Proper time for timelike intervals
==================================

In relativity, proper time along a timelike world line is defined as the time as measured by a clock following
that line. The proper time interval between two events on a world line is the change in proper time, which is
independent of coordinates, and is a Lorentz scalar.

**Notation:**

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

**Conditions**

#. The interval is timelike, i.e. :math:`\Delta s` is real.

**Links:**

#. `Wikipedia, equivalent to formula 2 in box <https://en.wikipedia.org/wiki/Proper_time#In_special_relativity>`__.

.. py:currentmodule:: symplyphysics.laws.relativistic.proper_time_for_timelike_intervals

.. py:data:: proper_time

    The :attr:`~symplyphysics.symbols.relativistic_mechanics.proper_time` interval between two events.

Symbol:
    :code:`Delta(tau)`

Latex:
    :math:`\Delta \tau`

Dimension:
    :code:`time`


.. py:data:: spacetime_interval

    The :attr:`~symplyphysics.symbols.relativistic_mechanics.spacetime_interval` between two events.

Symbol:
    :code:`Delta(s)`

Latex:
    :math:`\Delta s`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`Delta(tau) = Delta(s) / c`


    Latex:
        .. math::
            \Delta \tau = \frac{\Delta s}{c}