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Physical interpretation of the point-like dimension of elementary particles

 According to the Standard Model of particle physics, the most fundamental building blocks of our material world are electrons and quarks, e...


 According to the Standard Model of particle physics, the most fundamental building blocks of our material world are electrons and quarks, elementary particles with rest masses that are described as point-like in extent. There are practical and methodological reasons for this point-like characterization. The practical reason is that when we observe these particles, we experience their existence as point-like, and the methodological reason is that if we were to consider these elementary particles as non-point-like, we would have to assume an internal structure as a consequence of their physical extension, which would result in theoretical difficulties for us to interpret. Therefore, the most obvious approach is to consider the appearance of elementary particles as point-like. 

But elementary particles certainly cannot be point-like in reality. Both quantum theory and general relativity, as well as the general philosophical worldview, preclude the existence of any physical object as a point-like entity, anything that exists without physical extension. In addition to the fact that wave nature is a defining characteristic of elementary particles, and that it is impossible for a wave to exist as a single point, if anything were point-like in reality, it would appear to have infinite physical properties. The reality of the physical existence of elementary particles is further nuanced by the fact that quantum theory also characterizes the quantum world of elementary particles in such a way that a single entity can exist simultaneously in different places at the same time, and even everywhere in space at the same time with a definable probability. 

Theories have been developed to resolve the contradictory existence of elementary particles. The most widely accepted is the so-called Copenhagen interpretation, according to which elementary particles have a dual nature, they are wave-like when we do not look at them, do not measure them, do not interact with them, and then they can be in several places at the same time, and under certain circumstances they can even interact with themselves, and they can be localized, concrete, point-like in physical extension when we look at them, measure their state, interact with them.

The Copenhagen interpretation raises fundamental problems of natural philosophy, but it has also helped to make the most accurate predictions of science and to provide precise practical mathematical procedures for characterizing the quantum world as we experience it. But human reason objects to the idea that the actual way our world exists should be subjective, that the state of elementary particles should depend on what we do or do not do with them. 

The practical implications of the Copenhagen approach are undeniable, but the difficulties of the model in the philosophy of science have led to the development of other models that attempt to interpret the behavior of elementary particles. Perhaps the most extreme version of these models is the Many-worlds Hypothesis, whose main difficulty is not the practical interpretability of the many well-defined different probabilities of the quantum world, but because the wave functions of the particles in the model are never required to collapse and thus take on specific values, it is precisely the point-like nature of elementary particles, which is considered fundamental, that the hypothesis cannot interpret in an evidential way.

An accepted interpretation of the point-like reality of non-point-like elementary particles is more a compromise resulting from the actual limits of our knowledge than a recognition of reality. Can this contradiction in our view of elementary particles be resolved in a way that is consistent with reality?

Our world obviously exists without contradiction, and therefore the contradiction in the description of our world must arise from the imperfection of our picture of the world. We do not know our world accurately enough for this contradiction not to exist in our current description of our world. So let us examine what the reason for the point-like nature of elementary particles tells us about our knowledge of the world.

The methodological reason for the point-like extension of elementary particles is a rather epistemological aspect, related to the level of our knowledge. It is a reasonable assumption that there is no structure of elementary particles, but there is no fundamental difficulty in abandoning it if new knowledge would support it.

More fundamental is the practical reason for the problem of point-like nature, which is that every time we look at, study, or interact with elementary particles, we experience their existence as point-like. To explore this reason more deeply, let us analyze the actual physics of our particle physics experiments. The most obvious practical investigation might be to analyze the method of examining electrons. 

According to the Standard Model of particle physics, there are three different types of interactions between elementary particles: the strong, the weak, and the electromagnetic interaction. The electron is not involved in the strong interaction, and when we usually study the behavior of the electron, for practical reasons we usually use the electromagnetic interaction as a test tool rather than the weak interaction. The electromagnetic interaction takes place through the interaction with photons according to the theory of quantum electrodynamics. The particle involved in the electromagnetic interaction emits and absorbs photons (virtual and real), which is the process that creates the actual electromagnetic interaction behavior that we experience. 

When we look at and measure electrons, we typically look at them through electromagnetic interaction, so the experiment is done by interacting the electrons with photons, and everything we know from the experiment is a reflection of the state of the electrons from the moment of emission and absorption of the photons. And real photons that we can interact with are particles moving at the speed of light, so the change itself caused by the experiment, the origin of the interaction, happens extremely quickly and therefore takes place in an extremely small region of space. Since practically all of our knowledge of the properties of the electron in the study comes from this interaction, which is localized in an extremely small part of space, the extent of which may be practically the smallest scale of size we have, and below which there is no smaller extent of physical dimension that can be known, the spatiality of the interaction, and thus the recognized electron itself, necessarily appears to us to be point-like. 

The point-like extension of elementary particles is not necessarily the physical reality of the existence of elementary particles, but it is the physical dimension from which we can obtain information about them, typically through interaction, which appears to be the smallest physical size that exists for us.

How can we see non-elementary particles as complex if the interactions available to us about them can also be derived in a similar way, from the smallest possible size range that exists for us?

The internal structure of protons is typically studied by the electrons that collide with them, by studying their interaction with electrons of increasing energy. Since the existence of an electron can be described as a wave function, quantum mechanics describes the higher energy electron as a wave function in a more localized state, so that the point-like interactions with higher energy electrons can occur over a smaller range of physical dimensions. In the study of protons, we find that as the energy of the electrons is increased, the information from the interactions exhibits a characteristic distribution over a well-defined energy (size) range, which can be theoretically interpreted as the proton being a composite particle whose components are elementary particles, since as the size range of the possible interactions that can be created is reduced (using even higher energy electrons), the characteristic distribution of the information from the point-like region of the interactions does not seem to change. 

The appearance of the point-like nature of elementary particles comes from the smallest size range we have of the interactions that give us information about them, not from the actual form of existence of elementary particles. Elementary particles exist, can exist, only in a wave-like form. The collapse of the wave function never occurs, nor does it branch out to create new worlds, but simply the wave-like existences influence each other, interact with each other, and change, and it is from the moment of that change that we get information about the state of the wave function. The wave-like existence never ceases, but the states of the waves change through interactions, and the moments of change are our experienced world, including what we also describe as the macro-world, which is concrete and unambiguous through the concreteness and unambiguity of the moment of change. There is no contradiction between our experienced world, which exists unambiguously for us, and the quantum world of wave nature, which is characterized only by probabilities. There is, was, and will be only one world that we have and that exists.

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