New Approach to the General Theory of Relativity
by Jorge A. Franco Rodríguez
Electrical Engineer. Universidad Central de Venezuela (1975).
Master of Electrical Eng. Carleton University. Ottawa. Canada (1984).
Senior Member, IEEE. Communications and Information Theory Societies.
Edition: 4.7
Created: September 1998. Last Modified: Aug. 16, 2006.
URL: http//www.geocities.com/CapeCanaveral/Launchpad/6638/
shortcut URL: http://www.geocities.com/jorgefranco.geo/
Postal Address: Av. Libertador. Edificio Zulia, Piso 12. Apto. No. 123. Caracas 1050 Venezuela.
Preface.
This is a controversial work because it shows that Einstein was wrong in his definition of relativistic mass. This is a very strong statement, I know, but I think I have found a consistent and firm way to define the relativistic mass, and, I believe it had come from solid concepts. The problem with this is that all physics depends on this definition. As a consecuence, I had to redefine some concepts in Dynamics (the same thing occurred after Einstein had given his own mass definition: all physics had to be redefined).
The main body of this work (the first three parts) had been done between January '96 and September '96. After that, it was revised, corrected and ampled until December '97 (the last five parts), although Parts 5 and 8 have really been completed in May 99.
This last version, had been many times revised (with the help of some friends), before I have the boldness of presenting it to the scientific community, by using this fabulous mean as it is the internet pages. I would like to express my profound gratitude to Geocities for presenting me with the opportunity to promote this work. I hope not to be wrong!. If that is so (that I am in a correct way!), I believe I have to wait for a long, long time, before someone has the bravery (and luck) of demonstrating that in fact there is something wrong in Einstein's mass definition.
Before I put it in Geocities, I had sent it to many persons, and also to some authorized publications and I have not had any response. I think that this attitude responds to that Einstein's work has become untouchable and completely accepted, then, if anyone obtains that the Einstein's mass definition is erroneous, the obvious conclusion is that it is useless to spend time reading such work and that this guy must be crazy. What is worst, by reading the presentation of this page, someone can think: But, he is only an engineer!. No problem, I am glad that at least, already these notes are a public document through Internet, thanks Geocities. This means that they could be in the private library of each one of you, for studying, supporting and/or critizicing them, any time, anywhere.
In general, the presentation of this work admits that the reader can do his own calculations in order to check what is stated. But, it supposes the reader knows the basic concepts of Lorentz's Transformations, and has the normal comprehension of math and physics obtained in the secondary school. It is not necessary to know Tensor Calculus, Riemann Spaces nor Manifolds.
Also, I ask for your patience when reading my english.
Any comments will be highly appreciated. Please, send them to [email protected]. If you have any observation or you discover typing or conceptual errors in this work, it will be good for me to know them, in order to correct them, or realize that I have been working on wrong concepts, and that I have to discard this work because it is erroneous.
Registered in August 6, 1996, under the No. 00333 in the "Registro de la Propiedad Intelectual de la República Bolivariana de Venezuela" (Renewed in May 9, 1999).
Note: I have a new page in where I have tried to correct and simplify some of the lackings, mistakes and conceptual errors I did in this first work. I did not want to close this page because I wanted to leave a track about this work, in order to have a little bit of history. This page will have a better presentation with the articles in pdf. It will be available in November 2006
INDEX
--Lorentz transformation applied to rectilinear motion.
--Lorentz transformation applied to a curvilinear motion in two dimensions.
--Constancy of the speed of light.
--Lorentz transformation applied to three dimensional curvilinear motion.
--New definition of mass.
--Total Energy and Momentum.
--Demonstration that Einstein's definition of mass is wrong.
--Relativistic relationships between Physical Magnitudes.
--Discussion about the velocity of displacement of Fields.
--Conclusion.
--Bending of Light.
--Particular correction to Newton's Universal Gravitation Law.
--Two masses rotating around their Center of Mass.
--Derivation of the expression of equivalent mass Me.
--Three or more attracting masses in motion.
--General correction to Newton's Universal Gravitation Law.
--Precession.
--Are Black Holes visible?.
--How Black Holes looks like?
--Quantum Theory of Light.
--De Broglie's Wave-Particle Duality (1924).
--Schrödinger's Equation (1926).
--Modified Schrödinger's Equation.
--Conclusion.
--Effect of the Electric, Magnetic and Gravitationals fields on a pure mass m.
