Function transformation_matrix

physics/lorentz_transformation_four_vector.py:89–134

Calculate the Lorentz transformation matrix for movement in the x direction: | y -γβ 0 0| |-γβ y 0 0| | 0 0 1 0| | 0 0 0 1| where y is the Lorentz factor and β is the velocity as a fraction of c >>> transformation_matrix(29979245) array([[ 1.005037

(velocity: float)

def transformation_matrix(velocity: float) -> np.ndarray:
    """
    Calculate the Lorentz transformation matrix for movement in the x direction:

    | y  -γβ  0  0|
    |-γβ  y   0  0|
    | 0   0   1  0|
    | 0   0   0  1|

    where y is the Lorentz factor and β is the velocity as a fraction of c
    >>> transformation_matrix(29979245)
    array([[ 1.00503781, -0.10050378,  0.        ,  0.        ],
           [-0.10050378,  1.00503781,  0.        ,  0.        ],
           [ 0.        ,  0.        ,  1.        ,  0.        ],
           [ 0.        ,  0.        ,  0.        ,  1.        ]])
    >>> transformation_matrix(19979245.2)
    array([[ 1.00222811, -0.06679208,  0.        ,  0.        ],
           [-0.06679208,  1.00222811,  0.        ,  0.        ],
           [ 0.        ,  0.        ,  1.        ,  0.        ],
           [ 0.        ,  0.        ,  0.        ,  1.        ]])
    >>> transformation_matrix(1)
    array([[ 1.00000000e+00, -3.33564095e-09,  0.00000000e+00,
             0.00000000e+00],
           [-3.33564095e-09,  1.00000000e+00,  0.00000000e+00,
             0.00000000e+00],
           [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00,
             0.00000000e+00],
           [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
             1.00000000e+00]])
    >>> transformation_matrix(0)
    Traceback (most recent call last):
      ...
    ValueError: Speed must be greater than or equal to 1!
    >>> transformation_matrix(c * 1.5)
    Traceback (most recent call last):
      ...
    ValueError: Speed must not exceed light speed 299,792,458 [m/s]!
    """
    return np.array(
        [
            [gamma(velocity), -gamma(velocity) * beta(velocity), 0, 0],
            [-gamma(velocity) * beta(velocity), gamma(velocity), 0, 0],
            [0, 0, 1, 0],
            [0, 0, 0, 1],
        ]
    )


def transform(velocity: float, event: np.ndarray | None = None) -> np.ndarray: