PROF. Dr. Golden Gadzirayi Nyambuya | National University of Science & Technology (original) (raw)

articles by PROF. Dr. Golden Gadzirayi Nyambuya

At a most fundamental level, gravitomagnetism is generally assumed to emerge from the General The... more At a most fundamental level, gravitomagnetism is generally assumed to emerge from the General Theory of Relativity (GTR) as a first order approximation and not as an exact physical phenomenon. This is despite the fact that one can justify its existence from the Law of Conservation of Mass-Energy-Momentum in much the same manner one can justify Maxwell's Theory of Electrodynamics. The major reason for this is that in the widely accepted GTR, Einstein cast gravitation as a geometric phenomenon to be understood from the vantage point of the dynamics of the metric of spacetime. In the literature, nowhere has it been demonstrated that one can harness the Maxwell Equations applicable to the case of gravitation-i.e. equations that describe the gravitational phenomenon as having a magnetic-like component just as happens in Maxwellian Electrodynamics. Herein, we show that-under certain acceptable conditions where Weyl's conformal scalar [1] is assumed to be a new kind of pseudo-scalar and the metric of spacetime is decomposed as g µν = A µ A ν so that it is a direct product of the components of a four-vector A µ-gravitomagnetism can be given an exact description from within Weyl's beautiful but supposedly failed geometry. My work always tried to unite the Truth with the Beautiful, but when I had to choose one or the other, I usually chose the Beautiful.

Without using the common methodologies of quantum mechanics-albeit, methodologies that always inv... more Without using the common methodologies of quantum mechanics-albeit, methodologies that always involve some demanding mathematical concepts, we herein demonstrate that one can derive in a very natural, logical and trivial manner, Heisenberg's quantum mechanical uncertainty principle on the new phase-space whose name we have herein coined Stochastic Phase-Space. This stochastic phase-space-is a mathematical space upon which we previously demonstrated [2] the naturally implied existence of the First Law of Thermodynamics from Liouville's theorem. In addition to Heisenberg's uncertainty principle, we derive an upper limiting uncertainty principle and it is seen that this upper limiting uncertainty principle describes non-ponderable tachyonic particles. It must have been one evening after midnight when I suddenly remembered my conversation with Einstein and particularly his statement, 'It is the theory which decides what we can observe.' I was immediately convinced that the key to the gate that had been closed for so long must be sought right here. I decided to go on a nocturnal walk through Faelled

This is a Preprint article,This is the first instalment in a four part series, the aim of the wor... more This is a Preprint article,This is the first instalment in a four part series, the aim of the work being to introduce absolute motion into Einstein?s Special Theory of Relativity (STR). In the traditional treatment of Einstein?s famous twin paradox, it is argued that the stay at home twin will age more than the ?travelling? twin and the asymmetry is attributed to the fact that the travelling twin?s reference system is not an inertial reference system during the periods of acceleration and deceleration thus making it ?illegal? for the ?travelling? twin to use the STR in their reference system, hence ?resolving? the paradox altogether. From within the domains, confines and provinces of Einstein?s STR, we argue without considering the accelerations and decelerations, where we show that, indeed, it is the ?travelling? twin that is younger at the point of reunion. This brings us to a point of admission that there is indeed a twin who really does the travelling and another that does the staying at home. Hidden within the labyrinth of its seemingly coherent and consistent structure and fabric, does Einstein?s STR imply absolute motion ? we ask?

&lt;p&gt;Zambia has been thriving on hired space technology for telecommunication... more &lt;p&gt;Zambia has been thriving on hired space technology for telecommunication, weather prediction, land and radar surveillance which has resulted into the country spending a lot of money for these technological services. This also compromises the reliability of the space technologies that are being used as the country has no full control over them. This concept note gives an overview of the recent space science activities in Zambia and the efforts being made in developing a guiding national space science policy. We highlight current research in space weather, ionospheric total electron content (TEC) measurements, remote sensing and meteorological predictions. These are linked also to the academic programmes being developed in the leading higher education institutions in the country.&lt;/p&gt;

viXra, 2016

In the year 1928, the pre-eminent British physicist -- Paul Adrien Maurice Dirac, derived his ver... more In the year 1928, the pre-eminent British physicist -- Paul Adrien Maurice Dirac, derived his very successful equation now popularly known as the Dirac equation. This unprecedented equation is one of the most beautiful, subtle, noble and esoteric equations in physics. One of its greatest embellishments is embedded in that this equation exhibits a perfect symmetry -- which amongst others -- requires, that the Universe contain as much matter as antimatter, or that, for every known fundamental particle, there exists a corresponding antiparticle. We show here that the Dirac theory in its bare form -- without the need of the Pauli Exclusion Principle; can -- via, its internal logic -- beautifully explain the stability of the Dirac Void -- i.e., the empty Dirac Sea. There is no need for one to `uglify' Dirac's otherwise beautiful, self-contained and consistent theory by indiscriminately stuffing the Dirac vacuum with an infinite amount of invisible negative energy in-order to prev...

