantages in explaining a range of basic scientific ideas -- Gravity, Energy, Mass, Magnetism, and Antimatter (GEMMA).
Natural stable quantum points in talking about Mass and SEV (Spindle Energy Value)
The Standard Model gives us an easily visualized picture when talking about the Mass or Atomic Weight of an atom -- just count up the number of protons and neutrons, and that's your number.
Although we don't usually think about it, the proton/neutron idea allows to divide mass into quanta, into individual stable quantum points along the mass scale. It's like Lucretius started to do with the idea of matter -- he said it's not a continuous quantity, only certain divisions into parts are possible, and we call these atoms.
If now we want to look at atoms as spinning vortexes of energy, we don't currently have an intuitive way of dividing the energy involved into step-wise units, we think of energy as being a continuous quantity. But if energy is equivalent to mass, and mass is quantized, then energy must be quantized too, it must increase in fixed units. This fact is obvious, but not intuitive.
We actually passed by the units involved earlier, in the graphic about Einstein's mass-energy equivalence (Figure F11). There, at the bottom, one line gave the energy equivalent of 1 kilogram of mass. A second line gave the energy equivalent of 1 AMU, 1 Atomic Mass Unit,
An AMU is essentially the mass of a hydrogen nucleus, a proton. In stricter terms, "an atomic mass unit (symbolized AMU or amu) is defined as precisely 1/12 the mass of an atom of carbon-12. The carbon-12 (C-12) atom has six protons and six neutrons in its nucleus. In imprecise terms, one AMU is the average of the proton rest mass and the neutron rest mass". This slightly involved definition is needed because there is a very tiny difference between the masses of a proton and a neutron.
Earlier we talked about the energy of a spindle vortex atom as its SEV, its Spindle Energy Value, and how this was equivalent to its Atomic Weight. So it is clear that SEVs should be quoted in AMUs, as whole numbers. At least, this is so for particular isotopes of an element -- different isotopes will have different AW/AMU values.
To explain this a little, we can look at isotopes of the metal Lead. Lead has a huge number of isotopes, but its main 11 isotopes are shown in the table.
Figure BS802-F13. Table of Lead isotopes. From [22].
Four of these isotopes are stable, they are not radioactive and do not break down over time, even a very long time. The other seven have half-lives (the time needed for half the atoms of the isotope to decay into other elements) from a high of about 15 billion years down to about 26 minutes. Lead's other isotopes have shorter half-lives still, some measured in nanoseconds (billionths of a second) [22]. It's arguable as to whether such a brief interval counts as "existing".
On the Standard picture, atoms have quantized "Mass" (only whole numbers allowed), with the quantum units of two sorts, "Proton" and "Neutron". These two sorts differ in that Proton has a property called positive charge, and Neutron does not. Total Mass is total number of nucleons, called AW (Atomic Weight).
Looking at the most stable Lead isotope, Pb-208, the standard description is that it contains 82 protons and 126 neutrons, and thus a total nucleon count or AW of 208.
With the Vortex picture, atoms have quantized "Energy" (only whole numbers allowed), and since we are dealing with two aspects of the same situation, the Energy quantum units must also be of two sorts. We haven't yet speculated on the nature of the difference between the two sorts, only grouped them together as "Energy". Total Energy is the total of 2 sorts of as yet undescribed energy units, together called AMUs.
The Vortex description of Pb-208 says that it contains a total of 208 energy units or AMUs. So far we have made no split of these 208 units into different types. Let's have a preliminary stab at this.
Earthquakes are known to give off waves, and these (from a single event) may be of quite different types (P-waves, S-waves, etc). Of course these waves all express the movement of energy. In the same way, the movement of energy we see in Spindle Vortex rotation appears to fall into two categories, which we can call P-rotation and N-rotation, as the analog of the Proton and the Neutron in the Standard Model.
With this basic understanding in place, we can go on look at implications of the GEMMA or Spindle Vortex Model on standard views of gravity, energy, mass, magnetism, and antimatter.
Gravity
Gravity is a force which permeates our Universe, and we know quite a lot about it. The concept was invented back in the 1600s by Isaac Newton, supposedly from his observation of an apple falling from a tree.
Newton said that a force existed between any two masses in the Universe, and it was equal to the product of the masses divided by the square of the distance separating them, as in the diagram.
