Energy—momentum relation
========================

Relativistic momentum and total relativistic energy of a relativistic particle are related by a
linear equation.

**Conditions:**

#. Velocity :math:`\vec v` and momentum :math:`\vec p` must be parallel to each other.

**Links:**

#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation#Heuristic_approach_for_massive_particles>`__.

..
    TODO: find a more exact link

.. py:currentmodule:: symplyphysics.laws.relativistic.vector.energy_momentum_relation

.. py:data:: total_energy

    Total energy of the relativistic :attr:`~symplyphysics.symbols.basic.energy`.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`energy`


.. py:data:: momentum

    Vector of the particle's relativistic :attr:`~symplyphysics.symbols.classical_mechanics.momentum`.

Symbol:
    :code:`p`

Latex:
    :math:`{\vec p}`

Dimension:
    :code:`momentum`


.. py:data:: velocity

    Vector of the particle's velocity. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v`

Latex:
    :math:`{\vec v}`

Dimension:
    :code:`velocity`


.. py:data:: vector_law

    :code:`p * c^2 = E * v`


    Latex:
        .. math::
            {\vec p} c^{2} = E {\vec v}


.. py:data:: energy_law

    :code:`E = c^2 * norm(p) / norm(v)`


    Latex:
        .. math::
            E = c^{2} \frac{\left \Vert {\vec p} \right \Vert}{\left \Vert {\vec v} \right \Vert}