Shulou(Shulou.com)11/24 Report--

Take a metal rod and draw all the electrons to one end, where the electric field of the metal rod is a dipole field. Now cut the metal rod in half and we get a pair of charges: half negative and half positive, both of which have an electric field that radiates directly outward.

Now take another metal rod, magnetize it with a magnet, and we will get a dipole magnetic field that is very similar to the electric field of the dipole. But if we split the metal rod in half again, the ends of each half are still the North and South poles, and there will still be a dipole field. According to classical electromagnetism, no matter how many times the metal rod is cut, we will never get an isolated magnetic charge, that is, a magnetic monopole.

As early as 1269, the French scholar Petrus Peregrinus de Marincourt carried out this magnet slicing experiment for the first time, before we knew how the magnet was produced. Now that we know where magnetism comes from, we are not surprised that halved magnets produce two smaller magnets. In a ferromagnet, the magnetic field is the sum of the fields of countless tiny electron dipoles in the magnet atom. Another popular way to generate a dipole magnetic field is the electromagnet. According to classical electrodynamics, the moving charge is the source of the magnetic field.

The absence of the magnetic monopole in the classical theory is incorporated into the mathematics of classical electrodynamics, especially the Gaussian magnetic law (one of Maxwell's four equations), which indicates that the divergence of the magnetic field is zero. Divergence is a mathematical term that describes whether a point in a vector field is a source or a sink, and zero divergence means no source or sink. According to this law, we know that there is no magnetic monopole.

On the other hand, the Gauss law of the electric field tells us that the divergence of the electric field is not zero, it is proportional to the charge density. This charge is where the field lines can end-it forms their source or sink, so there is something like an isolated charge. If we take a quick look at the Maxwell equations, we will find that electricity and magnetism are not symmetrical. If we add something like a magnetic charge to the equations, we can also have symmetry between these equations.

Physicist Murray Gherman said: "everything that is not prohibited is mandatory." This means that if the mathematics of physical theory allows it to exist, then it exists in nature. Nothing in the Maxwell equation really shows that the magnetic monopole does not exist, except for the fact that Maxwell set the magnetic charge to zero because he does not believe it exists. But in principle, magnetic monopole can exist, at least according to classical theory.

Quantum theory, quantum mechanics? It has completely changed our understanding of electromagnetism by explaining it in terms of quantum fields rather than charges and forces. The great physicist Paul Dirac had a habit of staring at mathematics and discovering particles. As we discussed in previous articles, he predicted the existence of antimatter in this way in 1928. But then in 1931, just before his antimatter was verified, Dirac made another prediction-the existence of a magnetic monopole.

His argument is that starting with the dipole magnetic field, the monopole can be approximated by a magnetic line of force that separates the two ends far enough and disappears in some way. There is a way to do this, a coelectric solenoid will get a dipole field, and its connection line is limited to the line of the line. So the width of the coil is much smaller than the length, and it looks like two isolated magnetic charges. This structure is called the Dirac string, and Dirac's argument is that if the string part of the Dirac string is fundamentally undetectable, then the magnetic monopole can exist.

The second part of the argument is under what conditions the string cannot be detected. The magnetic field affects the charged particles, which is achieved by changing the phase of the particle wave function in quantum mechanics. Imagine a charged particle passing through a Dirac string, such as an electron. To draw this trajectory, you need to add up all possible paths for the electron, including the left and right paths on the string. The existence of the string and its magnetic field should introduce different phase shifts depending on which side of the string the electron passes through, which actually has a significant effect on the path of the electron. In other words, the string will be detectable.

But there is a situation where the string can never be detected: the amount of phase shift is proportional to the charge. For the value of the charge, the phase shift between the different sides of the string happens to be a wave period. This means that there is no observable difference, so it is undetectable for Dirac strings, and the final charge can only exist as an integral multiple of the basic charge. On the other hand, this is considered to be a prediction of charge quantization, which must be discrete as long as there is at least one magnetic monopole in the universe. Of course, we know that the charge is indeed quantized, and it can only be an integral multiple of the electron charge.

However, instead of using it as a prediction of charge quantization, we can also flip it: if the charge is quantized, the existence of a magnetic monopole is possible. The charge has been proved to be quantized, so quantum mechanics does not actually prohibit monopole.

The Great Unification Theory makes us fast forward for 40 years. In the early 1970s, physicists tried to explain weak forces and unify them with electromagnetism. After solving this problem, physicists are trying to include force through the so-called grand unification theory, which involves complex symmetry destruction. Facts have proved that magnetic monopole is inevitable in all grand unified theories.

In the electroweak theory, the Higgs field is a scalar field, which has two complex values everywhere. The interaction of these two "degrees of freedom" gives the Higgs particle mass. In the simplest grand unified theory, the Higgs field has three degrees of freedom instead of two. This means that the field can be a bit like a vector, even if it is really not a vector. It can have an internal arrow pointing in a specific direction-- not to the physical space, but to the space of the three degrees of freedom.

In 1974, Gerard t'Hooft and Alexander Polyakov also proposed that some points of the Higgs field can form some knots-the field arrows are pointing away from that point, these are topologically discontinuous points that cannot be removed by smooth deformation of space. It is proved that in the grand unified theory, these junctions in the Higgs field are particles with magnetic charge-magnetic monopole, which should be very large and should be formed spontaneously in a very high energy environment, such as in the very early universe.

It is exciting for these theories to predict the existence of magnetic monopole, but there are also problems. Because these theories predict that magnetic monopoles should have been produced in large numbers in the early universe, as many as protons and electrons, where are they now? And they should also be very large, trillions of times the mass of protons, so they should quickly re-collapse the universe.

In the experiment as early as 1982, physicist Blas Cabrera Navarro built a superconducting coil in his Stanford laboratory and managed to detect the magnetic monopole predicted by Dirac, but failed. There were also several different experiments on the large Hadron Collider, and magnetic monopole was also not found. The energy of the large Hadron Collider is about 100 billion times lower than that predicted by the grand unified theory to produce a monopole. People are also looking for magnetic monopoles from space, but again, there is no convincing evidence.

This article comes from the official account of Wechat: Vientiane experience (ID:UR4351), author: Eugene Wang

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