# What shape is the electron? What's the radius, what's the spin?

What is the shape of the electron?

Shape is perfectly suitable for describing angular macroscopic objects. But technically, electrons don't have a shape. The electron is an elementary particle, which means it has no internal structure and can't be divided into smaller things, or the interior of the electron is unknown.

Physicists also call electrons point particles. Point particles are particles of zero dimension that do not occupy space.

As we all know, one dimension is a line, two dimensions are a surface, and three dimensions are a volume. In three dimensions, each superposition of dimensions is an infinite number of superpositions of adjacent lower dimensions. For example, an infinite number of two-dimensional planes can add up to a three-dimensional solid. Similarly, the zero dimension is just a point, and an infinite number of zero dimension points form a one-dimensional line. So the 0 dimension doesn't have length, because if it has length, it's not 0 dimensional. It's like the idea of a particle in physics, a particle exists, but does a particle have a size? Of course not. A particle is just a concept.

Of course, when scientists say that an electron is a point particle, they don't mean that the electron is a particle. If we don't study the internal structure of the electron, we can think of the electron as a zero-dimensional point particle, and it doesn't take up space.

What is the radius of the electron?

Some people may question me: you just said that the electron is a zero dimensional point, why now talk about the size of the electron? In fact, you have fallen into the macro world of misunderstanding.

Electron is a microscopic particle, and its wave-particle duality is remarkable. Electrons are both particle and wave, and by electron radius, I mean one side of the particle.

In fact, wave-particle duality can be understood as follows. When not being measured, electrons act as both waves and particles. The wavelength of an electron is short, so the distance between its neighboring peaks is short. If the wavelength is very short, then the two peaks are so close together that it's hard to tell which one is which, and then the wave is more like a wave packet held together, and the wave packet is more like a particle.

For example, if you take a jump rope and shake one end so hard that the rope forms waves, the highest point of each wave being the crest. If you shake it harder, the distance between the peaks gets shorter and shorter, meaning the wavelength gets shorter and shorter. If I am strong enough to cause the wave length of the jump rope fluctuation is 0.001mm, then each wave peak looks connected together, so at this time the jump rope is like a rope wall, its fluctuation is not obvious. And when we measure the radius of an electron, we measure the particle side.

Ding Zhaozhong had done experiments to measure the radius of electrons. Normally we bombard other particles with electrons to measure their radii. When we measure the electron itself, we have no better particle to measure it with, so we measure the electron with the electron. Sending electrons to bombard the measured electrons, and using scattering to measure the space occupied by the electrons, the radius of the electrons can be measured.

But the awkward result is that the lower the energy of the electrons we emit, the larger the radius of the electrons we measure. The larger the energy of the emitted electron, the smaller the radius of the electron being measured. This is because the higher the energy of the emitted electron, the more energy will be transferred to the measured electron. As the measured electron absorbs the energy, the frequency of its fluctuations will increase, and the wavelength will be shorter, more like a particle, with a smaller radius.

The darker the electron, the more likely it is to find an electron

If we want to measure electrons of smaller radius, we need to bombard the measured electron with electrons of the same magnitude as the wavelength, and electrons of the same magnitude have shorter wavelength, higher frequency, and therefore higher energy.

And now we're stuck in a loop. To measure a more accurate radius of an electron, it requires a more energetic electron to bombard it, which results in a smaller radius absorbed by the measured electron, which requires a more energetic electron to bombard it in order to continue the measurement. Forcing the radius of the measured electron down to the lower limit of the Compton wavelength. So the radius of the electron measured by our existing instruments is about 10∧-15m. The real radius of the electron must be smaller than that, so in theory, the electron has a measurable radius.

At the same time, the electron is wave-particle duality, and it also has a wave side. And we can't measure both the velocity and the position of the electron, so we don't know where it's going to be next second, but we can only use probability to describe how likely it is that the electron will be at a certain point next second. Electrons have no real scale; we can only describe them in terms of probabilistic waves. In this sense, the volume of the electron is meaningless.

What is the spin of an electron?

When people think of spin, they think of the rotation of various spheres, like the Earth. But the spin of an electron is nothing like these spins, and its meaning is abstract.

As we know, in 1905, Einstein published the light quantum hypothesis, which states that the energy emitted by electrons is not continuous, but piecemeal. It radiates energy E=nhν(n is a positive integer, h is Planck's constant, ν is the photon frequency), so each energy is hν, one energy radiates n=1, two energy radiates n=2... And so on.

Later, scientists discovered that electrons also generate a magnetic field, which pushes the electrons back to spin.

When scientists start thinking about electron spins from the standpoint of classical physics, the first question they ask is what is the spin period?

This is awkward, because you can't measure the electron period at all, because electrons are point particles. Eventually physicists figured out that there was no period in the spin of an electron, that the spin of an electron was also quantized and discontinuous. A lot of people are probably confused, because this is a brand new concept.

Physicists discovered that the spin angular momentum of an electron is quantized. As we have said before, quantization refers to discontinuous and fundamental quantities. To express this quantization mathematically is to first find a fundamental quantity, such as hν, and then to apply a variable to the fundamental quantity, such as the N in the Planck formula E=nhν.

What is discontinuity?

We can say that the length of a rope is 100 meters, and that the rope has an infinite number of points, and all of these points together make a continuous rope. There's an infinite number of points from 0 to 100 meters. Such as 7.465161867... This number is somewhere between the seventh and eighth meter of this rope.

If I don't want to express all the points of this rope. I just want to know a particular set of points, so how do I write a formula for these discontinuities?

In fact, in mathematics, you can take any constant that you want to be a fundamental quantity, and let's say the constant is 2. Let's say that the expression for a particular set of points on this line x is equal to 2n, with n as a variable, and I can say that it can only pick integers between 1 and 50. So the value of x is 2,4,6.... 100.

I can also specify that the independent variable n is a half-integer between 1 and 50, in which case x=2n is 3,5,7..... . And that's where the discontinuity comes in. How basic quantities and variables are specified depends on the nature of the problem you are studying.

The quantization of the spin angular momentum means that the spin is discontinuous, so the value of the spin is also discontinuous. The angular momentum expression p=[J(J+1)]½ <e:2> (where is the reduced Planck constant with the value h/2π).</e:2>

So, here, "where" is the basic quantity, and "J" is the variable. If I limit the range of J, then the angular momentum expression can reflect the discontinuity of the spin angular momentum, which is the quantization, and J 1/2 is the spin angular momentum of the electron. If J can only take a semi-odd number (0.5,1.5, etc.), then the particles with such spins are fermions, electrons, neutrons, protons, etc. If J can only be an integer, then this kind of spin particle is a boson, such as a photon, gluon, etc.

That's the spin of an electron, and it's an intrinsic property of microscopic particles that doesn't have a classical physics equivalent. I can only explain this new concept in a more serious way, because there is absolutely no old concept that can help us understand them popularly.