As an introduction to this idea, I’ll provide background info from “Cosmos” magazine [1]:

“A robot engineered at Georgia Institute of Technology (Georgia Tech) has done the unthinkable and flouted a steadfast law of motion, suggesting that new laws need to be defined. Such new principles may have applications in new forms of locomotion without propellants. Newton’s third law states that for every action there is an equal and opposite reaction. So, when a human takes a step, we push against the Earth and the Earth pushes back, propelling us forward. But this only works thanks to friction. The same is true of all locomotion. Rockets, for example, eject massive amounts of matter at high speed to push themselves in the opposite direction. But the Georgia Tech robot has bypassed this need for a thrust in order to change momentum. It does this by making use of curved space.

Figure 1: Experimental “curved space-time robot” moving on a sphere with actuated motors on a freely rotating boom arm. Credit: Georgia Tech.

“We let our shape-changing object move on the simplest curved space, a sphere, to systematically study the motion in curved space,” says lead researcher Zeb Rocklin, assistant professor in the School of Physics at Georgia Tech. “We learned that the predicted effect, which was so counter-intuitive it was dismissed by some physicists, indeed occurred: as the robot changed its shape, it inched forward around the sphere in a way that could not be attributed to environmental interactions. The robot felt only slight forces due to friction and gravity, but the two effects were seen to hybridise with the curvature of the space itself to produce a strange dynamic with properties which could not have been produced by either friction or gravity on their own.

“While the observed effects due to curved space are small, the researchers believe that increasingly precise robotics will see these curvature-induced effects having practical applications. The principles of how the curvature of space can be harnessed for locomotion may ultimately be useful in circumnavigating the highly curved space around black holes. Because spacetime is very slightly curved, a device could actually move forward without any external forces or emitting a propellant – a novel discovery.”

(End of background info from “Cosmos”)

Alessandro Rizzo, my colleague at Research Gate, informed me about the close relationship between the Prandtl-Glauert equations for fluid flow, Einstein’s relativistic equation, and James Clerk Maxwell’s establishment of a powerful correlation between electromagnetic waves and fluid dynamics. This relation shows that the fluid relationship between gravitation and electromagnetism could also describe the flexibility, in Vector-Tensor-Scalar Geometry, of producing fermions or bosons at quantum scales through graviton-photon interaction, and of forming black holes or planets at cosmic scales.

The following method of building planets is preferred to collisions between rocks and dust in the solar system’s formative protoplanetary disk approx. four and a half billion years ago because most planetary systems seem to outweigh the protoplanetary disks in which they formed, leaving astronomers to re-evaluate planet-formation theories [2].

Figure 2: Parallelogram With Diagonal and Central Scalar Point (see text below – the momentum of photons and gravitons produces a pressure we identify as the solidity of mass and matter).

A vector is a quantity which possesses both magnitude and direction. Two such quantities acting on a point (represented by the red Scalar Higgs boson) may be represented by two adjoining sides of a parallelogram (e.g. CD and AD), so that the resultant diagonal^ (green line) also represents the vectors. The two sides and diagonal thus illustrate the graviton's spin 2 and the photon's spin 1. The resultant diagonal represents the interaction of the sides/vectors (1÷2 = the spin ½ of every matter particle). Tensor calculus changes the coordinates of the sides and diagonal into the coordinates of a single point (the scalar) on the diagonal. This scalar point is associated with particles of spin 0. If the mass produced previously happens to be 125 GeV/c^2, its union with spin 0 produces the Higgs boson - and relates the Higgs boson/field to the supposedly unrelated graviton/gravitational field (together with the latter's constant interaction with the photon/electromagnetic field).

^ The resultant diagonal of those two sides can be pictured as a boat being driven in, say, the vertical direction across a river while simultaneously being pushed horizontally by the river’s fast-flowing current. The interacting gravity and electromagnetism in VTS geometry produce mass e.g. they can form a Higgs boson or the strong/weak nuclear forces’ bosons as well as matter. On a cosmic level - if gravitational and electromagnetic waves focus on a protoplanetary disc surrounding a newborn star, the quantum spin of the particles of matter in the disc (1/2) could imprint itself on the waves’ interaction and build up a planet layer by layer from vector-tensor-scalar geometry’s 1/2 interaction. If the waves focus on a region of space where there’s no matter, the opposite interaction occurs and the graviton’s spin 2 is divided by the photon’s spin 1 to produce 2/1 (the quantum spin of gravitons composing the powerful gravitational fields of black holes). The mass produced has the spin inherent in each of the gravitons composing spacetime - and could be an alternative, or complementary, method to supernovas for producing the gravitational waves making up black holes. 

Quaternions were first described by Irish mathematician William Rowan Hamilton in 1843. Hamilton defined a quaternion as the quotient of two vectors [3]. In this case: the quotient of two vectors is 1/2, the division of the electromagnetic vector (photonic quantum spin of 1) by the gravitational vector (gravitonic quantum spin of 2). In other words, the term "diagonal" (like 1/2, the result of these 2 vectors interacting) in VTS Geometry can be replaced with the term "quaternion". (Of course, the vectors may be reversed to give the black hole quaternion of 2/1). A hologram’s appearance differs depending on which direction it’s viewed from. If the universe is holographic as proposed by Gerard‘t Hooft, Leonard Susskind, and AdS/CFT correspondence - if the 3rd dimension is the result of information in the 2nd dimension (in the 2D Mobius strip?) - a hologram’s property of looking different depending on the direction it’s viewed from might account for the matter-particle quaternion of 1/2 becoming the black-hole quaternion of 2/1.

It must be remembered that referring to space alone is incomplete. Living in space-time, it’s necessary to add some sentences about the time factor. The photon must interact with the graviton to produce the mass of the weak nuclear force’s W and Z bosons. To produce their quantum spin, the photon’s spin 1 needs to react with the graviton’s spin 2. That is, the photon’s turning through one complete revolution needs to be combined with the graviton’s being turned through two half-revolutions*. Incorporating the time factor as a reversal of time (Richard Feynman, 20th-century winner of the Nobel Prize in Physics, used reversal-of-time to explain antimatter) in the middle of the interaction: a gravitonic half revolution is subtracted from the photonic full revolution then the graviton’s time-reversal adds a half revolution (1-½+½ = the spin 1 of W and Z bosons). The strong nuclear force’s gluon’s quantum spin of 1 could arise in the same way as the spin 1 of weak-force bosons. The masslessness of gluons might be produced by retarded and advanced waves cancelling. They neutralize each other, producing a mass of zero and relating gluons to the Higgs boson whose zero quantity is its quantum spin.

Professor Stephen Hawking writes

"What the spin of a particle really tells us is what the particle looks like from different directions."  (3a)

Spin 1 is like an arrow-tip pointing, say, up. A photon has to be turned round a full revolution of 360 degrees to look the same.  

Spin 2 is like an arrow with 2 tips

1 pointing up, 1 down. A graviton has to be turned half a revolution (180 degrees) to look the same.  

Spin 0 is like a ball of arrows having no spaces. A Higgs boson looks like a dot: the same from every direction. 

Spin ½ is logically like a Mobius strip, though Hawking doesn’t specifically say so. This is because a particle of matter has to be turned through two complete revolutions to look the same, and you must travel around a Mobius strip twice to reach the starting point

The parallelogram can be converted by computer into the shape of Earth’s elliptical orbit, which means the vector/tensor/scalar relationship applies to this planet. One vector can be the magnitude and direction of the orbiting Earth itself. It and a second vector (Earth months later in its orbit – more about this at the paragraph’s end) are represented by two sides of the parallelogram as well as by the resultant diagonal. Being represented by the diagonal, Earth is naturally also represented by the diagonal’s central scalar point. Successful conversion of the parallelogram to an ellipse, followed by tensor analysis, means our planet is also a scalar object. This is equivalent to reducing the innumerable spins of particles composing the planet to spin 0. Such particles have no restriction on the number of them that occupy the same state. This state means Earth can possess magnitude occupying a literally infinite and eternal amount of space-time, thus having no need of direction and being capable of possessing the same state as any other material or immaterial body.

The idea of gravity reacting with electromagnetism to produce the mass of any particle (fermion or boson) is derived from two sources – a) 1915’s General Relativity, which modified Newtonian gravity: thus making it conceivable that gravity produces mass, instead of the currently accepted view that mass causes gravity, and b) Albert Einstein’s 1919 follow-up paper “Do Gravitational Fields Play an Essential Role in the Structure of the Elementary Particles of Matter?” Which implies matter may be united with General Relativity’s revised possibility of gravity producing mass. The works of 1915 and 1919 would then open the door to Einstein’s Unified Field Theory and his dream of unifying everything [4, 5].

Figure 3: Ellipse: Earth's Orbit around the Sun Is Elliptical.

Since they’d accommodate Earth’s infinity, the material bodies would similarly do the equivalent of reducing the innumerable spins of particles composing them to spin 0 (they’d only possess magnitude and would be scalar, infinite bodies). Occupying all space-time, vector-1 Earth must be united with vector-2 Earth. The condition of everything being infinite, superposed and existing everywhere/everywhen in space-time completely removes the need for any kind of universal contraction or expansion (and removes any need for the Big Bang, Inflation, or cyclic cosmology’s oscillations between Big Bangs and Big Crunches). Such a unified field sounds very strange because every object and event anywhere in space or time would be entangled with and capable of affecting any other object/event. However, it might add some common sense to quantum mechanics which has been repeatedly verified by experiment but makes no sense at all if we cling to the notion of finite, separate objects and events. The bits or binary digits used in traditional computers have one of two values (on/off, or 1 and 0). The qubits of quantum computers possess both values at the same time because any object is infinite and eternal (∞/∞t), merely appearing spatially and temporally finite. Since a quantum computer is ∞/∞t in actuality, it can use 1 and 0 simultaneously (a traditional computer, though ∞/∞t, is built and programmed to function in a more limited manner). How can any object be infinite yet appear finite? The finiteness corresponds to the scalar Higgs boson. This particle is actually an excitation of the Higgs field, which is depicted here as combination of the gravitational and electromagnetic fields. The Higgs field is a field of energy that is thought to exist in every region of the universe, [6] and could therefore be ∞/∞t.

Conversion of Fig.2’s parallelogram to Fig.3’s ellipse demonstrates that computers can also morph the shape-changing parallelogram into the shape of figure-8 Klein bottles (shapes in mathematical topology – aka “rubber-sheet geometry” – that are each a union of two Mobius strips). Immersed in the 3rd dimension, figure-8 Klein bottles possess self-intersections and self-interference (a photograph of a stapler is a 2- dimensional immersion of a 3-dimensional stapler). Perpendicular motion – or any fraction of it - of photons and gravitons (e.g. along adjoining sides in Fig.2) creates a pressure we identify as the solidity of mass and matter. The holographic-universe theory says the 3rd dimension is merely a projection of information from the second dimension (in this case, from the 2D Mobius strip). [7] If the 3rd dimension (the depth or height) of Fig.2’s parallelogram is deleted, the photons and gravitons can no longer travel on adjoining sides but must move along parallel sides. Should the photons and gravitons go in opposite directions (along sides that are now in contact and form the Mobius strip’s one surface), they’d produce resistance to each other’s motion * i.e. they’d produce friction.