As currently understood, the Dirac theory employs a 4 x1 type wavefunction. This 4x1 Dirac wavefu... more As currently understood, the Dirac theory employs a 4 x1 type wavefunction. This 4x1 Dirac wavefunction is acted upon by a 4x4 Dirac Hamiltonian operator, in which process, four independent particle solutions result. Insofar as the real physical meaning and distinction of these four solutions, it is not clear what these solutions really mean. We demonstrate herein that these four independent particle solutions can be brought together under a single roof wherein the Dirac wavefunction takes a new form as a 4x4 wavefunction. In this new formation of the Dirac wavefunction, these four particle solutions precipitate into three distinct and mutuality dependent particles that are eternally bound in the same region of space. Given that Quarks are readily found in a mysterious threesome cohabitation-state eternally bound inside the Proton and Neutron, we make the suggestion that these Dirac particles might be Quarks. For the avoidance of speculation, we do not herein explore this idea furth...

It is generally assumed that Einstein's General Theory of Relativity (GTR) is silent on the issue... more It is generally assumed that Einstein's General Theory of Relativity (GTR) is silent on the issue of planetary recession such as has been measured recently by Standish (2005); Krasinsky and Brumberg (2004) and as-well by Williams and Boggs (2009); Williams et al. (2004). In this short note, we demonstrate that the GTR is not silent on this matter, it does make a clear predictions albeit, predictions that is contrary with experience and for this task, we use the same solution that was and has been used triumphantly to explain the perihelion precession of the planet Mercury. From a pure standpoint of binary logic, we expect this solution to stand-up to all its predictions for both the precession of perihelion precession and as-well the expansion of orbits. At any rate imaginable, this apparent contradiction presents an interesting state of affairs for the GTR.

This is the second instalment in a four part series, the aim of the work being to introduce absol... more This is the second instalment in a four part series, the aim of the work being to introduce absolute motion into Einstein's Special Theory of Relativity (STR). Herein, we depart from the traditional case where one twin stays put while the other rockets into space, we consider the case of identically accelerated twins. Both twins depart at uniform relativistic speeds in opposite directions for a round trip from the Earth on their 21 th birthday destined into space to some distant constellation that is a distance L 0 in the rest frame of the Earth. A proper application of Einstein's STR tells us that the Earth bound observers will conclude that on the day of reunion, both twins must both have aged the same albeit their clocks (which where initially synchronized with that of the Earth bound observers) will have registered a duration less than that registered by the Earth bound observers. In the traditional twin paradox, it is argued that the stay at home twin will have aged more than the travelling twin and the asymmetry is attributed to the fact that the travelling twin's frame of reference is not an inertial reference frame during the periods of acceleration and deceleration making it "illegal" for the travelling twin to use the STR in their frame, thus "resolving" the paradox. This same argument does not hold in the case considered here as both twins will undergo identical experiences where each twin sees the other as the one that is in motion. This means, each twin must conclude that the other twin is the one that is younger. They will conclude that their ages must be numerically different, thus disagreeing with the Earth bound observers that their ages are the same. This leads us to a true paradox that throws Einstein's Philosophy of Relativity into complete disarray. "Our most trustworthy safeguard in making general statements. .. is imagination. If we can imagine the breaking of a Law of Physics-then, it is in some degree an Empirical Law. With a purely Rational Law we could not conceive an alternative. This ultimate criterion serves as an anchor to keep us from drifting unduly in a perilous sea of thought."

