Why is quantum mechanics important? We are used to seeing the world at the macroscopic level, our eye does not perceive what is really there at its microscopic level, and (maybe) it is better that way. We need a microscope or some other technology to detect the behavior of the smallest part of matter, the atom. The best description we have of the nature of the particles that make up matter is described by quantum mechanics. Subatomic particles such as electrons, neutrons, protons, quarks, and so on. We are made of matter, thus particles.

Every day, we humans dance the same quantum dance described by the physical laws that, during the 20th century, scientists such as Heisenberg, Bohr, Pauli, Einstein, Schrödinger, De Broglie tried to explain through their research and experiments. Heisenberg laid the foundations during his stay on the island of Heligoland, Germany, where he was able to calculate the matrix of numbers. Initially, he did not even know what this meant. A Neverland where seagulls screeched in the distance and where the insight of the waves is the only Gaussian noise you can hear. In the mid-1920s, quantum mechanics began with Heisenberg’s uncertainty and Born’s wave function.

Quantum theory was the brainchild of many people, as we have seen, but Bohr was the godfather, the man everyone admired. It was Bohr who first applied the notion of discontinuity within the atom. It was Bohr who had explained the behavior of the simplest atom, hydrogen. Even more, it was Bohr who had an almost demonic obsession with the truths of quantum theory and the dissemination of its fundamental principles to young scientists. He was the one who told Einstein: “Hey, Albert, look, God really plays dice!” In any case, Einstein remained convinced that, sooner or later, the strangeness of the quantum would be compensated by something else. He argued that there is a deterministic world that lies below quantum theory; Bohr, on the other hand, supported the idea that quantum theory is complete and that the quantum world is undeniably probabilistic.

Yes, you read that right. We are governed by ‘probability’.

The fundamental laws of modern physics provide statistical information. Heisenberg stated that precise information about the state of an object in the universe at a given time is not only impossible to determine, but that if it were possible, we would not have precise knowledge of both the future and the past, but only statistical information.

If you want to explain how electrons move through a computer chip, how photons of light transform into electrical current in a solar panel or amplify themselves in a laser in an optical fiber, or even just how the sun continues to burn, you will use quantum physics. Electronics is a science attributed as that branch of physics that studies the motion of electrons. Engineers and scientists have developed a whole series of macromodels such as BJT and FET to define the behavior of electrons to travel in certain states. Quantum mechanics tells us that an electron can only occupy certain energy levels. When looking at a large group of electrons, such as those found in semiconductors, these levels are “bands” or ranges of permissible energy values. When the semiconductor is connected to a voltage that is within the energy band, it conducts electricity. When connected to a voltage outside the allowable energy band, the device does not conduct electricity. It acts as an insulator. This is how the transistors turn on or off and the computer reads it as 1 or 0 bit.

Quantum physics characterizes simple things like the way the position or momentum of a single particle or a group of a few particles changes over time. In the case of high speeds, close to that of light, support is needed such as Albert Einstein’s theory of relativity, to which we will return later. Several quantum field theories deal with the fundamental forces through which matter interacts: Electromagnetism, which explains how atoms are held together; the strong nuclear force, which explains the stability of the nucleus in the heart of the atom; and the weak nuclear force which explains why some atoms undergo radioactive decay. Radioactive decay is a set of processes through which atoms change their states after a certain time, thus reaching lower energy but with more stability, and emitting particles of various kinds. The process continues (it is called the decay chain) until a condition of maximum stability is reached. In recent years, there have been theoretical and experimental studies to combine all these forces to arrive at the equation of God, a single simple equation that can describe nature as it is made. I’m talking about the standard model. One example is the discovery of the Higgs boson, the particle that explains why other particles have mass.

The first quanta we know well are photons (the particles of the sun), the elementary constituents of quantum mechanics, simple massless particles that bombard and heat us every day, and through which we are also able to produce electric current by exploiting the photoelectric effect with photovoltaic panels. The photoelectric effect explains the property of electrons to be ejected from the surface of a metal after being flooded with a stream of photons. The energy of the photons is transferred to electrons which acquire kinetic energy to change orbital, become photoelectrons, and get ready for a circuit to transfer electrical power.

The word “quantum” comes from Latin “Quanto” and reflects the fact that quantum models always imply something that arrives in discrete quantities. So it is not only probabilistic but also discrete. The energy contained in a quantum field comes in integer multiples of a certain fundamental energy. For the light, this is associated with the frequency and wavelength.

Planck created a mathematical formula for the frequencies of light energy emitted by a hot body. It showed that hot objects would emit ‘red’ frequencies. The hottest objects would emit frequencies of all visible colors, making them appear white. Planck’s formula worked, all thanks to a key idea. Before Planck, scientists believed that energy was on a continuous scale. They thought it was possible for an object to have an energy value on that scale. Planck’s radical hypothesis was that, at the subatomic level, hot objects could only emit energy in small units or “packets”. He called these quantum packets. Planck said that the amount of energy in a quantum increases with its frequency. Lower frequencies, such as red light, have less energy than higher frequencies, such as those in white light. However, Planck couldn’t find a reason to explain why energy was quantized in this way. In a letter to a friend, he wrote that this mathematical assumption in his formula was an “act of desperation”.

