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4dimensional optics, an alternative to relativity
, 2001
"... Received dd.mm.yyyy, accepted dd.mm.yyyy by ue Abstract. The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4dimensional space where time intervals are always a measure of geodesic arc lengths, i.e. c 2 ( ..."
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Cited by 6 (6 self)
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Received dd.mm.yyyy, accepted dd.mm.yyyy by ue Abstract. The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4dimensional space where time intervals are always a measure of geodesic arc lengths, i.e. c 2 (dt) 2 = gαβdx α dx β, with c is the speed of light in vacuum, t time, gαβ and the metric tensor; x α represents any of 4 space coordinates. The last 3 coordinates (α = 1, 2,3) are immediately associated with the usual physical space coordinates, while the first coordinate (α = 0) is later found to be related to proper time. The work shows that this principle is applicable in several important situations and suggests that the underlying principle can, in fact, be used universally. Starting with special relativity it is shown that there is perfect mapping between the geodesics on Minkowski spacetime and on this alternative space. The discussion than follows through light propagation in a refractive medium, and some cases of gravitation, including Schwartzschild’s outer metric. The last part of the presentation is dedicated to electromagnetic interaction and Maxwell’s equations, showing that there is a particular solution where one of the space dimensions is eliminated and the geodesics become equivalent to light rays in geometrical optics. A very brief discussion is made of the implications for waveparticle duality and quantization.
Can physics laws be derived from monogenic functions?, 2006, will appear in a book by Hadronic
"... This is a paper about geometry and how one can derive several fundamental laws of physics from a simple postulate of geometrical nature. The method uses monogenic functions analysed in the algebra of 5dimensional spacetime, exploring the 4dimensional waves that they generate. With this method one ..."
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This is a paper about geometry and how one can derive several fundamental laws of physics from a simple postulate of geometrical nature. The method uses monogenic functions analysed in the algebra of 5dimensional spacetime, exploring the 4dimensional waves that they generate. With this method one is able to arrive at equations of relativistic dynamics, quantum mechanics and electromagnetism. Fields as disparate as cosmology and particle physics will be influenced by this approach in a way that the paper only suggests. The paper provides an introduction to a formalism which shows prospects of one day leading to a theory of everything and suggests several areas of future development. 1
Dimensions in Special Relativity Theory a Euclidean Interpretation*
, 2005
"... A Euclidean interpretation of special relativity is given wherein proper time τ acts as the fourth Euclidean coordinate, and time t becomes a fifth Euclidean dimension. Velocity components in both space and time are formalized while their vector sum in four dimensions has invariant magnitude c. Clas ..."
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A Euclidean interpretation of special relativity is given wherein proper time τ acts as the fourth Euclidean coordinate, and time t becomes a fifth Euclidean dimension. Velocity components in both space and time are formalized while their vector sum in four dimensions has invariant magnitude c. Classical equations are derived from this Euclidean concept. The velocity addition formula shows a deviation from the standard one; an analysis and justification is given for that.
Maxwell’s equations in 4dimensional Euclidean space
, 2004
"... Abstract. The paper formulates Maxwell’s equations in 4dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector g0. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry radically different from that of special relativity, t ..."
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Cited by 1 (0 self)
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Abstract. The paper formulates Maxwell’s equations in 4dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector g0. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry radically different from that of special relativity, the paper derives relativistic electrodynamics from space curvature. Maxwell’s equations are then formulated and solved for free space providing solutions which rotate the vector potential on a plane; these solutions are shown equivalent to the usual spacetime formulation and are then discussed in terms of the hypersphere model of the Universe recently proposed by the author. PACS numbers: 41.20.Jb, 02.40.Dr, 04.20.CvMaxwell’s equations in 4dimensional Euclidean space 2 1.
A theory of mass and gravity in 4dimensional optics
, 2001
"... The paper deals with the concepts of mass and gravity in the formalism of 4dimensional optics, previously introduced by the author. It is shown that elementary particles can be associated with 4dimensional standing wave patterns with the Compton wavelength and both inertial and gravitational mass ..."
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The paper deals with the concepts of mass and gravity in the formalism of 4dimensional optics, previously introduced by the author. It is shown that elementary particles can be associated with 4dimensional standing wave patterns with the Compton wavelength and both inertial and gravitational mass are derived from this concept and shown to be attributable to an waveguide laid along the particle’s worldline; the same formalism is shown to accommodate also mass due to binding energy within compact bodies. Momentum exchange with accelerated bodies through gravitons is discussed and shown similar to mode exchange in optical fibers. Reported anomalies on the behaviour of the Foucault pendulum, both periodic and exceptional on the occasion of solar eclipses, are explained not only qualitatively but also on order of magnitude, resorting to graviton exchanges between Earth and the Sun or the Moon. It is argued that these effects provide experimental evidence of gravitons. 1
Kcalculus in 4dimensional optics
, 2002
"... 4dimensional optics is based on the use 4dimensional movement space, resulting from the consideration of the usual 3dimensional coordinates complemented by proper time. The paper uses the established Kcalculus to make a parallel derivation of special relativity and 4dimensional optics, allowing ..."
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4dimensional optics is based on the use 4dimensional movement space, resulting from the consideration of the usual 3dimensional coordinates complemented by proper time. The paper uses the established Kcalculus to make a parallel derivation of special relativity and 4dimensional optics, allowing a real possibility of comparison between the two theories. The significance of proper time coordinate is given special attention and its definition is made very clear in terms of just send and receive instants of radar pulses. The 4dimensional optics equivalent to relativistic Lorentz transformations is reviewed. Special relativity and 4dimensional optics are also compared in terms of Lagrangian definition of worldlines and movement Hamiltonian. The final section of the paper discusses simultaneity through the solution of a two particle headon collision problem. It is shown that a very simple graphical construction automatically solves energy and momentum conservation when the observer is located at the collision position. A further discussion of the representation for a distant observer further clarifies how simultaneity is accommodated by 4DO. Keywords: Kcalculus; alternative theories; 4dimensional optics; special relativity. 1
unknown title
, 2001
"... Received dd.mm.yyyy, accepted dd.mm.yyyy by ue Abstract. The paper deals with the concepts of mass and gravity in the formalism of 4dimensional optics, previously introduced by the author. It is shown that elementary particles can be associated with 4dimensional standing wave patterns with the Com ..."
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Received dd.mm.yyyy, accepted dd.mm.yyyy by ue Abstract. The paper deals with the concepts of mass and gravity in the formalism of 4dimensional optics, previously introduced by the author. It is shown that elementary particles can be associated with 4dimensional standing wave patterns with the Compton wavelength and both inertial and gravitational mass are derived from this concept and shown to be attributable to an waveguide laid along the particle’s worldline; the same formalism is shown to accommodate also mass due to binding energy within compact bodies. Momentum exchange with accelerated bodies through gravitons is discussed and shown similar to mode exchange in optical fibers. Reported anomalies on the behaviour of the Foucault pendulum, both periodic and exceptional on the occasion of solar eclipses, are explained not only qualitatively but also on order of magnitude, resorting to graviton exchanges between Earth and the Sun or the Moon. It is argued that these effects provide experimental evidence of gravitons.