Comment on feynman s proof of the maxwell equations by. Exact form of maxwells equations and diracs magnetic. Comment on feynman s proof of the maxwell equations by f. Feynmans derivation is wonderful, and i want to sketch why we would expect it to work, and what implicit assumptions its really making. Feynmans lectures are much more complete in that sense, even though as other comments on this thread note, the reader may not be able to use the learning to solve practical problems without going beyond feynmans. However, the proof of generalized maxwell equations involves some subtleties which remain unanswered. Feynman s proof of maxwell s equations get a copy of the paper feynman s proof of maxwells equations by freeman dyson published in ajp 58 3 march 1990. Relationship between magnetic field and defects field.
Derivation of maxwells equations via the covariance. Silagadze budker institute of nuclear physics and novosibirsk state university, 630 090, novosibirsk, russia mechanical maxwells demons, such as smoluchowskis trapdoor and feynmans ratchet and pawl need external energy source to operate. First we have the maxwell equationswritten in both the expanded form and the short mathematical form. Four simple vector equations or one tensor equation and an asssociated dual describe the uni. The basic equations of electromagnetism which are a collection of gausss law for electricity, gausss law for magnetism, faradays law of electromagnetic induction and amperes law for currents in conductors are called maxwell s equations. Feynmans proof of the maxwell equations, discovered in 1948 but never published, is here put on record, together with some editorial. Feynman nobel lecture nobel lecture, december 11, 1965. Dyson a proof of the lorentz force law and the homogeneous maxwell equations, which he obtained starting from newtons law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. We should remark, however, that there is an interesting consequence to this additional assumption.
I have seen a number of derivations of maxwells equations but this is the shortest, most illuminating and best i have come across it basically just uses covarience and as it says a little bit. We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. I was recently reading the paper feynmans derivation of maxwells equations and extra dimensions and the derivation of the maxwells equations from just newtons second law and the quantum mechanical commutation relations really intrigued me. Interesting derivation of maxwells equations physics forums. This video recounts a lecture by richard feynman giving an elementary demonstration of why planets orbit in ellipses. A version of this result is found to hold in classical mechanics, and it is shown that instead of. Get a copy of the paper feynmans proof of maxwells equations by freeman dyson published in ajp 58 3 march 1990. Maxwells theory based on faradays field lines concept employs only rank1 equations, for example the divergence of the electric field strength, e, is directly proportional to the charge density, q charge density is here defined as the charge per unit surface area, not the charge per unit volume. Derived equations are required to be covariant, and a simplicity criterion requires that the fourvector force on a charged particle be linearly related.
In particular tanimura2 has generalized the feynmans derivation in a lorentz covariant form with. Commutation relations in qm 2nd or 3rd year undergraduate to make the desired connection, one must have seen maxwells equations which some first year undergraduate physics textbooks include. But such generalizations are against the spirit of feynman s original derivation because they involve additional. In particular, the equation for the magnetic field of steady currents was known only as \beginequation \labeleq. Derivation of the maxwell equations and the relation. Work supported by department of energy contract deac0376sf00515. Did feynman ever say he tried to derive relativity himself. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. Maxwells equations are a set of linear partial differential equations that give the relationship between the classical electromagnetic field and its sources charge and current density. Feynmans proof of the maxwell equations hacker news. And then we present another derivation method using dirac decomposition, introduced by gersten 1998. Although maxwells equations would allow either possibility, we will put in an additional factbased on experiencethat only the outgoing wave solution makes physical sense.
The main focus of the present work is to study the feynmans proof of the maxwell equations using the nc geometry framework. One of these is the proper identi cation of evolution parameter which makes interpretation rather unclear. Together with the lorentz force law, they contain the entir. There are so many times that something leaves you stumped. The final chapter is about inducing electric and magnetic wave equations from maxwells equations.
The discovery and proof that light is an electromagnetic. In fact, it is the general solution of maxwells equations. Milo wolff first made me aware of the problems of maxwells equations. But the proof has a great virtue of being impressive and unexpected.
Maxwells equations and electromagnetic waves ii youtube. Then there is the conservation of charge, which is even written in parentheses, because the moment we have the complete maxwell equations, we can deduce from them the conservation of charge. Silagadze submitted on 21 jun 2001, last revised 29 jan 2002 this version, v2. This proof has many interesting points, not the least of which is that maxwell s equations appear to be derivable from newtons second law and the basic. They only derived the bianchi set, yet with slight tweakings with relativity, the other two can be derived. The development of the spacetime view of quantum electrodynamics.
