Principle of superposition and boundaries of its application

The principle of superposition is characterized by the fact that it occurs in many branches of physics. This is a certain provision, which is used in a number of cases. This is one of the general physical laws on which physics is built, as a science. This is also remarkable for scientists who apply it in different situations.

If we consider the principle of superposition in the most general sense, then according to it, the sum of the action of external forces acting on the particle will be composed of the individual values of each of them.

This principle is applied to various linear systems, i.e. Such systems, whose behavior can be described by linear relations. An example is a simple situation where a linear wave propagates in a certain medium, in which case its properties will be preserved even under the influence of perturbations arising from the wave itself. These properties are defined as the specific sum of the effects of each of the harmonious components.

Applications

As already mentioned, the superposition principle has wide enough scope. Most clearly, its effect can be seen in electrodynamics. However, it is important to remember that considering the principle of superposition, physics does not consider it a concrete postulate, but a consequence of the theory of electrodynamics.

For example, in electrostatics, this principle operates in the study of the electrostatic field. The system of charges at a particular point creates a tension that will be added up from the sum of the field intensities of each charge. This conclusion is used in practice, because with its help it is possible to calculate the potential energy of electrostatic interaction. In this case it will be necessary to calculate the potential energy of each individual charge.

This is confirmed by the Maxwell equation, which is linear in vacuum. This also implies the fact that light does not dissipate, but spreads linearly, so that individual rays do not interact with each other. In physics, this phenomenon is often called the principle of superposition in optics.

It is also worth noting that in classical physics the principle of superposition follows from the linearity of the equations of individual moving linear systems, and therefore is approximate. It is based on deep dynamic principles, but proximity makes it not universal and not fundamental.

In particular, a strong gravitational field is described by other non-linear equations, so the principle can not be applied in these situations. The macroscopic electromagnetic field also does not obey this principle, since it depends on the effect of external fields.

However, the principle of superposition of forces is fundamental in quantum physics. If in other sections it is applied with some errors, then at the quantum level it works quite accurately. Any quantum-mechanical system is depicted from wave functions and vectors of a linear space, and if it is subject to linear functions, then its state is determined by the principle of superposition, i.e. Consists of a superposition of each state and a wave function.

The boundaries of application are rather arbitrary. The equations of classical electrodynamics are linear, but this is not the basic rule. Most of the fundamental theories of physics are constructed from nonlinear equations. This means that in them the superposition principle will not be fulfilled, here we can include the general theory of relativity, quantum chromodynamics, and also the Yang-Mills theory.

In some systems, where the principles of linearity are only partially applicable, the superposition principle, for example, weak gravitational interactions, can be conventionally applied. In addition, when considering the interaction of atoms and molecules, the superposition principle is also not preserved, which explains the variety of physical and chemical properties of materials.