• General relativity says a light ray sent from a star and passing by the Sun is deflected 1.75 arcseconds from its original path by the Sun’s gravity. Also, Isaac Newton knew of gravitation’s effect on light more than 300 years ago. Like the “lock and key” mechanism in biological organisms of molecules engaging with cells’ receptors, gravity may deflect light because the latter’s photons are a key making up, and fitting into, the former’s graviton-locks of photons that need to be paired. This makes sense if trillions of Mobius strips make up a photon, and trillions of figure-8 Klein bottles make a graviton. Photons and gravitons fit together because Mobius strips couple with other strips to form figure-8 Klein bottles – the second topological shape is called a Mobius Doublet since it’s a joining of two strips.

Three things are essential for the movement of both the curved-space robot and what is called “topological propulsion” – shape changing, friction, and gravity. Future computers will take care of the first condition when they transform parallelograms into ellipses, topological shapes, etc. Friction is accounted for by deletion of the 3rd dimension (possible because of holographic-universe theory) plus topology’s single surfaces and self-intersections. And the third requirement is satisfied by general relativity’s statement that gravity is the curvature of space-time. Should the photons and gravitons go in opposite directions when the 3rd dimension is eliminated (along sides that are now in contact and form the Mobius strip’s one surface), they’d produce resistance to each other’s motion i.e. they’d produce friction and propulsion that isn’t mechanical, electrical, or chemical but exhaust-free and topological. There have been reports of Unidentified Flying Objects having no exhaust and experiencing g-forces (accelerations and decelerations) that are so high they could never be handled by the human body or present technology. Propulsion that’s topological wouldn’t produce g-forces on its crew because gravity acting alone does not produce g-forces: they’re a result of resistance to gravity by physical, tangible forces. This raises the question “Could Unidentified Flying Objects be a result of future human technology?” Of course, a Yes answer makes time travel necessary.

• All mass is composed of gravitational and electromagnetic waves, according to vector-tensor-scalar (VTS) geometry inspired by the title of Einstein's 1919 paper "Do gravitational fields play an essential role in the structure of elementary particles?" Both types of waves possess retarded and advanced ** components which travel forwards and backwards in time, causing cancellation in space-time and entangling all masses. Wick rotation (time) is built into the Mobius strips and figure-8 Klein bottles composing electromagnetism's photons and gravitation's graviton Therefore, all time (the entire past and present and future) is united into one thing just as all space and all mass are united into one thing. If time only passed rectilinearly - from past to present to future - the idea of waves travelling back in time would make no sense at all. But if time is curvilinear - with past, present, and future interconnected - time must be able to move from future to present to past. Unity of past/present/future may remove the issue of non-simultaneity – in special relativity – because the timing or sequence of events being different in different frames of reference can only exist if past/present/future are separate. The concepts of cause and effect are no longer separate when all periods of time are united, and everything can happen “at once”. This is similar to watching a DVD – every event on the DVD exists at once since the whole DVD exists but we’re only aware of sights and sounds occurring in each tiny fraction of a second.
• "When we solve (19th-century Scottish physicist James Clerk) Maxwell's equations for light, we find not one but two solutions: a 'retarded' wave, which represents the standard motion of light from one point to another; but also an 'advanced' wave, where the light beam goes backward in time. Engineers have simply dismissed the advanced wave as a mathematical curiosity since the retarded waves so accurately predicted the behavior of radio, microwaves, TV, radar, and X-rays. But for physicists, the advanced wave has been a nagging problem for the past cent" [8] Einstein's equations say gravitational fields carry enough information about electromagnetism to allow Maxwell's electromagnetic equations to be restated in terms of these gravitational fields. This was discovered by the mathematical physicist George Yuri Rainich [9].

Albert Einstein used Riemannian geometry when formulating his General Relativity. It should therefore be conceivable that another work by Georg Riemann (the Riemann Hypothesis published in 1859) might, with help from Wick Rotation and the inverse-square law, go beyond Special Relativity's statements about the light cone and the speed of light being a cosmic speed limit. Then time travel would be possible - I hope to show that travel can be into either the past or the future.

The Riemann hypothesis, proposed in 1859 by the German mathematician Georg Friedrich Bernhard Riemann, is fascinating. It seems to fit these ideas on various subjects in physics very well. The Riemann hypothesis doesn’t just apply to the distribution of prime numbers but can also apply to the fundamental structure of the mathematical universe’s space-time. In mapping the distribution of prime numbers, the Riemann hypothesis is concerned with the locations of “nontrivial zeros” on the “critical line”, and says these zeros must lie on the vertical line of the complex number plane i.e. on the y-axis in Fig. 8. Besides having a real part, zeros in the critical line (the y-axis) have an imaginary part. This is reflected in the real +1 and -1 of the x-axis in Fig. 8, as well as by the imaginary +i and -i of the y-axis. In the upper half-plane of Fig. 8, a quarter rotation plus a quarter rotation equals a half – both quadrants begin with positive values and ¼ + ¼ = ½. (The Riemann hypothesis states that the real part of every nontrivial zero must be 1/2.) While in the lower half-plane, both quadrants begin with negative numbers and a quarter rotation plus a negative quarter rotation equals zero: 1/4 + (-1/4) = 0. In the Riemann zeta function, there may be infinitely many zeros on the critical line. This suggests the y-axis is literally infinite. To truly be infinite, the gravitational and electromagnetic waves it represents cannot be restricted to the up-down direction but must include all directions. That means it would include the horizontal direction and interact with the x-axis – with the waves rotating to produce ordinary mass (and wave-particle duality) in the x-axis’ space-time,* and dark matter in the y-axis’ imaginary space-time.