I was invited to write an introduction to the new edition of feynmans classic book on quantum electrodynamics. I really love seeing derivations of the efes, maxwells equations, schrodinger equation etc. Maxwells equations in the context of the fock transformation and the magnetic monopole. Feynman s proof of the maxwell equations, discovered in 1948 but never published, is here put on record, together with some editorial comments to put the proof into its historical context. Some times ago dyson published a paper 1 about unusual proof of ho mogeneous maxwell equations feynman had shown him in 1948. Theres also an article about feynmans derivation of the. This book consists of five chapters, and the first four chapters deal with four maxwells equations, respectively. What is the relationship between jefimenkos equations and. A derivation of maxwell equations in quaternion space. Feynmans proof of maxwel ls equations get a copy of the paper feynmans proof of maxwel ls equations by freeman dyson published in ajp 58 3 march 1990. Freeman dyson is an englishborn american theoretical physicist and. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc.
Also, feynmans derivation of the lorentz force exclusively follows from its linearity in the charge velocity and from relativistic invariance. The fact that, unlike newtons laws, maxwells equations are already consistent with relativity is discussed. Stanford linear accelerator center stanford university, stanford, california 94309 submitted to american journal of physics. Many of us are familiar with feynmans proof of 1948, as revealed by dyson, which demonstrates that maxwell equations of electromagnetism are a consequence of newtons laws of motion of classical mechanics and the commutation relations of coordinate and momentum of quantum mechanics. In particle physics, quantum electrodynamics qed is the relativistic quantum field theory of electrodynamics. The purpose of this paper is to establish a connection between maxwells equations, newtons laws, and the special theory of relativity.
Generally covariant quantum mechanics on noncommutative. A students guide to maxwells equations students guides. First, he was talking about the general theory of relativity, not in any way the special theory. The interpretation of the feynmans derivation of the maxwells equations has aroused211 a great interest among physicists. Maxwells equations are a set of four differential equations, so they relate some function with its derivatives. To accomplish this task, we consider two kinds of noncommutativity. From feynman proof of maxwell equations to noncommutative quantum mechanics. Pdf it is shown that feynmans derivation of maxwell equations admits a generalization to the case of extra spatial dimensions. The real issue is that by switching back and forth between quantum and classical notation, feynman sneaks in physical assumptions that are sufficiently restrictive to determine maxwells equations uniquely. This proof has many interesting points, not the least of which is that maxwells equations appear to be derivable from newtons second law and the basic.
The maxwell equations are relativistically invariant, while the newtonian assumptions 1, 2, and 3, which feynman used for his proof, are nonrelativistic. As he explains, the failure of the maxwell equations in spherical coordinates can be imagined by saying, you cannot comb the hair on a tennis ball. Institute for advanced study, princeton, new jersey 08540. Fleisch focuses attention on the four maxwells equations in pages. Pdf noncommutative geometry framework and the feynmans. Maxwells equations cannot describe a spherical em wave. Therefore the purpose of the present paper is to derive a consistent description of maxwell equations in qspace. We generalize the previously given algebraic version of feynmans proof of maxwells equations to noncommutative configuration spaces. The proof begins with assumptions invariant under galilean transformations and ends with equations invariant under lorentz transformations. Does feynmans derivation of maxwells equations have a. In order to achieve this goal, we were inspired mainly by the special relativistic version of feynmans proof from which we constructed a formal approach more adapted to the. Feynmans different approach to electromagnetism iopscience. Feynmans derivation of maxwell equations and extra dimensions. Vol 2 was good though overly repetitive, iirc its 90 percent maxwells equations.
After having obtained previously an extended first approximation of maxwells equations in focks nonlinear relativity, we propose here the corresponding exact form. Such a formulation has the advantage of being closely connected to the physical situation. This is done with a derivation that begins with newtons verbal enunciation of his first two laws. Maxwells equations are a set of coupled partial differential equations that, together with the lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. And second, feynman did derive gr, but did so in a very different way to ei. Qed mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of. Later on, in 1966, in an interview for the american institute of physics with charles weiner 4,3 feynman said. Feynmans proof of the maxwell equations, discovered in 1948 but never published, is here put on record, together with some editorial comments to put the proof into its historical context. In fact tanimura had already given 8 an ndimensional generalization of feynmans proof along these lines. Well i could copy feynmans 21st lecture but i wont do that.