Principles of Invariance and Conservation Laws - History...

Invariance Principles and Conservation Laws

As you know, in physics, the principles that express the correlation (correlation) of the signs of processes are of great importance. But it is not enough to justify the correlation of signs. It is extremely important to point out their specificity. Which principles of physics deserve primary attention? It is essential that the principles of physics are realized not in any way, but in a quite definite way. According to the principle of least action, physical processes are performed in such a way that the extreme, as a rule, minimal, is the magnitude of the action (S), which is calculated by the formula

( 2 . 8 )

where L is the Lagrange function (Lagrangian), which, in the framework of classical mechanics, is equal to the difference between kinetic and potential energy.

Of course, it is also important to understand the mechanism for implementing the principle of least action. It is the process of interaction. And how is it realized? And this question is important. Let's try to answer it. Interacting objects are exchanged, in particular, by energy, masses, charges. It is interesting that the attributes exchanged between interacting objects are dynamic. Objects do not exchange either lengths, durations, or speeds. When considering the exchange nature of physical interaction, it is quite natural to assume the conservation laws. If the object A has passed a certain value to the object B , then it has not disappeared, but only changed its identity. Dynamic characteristics do not disappear, but only pass from one object to another. This fact is recorded by conservation laws, for example, by the laws of conservation of energy, mass, momentum, angular momentum, electrical and other charges.

As you can see, there is a close relationship between the dynamics of processes and the laws of conservation. The preservation of certain quantities is always realized in the processes of interaction. But, as it turned out, it correlates in a certain way with the operations of symmetry. The Greek word symmetry literally means proportionality. In physics, under symmetry is meant a change in the system, in which some of its characteristics remain unchanged, i.e. are invariants. In this regard, rather curious circumstances have emerged.

Issues of theory

The principle of least action is responsible for the law of conservation. The variation of the duration parameter entering into the principle of least action leads to the discovery of the law of conservation of energy. Variation of the length parameter leads to the law of conservation of momentum.

Variation of the parameter of the angular characteristic leads to the law of conservation of angular momentum.

As we see, under the aegis of the principle of least action there are three types of correlations: 1) change in duration - the law of conservation of energy; 2) change in the length - the law of conservation of momentum; 3) change in the angular characteristic - the law of conservation of angular momentum.

These correlations, of course, are not obvious. What is their meaning? Find an adequate answer to this question is not easy. But, as the author seems, it is quite possible. So, let's start his search.

Previously, it was noted that there is a certain subordination between physical parameters - not kinematics is primary, but dynamics: dynamics determines kinematics. Proceeding from this circumstance, it becomes evident that time is conditioned by acts of energy exchange. Accordingly, the length is determined by the acts of exchange of certain portions of the pulse. Finally, the angular characteristic is determined by the transfer of the angular momentum. So, our final conclusion is as follows: symmetry is determined by the dynamics.

It should be noted that the correlation described above between the variations of the kinematic variables in the composition of the principle of least action and conservation laws is often characterized with reference to the homogeneity of time and space, as well as the isotropy of space. Say, from the homogeneity of time follows the law of conservation of energy, from the homogeneity of space - the law of conservation of momentum, from isotropy of space - the law of conservation of the angular momentum. In this case, the homogeneity of time is understood as equal importance of all the moments and periods of time, the homogeneity of space - as an equal importance of all areas of space, and the isotropy of space - as the identity of its properties in all directions. In the author's view, such an explanation is not correct. Why?

The fact is that the principles of the theory are by definition ubiquitous. It is not true to say, for example, that in one area of ​​space they are true, but in another they are wrong. This means that the variation of the parameters of the length, duration, and angular characteristic of the principle of least action can not undo it. It is untenable to assert that the law of conservation of energy follows from the uniformity of time. Agreeing with this statement, we must assume that along with the homogeneity of time there is also its heterogeneity, which is allegedly incompatible with the law of conservation of energy. But it is impossible to introduce a correct definition of the inhomogeneity of time. The law of conservation of energy is in correlation not with the homogeneity of time, but with its entire nature. The opposition of homogeneity and inhomogeneity of time, as well as homogeneity and heterogeneity of space, as well as isotropy and anisotropy of space, is untenable. Not ignoring the principles of physical theory, it is impossible to give a consistent interpretation of the homogeneity and heterogeneity of time and space and, accordingly, the isotropy and anizotropy of space.

The principles of invariance are usually highly appreciated by physicists. In this connection, the conclusion to which Nobel laureate E. Wigner came: "It is the transition from one step to another, a higher one - from phenomena to the laws of nature, from the laws of nature to symmetry, as to the principles of invariance - what I call the hierarchy of our knowledge of the world around us. "

E. Wigner believes that cognition is three-step: single events laws principles of invariance.

Of course, he is in many ways right. Nevertheless, it may be appropriate to make some corrections to its conclusion. As emphasized above, in physics there is no more important concept than the original dynamic principle. In view of this circumstance, the Wigner scheme must be extended: single events → laws invariance principles dynamic principle.

And, of course, it is necessary to take into account that the Wigner scheme of cognition concerns only one stage of transduction, namely, to abduction. If we bear in mind the scientific explanation (deduction), then it does not end with a dynamic principle, but on the contrary, it begins: the dynamic principle → the principles of invariance laws → single events.


1. The dynamic principle is more important than the principles of symmetry. The symmetry is determined by the dynamics.

2. The conservation laws are derived from the principles.

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