Updated December 30, 2021

A subatomic particle is a component of matter smaller than one atom (1 ångström or 0.1 nanometer or 10^{−10} meter).

With E=mc^{2}, physicists realized that they could create particles by transforming energy into matter. Thus by accelerating corpuscles to a speed close to that of light, they were able to transform movement into particles. From then on, the bricks of reality have become radiance of extraordinary richness, they are no longer finite number of particles but energy composed of elementary particles or interactions.

E=mc^{2} does not include momentum i.e. kinetic energy. The equation which includes kinetic energy is E^{2}=p^{2}c^{2}+m^{2}c^{4} where p is the momentum.

Since we have squared the energy, in the mathematical sense there are two solutions to this equation. A positive solution and a negative solution and both make equal sense.

Intuitively this energy, E=√p^{2}c^{2}+m^{2}c^{4} does not make sense physical than positively. Negative energy makes no sense, just like negative mass or negative velocity.

However Paul Dirac (1902-1984) will consider the 2 solutions √ and -√ and above all take the negative solution seriously. Dirac understands that these values exist in the positive domain but also in the negative domain of energies.

In quantum physics the energies are quantified which implies that only certain particular values of the energy are possible.

Physical systems in general stabilize themselves by minimizing their energy, and find their equilibrium in the fundamental states of matter. But if negative energy states exist, the system should stabilize in these lower energy states, and therefore fall into negative energy states and then disappear from the real world !!!

Why doesn't an electron that is in a state of positive energy fall into a state of negative energy?

In 1925, Wolfgang Pauli (1900-1958) proposed a principle according to which electrons belonging to the same system cannot be simultaneously in the same quantum state. Subsequently, this principle will be generalized to any fermion or half-integer spin particle.

In other words, in quantum mechanics, 2 particles cannot be in the same quantum state at the same place at the same time (Pauli exclusion principle).

In 1931, Dirac will consider that all the states of negative energy are filled to infinity. Because if all the negative energy levels are filled, then it is impossible for other electrons to fall into the negative energy levels, which resolves the paradox. So there are particles in these energy levels that are called from the Dirac Sea.

Antimatter therefore exists and it will be measured experimentally by Carl Anderson (1905-1991) in 1933 by discovering the positive electron, or positron, in cosmic rays. *note: in quantum mechanics the state of a particle characterizes all the knowledge that is available if measurements are made on this particle. The state of the particle therefore contains all the information available about the particle. From this state, we can calculate the probability of finding such and such an angular moment, such energy, such speed or such impulse. It should actually be understood that the system is in a single quantum state, but that the measurements can give several different results, each result being associated with its probability of appearing during the measurement. *

The antiparticles are everywhere in the void around us and it is possible to communicate to them a certain amount of energy to make them appear in the real world of positive energies. The void is an infinitely deep sea of occupied energy levels.

Antiparticles are not the negative energy particles (red circle), they are the holes (red circle) left in the area of negative energy particles when a negative energy particle appears in the real world.

Dirac understands that this hole (antiparticle) has an energy that can be measured experimentally. Since energy and electric charge are conserved, the anti-electron must have a measurable charge opposite to that of the electron. What is remarkable is that this prediction will be verified in 1933 by Carl Anderson while he was doing research on cosmic rays.

To produce antimatter, enough energy is needed to cross the gap that goes from negative energies to positive energies. Indeed if we strike a virtual antiparticle with sufficient energy equal to twice the mass of the squared electron, we will create a particle of positive energy observable in the real positive world.

A particle for example an electron will appear in the positive world leaving a hole that is to say a positron in the world of negative energies.

This positron has the same mass as the electron but an opposite electric charge coming from the emptiness induced by the passage of the electron from the Dirac sea into the world of particles of positive energies.

When an electron encounters an antielectron, a positron, they annihilate into two photons of 511 kev.

With a Geiger counter (instrument for measuring a large number of ionizing radiation) we can see very weak lines of gamma photons with an energy of (511 keV/c2) which corresponds exactly to the mass of the electron.

As the mass of an electron is 511 kev it takes 1 Mev to go from n-1 (world of negative energies) to n1 (world of positive energies).

A proton has a mass of 938.27 MeV/c2, to create an antiproton, it will take 2 Gev. In other words, the more massive the particle, the more energy it takes to make it appear in the real world.

The antiparticles are well around us and even in us. Our own body emits some antiparticles (antineutrinos) when the potassium 40 in our body breaks down.

Are antiparticles really just holes in the Dirac Sea?

In the theory of Dirac a hole is not a particle but a lack of particle is an antiparticle of opposite charge, of opposite spin, of identical mass to the real particle. In quantum theory, antiparticles are real particles rather than holes. Which is mathematically equivalent to the Dirac Sea.

In summary, the hole can be thought of as a new type of particle, called an antiparticle which has opposite energy to the particle. If a particle is a fermion, then it must have a corresponding antiparticle. Antiparticles can be created with nothing but energy. If a particle and an antiparticle meet they can disappear in a burst of energy, the technical term is annihilation.

In 1933 the positron was discovered in cosmic rays by Carl Anderson (1905-1991). In 1955 the antiproton was discovered by Emilio Segrè (1905-1989). In 1956 the antineutron was discovered by Bruce Cork (1916-1994). In 1965 an antideuteron (nucleus of the antideuterium) was created in the CERN synchrotron. In 1995 the first atom of antimatter (antihydrogen) was created in a CERN laboratory. In 2011, the heaviest anti-nucleus (anti-helium-4) was observed.

The red circle represents the hole left in the infinite sea of Dirac by the electron going into the real world of positive energies.

A hole in a vacuum represents the absence of a state of negative energy and negative charge when an electron of positive energy and positive charge appears in the real world of positive energies.

A negative energy state is empty and a positive energy state is filled. A hole is perceived as a positron of positive energy.

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