^{3}.

We study properties of moving relativistic quantum unstable systems. We show that in contrast to the properties of classical particles and quantum stable objects the velocity of freely moving relativistic quantum unstable systems cannot be constant in time. We show that this new quantum effect results from the fundamental principles of the quantum theory and physics: it is a consequence of the principle of conservation of energy and of the fact that the mass of the quantum unstable system is not defined. This effect can affect the form of the decay law of moving relativistic quantum unstable systems.

Physicists studying the decay processes of unstable quantum systems moving with the velocity

Unfortunately, the experiments did not give any decisive answer for the problem which is the correct assumption:

In this paper, we analyze general properties of unstable quantum system from the point of view of fundamental principles of physics and quantum theory. Here, we show that the principle of the conservation of the energy does not allow any moving quantum unstable system to move with the velocity

The main information about properties of quantum unstable systems is contained in their decay law, that is, in their survival probability. Let the reference frame

Decay curve obtained for

Note that

Using relation (

A typical form of the instantaneous mass

In the general case, the mass (energy) distribution function

Now, let us consider the case when the unstable quantum system is moving with a velocity

From the fundamental principles, it follows that the total energy of the freely moving objects, both quantum and classical, stable and unstable, must be conserved. This means that if an experiment indicates the energy,

On the basis of this analysis, one can conclude that the rest mass

This situation has a simple explanation. Namely, despite the conclusions resulting from relation (

So in the case of the moving quantum unstable system, the principle of the conservation of the energy takes the following form:

The above conclusions result from the basic principles of the quantum theory. Taking this into account, one should consider a possibility that, in the case of moving quantum unstable systems, assumption (

From results presented in Figure

One more remark is as follows. Let us denote by

The last remark is as follows. It seems that the above-described effect can be relatively easily verified experimentally. It is because the conclusion that the velocity

The author declares that there is no conflict of interests regarding the publication of this paper.

The author would like to thank E. V. Stefanovich for valuable comments. The work was supported by the Polish NCN Grant no. DEC-2013/09/B/ST2/03455.