Particle Disintegration

The relativistic and the Newtonian model

Kostas Papamichalis Dr of Theoretical Physics

Theoretical analysis of the two models - Activities and Exercises: Particle Splitting.pdf

Synopsis
In the virtual environment of this application, the splitting of a particle to two distinct particles with masses different from zero is simulated, according to two different models: (a) a relativistic model and (b) a Newtonian model.
The motions of the particles are depicted with respect to two inertial reference frames: (1) the Lab Reference Frame (LRF) and (2) the Center of Mass Reference Frame (CMRF).
In windows 1 and 2, the relativistic model is simulated, in the LRF and the CMRF, respectively.
In windows 3 and 4, the Newtonian model is simulated, in the CMRF and the LRF, respectively.

The initial blue-colored particle P of mass m=1, is moving along the x-axis of the LRF with spatial velocity of magnitude v₀. When P is passing by the origin of the LRF, it is disintegrated in two particles: P1 (red-colored) and P2 (green-colored).
The value of v₀, the ratio 'lamda' of the mass m₂ of P2 over the mass m of P, the magnitude v_2CM of the P2-velocity with respect to the CMRF and its angle 'theta' with the x-axis of CMRF are controlled by the user.
It must be noted that in the relativistic model the splitting of P is not always possible. The splitting-condition concerns the values of the parameters lamda and v_2CM, and it is derived in the attached file "Particle Splitting.pdf". In the virtual environmenet of the simulation, for every value of v_2CM, the corresponding max permissible value of lamda is diplayed, for which the splitting is allowed. The user can check if splitting is possible or not, by running the simulation.

The light-velocity is c=1. The cordinates of the initial position of P in LRF are (-a,0,0), where: a=1.

In the virtual environment, the user will find measurement-tools for the quantities: (a) the P1-mass according to the relativistic model (m_1rel), (b) the P1-mass according to the Newtonian model (m_1N), (c) the P2-mass according to the relativistic model (m_2rel), (d) the P2-mass according to the Newtonian model (m_2N), (e) the magnitude of the P1-velocity in CMRF according to the relativistic model, (v_1CMrel), (f) the magnitude of the P1-velocity in CMRF according to the Newtonian model (v_1CMN), (g) the magnitude of the P2-velocity in CMRF according to the relativistic model (v_2CMrel), (h) the magnitude of the P2-velocity in CMRF according to the Newtonian model (v_2CMN), (i) the magnitude of the P1-velocity in LRF according to the relativistic model, (v_1Lrel), (j) the magnitude of the P2-velocity in LRF according to the relativistic model, (v_2Lrel), (k) the magnitude of the P1-velocity in LRF according to the Newtonian model (v_1LN) and (l) the magnitude of the P2-velocity in LRF according to the Newtonian model (v_2LN)

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