Energy—momentum relation

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

Conditions:

1. Velocity \(\vec v\) and momentum \(\vec p\) must be parallel to each other.

Links:

1. Wikipedia, derivable from here.

total_energy

Total energy of the relativistic energy.

Symbol:

E

Latex:

\(E\)

Dimension:

energy

momentum

Vector of the particle’s relativistic momentum.

Symbol:

p

Latex:

\({\vec p}\)

Dimension:

momentum

velocity

Vector of the particle’s velocity. See speed.

Symbol:

v

Latex:

\({\vec v}\)

Dimension:

velocity

vector_law

p * c^2 = E * v

Latex:

\[{\vec p} c^{2} = E {\vec v}\]

energy_law

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

Latex:

\[E = c^{2} \frac{\left \Vert {\vec p} \right \Vert}{\left \Vert {\vec v} \right \Vert}\]