--Effect of the Electric, Magnetic and Gravitational fields on a pure charge +q.
--Field produced by a photon.
--Field produced by a moving mass m.
--Curl of the Gravitational Field produced by a moving mass M.
--Gravitational waves do not exist!.
--Divergence of the Gravitational Field produced by a moving mass M.
--Two more Maxwell Equations.
--Conclusion
Introduction.
The concept of the variation of mass with its velocity, in rectilinear motion, m = Mo/(1 - v²/c²)1/2 , was established by Einstein in 1.905 (transversal mass). The dependence of the mass of a body with its velocity was one of the major outcomes of the Special Theory of Relativity, but the known relationship was obtained by Einstein from the classical concept of force, see Cincuant' Anni di Relativitá, 1905-1955, page 97, 1955:
"La definizione della forza qui data non è vantaggiosa, come per primo fu dimostrato da M. Planck. È assai più utile definire la forza in modo che il teorema dell'impulso e il teorema dell'energia assumano la forma piu semplice"
The possibility that this result be in error exists and at this moment there is not a convincible demonstration of its validity, General Relativity, Foster&Nightingale, 1979. page 176:
"It should be noted that we have not proved the celebrated formula E = g.m.c²; it simply follows from our defining E by p° = E/c.
Although this definition is standard in relativity, it is sensible to ask how it ever came about... "
In this work was obtained a new definition of mass, m = Mo/(1 - v²/c²)3/2, that coincides with the longitudinal mass also obtained by Einstein, but after discarded in his work.
The main idea followed in this work was the development of Lorentz transformation for a curvilinear motion in order to apply the Conservation of Angular Momentum Law and so to arrive at the previously mentioned definition of mass.
In Part 1, Lorentz transformation for Curvilinear Motion, in two and three dimensions, was achieved. Internal Angular Momentum (angular momentum measured respect to the center of mass of the system) for solid masses was developed and applied to curvilinear motion. From this, the "new" definition of mass was obtained.
In part 2, Total Energy, Kinetic Energy and Momentum of a body were redefined, which, at low speed of the bodies respect to the speed of light, reduce to the known classical expressions. The obtained relativistic new expressions of Energy and Momentum, when applied to particles without rest mass, also reduce to those currently used. Also, it is presented the variance or invariance of some physical magnitudes measured respect to the center of mass of the system under the obtained Lorentz transformations for curvilinear motion.
In Part 3, is demonstrated that the effect of Gravitational Field is instantaneous over all the space around the mass producing it. This surprising result, easily explains why gravitational forces are central. It is concluded, in general, that all kind of fields or forces have instantaneous effect, or a displacement at infinite speed. This fact joined to the restriction that particles or waves cannot go at a speed greater than that of light produce the conclusion that the property of that central forces, or forces in general, be conveyed by particles (Graviton, Gluon, Magneton, Photon, Bosons) is not true.
In Part 4, is discussed how application of Newton's equation of Universal Gravitation to the calculation of deflection of light conduces to an inconsistency. From this discussion a particular modification of the Law of Universal Gravitation for photons in movement was obtained, which reduces to its classical expression when movement is circular or radial.
In Part 5, General equations governing the movement of two or more bodies attracting among them with gravitational forces, were obtained. A general expression of the Law of Universal Gravitation for bodies in movement was obtained, similar to that obtained in Part 4. Applying it to the movement of attracting bodies a new expression of Precession was achieved.
In Part 6, is demonstrated that photons can be emitted from black holes. A modification of the Schwarzchild Radius was obtained. The expression of the maximum angle, respect to the radial line, in which photons can leave the black hole was calculated. From these results a discussion of the characteristics of photons imprinting telescopes at earth coming from black holes is done, and how to distinguish them among common stars, is presented. Examples of these bodies in the universe, responding to such characteristics, are given.
In Part 7, the new expression for kinetic energy was introduced in the Schrödinger's equation, giving a new shape to this equation. The Relativistic Hamiltonian was easily obtained, thanks the direct and explicit dependence on velocity of kinetic energy present in our equation, and the quantum operators correlated to, appear to be equal to those of Quantum Mechanics (except for the quantum operator of Energy). In this sense, the quantum-relativistic view of matter in an unified, exact and simple manner was achieved.
In Part 8, the Curl and Divergence of the Gravitational Field were obtained. The obtained espressions of these equations leads to the conclusion that Gravitational waves do not exist!.
See you later!
© 1997 [email protected]
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