What is the Dirac equation and why is it called the “formula” of love?

Have you ever heard of the Dirac equation as a formula for love? As Valentine’s Day approaches, it is common to see in publications that this equation shows how two systems that interact with each other and then separate can be described as two different systems, but at the same time as unique. That is, as if it is unbreakable love. Well you should know that it’s just popular culture mistake and that in reality the Dirac equation has no such meaning. Actually this explanation applies more to quantum entanglement than according to the Dirac formula.

However, even if this context is incorrect, you should know that the Dirac formula hides unique properties that make it the best ally of beauty and love. And it is the only equation, elegant and discreet, that manages to combine two sciences in one expression: quantum mechanics and the theory of relativity. Its author, Paul Dirac, combined both disciplines, which was unthinkable until then, and gave birth to unique expressionwhich manages to explain the behavior of electrons when they move at speeds close to light.

We’ll tell you all about it romantic equation and why its meaning is often confused with that of quantum entanglement.

SYNERGY OF TWO SCIENCES

Throughout the twentieth century, there were two disciplines in physics that completely revolutionized the science: general relativity and quantum mechanics. The combination of both made it possible to practically explain all phenomena which occurred in the Universe, but each of them had to be applied separately. Thus, quantum mechanics became a window into the microscopic world, and Einstein’s theory of relativity allowed us to study what happens in the macroscopic world, where stars and planets have enormous scales and particles reach enormous speeds.

However, in this new scientific panorama there were certain problem scientists did not know how to solve this problem. For example, Schrödinger’s quantum theory, non-relativistic in nature, could perfectly explain the behavior of electrons in traditional situations, but there seemed to be no correct way to consider them when these They have acquired very high speedclose to the light.

Erwin Schrödinger and his fascinating (though little known) philosophical side

In this context, scientists have puzzled over how to study tiny particles like electrons that respond to quantum behavior when they move at the speed limit contained in relativistic? Fortunately, Paul Dirac came up with a solution to the dilemma: synergy of both approaches in one equation.

THE MOST BEAUTIFUL EQUATION IN THE WORLD

Armed with a desire to model the behavior of relativistic electrons, Dirac formulated the Schrödinger equation to try transform it from wave to relativistic. To do this, he started from the conclusions of the Austrian physicist and applied Albert Einstein’s famous relativistic equation to them. Although in fact the process was something more complex Thanks to this, and requiring a lot of calculations, simulations and adaptation of equations, Dirac was finally able to unify the theory of relativity and quantum theory. one formula

.

With its help, Paul Dirac perfectly described the dynamics of these elementary particles with a spin mass of ½ when they move at speeds very close to the speed of light, that is, at relativistic movements.

Technically this is a formula that naturally explains existence of spin and antiparticles. In fact, although he did not realize it at the time, Dirac’s equation also holds for approximations with other particles such as protons and neutrons, since they are formed from quarks (elementary particles).

Quarks: small but chaotic subatomic particles

Soon the scientific community quickly nicknamed the famous formula “the most beautiful equation in the world“, thanks to the integration of two of the most important ideas in all of science: quantum mechanics and the theory of relativity. His conclusion was great milestone for the history of physics, and to this day the legacy of Dirac is still present in this magnificent formulation.

WRONG EXPLANATION

However, despite the fact that the synergy and connection between the two completely different approaches represented by the Dirac equation would be enough to call it the “equation of love,” popular culture accepts it. force this metaphor relating a formula to the meaning of terms that do not represent it, such as the term quantum entanglement.

This concept would argue that if two systems interact with each other for a period of time and then separate, they could be described as two different systems, but in a subtle way they return to one. unique system. That is, one state cannot be described independently of the other.

Well, it is not technically correct to combine both concepts. It must be taken into account that the Dirac equation is applicable only to one-electron behaviorand the interweaving and, therefore, the meaning that is mistakenly given to it is aimed at two particle dynamics.

It is possible that at some point in recent decades someone did not realize the uniqueness defining the Dirac equation and mixing various concepts within quantum theory, erroneously assigning this meaning to the equation.

So, you know, this Valentine’s Day, if you read somewhere that the Dirac equation is a love formula that explains the union of two particles, you will already know that this is not entirely true and that, in truth, love that it represents, is undoubted connection between quantum and the theory of relativity.