Keywords: energy-momentum 4-vector, relativistic frame invariants, relativistic systems of particles, relativistic energy-momentum, conservation, frame invariance, hybrid plasma gas, particle accelerators
Relativistic energy-momentum: the concepts of conservation versus frame invariance
The use of relativistic frame invariants is very well established, especially when it comes to the energy-momentum. In the following paper we clarify the terms 'conserved' and 'frame invariant' and we explain the differences between the two concepts. Our paper is divided into three main sections. In the first section we explain the notion of frame invariance. In the second section we explain the energy-momentum conservation. We end by giving a practical example (a hybrid plasma gas) of an open system, whereby energy and momentum are added from outside the system. We will show the interesting effects caused by adding photons to a system of massive particles. The new approach is extremely important in applications like particle accelerators where we can only work with directly measurable quantities, the kinetic energy KE and the momentum p.