Figure BS802-F14. The Gravitational Attraction formula. From [22].
In this formula, Fg is the gravitational force, m1 and m2 are the two masses involved, and d is the distance between them. G is the Gravitational Constant, a fixed number for any given system of units (usually masses are measured in kilograms, distance in metres).
This formula has been used and verified over the centuries and continues to serve. But it says nothing about what mass is, what causes an object to possess mass. This question has remained the subject of speculation -- the quantum-mechanics Standard Model suggests the possibility of a new sub-atomic "particle" which somehow endows mass.
Possibly for the first time, the new Spindle Vortex Model gives a palpable answer to the question of the nature of mass and gravity. It is in the nature of vortexes that they try to suck in stuff from around them. This suction is what we call gravity, and mass is the magnitude of this suction.
Vortex Suction
A universally-recognized property of vortexes is that they try to suck in material from outside them. These powerful forces are prominent in natural vortexes making up weather features on the Earth's surface -- cyclones, hurricanes, tornados, and the like.
Figure BS802-F15. A vortex sucking in material. From [4].
Vortex Suction in the seas and oceans can be a major hazard to ships in some areas. The strongest sea vortex (whirlpool or maelstrom) in the world is the Saltstraumen maelstrom located close to the Arctic Circle, southeast of the city of Bodo, Norway [17]. Navigation is dangerous in this strait, with only a small slot of time available each day for large ships to pass through.
Figure BS802-F16. The maelstrom off Norway as illustrated by Olaus Magnus on the Carta Marina, 1539. From [17].
Vortex Suction also occurs in the wider universe. Our Milky Way Galaxy behaves as a vortex, and slowly draws in stars at its current periphery, pulling them very gradually towards the AGN (supermassive black hole) at its centre [7]. Even our Solar System is a vortex, and it slowly accumulates material from the Oort Cloud within which it is moving -- more on this at P4: The Greater Averaged Universe (GAU): How the Solar System cannibalizes the Oort Cloud [19].
So it is no surprise that the Spindle Vortexes which represent atoms in our model also exert Vortex Suction. This is, then, the force which we call Gravity -- every atom has an attraction for every other atom in the Universe. So our model gives a very natural explanation of the origin of Gravity. In the Spindle Vortex Model, Gravity is merely the Vortex Suction expressed by the atom vortexes.
Proposition BS802-P3.
Vortex Suction can be a very strong force, while Gravity is often thought of as a relatively weak force in the Universe. We will look at this in more detail later on, but at the moment just suggest that much of the Gravity due to a set of atoms is neutralized by their placement one against the other, with individual suctions in opposing directions.
We can get a visual feel for this by looking at an aggregation of spindle-vortex atoms which happen to lie in the same plane.
Figure BS802-F17. An aggregation of spindle-vortex atoms.
In this image, the atoms are in essentially random orientations, some with their North Poles pointing up, pointing down, pointing into the image plane (so only the atom's South Pole is visible), and pointing left or right. Notice that ALL the Spindle Vortexes have the same sense of rotation -- clockwise when viewed from their South Poles. In fact, their direction of rotation defines what are the South and North poles.
Proposition BS802-P4.
It has been mentioned that gravity has been regarded as a relatively weak force, while vortex suction is thought to be quite strong.
The suggestion is, that when two or more atoms are placed together, their individual vortex suctions can largely cancel out, so what we perceive as gravity is only a small non-cancelled part of the force.
Some support for this idea comes from the concept of using monatomic hydrogen (isolated hydrogen atoms as opposed to the 2-atom hydrogen molecule) as a fuel. Such a fuel would, on the face of it, appear very powerful, but unfortunately its use is impracticable. Here's what [23] says about it.
"The specific impulse (ISP), a measure of efficiency which measures how much thrust you can get from a given propellant flow rate, could be as high as 1500 s. This is three times higher than the ISP of the Shuttle main engines. The big problem with this fuel is keeping it stable against it recombining into H2 when stored in its monatomic form".
What this amounts to is that when two isolated hydrogen atoms come close to one another, they are very strongly attracted, and join to form a hydrogen molecule. In the Spindle Vortex model, this can be represented as much of their individual vortex suctions cancelling out when they combine into a molecule.