Niels Bohr formulated the answer a couple of years later.

Bohr revolutionized the orbital model. He said the electrons had to be on a series of specific paths. These paths were like the orbits of the planets around the sun. He called them electron orbitals. Each orbital has an associated energy level. When an electron absorbs enough energy, it “jumps” from one orbital to the next larger one. When an electron “falls” from one orbital to a smaller one, it emits energy. The amount of energy emitted is exactly the difference in energy between the two orbitals. This is why energy exists in discrete values, as “quantum”, rather than on a continuous scale.

The earth revolves around the sun following its motions of rotation and revolution. As other planets do. Newton demonstrated what forces are at play, that is the gravitational attraction. Einstein tells us something more by introducing space-time. The microscopic level, i.e., the smallest part of matter, is practically the same. There is a nucleus similar to our sun, and then there are electrons located in orbits. Each orbit has a limited number of electrons with very specific characteristics in terms of spin. Well, with a similar analogy, orbitals are our planets and electrons its inhabitants.

When we observe the world, at the macroscopic or microscopic level, the substantial configuration is the same. Something controls everything (sun), something else follows the motion and keeps the atom alive. No particular reason why? We apparently don’t know. Electrons can jump from one orbit to another, and we see it as “observation”. In theory, we humans could also jump from one planet to another but with a considerable expenditure of energy. We might have done it already, we don’t know. The only problem is that it takes energy, orders of magnitude larger. Remember that, when an electron jumps from one orbit to another, we observe it through a photon that is emitted or absorbed as appropriate. That is, a ray of light that enters or leaves matter. In the first case, I think of a meteorite that enters the earth with force, thus changing evolution, forcing then to leave the house to take refuge elsewhere, in another orbital. We know that electrons of the same type cannot exist within an orbit, technically with the same spin. Without going into details, spin is related to the electromagnetic behavior of an electron. Two electrons on an orbit must have opposite spin, that is to say: two equal people in the same room fight, and it’s better to avoid that!

Pauli formalized this principle.

The mathematical description of a quantum system typically takes the form of a “wave function”, represented in the equations by the Greek letter psi: Ψ. There is much debate as to what, exactly, this wave function represents: Some think of the wave function as a real physical thing and some think of the wave function simply as an expression of our knowledge (or of the lack thereof) regarding the underlying state of a particular quantum object. Quantum physics is known for being strange because its predictions are dramatically different from our everyday experience (at least for humans). This happens because the effects involved get smaller as objects get larger: If you want to see quantum behavior, you basically want to see particles behaving like waves, and the wavelength decreases as the momentum increases.

Quantum mechanics is not local. What does that mean? The results of measurements made in a particular location may depend on the properties of distant objects and in a way that cannot be explained “normally”. This, however, technically does not allow information to be sent faster than the speed of light, although there have been several attempts to find a way to use quantum nonlocality. Quantum mechanics is the best theory we have for describing the world of subatomic particles. Perhaps the best known of its mysteries is the fact that the result of a quantum experiment can change depending on whether or not we choose to measure certain properties of the particles involved. When this was noticed, the scientists were deeply troubled. It seemed to undermine many concepts in practice with a world out there, independent of us. If the way depends on how – or if – we look at it, what can “reality” really mean? We can interpret this as parallel worlds.

The main advantage of the many-worlds interpretation is a realistic interpretation. It is often greeted with disbelief, as it implies that people (along with other objects) branch out constantly in countless copies, but this, in itself, is no argument against it. Every day, we venture into people who behave differently. However, the branching of people leads to philosophical difficulties regarding identity and probability. In addition to the parallel worlds, another explanation is contained in the hidden variables. What does it mean? The theory of quantum mechanics in its probabilistic nature is essentially due to physical mechanisms that are not yet known, or that is still incomplete. In any case, this theory is incompatible with some experiments conducted by Bell.

According to some studies, the universe could be described by a gigantic wave function that contains all possible realities within it. This “universal wave function” is a combination, or superposition, of all possible states of its constituent particles. As it evolves, some of these overlaps break up, making some realities distinct and isolated from each other. In this sense, worlds are not exactly “created” by measures. They are just separate. This is why we should not, strictly speak of a “splitting” of worlds, as if two were produced by one. Rather, we should speak of the unraveling of two realities that were previously only future visions of one reality.

At the beginning of the paragraph, I said that we are made of particles. We have our beautiful wave function that intersects with the others generating in turn many sub-functions. At the end of our life cycle, the particles recombine with the universe generating other wave functions, other molecules as a set of particles giving life to a new life, not necessarily what we mean, the human being.