It is possible to experimentally determine whether there are unaccounted for hidden parameters in quantum mechanics.

“God does not play dice with the universe.”

With these words, Albert Einstein challenged his colleagues who were developing a new theory – quantum mechanics. In his opinion, the Heisenberg uncertainty principle and the Schrödinger equation introduced unhealthy uncertainty into the microcosm. He was sure that the Creator could not allow the world of electrons to be so strikingly different from the familiar world of Newtonian billiard balls. In fact, over the years, Einstein played the role of devil’s advocate on quantum mechanics, inventing ingenious paradoxes designed to lead the inventors of a new theory to a standstill. Thus, however, he was doing a good deed, seriously perplexing theorists of the opposite camp with his paradoxes and forcing them to think deeply about how to solve them, which is always useful when a new field of knowledge is being developed.

There is a strange irony of fate in the fact that Einstein went down in history as a principled opponent of quantum mechanics, although initially he himself stood at its origins. In particular, he received the Nobel Prize in Physics in 1921 not for the theory of relativity, but for explaining the photoelectric effect on the basis of new quantum concepts that literally swept the scientific world at the beginning of the twentieth century.

Most of all, Einstein protested against the need to describe the phenomena of the microworld in terms of probabilities and wave functions (*cm.* Quantum mechanics), and not from the usual position of coordinates and velocities of particles. That’s what he meant by “dice.” He recognized that describing the motion of electrons in terms of their velocities and coordinates contradicts the principle of uncertainty. But, Einstein argued, there must be some other variables or parameters, taking into account which the quantum-mechanical picture of the microworld will return to the path of integrity and determinism. That is, he insisted, it only seems to us that God is playing dice with us, because we do not understand everything. Thus, he was the first to formulate *hidden variable hypothesis* in the equations of quantum mechanics. It consists in the fact that in fact electrons have fixed coordinates and velocity, like Newtonian billiard balls, and the uncertainty principle and the probabilistic approach to their determination within the framework of quantum mechanics are the result of the incompleteness of the theory itself, which is why it does not allow them for certain define.

The theory of a hidden variable can be visualized like this: the physical substantiation of the uncertainty principle is that it is possible to measure the characteristics of a quantum object, for example, an electron, only through its interaction with another quantum object; in this case, the state of the measured object will change. But, perhaps, there is some other way of measuring using instruments unknown to us so far. These instruments (let’s call them “subelectrons”) will probably interact with quantum objects without changing their properties, and the uncertainty principle will not be applicable to such measurements. Although there was no evidence to support this kind of hypothesis, they loomed ghostly on the sidelines of the main path of development of quantum mechanics – mainly, I believe, due to the psychological discomfort experienced by many scientists due to the need to abandon the established Newtonian ideas about the structure of the universe.

And in 1964, John Bell received a new and unexpected for many theoretical result. He proved that it is possible to conduct a certain experiment (details a little later), the results of which will make it possible to determine whether quantum mechanical objects are really described by wave functions of the probability distribution, as they are, or there is a hidden parameter that allows you to accurately describe their position and momentum, as at the Newtonian ball. Bell’s theorem, as it is now called, shows that, as if there is a hidden parameter in quantum mechanical theory that affects *any* physical characteristics of a quantum particle, and in the absence of such a serial experiment can be carried out, the statistical results of which will confirm or refute the presence of hidden parameters in the quantum mechanical theory. Relatively speaking, in one case the statistical ratio will be no more than 2: 3, and in the other – no less than 3: 4.

(Here I want to point out in parentheses that the year Bell proved his theorem, I was an undergraduate student at Stanford. Bell’s red-bearded, strong Irish accent was hard to miss. I remember standing in the corridor of the Stanford Linear Accelerator Science Building , and then he left his office in a state of extreme excitement and publicly announced that he had just discovered a really important and interesting thing. that day became an unwitting witness to its discovery.)

However, Bell’s experience turned out to be simple only on paper and at first seemed almost impracticable. The experiment had to look like this: under an external influence, the atom had to simultaneously emit two particles, for example, two photons, and in opposite directions. After that, it was necessary to catch these particles and instrumentally determine the direction of the spin of each and do this a thousandfold in order to accumulate sufficient statistics to confirm or deny the existence of a hidden parameter according to Bell’s theorem (in the language of mathematical statistics, it was necessary to calculate *correlation coefficients*).

The most unpleasant surprise for everyone after the publication of Bell’s theorem was the need to conduct a colossal series of experiments, which at that time seemed practically impossible to obtain a statistically reliable picture. However, less than a decade later, experimental scientists not only developed and built the necessary equipment, but also accumulated a sufficient data array for statistical processing. Without going into technical details, I will only say that then, in the mid-sixties, the complexity of this task seemed so monstrous that the likelihood of its implementation seemed equal to that if someone had conceived to plant a million trained monkeys from the proverb in the hope of finding among the fruits of their collective labor, a creation equal to Shakespeare.

When the results of the experiments were generalized in the early 1970s, everything became very clear. The wave function of the probability distribution perfectly accurately describes the movement of particles from the source to the sensor. Consequently, the equations of wave quantum mechanics do not contain hidden variables. This is the only known case in the history of science when a brilliant theoretician proved *opportunity* experimental verification of the hypothesis and gave justification *method* Such a test, brilliant experimenters, with titanic efforts, conducted a complex, expensive and protracted experiment, which in the end only confirmed the already dominant theory and did not even introduce anything new into it, as a result of which everyone felt cruelly deceived in expectations!

However, not all works were in vain. Quite recently, scientists and engineers, to their own surprise, have found a very worthy practical application of Bell’s theorem. The two particles emitted by the Bell source are *coherent* (have the same wave phase) because they are emitted synchronously. And this property of them is now going to be used in cryptography to encrypt highly secret messages sent through two separate channels. When intercepting and attempting to decrypt a message through one of the channels, the coherence is instantly violated (again due to the uncertainty principle), and the message inevitably and instantly self-destructs at the moment the communication between particles is broken.

And Einstein, it seems, was wrong: God still plays dice with the Universe. Perhaps Einstein still should have heeded the advice of his old friend and colleague Niels Bohr, who, once again hearing the old chorus about “dice,” exclaimed: “Albert, stop telling God what to do. ! “