This can be formalized by saying that in an aggregation of atoms, much of their individual vortex suction forces cancel out, and what we perceive as the gravity due to the aggregate is only the non-cancelled force.
Proposition BS802-P5.
The Spindle Vortex Simulator
To give an intuitive visual feel for the concept of atoms as rotating vortexes, the following interactive simulator has been designed and implemented.
1, 1 16, 256
VRN: 1/16, AW: 1/256
Figure BS802-F18. The Spindle Vortex with VRN slider.
In this simulator, the slider scale represents the rate of rotation of the atom. This value, the VRN or Vortex Rotation Number, varies in single steps from 1 to 16.
The scale beneath, marked AW for Atomic Weight, is the square of the VRN. This is because the energy of rotation varies as the square of the rate of rotation, and in the new model energy is perceived as mass. The AW scale also has some sample elements marked at the appropriate places, such as H, O, Cu, Nd (Neodymium), and Au (Gold),
Moving the slider along the scale will cause the spindle vortex image to increase in apparent rate of rotation, if your browser has the appropriate features.
It is a common concept, that if the rotation speed of a body is continually increased, eventually increasing stress will cause the body to break apart. Moving the slider to its extreme right point may cause the simulated atom to fly apart. This gives a nod to the idea that as atoms increase in mass, they may become more unstable and break down.
Emission of light from atoms
When we earlier looked at the Shell Model of different atoms (Figure F7), it was noted that the energies of light packets (quanta) given off or absorbed by particular atoms could be correlated with the energy levels of the different shells. A shell was represented as a holder of electrons, each shell holding a maximum number of electrons, usually 2 or 8.
So with an atom such as Sodium (with 3 shells), jumping of an electron from Shell 2 to Shell 3 would represent a specific change in the energy of the electron, and this change in energy would be directly proportional to the frequency (energy) of light waves emitted by Sodium.
This tying-in of specific light frequencies with specific elements ("Spectroscopy") has proved enormously useful in understanding physical and chemical behaviours of atoms, whether in the laboratory, everyday life, or in galactic space. Spectroscopy is perhaps the most useful of all scientific tools for many of the physical sciences.
But the Bohr/ Electron Shell Model (as in Figure F7) is not very intuitive in understanding the mechanism by which light quanta are produced or absorbed by the electron shells, or in estimating the energies of the quanta. In particular, the nature of the Electrons making up the shells is not readily understood.
In the original Bohr model of the Hydrogen atom, the single electron was envisaged as like a planet orbiting rapidly around its parent star. Later, multiple electrons were thought of as "smeared out" in rapid motion around their nucleus, and with the development of x-ray crystallography, images were derived of the varying density of the "electron cloud" around the atoms in a compound.
Figure BS802-F19. An electron-density map of a protein. From [16].
The figure shows one of these electron-density maps for a protein structure. The maps are not simulations, they are actual results of measurements presented in a certain way. Parts of the image can be thought of as parts of a contour map showing hills and plains in a given locality.
Roundish areas with close contour lines represent electron "hills", localities with a dense electron cover, maybe 8 or more electrons thick. They represent heavier atoms, which have more electrons. The straight lines (pentagon and arms), which have been added to the image, represent chemical "bonds", directions along which electrons are shared between atoms.
These representations of electrons in a molecule have been extremely useful in understanding atomic and molecular structures, but are not particularly helpful in grasping how the light quanta emitted or absorbed by an atom or a molecule are produced. The Spindle Vortex Model may give a more intuitive picture.
One of the limitations of the Bohr/ Electron Shell Model model is that it gives no indication of the direction in which a light quantum is emitted. The model has no defined axes or lines of movement along which emission might be preferred. In contrast, the Spindle Vortex Model has a strongly-defined axis, and it is natural to expect quantum emission to take place along this axis.
This is not only on symmetry grounds, but is the norm for another set of vortexes, that of large galactic bodies. During the course of their lives, most stars suffer a major explosion phase causing them to lose much of their mass. In some stars this event is called a "supernova". The star mass remaining behind is left in a very dense, rotating state, effectively a vortex [7].
