Is it a particle or a wave? -Describing quantum mechanical objects-

The electrons that appear in quantum mechanics are certainly completely different from classical particles, but it is not strictly correct to say that they are "both particles and waves." Furthermore, the explanation often found in various introductory books on quantum mechanics, which states that they are "neither," actually lacks accuracy as well. This is because the concepts of "particles," "strings," and "waves" exist independently within quantum mechanics. In this context, "wave" refers to a quantum field (Dirac field) such as an electromagnetic field. When the context and energy range are specified, "electron" refers to one of these three. So, is the electron concept first learned in quantum mechanics a particle, a string, or a wave? At least within the scope of non-relativistic quantum mechanics, it is described as a particle. It is a "particle," not a "string" or a "wave." Let us look at the reasons for this.

For example, in a single trial of the double-slit experiment, an electron is always a particle localized at a certain location, and it has never been observed as a wave in each individual trial. In the data obtained by repeating the same experiment many times, wave-like interference fringes are observed as a collective. However, in individual data, electrons are indeed observed as point particles. Even if you fire them one by one at the screen, wave properties are only seen in the data for the large collection finally obtained. The individual electron, not the collective, remains a "particle" throughout.

In the first place, the wave function in quantum mechanics is expressed as the inner product of the state vector describing the state of the system and the eigenstate vector indicating the independent events that the object can take.

Therefore, in the case of a zero-size particle localized at a certain location, such as a low-energy non-relativistic electron, the wave function can be written as a complex function regarding position coordinates. If it is an extended string or field, it becomes a wave functional where the function representing the shape of the string or field itself serves as the argument. These three are properly distinguished as theories.

Even in the double-slit experiment, because there is a premise that "the electron is a point particle," that single electron does not become a string or a wave in the first place. Therefore, it is clear that the statement "electrons become particles or waves" is not correct. Within the scope of this theory, the electron itself is always a particle and never turns into a wave. Also, "electrons are neither particles nor waves" is wrong, and at this level of discussion, it can be clearly stated that they are "particles."

Diffraction phenomena and interference phenomena are observed for the behavior of a collection of electrons governed by a wave function. Even in the double-slit experiment, by performing the experiment many times and accumulating data, the interference between the contribution of the history of passing through the upper slit and the contribution of the history of passing through the lower slit for particles that do not become waves leaves a striped pattern on the screen. This wave-like behavior for a collective occurs similarly for "particles," "strings," and "waves" (i.e., fields), but the concepts of individual particles, strings, or waves themselves are strictly distinguished from the behavior of their collective.

However, the picture described so far was for electrons in the theory of non-relativistic quantum mechanics. An electron in relativistic field theory is an excitation of a "wave" called the Dirac field. Also, in superstring theory, which is a candidate for quantum gravity theory, an electron is described as a "string" undergoing certain motions. In other words, the existence of an electron has diverse pictures in physics depending on the resolution we use to handle it. Furthermore, in recent theoretical physics, moving away from pictures that give a sense of some kind of reality like particles or waves, attempts are being made globally to describe electrons, other elementary particles, and even spacetime in a unified way as more fundamental "quantum information." As time passes, the understanding of "what is an electron?" is deepening. That is the kind of discipline physics, which is an empirical science, is.