The inverse-square law states that the force between two particles becomes infinite if the distance by which they’re separated goes to zero. Remembering that gravitation partly depends on the distance between the centres of objects, the separation only goes to zero when those centres occupy identical space-time coordinates ^ (not merely when the objects’ sides are touching). That is – infinity equals the total elimination of distance, or zero. The infinite, eternal cosmos could possess this absence of distance in space and time (deletion of the 3rd dimension) via the electronic mechanism of binary digits which would make the universe as malleable and flexible as any image on a computer screen. If infinity is the total deletion of distance in space-time, there is nothing to rule out instant intergalactic travel or time travel to the past and future. Infinity does not equal nothing – nor does zero. ^^ Zero would be something if it’s paired with one to form the binary digits used in computers and electronics. Could the universe, and life, have begun with all the brains of past and future history acquiring increasingly sophisticated knowledge of time and space? Then an extra-dimensional hyperspace might be used to access the infinite past and purposely switch the digits composing the universe from 1 to 0 or vice versa (this switching would be comparable to the quantum fluctuations associated with Big Bang theory).

• Quantum mechanics forbids two particles of matter to occupy identical coordinates. But in a universe that is purely mathematical, matter has the same freedom as photons and gravitons (unlimited numbers can be in the same place).
• The best physics paper of recent weeks comes from a group of physicists in Japan and the United States who found a new way to create matter from light [1a]. Electrical engineer Hong Tang and his team at Yale University demonstrated that, on nano-scales, light (electromagnetism) can attract and repel itself like electric charges or magnets [2a]. This is the Optical Bonding Force. Articles I’ve written propose that light can attract itself because a photon, the quantum of electromagnetism, is composed of trillions of Mobius strips (a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist). In attraction, a pair of strips can fit together and form a Klein bottle (another example of mathematics’ topology or “rubber-sheet geometry” which, if travelled upon, could be followed back to the point of origin while flipping the traveller upside down). The Klein bottle is a two-dimensional manifold mathematically immersed – not embedded – in the third dimension (an immersion may have self-intersections; embeddings have no self-intersections). Trillions of bottles form a graviton, the quantum of gravity (when a graviton dissociates or separates into Mobius strips, the building blocks of photons adopting different paths, light repels itself). If this explanation of a science experiment's results is correct, the shared topology making up photons and gravitons would indicate electromagnetic-gravitational unification. If the pressure of interacting photons and gravitons produces mass, the explanation suggests a supersymmetrical correspondence between fermions and bosons. Einstein's equations say gravitational fields carry enough information about electromagnetism to allow Maxwell's electromagnetic equations to be restated in terms of these gravitational fields. This was discovered by the mathematical physicist George Yuri Rainich. Therefore, gravitational waves might also be capable of attracting and repelling. Suppose all the gravitational and electromagnetic waves composing space-time between a spaceship and a distant galaxy were compressed by attraction or repulsion into a flat plane. Then there'd be no distance between astronauts and, say, the Andromeda galaxy and they could travel there instantly (instead of making a journey that takes more than 2 million years at the speed of light).

Figure 4: Two-Dimensional (2D) Mobius strip and Figure-8 Klein Bottle (Immersed in 3D), Which May Respectively Form the Photon and Graviton. Following Einstein and Rainich and de Broglie, these in Turn May Form Mass. Wick Rotation Might Denote Time, the 4th Dimension of Space-time.

If light can interact with itself, you would not need a virtual exchange particle (see next paragraph) to facilitate the interaction between the photons that create matter from light.  The photon itself would be the required charged particle because of its ability to attract and repel itself like electric charges or magnets. Also, two photons aren’t necessary to produce an electron and positron. We saw how gravitation’s graviton can be topologically closely related to electromagnetism’s photon (gravitons can “dissociate” into photons). This dissociation means a graviton and photon can interact to produce an electron and positron (see next paragraph). According to Vector-Tensor-Scalar Geometry (discussed on pp.3-5), they can produce the mass and quantum spin of any particle.

Space has to exist if Relativity is right about gravity being the curvature of space (we all know gravity exists). Maybe the virtual particles currently theorised to fill space don't exist. And the model of space and time being inseparable says there must be an entity called time if there's an entity called space (which would be filled with real particles called gravitons and photons). (Those particles would share elements of their composition, thus being interactive electromagnetically and topologically). Einstein’s 4-dimensional mathematical existence of spacetime wouldn't perfectly represent its physical existence, as made clear by Einstein's publication in 1919 of an article suggesting gravity plays a role in the composition of elementary particles. This might mean (a) gravity and electromagnetism can undergo a particular interaction to form particles with mass, and (b) space, while filled with gravitons and photons, is nothing but the absence of the mass-generating interaction. There can be no curvature of something that has no existence itself. The phrase "curvature of space" would technically mean "gravitons and photons filling space follow curved paths". However, it’s very convenient to simply speak of curved space – just as we say the Sun rises and sets while neglecting to mention Earth’s rotation … or speak of waves travelling without referring to excitation of pre-existing gravitons or photons.