The remnants of smaller stars end up as "white dwarfs", medium-mass stars become "neutron stars", higher-mass stars end up as "black holes". In galaxies, mass accumulates at the centre to form "supermassive black holes" or AGNs (Active Galactic Nuclei). All these vortex formations emit light from both ends of their vortex axes, and with increasing mass, these emissions include higher-energy light quanta and mass particles such as protons [7]. With galaxies, the emission beams show up as "astrophysical jets", and are the sources of high-energy cosmic rays (although this is not always generally acknowledged).
So when we look at light quanta emitted from a Spindle-Vortex atom, it is natural to expect this to occur along the axis of the vortex, as in the following graphic.
Here the light quanta are shown as sections of helical springs, emanating from the caps of the atom. As they rotate in the same direction as the caps they spring from, the quanta have opposite sense of rotation (are oppositely polarized).
Here our new model gives a notably superior visual picture of the emission of quanta of fixed energy from an individual atom, compared with the Standard Model. In the model, emission of light quanta from an atom takes place at both ends of the vortex axis, and the quanta are oppositely polarized.
Proposition BS802-P6.
Magnetism
Magnetism is the ability of some bodies to attract iron and certain other metallic objects towards them. It was noticed and brought to use by the Chinese, possibly as early as 200 BC.
The bodies used by the Chinese were naturally-occurring lumps of iron-bearing rocks called lodestones [25]. Small pieces of lodestone were used in navigational compasses from the mid-1000s, again first by the Chinese.
Figure BS802-F21. Lodestone in the Hall of Gems of the Smithsonian. From [25].
A piece of lodestone could be made into a needle or lozenge shape such that, if freely suspended, one end of the lozenge would point towards the Earth's North magnetic pole, and the other towards the South. Suspension could be from a string, or on a tiny raft floating on a liquid.
Figure BS802-F22. A piece of lodestone suspended from a string. From [26].
Microscopic examination of lodestones has found them to be made of magnetite (Fe3O4) with inclusions of a mineral called maghemite (cubic Fe2O3), often with impurity metal ions of titanium, aluminium, and manganese. Magnetite is a common iron mineral, and is not magnetic unless treated.
How do lodestones get magnetized? The leading theory is that lodestones are magnetized by the strong magnetic fields surrounding lightning bolts when they hit magnetite rocks -- lodestones are almost always found near the surface.
Electromagnetism. In the early 1800s, researchers found that a magnetic field was created around an electric current flowing in a wire. Unlike the lodestone, the magnetic field was not permanent, but disappeared when the electric current was switched off.
So, magnetism is a property of some bodies, either natural or created by the proximity of an electric current. When it occurs, one end of a suspended magnetic body tends to point towards Earth's North Magnetic Pole, and the other towards the South Magnetic Pole.
What causes a body to exhibit magnetic behaviour? Surprisingly, science has till now not had a ready answer to this question, although magnetism is a thoroughly researched and understood phenomenon. Here is some of what Wikipedia says [24].
"The magnetic properties of materials are mainly due to the magnetic moments of their atoms' orbiting electrons. Ordinarily, the enormous number of electrons in a material are arranged such that their magnetic moments cancel out. This is due to electrons combining into pairs with opposite intrinsic magnetic moments and combining into filled subshells with zero net orbital motion".
This somewhat echos the picture we gave above as to how Gravity influences matter, but does not give any origin for the "magnetic moments" which underlie magnetism.
Magnetism and Gravity
The connection between magnetism and gravity, if it exists, has long intrigued the scientific community. There are obvious similarities, with the ability of one object to draw another towards it. But there are also stark differences -- magnets always have North and South poles, and magnetism can show up as repulsion, as well as attraction.
There is also a great apparent difference in their strengths. Vehicle scrapyards may have giant electromagnets which can lift a big car with ease. I have had the opportunity to travel on the Shanghai Maglev train, which connects the city of Shanghai in China with its airport.
Figure BS802-F23. The Shanghai Maglev train. From [27].
This train, of conventional size with carriages weighing many tonnes, has no wheels. Instead, in operation it is suspended electromagnetically as much as 10 cm above its track. Electromagnets and coils at the base of the train and within the concrete track both lift the carriages when in use, and supply the propulsive power to pull the train along at speeds well above 300 km/hr.
