洛伦兹变换:
\( \gamma^2 = \frac{c^2}{c^2-v^2} \),即:
\( \gamma^2 c^2 = \gamma^2 v^2 + c^2\),
两个同时乘以静止质量\(m_0\),得:
\( \gamma^2 m_0^2 c^2 = \gamma^2 m_0^2 v^2 + m_0^2 c^2 \)
我们令 \( m=\gamma m_0 \),于是:
\( m^2 c^2 = m^2 v^2 + m_0^2 c^2 \),即:
\( (mc)^2 = (mv)^2 + (m_0 c)^2 \),或:
\( (mc^2)^2 = (mv)^2 c^2 + (m_0 c^2)^2 \),或:
\( (mc^2)^2 = (pc)^2 + (m_0 c^2)^2 \)