Shailendra Rajput and Asher Yahalom

Ariel University

Relativistic Dynamics

The 12^{th} Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and
Fields

Previously, we have shown that Newton’s third law cannot strictly hold in a distributed system due to the finite speed of signal propagation. Hence, action and reaction cannot be generated at the same time due to the relativity of simultaneity. As a result, the total force does not add up to zero at a given time. It was demonstrated in a specific example of two current loops with time-dependent currents, and the analysis led to the possibility of a relativistic engine. The system is not composed of two material bodies but a material body and field. As the system is affected by a total force for a finite period, hence the system acquires mechanical momentum and energy. Here, the question arises that we need to abandon the law of momentum and energy conservation. It was also demonstrated that any momentum gained by the material part of the system is equal in magnitude and opposite in direction to the momentum gained by the electromagnetic field. Hence the total momentum of the system is conserved. We also briefly discussed the material composition, structure, and properties of metals that should be used in a relativistic engine. Preliminary magnetic energy considerations in the relativistic engine were also discussed. Here, we give a detailed analysis of energy conservation in a relativistic engine, including radiation losses and the exchange of energy between the mechanical part of the relativistic engine and the electromagnetic field. It is observed that the field energy expenditure is six times the kinetic energy gained by the relativistic motor. Two times comes at the expense of the electric field energy and four times at the expense of the magnetic field energy. The relativistic engine may have radiation loses which are of order , those loses may be avoided by cleverly constructing the loop coils orthogonal to each other. We also provide relativistic corrections to the mutual inductance expression up to the order of .