What is the source of the relatively large force of Magnetism? Earlier it was suggested that Vortex Suction could potentially exert strong forces, but these forces were usually largely cancelled out in aggregates of atoms by the dispositions of the atoms -- Gravity was just a residual effect left over from marginally incomplete cancellation.
Here then, in the new Spindle Vortex Model, is a possible origin of magnetism. It is an effect which occurs when the atoms in an aggregate become markedly distorted in their relative positioning, so that vortex suctions are no longer largely cancelled out.
We can represent this situation in a graphic showing a body which has an appreciable excess of North-pointing (Green) poles in one area, balanced by a similar excess of South-pointing (Red) poles in another. Vortex suction cancellation is still occurring, but much more imperfectly, which allows leakage of the suction at a macroscopic scale.
Figure BS802-F24. Preferential spindle vortexes alignments giving magnetic effects.
This representation does tie in with real-life observations. It is suggested that in lodestones, the usual good matching of atoms or vortexes at the everyday scale has been disrupted, possibly by lightning strike. Heating of a lodestone (making its internal vibrations increase) eventually causes it to lose its magnetic properties. The same is true of permanent magnets prepared by exposing certain iron alloys to strong magnetic fields.
In essence, the crystal structures of the magnets have become twisted by application of strong fields. It might be anticipated that applying a strong field to a magnetizable body would cause it to alter shape slightly. Such an effect is known, called Magnetostriction [28].
It is magnetostriction which is responsible for the humming sound which comes from some transformers. The process causes small changes in the shapes of the equipment parts, and these show up as a humming.
In summary, In the new model, we can say that magnetism is caused by macroscopic misalignments of vortexes, leading to very poor cancelling of vortex suctions.
Proposition BS802-P7.
Matter and Anti-Matter
Standard physics has it that the material substances of the Universe consist of two sorts, Matter and Anti-Matter. Overwhelmingly, the sort we encounter in our present Universe is Matter. This matter is made up of atoms and particles like protons, neutrons, and electrons, as mentioned in many of the above descriptions.
But the other sort, Anti-Matter, does exist as a sort of mirror equivalent of the familiar Matter which we see everywhere. Every sort of particle and atom we know about has a theoretical mirror equivalent, usually with opposite characteristics to the everyday sort.
So the proton, the essential basis of the Hydrogen atom, has a twin equivalent, the Anti-Proton, which has a negative charge instead of the positive charge of the proton. The tiny electron, with its negative electrical charge underlying much of basic physics, has a mirror twin with positive charge, the Positron. Join together an anti-proton and a positron, and you form an atom of anti-hydrogen. Other anti-atoms of higher mass (such as anti-helium) are also possible, but for reasons given below are seldom researchable.
Figure BS802-F25. A concept of Matter and Antimatter. From [31].
The main reason why research is difficult is because matter and anti-matter are almost totally incompatible, when they come together they annihilate each other very quickly, turning their total masses into energy.
Here is some of what [30] says about the topic, in particular proton-antiproton annihilation.
"When a proton encounters its antiparticle the reaction is not as simple as electron-positron annihilation. Unlike an electron, a proton is a composite particle consisting of three "valence quarks" and an indeterminate number of "sea quarks" bound by gluons. Thus, when a proton encounters an antiproton, one of its quarks may annihilate with an antiquark to produce a gluon, after which the gluon together with the remaining quarks, antiquarks, and gluons will undergo a complex process of rearrangement into a number of mesons, which will decay in a series of reactions that ultimately produce only gamma rays, electrons, positrons, and neutrinos.
Since the absorbed energy can be as much as ~2 GeV, it can in principle exceed the binding energy of even the heaviest nuclei. Thus, when an antiproton annihilates inside a heavy nucleus such as uranium or plutonium, partial or complete disruption of the nucleus can occur, releasing large numbers of fast neutrons. Such reactions open the possibility for triggering a significant number of secondary fission reactions in a subcritical mass, and may potentially be useful for spacecraft propulsion".
Plenty more jargon here, but the main gist is that when an anti-particle meets its normal-matter twin, they both disappear leaving behind a huge amount of energy. When energy is produced by converting mass in a hydrogen bomb, only a tiny amount of mass is used up. Here the total mass of both particles is turned into energy.
This case of Mutually Assured Destruction in the atomic world is the main reason why anti-matter is very seldom met with in the real world -- if it is being produced by some process, it's not likely to last long once it meets normal matter.