Should the photons and gravitons go in the same direction when the 3rd dimension is eliminated (along sides that are now in contact and form the Mobius strip’s one surface), they’d produce a superconductor that wouldn’t rely on low temperature or high pressure because it’s mathematical (topological). To begin discussion of topological superconductors, let’s start with a few words about the related topological insulators. A topological insulator is a material that behaves as an insulator in its interior but whose surface contains conducting states. However, the conducting surface is not the unique character of topological insulators, since the ordinary band insulators can also support conductive surface states. What is special is that the surface states of topological insulators are symmetry protected. Symmetry Protected Topological (SPT) Order is a kind of order in topological insulators where, if symmetry is preserved during the deformation undergone in topology (also known as rubber-sheet geometry), a phase transition from one state of matter to another must occur (in this case, between insulation and conduction). In other words, if the shape of a Möbius strip (or the union of two strips into a Klein bottle) is preserved, phase transition must occur just as orientation-reversing curves occur in the Möbius and Klein.

The General Theory of Relativity will be useful in this article. Specifically – the analogy of the theory’s curvature of space-time to a rubber sheet. A small body like the Earth is said to warp space-time only a little and create a dimple in the sheet. A larger body such as the Sun curves space-time much more and forms a deep valley in the rubber. And a black hole is often pictured as warping space-time so much that it tears a hole through the rubber fabric. Transferring the analogy to the quantum realm – the motion of electrons can be visualized as their gliding across hills and valleys of pure energy (gravitational energy). This is because Relativity says gravity is caused by the curvature of space-time. Therefore, gravity ... gravitational energy ... IS space-time. Materials that don’t conduct electricity (insulators) have deep valleys which electrons struggle to escape from. In 2004, U.S.A. physicist Charles Kane noticed something strange in his computer simulations of electrons flowing through different materials: an insulator whose quantum state had the equivalent of a hole. Kane had not found the first quantum black hole but had discovered the first topological insulator – a then theoretical material that could conduct electricity on its surface but not within its interior. (In 2007, American physicist M. Zahid Hasan led the team that made the first 3D topological insulator.) About 90 years ago, while experimenting with the equations of quantum physics, German physicist Hermann Weyl showed that a massless and charged particle (now called the Weyl fermion) could theoretically exist. (10) In topological insulators, the hole in its quantum state causes electrons to come together and behave like a single particle called a Weyl fermion. The Weyl fermion can be related to Topological Insulators (TI), the Majorana fermion^ can be related to quantum computers’ Topological Superconductors (TS), while topological insulators and topological superconductors may be regarded as the (Mobius dependent) inverse of each other. This state of topological materials and “unnatural” fermions can be expressed by another phenomenon which is called here vector-tensor-scalar geometry: in which matter, and the Higgs boson, both emerge from photon-graviton interaction. This means the Higgs boson is related to the graviton, and the Higgs field is therefore united with the gravitational field (together with its constant interaction with the electromagnetic field).

• The Majorana fermion was predicted in 1937 by Italian physicist Ettore Majorana playing with the same quantum math that had intrigued Weyl. Like a Weyl fermion, a Majorana fermion has no mass. It also has no charge, despite being made of a bunch of negatively charged electrons [11].

Figure 5: Mobius Dependent Inversion of Figure 6.

Figure 6: Mobius Dependent Inversion of Figure 5.

• Topological insulators can also be composed of Mobius strips but the union of tiny “cyclone” motions (the union in Mobius fashion of surface and cavity, or hole) is a topological quantum number (also called topological charge) that can be created or destroyed during the phase transition between insulator and superconductor.

Relating Fig. 5’s Weyl fermion and Fig. 6’s Majorana fermion to VTS Geometry (Figure 2) -

Side DC of parallelogram = Vector 1 electrons; Side DA = Vector 2 electrons

Referring to Fig. 2, the two vectors (two groups of charged electrons) interact to form the resultant diagonal DB (the electrons travel ADB and CDB, coming together to behave like a single charged particle called a Weyl fermion). Tensor calculus converts the points on the sides and diagonal into a single scalar point on a nominated side (say, in the centre of the diagonal). And the mass of the vector 1 electrons minus the mass of the vector 2 electrons [(x MeV/c^2) - (x MeV/c^2)] equals zero, and the massless Weyl.

In the case of the Majorana fermion, the electrons flow in the reverse direction. They go in the BD direction, then split and follow the paths DA and DC. This preserves information if one pathway is interfered with. They produce the chargeless Majorana because the negative vector-1 electrons minus the negative vector-2 electrons equal (-y) - (-y) = 0. The Majorana’s lack of mass is attributed to the same process by which the Weyl particle becomes massless (see previous paragraph).

Why is subtraction essential? This appears to be a consequence of matter, and the Higgs boson, both emerging from photon-graviton interaction. Two adjoining sides of a parallelogram represent the vectors of the photon’s spin 1 and the graviton’s spin 2. The resultant diagonal represents the interaction of the sides/vectors (1÷2 = the spin ½ of every matter particle: and division is merely repeated subtraction e.g. 4 subtracted from 20 five times equals zero, therefore 20 ÷ 4 = 5).

The Meissner effect (or Meissner–Ochsenfeld effect) is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the Meissner effect in 1933. Regarding the Meissner effect: Think of the electromagnetic wave relativistically. In General Relativity, the simple analogy of space-time being regarded as a rubber sheet is commonly used. Instead of resorting to complex and lengthy relativistic mathematics, we can simply picture an electromagnetic wave as a cylinder made of rubber. If two sides of the cylinder are pushed in with your fingers (say, the ones representing the electric component), the sides in the perpendicular direction (representing the magnetic component) will bulge outwards - this can be verified by placing a ruler behind the cylinder. Compressing the electric component will force the magnetic component to bulge outwards i.e. there will be little or no magnetic field within the superconductor, only an external magnetic field. An externally applied magnetic field also conforms to the bulging outwards and is expelled from within the superconductor. 

