World lines transform: the relativistic and the Newtonian point of view

Kostas Papamichalis PhD of Theoretical Physics

Download the explanatory pdf-file: The theoretical background

In this simulation, the user can watch and study the motion of a particle in two inertial frames, and in the context of two different theories: a) the Einstein's Special Relativity and b) the Newtonian Mechanics.
In the initial frame (O) the user can choose two motions for the particle: a) a uniform linear, or b) a uniform circular. These choices are accomplished by pressing the button at the end of the text: "Linear world line"/"Circular world line".
The left windows depict the motions in the (O) frame, and the right in the (O') frame. The origin O of the (O) frame is moving with respect to the (O') frame along the x-axis with velocity v₀, controlled by the user.
For the case of the linear motion, the particle's velocity magnitude and the angle forming with x-axis in (O) frame, are also selected by the user. The corresponding values in the (O') frame are given by the output tools in the control panels of the simulation.
The clocks attached in every window measure the world time for the corresponding inertial frame, and the particle's time coordinate.

The user is prompted to justify the characteristics of the particle's world line in the (O') frame depicted in the virtual environment of the simulation, for any selected, given or getting calculated set of initial conditions.

By double click on the sim-windows, you can run or pause the simulation
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