There is a rare instance in which the average person may encounter anti-particles in use. In the hospital diagnostic imaging procedure called PET Scanning, use is made of positrons (positive electrons) given off by certain radio-isotopes. The procedure, Positron Emission Tomography in full [33], aims to give a 3-D picture of a part of the body which has been dosed with a tiny amount of the radio-isotope.
In theory, an Anti-Universe could exist, almost entirely made up of anti-matter, with virtually the same physical laws operating. Electric current flow in metals would be of anti-electrons (positrons), and the nucleus of anti-Uranium would contain 92 anti-protons.
We have seen above why anti-matter finds it hard to survive in a world where it is swamped by normal matter. Is there anywhere in the Universe where anti-matter is being produced in quantity?
In UG101: Recycling the Universe -- Neutron Stars, Black Holes, and the Science of Stuff [7], I suggest that the AGNs which lie at the hearts of all galaxies are recycling factories, taking in matter and energy and streaming out processed energy and mass in galactic jets, the origin of highest-energy cosmic rays. These jets are known to contain antimatter in the form of antiprotons and positrons, in addition to the protons, electrons, helium, and diffuse gamma rays [29].
Because these jets encounter normal matter as they stream out into the existing Universe, most of their anti-matter will become annihilated, and surviving anti-matter will be sparse. As a whimsical aside, in two separate places above it was mentioned that monatomic hydrogen and proton-antiproton annihilation would each form the basis of very powerful fuels. So a bucket of monatomic anti-hydrogen should take you a long way, if only you could control it.
Why does our Universe contain mostly matter rather than antimatter?
Here is a question which has occupied thinking people for almost as long as the existence of anti-matter has been known. The actual processes were explained in the previous paragraph -- both matter and anti-matter are believed produced from the AGNs at the centres of galaxies, and this is thrust out into a predominantly Matter world, so most antimatter is lost in annihilation with normal matter.
But this explanation still leaves some wondering about Symmetry considerations, there is a nagging feeling that somehow the totals of normal matter and anti-matter in a sufficiently large area of the Universe ought to be equal, there should be a symmetry of mass. But the surprising truth is, the Universe is not symmetrical. In fact, it is left-handed.
Until 1956, most scientists believed that Nature at its most basic level cannot discern right from left, up from down, in from out [35]. When a nuclear particle undergoes a metamorphosis, it was supposed, the process should be unaffected by reversing all the mathematical coordinates that define the particle -- by turning the particle inside out, so to speak.
This assumed indifference was a consequence of the Conservation of Parity, one of the central beliefs of 20th-century physics. Conserved parity was a beautiful and elegant idea that appealed to mystics and philosophers as well as hard-nosed physicists. For one thing, it fitted the Confucian world view, in which all things consist of precisely equal dollops of Yin and Yang, the universal complementary opposites.
But the beautiful notion of conserved parity turned out to be wrong. Two physicists working on decay of atomic particles, Tsung-Dao Lee and Chen Ning Yang, proved that long-held assumptions about the symmetry of emissions from the particles were wrong -- the way the particle decays depends upon its orientation. For this work, they were awarded the 1957 Nobel Prize in Physics [35].
There is further thought in [7], where mass/energy items are put into 4 classes, called Stuff1, Stuff2, Stuff3, and Stuff4. Of these, Stuff2 is matter, and can exist in normal- or anti- forms, while the other three Stuffs do not include this characteristic. So converting matter into another form of energy causes it to lose its normal/anti character.
Anti-Matter and the Spindle Vortex Model
When considering the nature of anti-matter, the Spindle Vortex Model has a considerable advantage over the conventional Standard Model. In the latter, the mutual annihilation of, say, a proton and an antiproton is known but not readily explained. With the new model, anti-matter spindle vortexes are just like normal ones, but they rotate in the opposite sense.
Proposition BS802-P8.
In an encounter between a vortex and an anti-vortex, mutual annihilation would be the normally expected outcome. If the mirror vortexes were exact twins, total annihilation would be the anticipated result. If the match was not exact, say an anti-proton encountering a normal neutron, then some smaller debris such as mesons or positrons might occur.
The Spindle Vortex Model thus gives a much more satisfactory representation of the nature of anti-matter than do earlier models.
