Foreword

The Past and Future of Magnetic Monopoles

G. Lochak

1. A Brief History of Electricity and Magnetism

The observation of electricity and magnetism began in ancient times. It is attributed to the Greeks and the Chinese. Around 600 B.C., Thales noticed that amber had the ability to attract light bodies when rubbed with a cat skin. But the Greeks also knew about magnets, whose name is magnes in Greek. And thus, since amber is called elektron, they passed down to us not only the beginning of the study of electromagnetism, but also the etymology. The Chinese did not know about electricity, but they knew about magnets: probably both they and the Greeks found magnetite mines (i.e., a magnetic iron oxide). But the Chinese also discovered the Earth's magnetism. They invented the compass (1000 B.C.), and merchant ships brought it to the rest of the world. Nevertheless, the observation of things and the use of them was not yet a science, which is the explanation of the behavior of things and their inclusion in an image of the world. The Greeks had done this in astronomy, but not in electricity and magnetism. The science of electricity and magnetism started with André-Marie Ampère, and was developed by James Clerk Maxwell, who considered Ampère the greatest physicist since Isaac Newton. But then Ampère lost that distinction when Einstein declared that the greatest was actually Maxwell. And Maxwell lost that title to Einstein. Records are fragile! Now, it may be said that, despite the contributions from many others in these fields, the science of electricity and magnetism owes its fundamental ideas to three men: Ampère, Maxwell, and Michael Faraday. Consider the following points: 1. Starting from experiments of Oersted and others, Ampère and Faraday gathered electricity and magnetism in a single doctrine that claims that: a. An electric current produces magnetism (Ampère). b. A variation of magnetism produces electricity (Faraday).     These two statements are not reciprocal because in the first case, the electric current may be static, while in the second case, magnetism must vary. 2. The next discovery was the notion of field, born in the same years. The idea appeared in two steps: a. At first, Ampère's and Faraday's attention was drawn to the lines of magnetic or electric forces. Ampère based his "Electrodynamics" on the interactions between small elements of currents and introduced a vector, known in French as the directrice, which today is called the magnetic field.     Faraday observed figures drawn by iron filings scattered on a sheet of paper above a magnet. He interpreted them as lines of force and then as lines of field, a concept that is now taught in every textbook. b. The second step is due to Faraday alone. He introduced the entirely new idea that an electric or a magnetic force acts owing to a new property of the surrounding space: the electromagnetic field. This idea required a new type of mathematics that was capable of gathering electric and magnetic properties in a new image of the world. This was the achievement of Maxwell's equations, which are engraved into the pantheon of science and are the object of universal admiration, as expressed by Ludwig Boltzmann in his Treatise of Electromagnetism, quoting a verse of Goethe's Faust: "War es ein Gott der diesen Zeilen schrieb ?" (Was it a god who wrote down these signs?)1. Thus, beside the empty world inherited from Democritus, filled with material points obeying Newton's laws of mechanics, appeared another physical world: a resurgence of the world of Anaxagoras, filled with fields. Maxwell's equations became the counterpart of Newton's mechanics. But these contradictory worlds were destined to concur as follows: In 1905, the Einstein photon brought the corpuscles back into the theory of light, from which they had been expelled by the wave theory of Maxwell, Christiaan Huygens, and Augustin-Jean Fresnel. Einstein proved that the still-mysterious photoelectric effect was a consequence of his hypothesis. Conversely, in 1923, Louis de Broglie discovered that material corpuscles have wave properties. He gave the first formulas for matter waves, interpreted the spectrum of Niels Bohr's atom in terms of stationary electron waves, and predicted the diffraction of electrons. Matter and Light, the title of one of his books, became the symbol of the new quantum world: wave-particle dualism.

2. The Fathers of the Magnetic Monopole

2.1. Maxwell (1873)

We have already noted the absence of symmetry between the Ampère and Faraday laws, which favors electricity, since we can create magnetism with a stationary electric current (the electromagnet), whereas we need a variation of magnetism to create an electric current (Faraday's induction). This asymmetry occurs because we can produce an electric current, but not a magnetic current. Nevertheless, in 1785, Charles-Augustin de Coulomb measured his law of force in /r2, not only for electric charges but for magnetic charges even though he possessed only what he called "electric poles " (small, charged objects), but no "magnetic poles." So he used long magnetic wires, whose extremities could not interact, as Maxwell explained in his Treatise on Electricity and Magnetism. Maxwell gave a central place to Coulomb's law not only for electricity, but also for magnetism. Magnetic poles are described at the beginning of volume 2 of his Treatise, which shows that electric and magnetic charges have the same physical dimensions and are thus expressed in the same units. But neither in the electric case nor in the magnetic case are particles mentioned in the sense that we now understand them (as localized microobjects). The experimental discovery of the electron as a particle-the fruit of numerous works-was announced by J. J. Thomson in 1897. A first theory came from Hendrik Lorentz at this time, but the true theory came later, with the Dirac equation in 1928. The Maxwell poles were only a rough draft, but Maxwell was the first to understand that vectors representing electricity and magnetism are of a different nature. The first is a polar vector, of the same kind as a velocity, while the second is an axial vector of the same kind as a rotation axis. Despite some analogies, electricity and magnetism are fundamentally different; this difference appears in their symmetry properties. The image of a magnetic field in a mirror perpendicular to it is the field itself, while the image of an electric field perpendicular to a mirror is inverted. That is, the image is the mirror image of the object. Conversely, the image of a magnetic field parallel to a mirror is parallel to the field, but inverted, while the image of an electric field parallel to a mirror is the field itself. In other words, there is no exact analogy between electricity and magnetism, contrary to what is often claimed and to the analogy falsely attributed to Maxwell's equations. These errors arise because polar and axial vectors are represented by the same symbols. Maxwell knew this, and Pierre Curie tried to impose different notations for these reasons, but in vain. Through the discovery (quickly forgotten!) of the difference between polar and axial vectors, Maxwell was the second (after Louis Pasteur) to approach the fundamental property of enantiomorphism, or chirality; i.e., the difference between left and right, such as the left and right hands. Chiral comes from the Greek kheir (hand). Actually, Pasteur was the first to discover this phenomenon in another field, not in electromagnetism but in crystallography. He discovered that there are two kinds of crystals of tartaric acid: left and right. Each of them is not its own mirror image, but the image of the other in a mirror, like two hands. When Pasteur made this discovery, he was still a student at the Ecole Normale Supérieure. In a state of great excitement, he immediately went out of the room where he worked, declaring with enthusiasm in the corridor, "The Universe is not symmetric to itself !" He was immediately convinced of the universal character of his result. And when he said that to his old master, Jean-Baptiste Biot, the latter replied: "I am moved to tears by what you are telling me !" This discovery lay at the origin of the biological achievements of Pasteur, and it must be remembered that a few years before these lines were written, a Nobel Prize was awarded to William Knowles, Ryoji Noyori and Barry Sharpless for a discovery of great importance for medicine: the chiral catalysts, able to separate left and right synthetic molecules. A whole generation remembers the drama of a mildly sedative medicine, thalidomide, prescribed to pregnant women, who gave birth to children without arms or legs as a result of the drug. The reason for this was that the synthetic molecules were a mixture of left and right molecules, one group of which (and only one) being teratogenic. And we shall see what followed from the discovery of chirality in physics: it happened that beta radioactivity is chiral too, and it introduces enantiomorphism just like tartaric acid and magnetism. In my opinion, it may be asserted that...