A Short Introduction to the Magnetic Monopole Problem

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The essence of a theoretical physics work is an attempt to come up with a new idea that helps solving problems or a new solution to a known problem. In my opinion, the preliminary efforts of such a work should be dedicated to the identification of the problem and casting it into a clear form. Only after accomplishing this task, one should try to solve the problem. This approach is used here in an examination of the magnetic monopole (called briefly monopole) issue. The following lines are expected to be understandable to readers of popular science texts.

The fundamental difference between electric charge and monopole stems from the fact that electric charge has been found in laboratory whereas a monopole has not been found yet. Therefore, the monopole issue is a subject of a theoretical work. Here one relies on basic properties of electrodynamics and in particular on the well known relationships between electric charge and electric field. Thus, one expects that analogous relationships exist between magnetic charge and magnetic field. Hereafter, this correspondence is called charge-monopole analogy.

A brief survey of the literature is a good starting point. Let us take two very well known textbooks on classical electrodynamics: Landau and Lifshitz, The Classical Theory of Fields and Jackson, Classical Electrodynamics. Here one finds that Landau and Lifshitz do not mention monopoles at all whereas Jackson dedicates to monopoles only a very small portion of his book.

Wikipedia is a very well known source of information. According to its principles it describes ideas that are consistent with the current consensus. Thus, the Wikipedia item of electric charge describes properties of one kind of physical object (which can be either positive or negative). On the other hand, the monopole item of Wikipedia describes several kinds of monopoles.

The previous lines show that the status of the electric charge is completely different from that of the magnetic monopole. This difference is incompatible with the charge-monopole analogy which is expected to be valid. Therefore, it is clear that the present consensus about magnetic monopole has not said the last word on this subject. For this reason, monopoles look like a promising subject for a theoretical research.