Rounding-Out GEMMA
The representation of atoms as spindle vortexes as given above is perhaps the first such representation with the degree of detail included. As such, it is still rather rough in parts and capable of improvement and development.
In particular, it should not be assumed that images and graphics used here are the literal equivalents of the underlying structures. A brief list follows of the main points and riders to the model.
Basics of the Spindle Vortex Model.
1. Matter is made up of vortexes.
2. Atoms are single vortexes. Their masses/rotation speeds increase with atomic weight.
3. These masses/rotation rates are somewhat quantized, giving whole-number atomic weights.
4. With standard matter, all vortexes rotate in the same sense, arbitrarily defined as Clockwise when viewed from the lower terminal point "South Pole".
5. With Antimatter, all vortexes rotate Anticlockwise. Hence the mutual incompatibility of matter and antimatter in contact.
6. Vortexes are 3-dimensional, but not necessarily the same 3 dimensions as ordinary space. The spherical representations and symmetries used here are most likely inaccurate -- a spinning-top shape as in Figure F25 is one possibility.
7. With magnetism, clumps of material have a somewhat preferred vortex orientation in space, ie the clump has an actual non-zero axis vector. This must be matched by a similar summed axis vector in the opposite direction in another clump or clumps.
8. In non-magnetized material, the vortex axis moments and axis vectors sum up to zero over a given small volume.
9. Radioactivity occurs as atom-vortex rotation rates increase to higher levels, with lowered stability.
10. Gravity is the consequence of interaction of the rotating fields of spindle-vortexes.
11. Sub-atomic particles are vortex fragments, usually unstable.
12. The shapes of spindle-vortexes are not necessarily similar to those of larger real-world vortexes.
13. Atom-vortexes in close proximity may be randomly oriented, but their contact surfaces will interact sympathetically.
14. Protons are hydrogen nuclei and thus standard vortexes.
15. Photons are emitted from spindle axis ends as sinusoidal photon hoops. The atom "twitches" slightly.
16. Rotational energy and mass are equivalenced at the spindle-vortex scale.
17. Newtonian gravity is based on point masses. Some sort of tensor maths is needed to describe interaction of rotating masses.
18. In the images presented here, the rate of rotation is assumed the same throughout the Spindle Vortex. This may not be true.
There is Nothing New Under The Sun
Every scientist who comes up with a brilliant new theory, every inventor who devises an astounding new instrument, every manager who comes up with a dazzling new approach, all are subject to the scrutiny of the world, including some who have the temerity to point out "But so-and-so did it years ago".
Sometimes, as with patents, this mechanism of criticism has a formal structure. The story goes that the inventor of a new technique for raising sunken ships by pumping in air-filled balls had his patent application knocked back, because the Patent Examiner had seen a Mickey Mouse cartoon where the hero had raised a sunken boat by putting in table-tennis balls.
Quotation BS802-Q1.
And so with the Spindle Vortex Model. Some preceding efforts have been described above, but one with uncanny prescience dates back to 1644.
In that year, the brilliant French scientist, mathematician, and philosopher Rene Descartes (after whom Cartesian Geometry is named) came up with a description of matter and space entitled "Aether vortices around celestial bodies" [32]. Here are some extracts about it..
"Rene Descartes proposed in 1644 that no empty space can exist and that space must consequently be filled with matter. The parts of this matter tend to move in straight paths, but because they lie close together, they can not move freely, which according to Descartes implies that every motion is circular, so the aether is filled with vortices. Descartes also distinguishes between different forms and sizes of matter in which rough matter resists the circular movement more strongly than fine matter".
Figure BS802-F26. Portrait of Rene Descartes. From [34].
"Due to centrifugal force, matter tends towards the outer edges of the vortex, which causes a condensation of this matter there. The rough matter cannot follow this movement due to its greater inertia -- so due to the pressure of the condensed outer matter those parts will be pushed into the center of the vortex".
Figure BS802-F27. Vortexes in 1644. From [32].
"According to Descartes, this inward pressure is nothing else than gravity. He compared this mechanism with the fact that if a rotating, liquid filled vessel is stopped, the liquid goes on to rotate. Now, if one drops small pieces of light matter into the vessel, the pieces move to the middle of the vessel".
