R2: Relativity Theories Toolbox

This package aims to implement some tools and objects of relativity theories in order to observe the relativistic effects on physical cases.

from r2 import Constants, VelocityVector
velocity = Constants.LIGHT_VELOCITY * VelocityVector(
        1 / 9,
        1 / 2,
        1 / 4,
)
print(f"The velocity vector is:\n{velocity}\n")
print(f"It's norm is the {velocity.compute_beta()} fraction of light velocity.")

The velocity vector is:
[[3.33102731e+07]
 [1.49896229e+08]
 [7.49481145e+07]]

It's norm is the 0.5699523480189775 fraction of light velocity.

from r2 import VelocityQuadriVector
velocity_quad = VelocityQuadriVector.from_space_vector(velocity)
print(f"The velocity quadri-vector built from the previous velocity vector is:\n{velocity_quad}\n")
velocity_quad_proper_ref = velocity_quad.lorentz_transform(velocity)
print(f"This quadri-vector in it's proper reference frame is:\n{velocity_quad_proper_ref}")

The velocity quadri-vector built from the previous velocity vector is:
[[3.64854055e+08]
 [4.05393394e+07]
 [1.82427027e+08]
 [9.12135137e+07]]

This quadri-vector in it's proper reference frame is:
[[2.99792458e+08]
 [0.00000000e+00]
 [0.00000000e+00]
 [0.00000000e+00]]

from r2 import ImpulseQuadriVector
mass = 2
impulse_quad = ImpulseQuadriVector.from_space_vector(velocity_vector=velocity, mass=mass)
print(f"The impulse quadri-vector of a {mass}kg mass with the previous velocity vector is:\n{impulse_quad}\n")
print(f"It's energy is {impulse_quad.compute_energy()}J.\n")
impulse_quad_proper_ref = impulse_quad.lorentz_transform(velocity)
print(f"In it's proper reference frame the same impulse quadri-vector is:\n{impulse_quad_proper_ref}\n")
print(f"In this frame it's energy is {impulse_quad_proper_ref.compute_energy()}J. The reference frame is the frame where the energy is the lowest (no kinetical energy).")

The impulse quadri-vector of a 2kg mass with the previous velocity vector is:
[[7.29708110e+08]
 [8.10786789e+07]
 [3.64854055e+08]
 [1.82427027e+08]]

It's energy is 2.1876098782138845e+17J.

In it's proper reference frame the same impulse quadri-vector is:
[[5.99584916e+08]
 [0.00000000e+00]
 [0.00000000e+00]
 [0.00000000e+00]]

In this frame it's energy is 1.7975103574736355e+17J. The reference frame is the frame where the energy is the lowest (no kinetical energy).

from r2 import ImpulseQuadriVector
_lambda = 800e-9
energy = Constants.LIGHT_VELOCITY * Constants.PLANCK_CONSTANT / _lambda
photon_velocity = Constants.LIGHT_VELOCITY * VelocityVector(
        1,
        0,
        0,
)
impulse_quad = ImpulseQuadriVector.from_space_vector(velocity_vector=photon_velocity, energy=energy)
print(f"The impulse quadri-vector of a null mass particule is defined from it's energy. For instance a photon with a {_lambda}m wavelength with the following velocity vector:\n{photon_velocity}\n")
print(f"Has the following impulse quadri-vector:\n{impulse_quad}\n")

The impulse quadri-vector of a null mass particule is defined from it's energy. For instance a photon with a 8e-07m wavelength with the following velocity vector:
[[2.99792458e+08]
 [0.00000000e+00]
 [0.00000000e+00]]

Has the following impulse quadri-vector:
[[8.28258755e-28]
 [8.28258755e-28]
 [0.00000000e+00]
 [0.00000000e+00]]

The proper reference frame is not defined for this quadri-vector because by definition the speed of light is absolute. You can't find a reference frame where the photon is not moving in space. But, you can observe the compatibility of the Lorentz Transform with the light speed absolutism:

impulse_quad.lorentz_transform(velocity)
print(impulse_quad)

[[8.28258755e-28]
 [8.28258755e-28]
 [0.00000000e+00]
 [0.00000000e+00]]