×ØÖ Øº This reading is a continuation of the earlier reading Nyambuya (2008); where three new Cur... more ×ØÖ Øº This reading is a continuation of the earlier reading Nyambuya (2008); where three new Curved Spacetime Dirac Equations have been derived mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of fermions and the suggestions is that particles including the Electron, which is thought to be a point particle, do have a finite spatial size and this is one of the reasons for the observed anomalous gyromagnetic ratio. Combining the idea in Nyambuya (2008) which lead to the derivation of the three new Curved Spacetime Dirac Equations, and the proposed Unified Field Theory (Nyambuya 2007), a total of 12 equations each with 16 sub-components are generated thus leading to a total of 192 equations for the Curved Spacetime Dirac Equation. Some symmetries of these equations are investigated, i.e., the Lorentz symmetry, charge conjugation symmetry (C), time reversal symmetry (T), Space reversal (P) and a combination of the C, P &T-symmetries. It is shown that these equations are Lorentz invariant, obey C-symmetry and that some violate T and P-symmetry while others do not and that they all obey PT-symmetry. These symmetries show (or modestly said-seem to suggest) that anti-particles have positive mass and energy but a negative rest-mass and the opposite sign in electronic charge. Through the inspection of these symmetries, a suggestion is (here) made to the effect that the rest-mass of a particle must be related to the electronic charge of that particle thus leading us to a possible resolution of whether or not Neutrinos do have a none-zero rest-mass. Additionally, we demonstrate that these equations have the potency to explain naturally the observed lepton generation phenomena.

The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a sin... more The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a single roof via an extension of Reimann geometry to a new geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both the length and the angle of a vector under parallel transport. The affine connection of this new geometry-the Reimann-Hilbert Space, is a tensor and this leads us to a geodesic law that truly upholds the Principle of Relativity. The geodesic law emerging from the General Theory of Relativity (GTR) is well known to be in contempt of the Principle of Relativity which is a principle upon which the GTR is founded. The geodesic law for particles in the GTR must be formulated in special (or privileged) coordinate systems i.e. gaussian coordinate systems whereas the Principle of Relativity clearly forbids the existence of special (or privileged) coordinate systems in manner redolent of the way the Special Theory of Relativity forbids the existence of an absolute (or privileged) frame of reference. In the low energy regime and low spacetime curvature the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the none-abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac Equation. Further, to the already existing four known forces, the theory predicts the existence of yet another force. We have coined this the super-force and this force obeys S U(4, 4) gauge invariance. Furthermore, unlike in the GTR, gravitation is here represented by a single scaler potential, and electromagnetic field and the nuclear forces are described by the electromagnetic vector potential (A µ) which describes the metric tensor i.e. g µν = A µ A ν. From this (g µν = A µ A ν), it is seen that gravity waves may not exist in the sense envisaged by the GTR.

In an earlier reading, we argued from a physical and number theoretic standpoint that an upper bo... more In an earlier reading, we argued from a physical and number theoretic standpoint that an upper bound speed limit such as the speed of light implies the existence of a lower limit to the duration of events in the Universe. Consequently, this leads to a minimum characteristic length separation for events in the Universe. Herein, we argue that matter and energy that is in compliance with and in observance of the upper bound light speed limit is governed by the lower limiting uncertainty principle of Professor Werner Heisenberg. If there is a lower limiting uncertainty principle, we ask the natural and logical question 'What would an upper bound uncertainty principle mean?' We come to the interesting conclusion that an upper bound uncertainty principle must apply to particles that travel at speeds, equal to, or greater than the speed of light. Further, we argue that consequently, a tachyon must exist in a permanent state of confinement and must be intrinsically and inherently unstable in which event it oscillates between different states. These two requirements place quarks in a position to be good candidates for tachyons.

This reading expounds with expediency on the recently proposed Azimuthally Symmetric Theory of Gr... more This reading expounds with expediency on the recently proposed Azimuthally Symmetric Theory of Gravitation (ASTG) setup earlier. At its inspection, it was demonstrated that the ASTG is capable (among others solar anomalies) of explaining the precession of the perihelion of solar planets. In the present, we show that the ASTG is capable of explaining the puzzling observations of flyby anomalies, i.e. the anomalous asymptotic speed increases of the osculating hyperbolic speed excess. It is shown that these flyby anomalies occur naturally in the ASTG. We derive the empirical formula proposed by Anderson et al. in 2008, which up to now has no physical or foundational basis except that experience suggest it. If the ASTG model is correct, then for the first time the Anderson et al. formula is given a physical meaning.

