According to Newton’s third law, there is a reaction of equal magnitude for every action in the opposite direction. Thus the total force in a closed system that is not affected by external forces is zero. However, the principle of relativity states that the propagation speed of any signal cannot be higher than the speed of light. Hence, the total force in the system cannot add up to zero because of the finite speed of signal propagation. Retardation in special relativity was thus suggested as a basis for relativistic engine. In our previous works, we have demonstrated this phenomenon in a specific example of two current loops with time dependent currents in one of the loops [1]. An assembly of a permanent magnet and one-time dependent loop current was also utilized [2, 3]. The total force on the system is not zero for a finite period, hence the system obtains mechanical momentum and energy. Now the important question is how the law of momentum and energy conservation holds. In one of our previous works, we have shown that the momentum is conserved if the field momentum considered and not just the mechanical momentum of the material part of the device [4]. Here we give a detailed analysis of the energy conservation in a relativistic engine including radiation losses and exchange of energy between the mechanical part of the relativistic engine and the electromagnetic field.

Keywords: Newton’s Third Law; Relativity; Electromagnetism; Energy conservation.

References:

[1]     Miron Tuval, and Asher Yahalom. “Newton’s third law in the framework of special relativity.” The European Physical Journal Plus, 129 (2014) 240.

[2]     Asher Yahalom. “Retardation in Special Relativity and the Design of a Relativistic Motor.” Acta Physica Polonica A, 131 (2017) 1285.

[3]     Miron Tuval, and Asher Yahalom. “A Permanent Magnet Relativistic Engine.” In Proceedings of the Ninth International Conference on Materials Technologies and Modeling (MMT-2016) Ariel University, Ariel, Israel. 2016.

[4]     Miron Tuval, and Asher Yahalom. “Momentum conservation in a relativistic engine.” The European Physical Journal Plus, 131 (2016) 374.