About a hundred years of quantum field theory - about the theory that changed the world

In the XNUMXs, quantum theory entered the mainstream of physics and brought science and technology to new heights. In this article we will summarize the successes and failures of the Torah that revolutionized the world.

Somewhere in northern Spain in 1879, like Moses being led to the burning bush, the archaeologist Marcellino was led by his eight-year-old house to the Altamira cave. In a cave that is almost 300 meters long, impressive wall paintings were discovered that documented the lives of humans from the Paleolithic period. The history is more than ten thousand years old, which was preserved thanks to the dry conditions and little exposure to the sun, providing a wonderful testimony to the intricacies of the psyche of the people from the prehistoric period. The wildlife, the palms, and the use of the natural contours of the caves to create a three-dimensional visual show how curious humans were about themselves and their surroundings. The historical documentation corresponds with the abstract thinking that developed over the years and allowed us to express our curiosity about the universe with the help of verbal language and visual documentation.

Throughout two thousand years of documented research, two basic questions still remain open: how did it all begin and what are we all made of? At the same time, there is no doubt that we have made significant progress in solving these problems. Today, physicists believe that the language of the universe is written with the help of quantum fields from which the process of creation can be described. The Wonderful Torah began its journey in the twenties of the last century with the aim of uniting quantum mechanics and Einstein's special theory of relativity. Simply put, the Torah implies that the most basic structure of the universe is a field, similar to a magnetic or electric field. If a field is "quantized", i.e. if the field is described in the language of quantum mechanics, it can be shown that waves in the medium describe what we usually call "particles".

The concept of field - the innovation of the 19th century

At the beginning of the twentieth century, the concept of "particle" and "field" described completely different physical quantities. Before the nineteenth century the concept of a field did not exist at all. For Newton, for example, there is no meaning in claiming that the Earth creates a gravitational field and curves space. The statement that the Earth attracts the Moon is sufficient. The concept of "field" first appeared when James Clark of Quasel showed that electromagnetic waves travel at the speed of light. From this unique connection, physicists were forced to assume that fields are more than just a useful mathematical description.

Not everyone swallowed the idea easily. Maxwell himself insisted that electromagnetic waves move on a medium called "the ether" and refused to consider the electromagnetic field as an independent entity. Along with the experimental failures to prove its existence, the idea of ​​the ether faded away completely when Einstein first presented the special theory of relativity. Albert's Torah denies the existence of a cosmic axis system relative to which all objects in the universe move. The belief in the existence of fields was significantly strengthened with the publication of the general theory of relativity which claims that the fabric of the universe is the gravitational field that dictates the movement of bodies. The new paradigm led the physicist Theodore Clause to assume that the electromagnetic force behaves equidistantly. Klose showed that a fifth dimension added to the universe could explain the electromagnetic force similar to the curvature of the four natural spaces (three spatial dimensions and one temporal dimension). The impressive theoretical success led the physicists to the hypothesis that it is possible to mathematically unify all forces in nature.

The fundamental change of physics in the 20th century

At that time, another revolution took place - quantum mechanics began to raise its head and play the cards. Planck's solution to the black body problem revealed a discrete structure to the universe. Planque's success led other scientists such as Born to describe the classical electromagnetic fields using quantum mechanics. In 1926, researchers showed that from the quantum description it follows that light comes in packets, exactly the same packets that Planck predicted to solve the black body problem. Later, the famous physicist Paul Dirac showed how quantum mechanics explains the spontaneous emission of radiation from energetic atoms. From this point on fields became commonplace in physics, but were still seen as objects distinct from particles. On the one hand, the material particles are "immortal" and on the other hand, force-carrying particles, such as the photon, can be absorbed and created without limit. The significant step towards the unification of ideas came relatively quickly in the XNUMXs by Jordan Wigner and in a separate article published by Pauli and Heisenberg. Physicists have shown that, on balance, the particles of matter are described with the help of waves in quantum fields. The practical uses for field theory were not long in coming - from radioactive decays, to proving the existence of neutrinos, to the discovery of anti-particles. Despite the successes, there were sometimes calls against those who believe that the field theory is only part of reality, even Dirac believed that the theory could not describe matter particles at the same time because the existence of the anti-particles forced Dirac to add an "infinite sea" of negative energy to the universe. The counter reaction was repelled by a series of articles by Pauli and Oppenheimer who managed to describe the antimatter from field theory in a natural way without adding "crazy" ideas. From then on, the scientific community changed the position of quantum field theory as a pillar for describing reality: the entire universe is made up of fields that obey quantum mechanics and private relativity, everything else comes from the dynamics of these fields.

The challenges of field theory

Field theory raised the suspicion that the interaction of the hydrogen atom with the electromagnetic field changes its emission spectrum. In the late thirties, Oppenheimer heroically showed that the interaction of the hydrogen atom with the electromagnetic field adds an infinite amount of energy. Infinite sizes (perhaps apart from the assumption of the size of the universe), have never been measured, certainly not in the simple hydrogen atom. The catastrophe of measurable quantities, somewhat reminiscent of the black body problem, shattered physicists' hopes of finding a unifying description of nature. To solve the problem physicists have proposed a wide variety of far-reaching explanations. Dirac himself argued that negative probabilities should be generalized to correct for the infinite contributions in the energy change of the hydrogen atom.

