In mathematics it is possible to treat and operate with both infinitely large and small quantities. Thus, when it comes to the infinitely small, we have the definition of “point”, which is described as an element devoid of dimension, volume or area, that is, it has no size and determines a position in space. However, although they have no dimension, the points are fundamental in mathematical calculations.

In physics, on the other hand, when it comes to real objects, if they are so small - smaller than Quarks, for example, which are basic elements that make up matter - formulas do not work, bringing strange results, usually infinite. So when we try to describe something of the proportion of a point reacting to the forces present in a tiny space, things get complicated.

Although mathematicians are totally comfortable dealing with infinitely small sizes and distances, physicists wonder if there is a limit to the smallest possible object or whether there is an infinitely small space. If we consider gravity in these conditions, in infinitely small dimensions, this force becomes infinite, destroying the “fabric” that forms space and creating a foam of black holes.

Points

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Throughout history, humanity discovered - with the Greeks - that matter was made up of atoms, and later (with JJ Thomson) that atoms are made up of electrons. Then in the 1930s Walton and Cockcroft, a pair of British physicists, managed to separate the atomic nucleus with a particle accelerator. That was just the beginning ...

Since then, through successive experiments and technological development - and the construction of increasingly powerful particle accelerators - we find that the nuclei of atoms are made up of protons and neutrals, and these in turn are composed by the quarks.

However, while it seems that the basic building blocks of matter are “particles, ” it has not yet been possible to divide quarks and electrons through today's particle accelerators.

Theories

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To circumvent this problem and deal with infinitely small proportions and spaces, quantum physics relies on some parallel alternatives - theories - such as Wave-Particle duality or Heisenberg's Uncertainty Principle, which deals with the impossibility of determining simultaneously what is the velocity (or energy) and position of a particle at a given instant.

There are two theories - which have not yet been proven in practice - in this regard. One assumes that the smallest "thing" in the universe is much smaller than quarks. In fact, this thing would be something real and tangible, finite in size, though much, much smaller than any known particle, and it was trying to prove this theory that the Higgs Boson was discovered.

Image Source: Reproduction / CERN

The other theory is strings and superstrings, in which physicists theorize that instead of particles, the smallest things in the universe would be infinitely thin strings - but of some length - that would be vibrating like the strings of a violin. Each type of vibration would correspond to a particle described by the standard model, that is, an electron, a quark and so on, not to mention that in these theories one works with the idea of ​​up to eleven dimensions, suggesting the possibility that there are parallel universes.

Answers?

However, while they are fascinating and potentially explain what is, after all, the smallest thing in the universe - and what would be the fundamental element that makes up matter - these theories, to be proven, need to be replicated in the laboratory. And while physics has come a long way in recent decades, we are still far from answering such questions as “how infinitely large” and “how infinitely small” the universe is.