This is the first instalment in a four part series, the aim of the work being to introduce absolu... more This is the first instalment in a four part series, the aim of the work being to introduce absolute motion into Einstein's Special Theory of Relativity (STR). In the traditional treatment of Einstein's famous twin paradox, it is argued that the stay at home twin will age more than the "travelling" twin and the asymmetry is attributed to the fact that the travelling twin's reference system is not an inertial reference system during the periods of acceleration and deceleration thus making it "illegal" for the "travelling" twin to use the STR in their reference system, hence "resolving" the paradox altogether. From within the domains, confines and provinces of Einstein's STR, we argue without considering the accelerations and decelerations, where we show that, indeed, it is the "travelling" twin that is younger at the point of reunion. This brings us to a point of admission that there is indeed a twin who really does the travelling and another that does the staying at home. Hidden within the labyrinth of its seemingly coherent and consistent structure and fabric, does Einstein's STR imply absolute motion-we ask? This is the question that we leave hanging in the mind of the reader. In the next reading, we propose a new version of the twin paradox, where the scenario is truly symmetric from either of the twin's reference systems-we have coined this, the "Symmetric Twin Paradox (STP)". This version (STP) unearths an irretrievable contradiction hidden at the deepest and subtle level of Einstein's STR. It is shown that Einstein's STR is unable to resolve this irretrievable contradiction, even if the accelerations and decelerations are taken into. Not even Einstein's General Theory of Relativity can be brought to the rescue in the case of the STP. In our third instalment, we shall setforth a new version of the STR where absolute motion is permitted. This version solves the symmetric twin paradox and any known paradox of relativity. Lastly, we apply this new STR where absolute motion is permitted to experimental efforts that have been made to measure absolute motion. Most well trained physicists tend to ignore completely, readings purporting to go against Einstein's STR. We would like to persuade our reader to make a brief stop and consider for a minute, what we have to say in our four part series of readings. "At the heart of science is an essential balance between two seemingly contradictory attitudes-an openness to new ideas no matter how bizarre or counterintuitive they may be, and the most ruthless skeptical scrutiny of all ideas, old and new. This is how deep truths are winnowed from deep nonsense."-Carl Sagan (1934 − 1996) * When Einstein first submitted his revolutionary paper, its initial title was "The Theory of Invariants". Planck, a founder and the first editor of the * See e.g. http://twinparadox.net/, visited on this day 14 Aug. 2013@15h55 GMT+2. A survey and perusal of this site will-amongst others, reveal why the Twin Paradox can not be considered a solved problem. Debates on this problem are still very much alive.

In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purp... more In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purpose of this reading is to make a valid and justified mathematical modification to the Dirac Equation so that it describes any spin particle. We show that this mathematical modification is consistent with the Special Theory of Relativity (STR). We believe that the fact that this modification is consistent with the STR gives the present effort some physical justification that warrants further investigations. From the vantage point of unity, simplicity and beauty, it is natural to wonder why should there exist different equations to describe particles of different spins? For example, the Klein-Gordon equation describes spin-0 particles, while the Dirac Equation describes spin-1/2, and the Rarita-Schwinger Equation describes spin-3/2. Does it mean we have to look for another equation to describe spin-2 particles, and then spin-5/2 particles etc? This does not look beautiful, simple, or at the very least suggest a Unification of the Natural Laws. Beauty of a theory is not a physical principle but, one thing is clear to the searching mind-i.e., a theory that possesses beauty, appeals to the mind, and is (posteriori) bound to have something to do with physical reality if it naturally submits itself to the test of experience. The effort of the present reading is to make the attempt to find this equation.

We take – albeit, with an all-important and subtle difference; a closer and meticulous look at th... more We take – albeit, with an all-important and subtle difference; a closer and meticulous look at the motion of light in a Newtonian gravitational field in exactly the same manner as has been conducted by past researchers leading them to conclude that for light grazing the limb of the Sun, its path must suffer a deflection of ∼ 0.875 ′′ from its otherwise straight path. The difference between our approach and that of past researchers, is that, at the outset of the derivation of the resultant equations of motion, we do not assume the equity of gravitational (mg) and inertial mass (mi). The ratio of the gravitational to inertial mass (γ = mg/mi) is persistent in the equations, it does not cancel out or disappear. Eventually, this ratio emerges in the final equations of motion. When these resultant equations of motion are inspected, it is seen that the factor two difference needed to bring Newtonian gravitation into harmony with observations can be attributed to a photon’s gravitational to inertial mass ratio. This leads us directly to question the validity of the equivalence principle. This finding, we believe, demonstrates or hints to a much deeper reality that the gravitational and inertial mass, may – after all; not be equal as we have come to strongly believe. This rather disturbing (perhaps exciting) conclusion, if correct; may direct us to closely re-examine the validity of Einstein’s central tenant – the Equivalence Principle, which stands as the strong foundational basis of his beautiful and celebrated General Theory of Relativity (GTR).