At least he didn't say anything about anti-matter. Or about emission of light quanta.
* * * * * * * * * * * * * * * * * *
References and Links
[1]. Lord Kelvin. On Vortex Atoms. https://zapatopi.net/kelvin/papers/on_vortex_atoms.html .
[2]. William Thomson (1824-1907), Lord Kelvin, Physicist. https://www.artuk.org/discover/artworks/william-thomson-18241907-lord-kelvin-physicist-126219 .
[3]. Sucked Into The Research Vortex.
http://publishingbones.com/2016/07/20/sucked-into-the-research-vortex/ .
[4]. #vortex. https://wifflegif.com/tags/10840-vortex-gifs .
[5]. Lucretius. https://plato.stanford.edu/entries/lucretius/ .
[6]. Lucretius. https://www.laphamsquarterly.org/contributors/lucretius .
[7]. David Noel. UG101: Recycling the Universe: Neutron Stars, Black Holes, and the Science of Stuff. http://www.aoi.com.au/Recycling/ .
[8]. Planes clouds and vortices. https://www.youtube.com/watch?v=dfY5ZQDzC5s .
[9]. David Noel. P3: Living In The Universe: (What CMBR tells us about Dark Matter, and much more). http://aoi.com.au/Living/ .
[10]. Bohr model. https://en.wikipedia.org/wiki/Bohr_model .
[11]. Bohr atomic model. https://www.britannica.com/science/Bohr-atomic-model .
[12]. Shell Model. https://physics.tutorvista.com/modern-physics/shell-model.html .
[13]. The Standard Model. http://electron6.phys.utk.edu/phys250/modules/module%206/standard_model.htm .
[14]. Quantum chromodynamics. https://en.wikipedia.org/wiki/Quantum_chromodynamics .
[15]. Richard Feynman. https://en.wikipedia.org/wiki/Richard_Feynman .
[16]. David Noel. The Photon Hoop Model for light: A new model to aid analysis and computation of light reflection and refraction phenomena, and towards a resolution of the dichotomy between wave models and particle models for light. http://aoi.com.au/bcw/PhotonHoop/index.htm .
[17]. Whirlpool. https://en.wikipedia.org/wiki/Whirlpool .
[18]. Einstein's mass - energy equivalence. http://qqnvr.com/assets/download.php?file=/../data/17/e-mc2-worksheet/e-mc2-worksheet-23.jpg .
[19]. David Noel. P4: The Greater Averaged Universe (GAU): How the Solar System cannibalizes the Oort Cloud. http://www.aoi.com.au/GAU/index.htm .
[20]. Periodic Table of Elements Reference Card. https://www.coop.com.au/periodic-table-of-elements-reference-card-chm001/5555000095488 .
[21]. Force of Attraction Formula. https://formulas.tutorvista.com/physics/force-of-attraction-formula.html .
[22]. Isotopes of lead. https://en.wikipedia.org/wiki/Isotopes_of_lead .
[23]. Monatomic hydrogen as fuel. http://www.chemicalforums.com/index.php?topic=7789.0.
[24]. Magnetism. https://en.wikipedia.org/wiki/Magnetism .
[25]. Lodestone. https://en.wikipedia.org/wiki/Lodestone .
[26]. About Our Name. https://www.lodesys.com/2008/05/about-our-name/ .
[27]. Maglev Train. http://www.visitourchina.com/shanghai/attraction/maglev-train.html .
[28]. Magnetostriction. https://en.wikipedia.org/wiki/Magnetostriction .
[29]. Secondary antiprotons and propagation of cosmic rays in the Galaxy and heliosphere. https://arxiv.org/abs/astro-ph/0106567 .
[30]. Annihilation. https://en.wikipedia.org/wiki/Annihilation .
[31]. Antimatter. http://www.crystalinks.com/antimatter.html .
[32]. Mechanical explanations of gravitation. https://en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation#Vortex .
[33]. Positron emission tomography. https://en.wikipedia.org/wiki/Positron_emission_tomography .
[34]. Rene Descartes. https://en.wikipedia.org/wiki/Rene_Descartes .
[35]. Malcolm W Browne. Left-Handed Universe. https://www.nytimes.com/1986/11/25/science/left-handed-universe.html .
