Source code for irfpy.util.sprel

''' Formulae of special relativity.

.. codeauthor:: Yoshifumi Futaana

.. autosummary::
    
    time_dilation
    length_contraction
    energy
'''

from irfpy.util import constant as k
from irfpy.util import lorentztrans as lt
from irfpy.util import unitq as u

def time_dilation(t0, v):
    r''' Calculate the time dilation

    :param t0: Time in the rest frame (moving with the object) in ``s``.
    :param v: Velocity of the object in ``m/s``.
    :returns: ``t1``, time observed by an observer moving with relative to the object (``s``).

    .. math::

        t_1 = \gamma t_0

    >>> print('%.3f' % time_dilation(1, 42300000.))
    1.010

    Unitful version, too.

    >>> u.pprint(time_dilation_u(1 * u.s, 42300000. * u.m / u.s), fmt='%.8f')
    1.01010541 s
    '''
    return t0 * lt.gamma(v)


time_dilation_u = u.make_unitful_function(time_dilation, [u.s, u.m / u.s], u.s)
''' Unitful version of :func:`time_dilation`
'''

def length_contraction(l0, v):
    r''' Calculate the length contraction (Lorentz contraction)

    :param l0: The proper length (length of the object in the rest frame) in ``m``.
    :param v: Velocity of the object relative to the observer (``m/s``).
    :returns: ``l1``, length observed by an observer moving relative to the object (``m``).

    .. math::

        l_1 = \frac{l_0}{\gamma}

    >>> print('%.4f' % length_contraction(1, 13400000.))
    0.9990
    >>> print('%.4f' % length_contraction(1, 42300000.))
    0.9900

    Unitful version, too.

    >>> u.pprint(length_contraction_u(1 * u.km, 42300 * u.km / u.s).rescale(u.km), fmt='%.9f')
    0.989995689 km
    '''
    return l0 / lt.gamma(v)

length_contraction_u = u.make_unitful_function(length_contraction, [u.m, u.m / u.s], u.m)
''' Unitful version of :func:`length_contraction`.
'''

def energy(m):
    r''' Return the total energy

    :param m: Mass of the object in ``kg``.
    :returns: The rest energy, **E**, in ``J``.

    .. math::

        E = m c^2

    >>> me = 9.11e-31     # Electron mass
    >>> print('%.3e' % energy(me))
    8.188e-14

    >>> ene_u = energy_u(me * u.kg)
    >>> print('%.3f keV' % ene_u.r(u.keV))
    511.034 keV

    >>> print('%.3f MeV' % energy_u(u.k.proton_mass).r(u.MeV))
    938.272 MeV
    '''
    return m * k.c ** 2

energy_u = u.make_unitful_function(energy, [u.kg], u.J)
''' Unitful version of :func:`energy`.
'''

import unittest
import doctest


def doctests():
    return unittest.TestSuite((
        doctest.DocTestSuite(),
        ))
if __name__ == '__main__':
    unittest.main(defaultTest='doctests')