![]() ![]() ![]() In order to let the sun shine there needs the absorbers. Wave can be supposed, but it is clear that the particle cannot be supposed.įeynman and his doctor father Wheeler tell us if the space is empty, the sun cannot shine. Radiation is a very complicated phenomena, our today's theory still does not answer the problem of wave-particle duality problem. Can the retarded wave and advanced wave be supposed? This is not clear. This current should produce some wave, if this wave is retarded wave, the receiving antenna actually is a transmitting antenna but not a receiving antenna. We know there is current in the receiving antenna when it receives wireless waves. The mutual energy flow theorem also supports the advanced wave. However the absorber theory of Wheeler and Feynman, Transactional interpretation of John Cramer supports the advanced wave. Most scientists do not accept the advanced wave because of the causality problem. The receiving antenna sends the advanced wave. As I know the transmitting antenna sent retarded wave. They are the solutions of Maxwell equations. However it is difficult to prove the radiation field can be superposed.įor radiation fields, there are two kind of fields retarded potential and advanced potential. Hence Lorenz should get the respect similar to Maxwell.Īs I know the suppositions of the static field electric field and static electric magnetic field is self-explained. Lorenz introduce the retarded potential is base on his study in optic and elastic wave. The concept of retarded potential is equivalent to the displacement current of Maxwell. He also introduced retarded potential in the same paper. Only a few years later than Maxwell's theory. Lorenz gauge should be as 5th Maxwell equations. Hence in order to solve the electromagnetic problem, Lorenz gauge is required. ![]() Hence superposition principle is an independent principle. Actually Maxwell equation + Lorenz gauge + superposition principle together solve the current electromagnetic problems. Maxwell's equations did not answer all electromagnetic theory. what piece of knowledge is fundamental rather than derived). When we learn all this physics today we sometime forget the history, how our knowledge is connected to history, and what comes first (i.e. This is how we know that the field behaved linearly. The more fundamental equation is Coulomb's law, which was discovered as an empirical law, along with its linearity, by experiments conducted by Coulomb. You state using Gauss' law to calculate the field. Once you "prove" that a set of equations is in fact linear you can immediately apply this result. The proof can be found in most math texts on ordinary or partial differential equations, also linear algebra or operator theory. Linearity means that if F1 is a solution for S1, and F2 is a solution for S2 then F1 + F2 is a solution for S1 + S2. Where D() is some abstract differential linear operator. Maxwell's equations are just one of many that fall into this category. It is a mathematical principle and it holds for any linear equation or system of equations. Paris 116 (1893), 964.To put it simply superposition does NOT follow from Maxwell's equations. Guldberg, A.: Sur les équations différentielles que possedent un système fundamental d'intégrales, C.R. Vessiot, E.: Sur une classe d'équations différentielles, Ann. E.: Introduction to Lie Algebras and Representation Theory, Springer, New York, 1972. Jacobson, N.: Lie Algebras, Interscience Publishers, New York, 1961. and Winternitz, P.: Classification of systems of ordinary differential equations with superposition principles, J. Winternitz, P.: Comments on superposition rules for nonlinear coupled first-order differential equations, J. Wolf (ed.), Nonlinear Phenomena, Lecture Notes in Phys. Winternitz, P.: Lie groups and solutions of nonlinear differential equations, In: K. and Marle, Ch.-M.: Symplectic Geometry and Analytical Mechanics, D. ![]() Lie, S.: Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen (revised and edited by Dr G. and Norman, E.: On global representations of the solutions of linear differential equations as a product of exponentials, Mem. and Norman, E.: Lie algebraic solution of linear differential equations, J. and Ramos, A.: Integrability of Riccati equation from a group theoretical viewpoint, Internat. F.: Related operators and exact solutions of Schrödinger equations, Internat. and Nasarre, J.: The nonlinear superposition principle and the Wei-Norman method, Internat. M.: A generalization of Lie's 'counting' theorem for second-order ordinary differential equations, J. ![]()
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