Motion of particles in a uniformly accelerated reference frame: the relativistic and the Newtonian point of view
Kostas Papamichalis Dr. of Theoretical Physics

Download the theoretical background and activities: The theoretical model

Six point-particles move in a Cartesian, inertial coordinate system of a Minkowski space M with the same constant velocity u, along straight lines which are parallel to the x-axis of the coordinate system.
Consider a uniformly accelerated frame (UAF) moving along the positive y-axis with acceleration g (see the "Theoretical model" pdf-file). In the simulation, the motion of each particle is depicted in the UAF, according to the relativistic and the Newtonian point of view.
The user is prompted to notice the existence of an “event horizon” in the context of the relativistic model and the difference rate of time measured by two similar clocks attached, at the origin O' of the UAF and at a certain moving particle. To choose the particle you want to measure its proper time, click at a point of the relativistic-model-window with y-coordinate close to the particle’s initial y-coordinate; then, the particle’s color turns to red and the proper time of the selected particle is being measured by the red tool of the simulation’s control-window.
The world time t' in both, the relativistic and the Newtonian environment is measured by the same clock placed at the origin O' of the uniformly accelerated frame (UAF).
By double-clicking on the window of the Newtonian virtual environment, the user can start or pause the application.
The user controls the common value of the initial x-position and the initial velocity of the particles, as well as the acceleration of the UAF. The light velocity equals to 1: c=1.

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