![]() The key point is that the local symmetry group in QED, which is U(1), is Abelian. In quantum electrodynamics(QED), there is one gauge field called the photon and is denoted by $A_\mu$. Interactions in a theory are mediated by gauge fields. The answer to why you could add electric fields in the first place, or more precisely, what causes the equations of motion to become linear (instead of something else random), comes from symmetry. It needs to be tested again and again in case there is some new theory developed in electromagnetic field theory or quantum mechanics.įirst, superposition principle and linearity is the same thing, exactly how Code wrote in a comment above. Summary: Maxwell theory is not a complete theory (Otherwise do not need QET), superposition principle should be an independent principle to Maxwell equations. Can this kind wave be supposed? It is not clear. As I know the wave collapse is related to the concept of time-reversal waves. The wave collapse process if it exists should be some kind of waves. Anyway superposition principle is not tested like Coulomb's law. There are some publications that tell us the supposition principle is correct at 15%, (I forget the cite place). If something is wrong we first need to test whether or not the superposition principle is correct. ![]() This means something is wrong in classical electromagnetic field theory. Our current electromagnetic field theory (Maxwell theory) did not reflect this point of view. 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. To put it simply superposition does NOT follow from Maxwell's equations.
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