Elastic collision between particles: the relativistic and the Newtonian point of view

Kostas Papamichalis Dr of Theoretical Physics

The theoretical background

Synopsis

In the virtual environment of the simulation, the elastic collision of two distinct particles is depicted according to two different models: a) a relativistic model and b) a Newtonian model.
The motion of the system which is consisted by the blue and the purple particle, is considered in the lab inertial system (LS) (cyan windows) and in the center-of-mass frame of the two particles (CMS) (yellow windows). The particles P1 and P2 in both models have the same initial conditions in the lab system: the initial position of P1 is (-1,0,0) and that of P2, (0,0,0). The corresponding initial velocities are (v0,0,0) for P1 and (0,0,0) for P2. The motion is taking place on the Oxy plane of the lab system.
The user controls the initial velocity of P1, the fraction "lamda" of the particles' masses, and the scattering angle "Theta" of P1 in the CMS. Note that Theta is a parameter concerning the mechanism of the P1-P2 interaction. Nevertheless, The particles during their interaction merge in a point of the Minkowski space-time and then emerge, following different directions (see the "Theoretical background" pdf file). In the P1-P2 interaction, the total energy and the spatial momentum of the system are conserved.
In the virtual environment depicting the relativistic model in the LS and the CMS (first and second window) of the Minkowski space, the user can notice the deformation of the moving particles along the direction of each motion. In addition, the world time of CMS runs in different rate compared to the world time of the LS (see the attached pdf file). The world time in each reference frame is measured by a chronometer attached to the corresponding frame.
The user compares the directions and the magnitudes of the particles' final velocities predicted in the context of each model, and by accomplishing the activities found in the attached file, can evaluate his/her observations and conclusions.

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-160-140-120-100-60-40-20020406080100120140160180-80-180angledegx:undefined,y:undefinedtime= 0.000Lab Frame - Relativistic model-160-140-120-100-60-40-20020406080100120140160180-80-180angledegx:undefined,y:undefinedtime= -0.232Center of Mass Frame - Relativistic model-160-140-120-100-60-40-20020406080100120140160180-80-180angledegtime= 0.000Lab Frame - Newtonian model-160-140-120-100-60-40-20020406080100120140160180-80-180angledegtime= 0.000Center of Mass Frame - Newtonian model

The Relativistic model

The Newtonian model



Title and author:

Elastic Relativistic Collisions
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author image kostas papamichalis