In traditional Newtonian physics, matter and energy are two essential but very different concepts. Matter corresponds to physical objects, the movement of which is intended to be described quantitatively, and which are characterized by their mass, that is, their inertia in the face of changes in the state of motion. On the other hand, energy is a more abstract entity, and it can be understood as the ability to do work, that is, to exert forces on matter (thus, the kinetic energy of movement of one object can exert forces on another by shock; likewise, the potential energy of an object describes the storage of this capacity, and produces movement when released.) It is a familiar and everyday principle that both matter (or mass) and energy are neither created nor destroyed, only transformed.
However, these seemingly immovable principles are only approximations to a deeper reality, which clearly manifests itself only when trying to describe objects with speeds close to the speed of light, the realm of Special Relativity. One of the most profound results of Einstein's Special Theory of Relativity is the relationship between matter (or mass) and energy. In summary, any form of energy present in a system contributes to its mass, understood as inertia with respect to the change in its state of motion. For example, consider a hollow metal ball, filled with water at rest, and an identical ball but filled with water in agitated motion. In Special Relativity, the kinetic energy of the movement of water in the second case manifests itself in that the mass of the second filled ball is slightly greater than that of the first (in general, with such an enormously small difference that it is unobservable in mechanical experiments with hollow balls, but not null in principle). Likewise, a hollow ball filled with electromagnetic radiation has a mass slightly more than an empty hollow ball, due to the energy of the electromagnetic field in the first case. As a final example, this principle is related to the existence of a maximum speed (that of light c = 300,000 km / s) in Relativity. When an object has high speed, its kinetic energy can be translated into an increase in its mass (inertia), making it much more difficult to accelerate it further. As the speed of light approaches, the contribution of the kinetic energy to the mass / inertia approaches infinity, so it is never physically possible to reach that limit speed.
Focusing on objects at rest, the above ideas are summarized in the famous equation E = mc2, which relates the contribution of an energy (of any type) "E" of a system with its contribution to the mass "m" of that system. Alternatively, it also states that a particle with mass (at rest) "m" has, simply because it exists, an amount of energy "E". This energy can be imagined as potential energy, which can be released when the system (the particle) undergoes any change in its mass. Therefore, mass and energy are interchangeable concepts. And the principle of conservation of mass and energy as independent entities is meaningless, and is replaced by the principle of conservation of mass-energy. That is to say, the existence of processes in which a certain amount of mass is released in the form of energy is perfectly possible, and conversely, of processes in which a certain amount of energy is transformed into mass of new objects or particles.
The processes in which a certain amount of mass from a system is released in the form of energy are familiar to us, since they occur in nuclear reactions. An example in the cosmic context is the fusion of hydrogen into helium in the hearts of stars, such as the Sun. The mass of a hydrogen nucleus (a proton) is 1.67 x 10-27 kg, while a nucleus of helium (two protons and two neutrons attached) is 6.64 x 10-27 kg. The Sun's nucleus is a factory that converts groups of four protons into helium nuclei. The process by which two of these protons are transmuted into two neutrons is mediated by the weak interaction, which is discussed in other chapters; likewise, in the fusion process they go through other intermediate states, with deuterium nuclei, etc. Fortunately, we are only interested in the energy balance between the initial state and the final state, which is independent of the intermediate steps. The difference in mass is approximately 0.04 x 10-27 kg, which corresponds to an energy difference of 0.36 x 10-11 Joules. Taking 1 kilogram of material we obtain an energy of the order of 1015 Joules, approximately 1 Megaton. The Sun burns approximately 6 x 1011 kilograms every second, so it emits 1011 Megatons per second, thanks to which our Earth is a suitable planet for our existence.
A similar calculation would allow us to calculate the energy released in a nuclear fusion bomb; or in a more beneficial way for Humanity, in future nuclear fusion plants, when this process can take place in a controlled way. Another example is that of fission reactions, such as those that occur in nuclear bombs, or in nuclear power plants. In this case, when a uranium-235 nucleus captures a neutron, it decomposes into, for example, a barium-141 nucleus and a krypton-92 nucleus, with the emission of three neutrons. The difference in masses between the initial and final systems is transformed into emitted energy, on the order of 1 Megaton per kilogram.
A final example closer to particle physics is the annihilation of matter particles with antimatter particles. For every known particle there is an antiparticle, a particle with exactly the same mass, but with opposite charges. When a particle and its antiparticle collide, they annihilate and release their entire mass in the form of energy, for example by emitting photons (electromagnetic radiation). As usual, we introduce energy units adapted to particle physics, specifically 1 GeV = 1.6 x 10-10 Joules. The energy equivalent of the mass of a proton is 0.938 GeV, so an annihilation of a proton and an antiproton at rest releases an energy of 1,876 GeV, about 100 times higher than fusion reactions.
Examples of nuclear reactors or bombs can lead us to speculate (as has been the case in certain works of fiction) with the possibility of building antimatter-based destruction artifacts. However, this is not feasible since antimatter is not found naturally on Earth (or in our observable universe), except in ephemeral phenomena such as natural radioactivity or cosmic rays. And the production of antimatter in laboratories is energetically very expensive, and highly inefficient. For example, CERN's Antiproton Decelerator experiment, Geneva, Switzerland, produces anti-hydrogen atoms; in its entire history it has managed to accumulate only 10 nanograms (that is, 10-8 grams), whose annihilation would produce the very small amount of energy of 10,000 Joules (equivalent for example to the consumption of a 60W bulb for 4 hours).
So far we have described processes in which mass is converted into energy. But there are many processes and phenomena in which energy is converted into mass. One of the most common (and therefore unnoticed) lies in the mass of a proton itself. A proton is a composite particle, made of three quarks (two "up" type quarks and one "down" type quark). However, the quark mass at rest is much, much smaller than the mass of a proton, only about 1%. The mass of the proton is in its 99% the manifestation of the energy of the very intense fields of the interaction of color (gluons) that hold the quarks together forming the proton. It is a physical embodiment similar to our previous academic example of a hollow ball filled with radiation, with the exception that in this case the (colored) radiation field is not an insignificant contribution (but the dominant one) to the mass.