The General Theory of Relativity (GTR) is essentially a theory of gravitation. It is built on the... more The General Theory of Relativity (GTR) is essentially a theory of gravitation. It is built on the Principle of Relativity. It is bonafide knowledge, known even to Einstein the founder, that the GTR violates the very principle upon which it is founded i.e., it violates the Principle of Relativity; because a central equation i.e., the geodesic law which emerges from the GTR, is well known to be in conflict with the Principle of Relativity because the geodesic law, must in complete violation of the Principle of Relativity, be formulated in special (or privileged) coordinate systems i.e., Gaussian coordinate systems. The Principle of Relativity clearly and strictly forbids the existence/use of special (or privileged) coordinate systems in the same way the Special Theory of Relativity forbids the existence of privileged and or special reference systems. In the pursuit of a more Generalized Theory of Relativity i.e., an all-encampusing unified field theory to include the Electromagnetic, Weak & the Strong force, Einstein and many other researchers, have successfully failed to resolve this problem. In this reading, we propose a solution to this dilemma faced by Einstein and many other researchers i.e., the dilemma of obtaining a more Generalized Theory of Relativity. Our solution brings together the Gravitational, Electromagnetic, Weak & the Strong force under a single roof via an extension of Riemann geometry to a new hybrid geometry that we have coined the Riemann-Hilbert Space (RHS). This geometry is a fusion of Riemann geometry and the Hilbert space. Unlike Riemann geometry, the RHS preserves both the length and the angle of a vector under parallel transport because the affine connection of this new geometry, is a tensor. This tensorial affine leads us to a geodesic law that truly upholds the Principle of Relativity. It is seen that the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the non-Abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac equation.

Herein, we argue that the observed +38 mm/yr secular Lunar drift from the Earth does-to an admira... more Herein, we argue that the observed +38 mm/yr secular Lunar drift from the Earth does-to an admirable degree of agreement between theory and observations; explain the observed secular increase in the Lunar eccentricity. At present, the recession of the Moon from the Earth is not any more considered as an anomaly as this is believed to be well explained by conventional physics of Lunar-Earth tides. However, the same is not true when it come to the observed increase in the Lunar eccentricity which is considered to be an anomaly requiring an explanation as to what is the cause behind this phenomenon. We not only demonstrate an intimate connection between these two seemingly unrelated phenomenon, but show that the intimate relationship that we deduce fits so well with observations to a point that-logic dictates that, the Lunar drift must surely be the cause of the secular increase in the Lunar eccentricity.

Exactly 100 years ago, German scientist-Alfred Lothar Wegener, sailed against the prevailing wisd... more Exactly 100 years ago, German scientist-Alfred Lothar Wegener, sailed against the prevailing wisdom of his day when he posited that not only have the Earth's continental plates receded from each other over the course of the Earth's history, but that they are currently in a state of motion relative to one another. To explain this, Wegener setforth the hypothesis that the Earth must be expanding as a whole. Wegener's inability to provide an adequate explanation of the forces and energy source responsible for continental drift and the prevailing belief that the Earth was a rigid solid body resulted in the acrimonious dismissal of his theories. Today, that the continents are receding from each other is no longer a point of debate but a sacrosanct pillar of modern geology and geophysics. What is debatable is the energy source driving this phenomenon. An expanding Earth hypothesis is currently an idea that is not accepted on a general consensus level. Antiproponent of the expanding Earth mercilessly dismiss it as a pseudo or fringe science. Be that it may, we show herein that from the well accepted law of conversation of spin angular momentum, Stephenson & Morrison (1995)'s result that over the last 2700 years or so, the length of the Earth's day has undergone a change of about +17.00 µs/yr, this result invariably leads to the fact the Earth must be expanding radially at a paltry rate of about +0.60 mm/yr. This simple fact, automatically move the expanding Earth hypothesis from the realm of pseudo or fringe science, to that of real and ponderable science.

Advances in Pure Mathematics, 2016

English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and c... more English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat's Last Theorem which had for 358 years notoriously resisted all gallant and spirited efforts to prove it even by three of the greatest mathematicians of all time-such as Euler, Laplace and Gauss. Sir Professor Andrew Wiles's proof employs very advanced mathematical tools and methods that were not at all available in the known World during Fermat's days. Given that Fermat claimed to have had the 'truly marvellous' proof, this fact that the proof only came after 358 years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat's time, this has led many to doubt that Fermat actually did possess the 'truly marvellous' proof which he claimed to have had. In this short reading, via elementary arithmetic methods, we demonstrate conclusively that Fermat's Last Theorem actually yields to our efforts to prove it. This proof is so elementary that anyone with a modicum of mathematical prowess in Fermat's days and in the intervening 358 years could have discovered this very proof. This brings us to the tentative conclusion that Fermat might very well have had the 'truly marvellous' proof which he claimed to have had and his 'truly marvellous' proof may very well have made use of elementary arithmetic methods. "Fermat said he had a proof. I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.