Analysis of the Variety of the Relativistic Approach Velocity of Objects Based on the Data of the Large Hadron Collider

Abstract

Relevance and formulation of the problem. The number of areas of scientific and practical activity in which it is necessary to consider relativistic corrections is steadily growing. In many cases, two objects under study move towards one another. This takes place both in relation to astronomical objects and in relation to quantum particles, including in colliders—accelerators of charged particles in colliding beams. With counter relativistic motions, the relative velocity does not coincide with the approach velocity. However, considering relative velocity alone limits the arsenal of research tools and methods. As opposed to relative velocity, which is determined in accordance with the relativistic formula for velocity addition, the approach velocity of unaccelerated objects is defined as the ratio of the distance between them to the time it takes to cover it. The purpose of this work is to analyze the variety of the relativistic approach velocity of objects depending on the choice of inertial reference frames based on the data of the Large Hadron Collider. Results. At the Large Hadron Collider, the approach velocity of protons is almost twice as high as the speed of light in the laboratory reference frame. In frames of reference associated with moving protons, depending on the options of relativistic transformation of segments of lengths and time intervals, the maximum approach velocity of protons is 1.1 × 10⁸с, and the minimum is 1.2 m/s. In accordance with the technique based on the relativistic velocity addition formula, the approach velocity in reference systems associated with moving protons is almost equal to the speed of light. In this case, the approach velocity becomes equal to the relative velocity, which should not be considered as a generalization of the classical mechanics rule on the indistinguishability of these velocities to relativistic mechanics. Practical significance. The results obtained may be of interest in assessing the approach velocities of astronomical objects, including the Earth and asteroids, as well as significantly expand the variability of hypotheses when processing experimental data arrays obtained at elementary particle accelerators, including the Large Hadron Collider.