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Conservation of the energy-momentum. A simple demonstration of the no-interaction theorem in classical physics. (English) Zbl 1411.81233

Summary: In Relativity the sum of 4-vectors in different points does not generally represent a 4-vector. By using this result, it is shown by simple methods that the total energy-momentum of a system of point particles represents a well-defined 4-vector if the particles do not interact. It is proved that this is equivalent to the no-interaction theorem in Classical Physics. This theorem difficulties the study of a system of interacting particles since it is not even possible to define the total energy-momentum nor the reference frame where the system is at rest. This impediment is avoided by adding to the energy-momentum tensor the stress tensor describing the interaction. As an example, this is applied to a system of charged particles. In the process, the equation of motion for a charged particle including the self-force is formally obtained. However, when a thermodynamic system is analyzed from two different reference frames with a relativistic relative velocity, the interaction between the particles and the walls of the volume cannot be described by means of a covariant stress tensor and consequently the proposed technique is not feasible. Despite the above mentioned drawbacks, a covariant theory of the relativistic transformation laws of the thermodynamic quantities is developed.

MSC:

81V19 Other fundamental interactions in quantum theory
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
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