Figure 7: An electromagnetic wave showing electric and magnetic fields, and the wavelength (λ) which is the distance between crests of a wave.

An electromagnetic wave can have its electrical part compressed through e.g. introduction of copper-and-oxygen compounds called cuprates or use of hydrogen sulfide (speaking of molecules as well as waves refers to quantum mechanics' wave-particle duality). This means the explanation of superconductivity developed by John Bardeen, Leon Cooper, and John Schrieffer in 1957 (for which they shared the 1972 Nobel Prize) need not depend on the Cooper pair or BCS pair - a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper [12]. In a Cooper pair, an electron in a metal attracts the positive ions that make up the rigid lattice of the metal. This positive charge can attract other electrons, and it has also been recently demonstrated that a Cooper pair can comprise two bosons. [13].

Two-time co-winner of the Nobel Prize in Physics (in 1956 for invention of the transistor, in 1972 for a fundamental theory of conventional superconductivity) John Bardeen comments –

"The idea of paired electrons, though not fully accurate, captures the sense of it."

(14).

Phrased informally, a more accurate description of superconductivity might refer to the illustration above of an electromagnetic wave. If compression is sufficient; the orange-coloured electric component no longer follows the long, curved path outlined by its peaks and troughs but is compressed to the arrow showing the direction of propagation. Its path is now linear and follows the shortest distance between two points. In other words, a superconductor that operates at room temperature and normal atmospheric pressure has been manufactured. Any resistance to the flow would, like a rock in the bed of a stream causing water to flow around it, lengthen the distance and mean the compound is not a perfect superconductor. This analogy to "a rock in the bed of a stream" refers to the relative non-movement of paired electrons. Superconductivity is a wave motion, where energy is transferred from one place to another without involving an actual transfer of matter.

The idea of compressed electric fields (they could be compressed by combined gravitational-electromagnetic waves) and bulging, expelled magnetic fields is a plausible alternative to Earth's geodynamo.* Venus' core is thought to be electrically conductive and, although its rotation is often thought to be too slow, simulations show it is adequate to produce a dynamo. Yet it has no detectable intrinsic magnetic field. It could follow Alternating Current and use reversal – instead of compressing electrically and expelling magnetically, the planet would undergo compression of electromagnetism's magnetic component with expulsion of the electric component. Venus would have no intrinsic magnetic field as a result. But it would have a strong electric field – and the European Space Agency's Venus Express spacecraft did detect one [15].

* The cause of Earth's magnetic field is said to be the geodynamo, also called the magnetic dynamo theory. The heat from the solid inner core puts the liquid outer core in motion, and the movements of the outer core's electrically conducting fluids (such as molten iron) generate the planet's magnetic field. Electrically conducting fluids occur in the Sun, other stars and most planets – and are, at present, the scientifically accepted mechanism for magnetic fields.

'Scientists using Venus Express have identified another difference between the planets: Venus has a substantial electric field, with a potential around 10 V. This is at least five times larger than expected. Previous observations in search of electric fields at Earth and Mars have failed to make a decisive detection, but they indicate that, if one exists, it is less than 2 V. “We think that all planets with atmospheres have a weak electric field, but this is the first time we have actually been able to detect one,” says Glyn Collinson from NASA’s Goddard Space Flight Center' [16].

How does this alternative account for magnetic-field reversals? The incoming weak gravitational waves and powerful electromagnetic waves – 10^36 (a trillion trillion trillion) times stronger - can compress electric fields, resulting in a strong magnetic field. As motions in planetary cores occur, relocated electric waves can be compressed less, causing reduced expelling of the magnetic waves and weakening of Earth's field. Electromagnetic waves can change orientation by 180 degrees, causing the expelled magnetism's polarity to reverse. The presence of electric and magnetic fields does, of course, require the presence of the accepted geodynamo theory’s electrically conducting fluids but not of Type-l superconductors which operate at temperatures close to absolute zero or 0 K. There are other superconductors e.g. high-Tc (high temperature aka Type-II superconductors) as well as this article’s proposed topological superconductivity.

The topological version operates mathematically and is able to remove the uncertainty regarding the cause of the planet Mercury’s magnetic field.

The planet probably rotates too slowly (once every 58? earth days) for the dynamo effect to occur [17]. (Earth’s dynamo is called the geodynamo.)

Agreement is added by “The magnetic field itself is thought to originate from the dynamo mechanism, although this is uncertain as yet” [18].

Mercury’s rotation on its axis may be too slow for the dynamo effect to occur … too slow to sufficiently stir the electrically conducting fluids within the planet. So how can those conducting fluids be stirred and activate Mercury’s weak magnetic field? This involves a few sentences on pp. 7-8.

“Should the photons and gravitons go in opposite directions when the 3rd dimension is eliminated (along sides that are now in contact and form the Mobius strip’s one surface), they’d produce resistance to each other’s motion i.e. they’d produce friction and propulsion that isn’t mechanical, electrical, or chemical but exhaust-free and topological.” And “Should the photons and gravitons go in the same direction when the 3rd dimension is eliminated (along sides that are now in contact and form the Mobius strip’s one surface), they’d produce a superconductor that wouldn’t rely on low temperature or high pressure because it’s mathematical (topological).”

