In mathematical expressions that describe the basic properties of matter and the laws of nature, there are always some constant coefficients of a universal nature - fundamental physical constants. They express the limit values of the most important quantities, determined empirically, and set the natural scale for the mathematical description of physical processes. Such coefficients include, for example, Planck's constant, elemental electric charge or the speed of light.
There are also dimensionless constants. Whatever system of units we choose, their numerical value remains unchanged. One of these constants is the fine structure constant, which expresses a measure of the intensity of electromagnetic interaction.
Mathematical definition
This constant, denoted by the Greek letter "alpha", in the form of a ratio combines several fundamental constants. In different systems of units, it is defined differently, but always has the same numerical value.
In the SI system, the formula for the fine structure constant is as follows: α = e 2 / 2ε 0 hc. Here e is the elementary amount of electricity (electron charge), ε 0 is the electric constant, h is the Planck constant, and c is the speed of light in vacuum.
In the GSSE system, ε 0 = 1, and the constant is determined by the formula α = e 2 / ħc, where ħ is the reduced Planck constant (ħ = h / 2π).
The numerical constant of the fine structure is approximately 1/137; its value is constantly being refined. Currently, it is calculated to the nearest billionth and equal to 1 / 137.035999710.
History of the introduction of a new constant
In 1916, long before formalizing the theoretical foundations of quantum mechanics, the German physicist A. Sommerfeld worked with the Bohr model of the atom. Within the framework of this model, the scientist was looking for an explanation for the appearance in the atomic spectra of the so-called fine structure - splitting of spectral lines (i.e., energy levels of electrons).
Sommerfeld suggested that the fine structure arises as a manifestation of the relativistic effects of electron motion. In the calculations, he obtained a dimensionless quantity close to 1/137, reflecting the ratio of the speed of an electron located in the lowest orbit (the Bohr model still operated with the concept of “orbit” for electrons) to the speed of light. Therefore, sometimes the constant "alpha" is also called the Sommerfeld constant, in honor of the scientist who introduced it to physical science.
The explanation of the fine structure of the spectrum
The development of ideas about the fine structure constant is associated with the further progress of quantum physics, in particular with the concept of spin — the intrinsic angular momentum of a particle. It turned out that the fine splitting of the spectral lines is caused not only by the relativistic motion of the electron in the atom, but also by the interaction of its spin moment with the orbital moment. Depending on the orientation of the spin, it can be described by either a vector sum or a difference, as a result of which small differences in energy values arise, leading to a splitting of the line in the spectrum.
As for the constant "alpha", then it (or rather its square) is included as a coefficient in the equation of spin-orbit interaction, which gives a correction to the energy of an atomic electron. In other words, this constant determines the size of the fine splitting of the spectrum lines. However, this does not clarify its physical nature.
Coupling constant
The physical meaning of the fine structure constant is revealed by quantum field theory. This value refers to the so-called coupling constants - measures of the intensity of interaction. In other words, it characterizes the probability of an interaction act, which quantum electrodynamics interprets as the emission (absorption) of a charged particle - for example, an electron - of a virtual quantum of the electromagnetic field (photon). These photons form the electric field of the particle, through which it "communicates" with other brothers who have an electric charge.
Thus, "alpha" controls the force with which charged particles interact with each other, for example, the repulsive force of electrons or the force of their attraction by the nucleus, which in turn determines the size of the atom, the speed of the electrons in it and the spatial arrangement of electron clouds.
Nevertheless, in the modern theory of elementary particles, which is not too well called the "Standard Model", the fine structure constant, along with a number of other world constants, is included as an external parameter. The theory takes this combination of empirically obtained critical quantities as a given: their numerical value does not follow from anything, it just is as it is. Some modern theoretical constructs, such as the chaotic theory of inflation and string theory, suggest that the set of fundamental constants was realized randomly in our Universe. They allow and even require the existence of a huge variety of other universes with different sets of constants.
The question of the constancy of "alpha"
Our Universe has gone through several stages in its evolution. According to a number of physical theories, a change in these phases of development should have been accompanied by a change in the value of world constants, including the fine structure constants. In addition, these values may differ in remote areas of the universe (which were closer in earlier eras). It is very important for physicists to know whether fundamental constants evolve, and if so, how.
It is possible to obtain answers to these questions by observing ultra-long-range objects of space, such as quasars. So, in 2010 there were reports of observational results indicating that alpha may have increased in some areas, and in others, decreased from 10 billion years away from modern times. However, it is too early to draw final conclusions on these results.
At the beginning of 2018, data were published on the study of the galaxy, which is separated by 2.94 billion light-years from us. They indicate that during the corresponding period of time the fine structure constant has not changed. So, if it, along with other basic parameters of our world, has evolved, then this most likely happened at the very early stages of the existence of the Universe. Further research will no doubt shed light on this interesting question.