Movement and Uncertainty of the Center of Relativistic Energy in an Isolated Frame of Reference

We study, based on a thought experiment, whether the center of relativistic energy (CRE) is always constant in an isolated frame of reference (IFR). First, we assume that two objects, in a moving IFR (MIFR), move parallel to and very close to a coordinate axis from opposite directions and with equal speed. Each length in the direction of travel of the objects is much longer than that perpendicular to the direction of travel of them. Here it is assumed that the location of the CRE (LCRE) of each object, in the initial condition, is very close to the coordinate axis. When they become perfectly symmetric with respect to the coordinate axis, the forces perpendicular to the direction of travel of the objects are applied to each CRE and thereby a perfectly inelastic collision between them occurs on the coordinate axis. The combined object (CO) resulting from the perfectly inelastic collision begins to rotate because the momentum of the object before the combination acts like the moment of force on the CO. For simplicity, we examine the energy distribution of the CO when it becomes perpendicular to the coordinate axis due rotation. The magnitude of velocity of each minute portion (MP) symmetrical with respect to the coordinate axis is different depending on whether the direction of each rotational velocity is the same or opposite to the direction of travel of the MIFR. Then the energy of each MP is not the same. As a result, we quantitatively demonstrate that the LCRE of the CO significantly moves from the vicinity of the coordinate axis. Therefore, we conclude that the LCRE in the MIFR is not necessarily invariant. Furthermore, we carry out the above thought experiment in a gravitational field (GF). The amount of potential energy of the CO changes due to the movement of the center of mass (CM), in other words, the center of gravity (CG). Therefore, we find that the law of conservation of energy can be violated in an isolated GF. Second, we suppose a process in which a force causes a negative acceleration on a moving object (MO) and thereafter the MO eventually comes to rest. What is considered here is the LCRE when the MO comes to rest and Lorentz contraction of it disappears. We pay attention to the position of the force applied to the MO because the transmission time of force (TTF) inside the MO may vary depending on the position of the MO where the force is applied. As a result, we find that the position at which the MO comes to rest differs depending on the TTF inside the MO. Therefore, we conclude that the LCRE in an IFR differs depending on the position of the MO where the force is applied, in other words, it in an IFR is not necessarily uniquely determined.