Relativistic time dilation
==========================

Time dilation is the difference in elapsed time as measured by two clocks,
either due to a relative speed between them (special relativity),
or a difference in gravitational potential between their locations. This law only
covers the special relativistic time dilation due to acceleration.

**Notation:**

#. :math:`c` (:code:`c`) is :attr:`~symplyphysics.quantities.speed_of_light`.

**Links:**

#. `Wikipedia, formula in box <https://en.wikipedia.org/wiki/Time_dilation#Simple_inference>`__.

.. py:currentmodule:: symplyphysics.laws.relativistic.relativistic_time_dilation

.. py:data:: proper_time

    :attr:`~symplyphysics.symbols.relativistic_mechanics.proper_time`, which is measured by clocks stationary in the proper reference frame.

Symbol:
    :code:`tau`

Latex:
    :math:`\tau`

Dimension:
    :code:`time`


.. py:data:: speed

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the object.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: relativistic_time

    Relativistic :attr:`~symplyphysics.symbols.basic.time`, which is measured by clocks stationary in the external reference frame.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`t = tau / sqrt(1 - v^2 / c^2)`


    Latex:
        .. math::
            t = \frac{\tau}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}