The size of the electron is unknown, and it cannot be found. How should this be understood?

One of the favorite subatomic particles of all who know the structure of matter is electron. There have been all sorts of conversations about it. That it does not exist, that it is not a particle even if it does exist, and so on. Not so long ago it was discussed that the electron is not a lepton at all, and therefore can also be divided into subparticles. In each such “strange” version there is a share of real science. But a special measure of quantum mockery of the consciousness of an ordinary person hidden in an attempt to describe the size of an electron.

Wait a minute… We did some problems at school and used table sizes for the electron. What's wrong with that? Where did they come from then? In general, everything is fine. Except that these values ​​are not that precise, and then I remember Eddington joke. He also derived the magic number 137 in strange ways. But with the electron everything is more interesting and “scientific”. Let's figure it out.

All contradictions are observed from the moment where it begins the quantum nature of this particle is especially actively manifested. The electron, which we remember from our general physics course as a ball rotating around the nucleus of an atom in Rutherford's model, suddenly becomes a field oscillation or a form of energy. And then everything turns upside down. From now on, it is not quite a particle.

Dimensions of an electron – this is one of the most striking and strange manifestations of its amazing nature. Let's start from afar.

If there is a particle that exists in the “physical” world, then it has a size. It can be measured and even touched. But with the electron, everything is very interesting here too.

Let's turn to to the same information from the textbook and let's try to determine its size. Most likely you will find one of the standard images of this type:

But since the electron is not a “ball” with a clearly defined boundary, its radius is rather a theoretical valuebased on various physical models. It would be appropriate to say that the electron simply has no size. The same quantities that we use in calculations are derived from some theoretical idea of ​​the issue under study. I do not want to say that this is wrong, but this is not the physical size of the particle in the direct sense of the word.

In particle physics, there are at least three main approaches to determining the size of an electron. Let's call them the classical method of determining the radius of an electron, comparison with the Compton wavelength and determination according to the standard model.

Classical radius of the electron is obtained from the theory of electromagnetism. It is approximately equal to 2.8179403227×10^−15 meters. This value does not correspond to reality, since does not take into account the quantum nature of the electronHowever, if we turn to specific calculations, the value floats and seems to hint at some inaccuracy and strangeness.

This value is calculated based on what size the sphere of negative charge formed by a current moving at the speed of light would have to be when the energy transferred to the system. For different processes this is a different indicator.The extremely small diameter is observed in accelerators (up to 10 ^-18 meters), the extremely large size is observed in the electron shells of atoms (10 million times greater than the noted value).

If we take into account the quantum nature of the electron, then it is subject to probabilistic characteristics and describing it as a particle is meaningless. Actually, even based on different calculated values, it is quite expected. Read it as “the electron has no specific size”. But, with all this, the particle must be characterized somehow in calculations. Here is used Compton wavelength and size is compared with it. This value is defined as the ratio of Planck's constant to the mass of an electron multiplied by the speed of light. It is approximately 2.42631023867×10^−12 meters. Compton wavelength can be considered as the minimum size that an electron can haveIn fact, it is this value that is used as the main one in “quantum research” for some assessment.

There is more one interesting approachwhich considers the size of an electron to be the region of existence of the process that generates the electron and has an energy equal to the rest energy of the electron, 0.511 MeV. This size is millions of times smaller than the electromagnetic one.

In this case, if refer to the standard model (and we remember that it is the standard model that is accepted as the unspoken boundary between the hypothetical and the experimental), then everything is very interesting here. According to the standard model of particle physics, an electron is just a point particle, that is, its size is zero. It is extremely difficult to experimentally determine the size of an electron with high accuracy, since it is much smaller than can be measured even with modern instruments. This means that it is a point that cannot be measured.

Probably the most important thing of all is – This is a strange specificity that is very difficult to imagine and work with.

The radius of an electron is not just a “size” in the usual sense of the word, but rather a quantity that characterizes its quantum behavior. It is almost impossible to experimentally determine the size of an electron with high accuracy, and, as we have found out, it can be calculated in different ways. Just imagine that you are trying to measure the size of a shadow. The electron, like a shadow, exists, it has a shape, it interacts with the world, but when you try to determine its exact dimensions, it becomes elusive. This is a probability smear or quantum phantom that defies our intuition. From now on, particles should be perceived as a foggy cloud of particle existence, not an object.

This does not mean that the electron is infinitely small or that it does not exist at all. It does mean that its size is not a well-defined concept in the classical sense of the word.

Well, as usual, I'll be glad. invite you to my project's Telegram channelwhere I try to understand the most interesting “wilds in physics”.