In Mercury’s case, generation of the planet’s magnetic field doesn’t totally depend on electrical and chemical factors like electrically conducting fluids – nor does it rely on mechanical rotation. Similar to the topological propulsion that’s free of exhaust and g-force, a superconducting mechanism that’s independent of temperature and pressure conducts the effects of the electrically conducting fluids to create global magnetism.* In the event that the dynamo theory is considered inadequate for explaining magnetism of other bodies, it’s worth remembering that the effects of molten iron and nickel in Earth’s outer core could create a magnetosphere.

Figure 8: Wick Rotation or the Circle Of I: “The complex plane reveals i’s special relationship with cycles via the circle of i, also known as Wick rotation. Whenever a point on the complex plane is multiplied by i, it moves a quarter rotation around the origin or center of the plane” [19].

Scientists noted that Mercury's magnetic field can be extremely "leaky". (20) A century ago the founder of Wave Mechanics, Louis de Broglie, treated electrons as standing waves, thus introducing matter waves and wave-particle duality. Thanks to Einstein, Rainich, and de Broglie; mass can be regarded as an extension of electromagnetic (plus gravitational) waves, too. Using de Broglie’s matter waves and the usefulness of imaginary numbers / Wick rotation in engineering, electric current can be viewed as rotation of electromagnetic and gravitational waves in the Circle of i. (AC’s periodic reversal of direction would be counterclockwise motion alternating with clockwise.) How can Wick rotation explain physics’ dark matter and dark energy? (The relevance of these to electric current will be apparent later in this paragraph) The counterclockwise rotation of gravitational and electromagnetic waves between the x- and y-axes in Figure 7 can be viewed as responsible for the gravitational/electromagnetic energies forming all mass in space-time or, as dark energy, forming all mass in imaginary time – described by “imaginary” numbers like i2 = -1. Since time and space can never be separated, imaginary time is linked to an imaginary space and the mass in that space is known as dark matter. Just as waves “leak” from the x- to the y- axis to become dark matter, loss of power in electrical transmission can also be seen as leakage from the x- to the y- axis. And loss of power in Mercury’s topological superconductance can be seen as the extreme leakiness of the magnetic field which leads to the magnetic "tornadoes" encountered by the MESSENGER spacecraft during its second fly-by on October 6, 2008.

To summarize the statements about Mercury’s magnetic field, and also to lead into the next part about the Sun -

Look at the diagram of the parallelogram (bottom of page 3). The top and bottom of the figure could be compressed by gravitational waves, and 10^36 times as strong electromagnetic waves. This would form a single line in which particles (partially composed of topology's Mobius strips) could either (a) travel in opposite directions, causing interference and friction, or (b) all travel in the same direction, with no friction or resistance resulting. I call (a) topological propulsion, since UFOs might use it, and (b) is called topological superconductivity, which is obviously related to the other electrical entity of alternating current (AC). Should the photons and gravitons go in the same direction when the 3rd dimension is eliminated (along sides that are now in contact and form the Mobius strip’s one surface), they’d produce a superconductor that wouldn’t rely on temperature or pressure because it’s purely mathematical (topological).

In the sun's case, generation of its magnetic field doesn’t totally depend on electrical and chemical factors like electrically conducting fluids – nor does it rely on mechanical rotation. Similar to the topological propulsion that’s free of exhaust and g-forces, a superconducting mechanism that’s independent of temperature and pressure conducts the effects of the electrically conducting fluids to create magnetism. This superconducting mechanism may be powered by the quantum entanglement of alternating current’s sine waves on the single side formed by compression of Vector-Tensor-Scalar Geometry’s parallelogram. The model for our star’s behaviour could be used by technology to generate controlled “fusion” power on Earth. Instead of fusion produced by physically squeezing hydrogen with enormous pressures and temperatures, sine waves could be quantum-entangled to fuse quantum systems and produce power under normal atmospheric pressure and room temperature.

The planet Mercury might also use topological superconductivity to explain how it can have a magnetic field when its rotation on its axis is too slow to create a magnetic field. After the MESSENGER spacecraft visited the planet, scientists noted that Mercury's magnetic field can be extremely "leaky". And loss of power in Mercury’s topological superconductance can be seen as the extreme leakiness of the magnetic field which leads to the magnetic "tornadoes" encountered by the MESSENGER spacecraft during its second fly-by on October 6, 2008. The "tornadoes" might result from magnetism leaking into certain locations and getting concentrated there. If you read this article's section about Vector-Tensor-Scalar Geometry, that will explain how the leakage can also be viewed as responsible for the gravitational/electromagnetic energies forming all mass in space-time or, as dark energy, forming all mass in imaginary time – described by “imaginary” numbers like i^2 = -1. Since time and space can never be separated, imaginary time is linked to an imaginary space and the mass in that space is known as dark matter.

“Entangling electrons with heat”- says,

“In quantum computing, entanglement is used to fuse individual quantum systems into one …” [21].

Quantum entanglement is defined as “the phenomenon whereby the act of measuring one of a pair of particles determines the result of measuring the other, even when at a distance from each other”. Fusion – short for “nuclear fusion” - is defined as “a reaction in which atomic nuclei of low atomic number fuse to form a heavier nucleus with the release of energy”. Both are forms of fusion – the first is quantum mechanical and the second is classically mechanical. They are thus capable of being mistaken for each other. Waves can not only be described by mathematics but, according to this article, they can literally be the result of maths. * Then, Fourier analysis or v=f    would not merely be descriptions of waves created by interacting particles. In conjunction with the base 2 maths aka binary digits and topology addressed in this article, they’d be part of the “blueprint” for forming waves which, via VTS geometry, produce particles. Interacting particles can produce waves just as masses can create the gravitational waves of gravitation by curving spacetime. VTS plausibly explains the inverse – it doesn’t regard mass as the producer of gravity but regards gravity, partnering with electromagnetism, as producer of mass. Inverting quantum mechanics, the inverse law states that waves produce particles. Waves of any nature are known to transfer energy. If the power of one wave is entangled with the energy of all the other waves in the Sun, the entanglement produces phonons which manifest as vibrations apparent in its rising and falling convection cells.

* A 3D cube can be regarded as an image of reality coded on a 2D surface (a projection from a square). The cubic shape would be a linear projection resulting from adding, in one direction, multiple layers of the information in the square. The 2D square would be a nonlinear (angular) projection resulting from adding 4 lines, each one being separated from those adjoining it by 90 degrees. A one-dimensional line is a set of points obeying a linear relationship. A point’s an exact position or location. It’s important to understand that a point is not a thing, but a place. It possesses zero size and no matter how far we zoomed in, it’d remain dimensionless with no width. Instead of programming a set of points to follow a straight line, suppose they’re represented curvilinearly as a waveform described by Fourier analysis or v=f  .

“In general, when we combine two waves to form a composite wave, the composite wave is the algebraic sum of the two original waves, point by point in space [Superposition Principle]. When we add the two waves we need to take into account their: • Direction • Amplitude • Phase” [22].

In many waves in the Sun, these 3 must be identical and this state is achieved via “eVTS – elliptical Vector Tensor Scalar – Geometry”. Of course, not all the waves can be identical since there needs to be some variation to allow for e.g. the different frequencies/wavelengths of radio, microwave, infrared, visible colours, ultraviolet, X-ray, and gamma.

The section eVTS (elliptical vector-tensor-scalar) GEOMETRY uses Earth as the example of eVTS but the same condition and quantum state applies to our star where many, not all, waves’ Direction, Amplitude, and Phase are unified into an identical state instead of randomly interfering with one another (some interference is necessary to produce varying electromagnetic frequencies). Now to return to the Sun.

Supporting the quantum-entanglement interpretation - it’s been claimed that things like the brain, Sun, and stars could probably only possess quantum behaviour if they function at temperatures near absolute zero (−273.15° on the Celsius scale, which equals −459.67° on the Fahrenheit scale) [23]. This is because, in laboratories, quantum mechanical states like entanglement and superposition are very fragile and can only be achieved by using temperatures near absolute zero to isolate a quantum system from heat. However, that fragility wouldn’t apply if a deeper understanding of nature reveals the following quote from “New Scientist” to be correct –

‘Physicists now believe that entanglement between particles exists everywhere, all the time, and have recently found shocking evidence that it affects the wider, “macroscopic” world that we inhabit’ [24].

This is supported by these sentences from a transcript by “The Science Show” - “Entanglement is actually everywhere. Any two subatomic particles that interact in some way become entangled. When you see light coming from a faraway star, for instance, the photon, the particle of light, is almost certainly still entangled with the atoms way up there in the star that emitted it” [25]

Such macro-entanglement was confirmed in 2020 when researchers reported the quantum entanglement between the motion of a millimetre-sized mechanical oscillator and a disparate distant spin system of a cloud of atoms [26]. Later work complemented this work by quantum-entangling two mechanical oscillators [27].

Earlier, it was pointed out that fusion and quantum entanglement can be mistaken for each other. Could it be that Hans Bethe and Charles Critchfield confused classical and quantum mechanics in 1938 when they decided the Sun and stars are powered by nuclear fusion? Maybe the proton-proton reaction they contemplated – as well as other reactions such as beryllium-boron – are not a union caused by extreme temperature and pressure. Maybe the reactions are a quantum-mechanical union of solar sine waves. * If the Sun operates quantum mechanically, it would be more evidence of macroscopic entanglement as well as, possibly, quantum entanglement being deterministic in some circumstances. Its apparent probabilistic nature might mean it’s related to Chaos theory, where there’s hidden order within seeming disorder. This would revolutionize present ideas regarding the future of the solar system.

Vector-Tensor-Scalar (VTS) Geometry suggests matter is built up layer by layer from the 1 divided by 2 interaction described in the article. The Sun and stars are a special case of VTS geometry in which stellar bodies are built up layer by layer with AC waves in addition to matter such as hydrogen and helium etc (in accordance with wave-particle duality, electromagnetic waves – including solar sine waves – exhibit particle-like properties and the AC waves manifest stars’ chemical elements). If the Sun only used 1 / 2 (without the AC interaction), it’d be powered by high temperatures and pressures compressing its particles by nuclear fusion. When powered by AC waves, the half-periods entangle to produce phonons which manifest as vibrations apparent in its rising and falling convection cells of, respectively, hot and cooler plasma.

In about 5 billion years the Sun is supposed to expand into a red giant and engulf Mercury and Venus and possibly Earth (the expansion would probably make Earth uninhabitable in less than 1 billion years). It's entirely possible that there may not even be a red giant phase for the Sun. This relies on entropy being looked at from another angle - with the apparent randomness in quantum and cosmic processes obeying Chaos theory, in which there's a hidden order behind apparent randomness. Expansion to a Red Giant could then be described with the Information Theory vital to the Internet, mathematics, deep space, etc. In information theory, entropy is defined as a logarithmic measure of the rate of transfer of information. This definition introduces a hidden exactness, removing superficial probability. It suggests it's possible for information to be transmitted to objects, processes, or systems and restore them to a previous state - like refreshing (reloading) a computer screen. Potentially, the Sun could be prevented from becoming a red giant and returned to a previous state in a billion years (or far less) - and repeatedly every billion years - so Earth could remain habitable permanently.

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