A decade after the publication of the article, the solution has arrived, and it is much less exciting than what Dirac proposed. It is true that the parameters in theory are infinite, but they do not represent the quantities measured in the laboratory. Under redefinition of the parameters, the infinite expressions can be eliminated and the measured magnitude can be obtained. This method proved itself when Schweigner calculated for the first time in 1949 the magnetic moment of the electron - a quantity indicating the degree of rotation of the electron under the influence of external magnetic fields. Today the magnetic moment is calculated up to the ninth digit and corresponds exactly to the experimental results. The magnetic moment of the electron is a resounding success by any scientific standard.

The re-bloom

The heyday of field theory began in the seventies of the last century. In an article that won the Nobel Prize, David Gross and his colleagues developed the "color theory", or in other words, the mechanics of the strong nuclear force. The researchers proposed for the first time an explanation for the attraction of the particles charged with "color" (the charge of the strong force). Thanks to the phenomenon known as "free asymptotics", the same particles are attracted less as the relative distance between them is smaller (contrary to conventional wisdom, the force usually decays with the distance). At the same time, measurements of cosmic radiation, the multitude of accelerators, and the multitude of evidence from radioactive decays helped in the creation of the great particle catalog of nature and in building the infrastructure for the standard model. On the other hand, the "zoo" of the particles caused confusion and bewilderment among the physicists. The huge amount of particles created a sense of disorder and randomness in nature. The picture became clear thanks to Gal-Man's genius, when a fundamental pattern for particles in nature was revealed to him. The model that claims to unify all the forces and particles in nature under a single mathematical formalism could not complete the task without the recognition of the enormous importance of symmetry in nature. Symmetry dictates the laws of nature and draws the mathematical pattern for describing the interactions of the particles with themselves and their environment. Thanks to Gellman's recognition of symmetry as a cornerstone in physics, he revealed an internal structure to particles that had been considered elementary until now. The protons and neutrons are made up of quarks, particles that carry a fractional electric charge and a color charge. After Gelman's discovery, it seemed that field theory had reached its golden age. The standard model that brings together all fields and elementary particles manages to explain nature at the most basic level. Now we can finally ask the really hard questions - how did it all start? A host of evidence and an impressive theoretical understanding created the following picture: the universe began in an unimaginably dense area with an unprecedented energy density. The fabric of the universe unraveled thanks to a random quantum process that released the concentrated energy. The swelling known as "inflation" cooled the universe and reduced the degree of symmetry expressed by the laws of nature. Thanks to gravity, in a long and drawn-out process cosmic structures, galaxies, suns and planets came together.

Question marks are on the way

The scientific story is attractive and fascinating, but many question marks still exist. The dark matter and dark energy that are able to theoretically explain the rotation speed of the galaxies, the cosmic radiation spectrum and the expansion of the universe, are not included in the standard model. The revolutionary ideas receive daily articles in the scientific community dealing with theories "beyond the standard model". Whether the dark matter is a liquid that fills the universe, a heavy or light particle, perhaps a neutrino or a completely different phenomenon, they are all explained under field theory models. It is likely that these will receive an adequate solution as soon as a suitable quantum theory for gravity is found. As a matter of fact, quantum theories for weak gravitational fields exist on the market and they fit nicely with past assumptions. The remaining challenge is to describe a quantum theory for gravity when the field strength is greater than all the parameters of the system. In this case, the mathematical tools we have are unable to solve the infinities that appear in the calculations, the mathematical consistency is broken and we have to look for new ways to describe the system. In the last decades, they tried to circumvent the mathematical problem by means of the principle of duality. Physicist Maldesena showed that gravitational calculations can be converted into gravity-free field theory calculations with conformal symmetry (in general, this is Lorentz symmetry together with stretching symmetry) in one less dimension. This method was a resounding success and with its help we were able to understand a little more about the nature of black holes and universes in the presence of strong gravity. Unfortunately, the method is only correct for universes with negative concavity, the opposite of the universe we live in. It turns out that the principle of duality is also used by physicists outside of gravitational forces - mapping difficult problems to parallel problems that are easy to solve is not a simple thing, but if it is at hand it is extremely powerful. Another challenge beyond strong gravity is the strong force, which prevents physicists from performing mathematical calculations at low energies. The reason for this stems from the fact that physicists tend to perform perturbative calculations, i.e. around a system that they know how to fully describe. The perturbative method examines how small changes will affect the dynamics and physical quantities. In cases where strong forces are involved, weak perturbations do not exist at all. Physicist T. Hoft managed to circumvent the problem in an article he published in 1974 in which he introduced a new small parameter that helped physicists predict measurable quantities with the help of perturbative methods. Another powerful method to bypass the perturbative calculation is with the help of topology. It turns out that behind the mathematics of field theory are hidden real gems from the world of topology with the help of which physical quantities can be calculated only thanks to the spatial conditions that a system is forced to exist. Quantum topology led to the Aaronov-Bohm effect, the quantum Hall effect, exotic substances and many other phenomena that moved physicists forward towards the unification of general relativity and quantum mechanics.

We are just at the beginning of the search for new methods to describe the universe, ones that are not based on the principles of the past and require thinking outside the box. In truth, you don't have to go too far, the new methods we have already discovered are just beginning to scratch the surface and the hidden potential is slowly beginning to be revealed. Theoretical physics is at the dawn of a new century characterized by a sense of accomplishment, boldness and audacity to search for new ideas that may bring about another scientific revolution.

Scientific history is taken From Steven Weinberg's article

More of the topic in Hayadan:

• A quantum threat to special relativity / David Z. Albert and Rebecca Gal Chen
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