E=mc², formulê elaqeyê enerci u kutleya.
KE=mc2−m0c2{\displaystyle KE=mc^{2}-m_{0}c^{2}}
KE=mc2−m01−v2c2c2=mc2−m0cc2−v2{\displaystyle KE=mc^{2}-{\frac {m_{0}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}c^{2}=mc^{2}-{\frac {m_{0}c}{\sqrt {c^{2}-v^{2}}}}}
m0v1−v2c2{\displaystyle {\frac {m_{0}v}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}
E2=m02c4+p2c2{\displaystyle E^{2}=m_{0}^{2}c^{4}+p^{2}c^{2}} E=m02c4+p2c2{\displaystyle E={\sqrt {m_{0}^{2}c^{4}+p^{2}c^{2}}}} rê dengo. E=mc^2
E=m02c4+p2c2{\displaystyle E={\sqrt {m_{0}^{2}c^{4}+p^{2}c^{2}}}} n pc pc=p02−m02c4{\displaystyle pc={\sqrt {p_{0}^{2}-m_{0}^{2}c^{4}}}}
p2c2=m02v2c21−v2c′=m02v2c2c41−v2c2{\displaystyle p^{2}c^{2}={\frac {m_{0}^{2}v^{2}c^{2}}{1-{\frac {v^{2}}{c^{'}}}}}={\frac {m_{0}^{2}{\frac {v^{2}}{c^{2}}}c^{4}}{1-{\frac {v^{2}}{c^{2}}}}}}
Hesabo peyên:
p2c2=m02c4[v2c2−1]1−v2c2=m02c41−v2c2=−m02c4+m2c4=(mc2)2⇒E=pc{\displaystyle p^{2}c^{2}={\frac {m_{0}^{2}c^{4}[{\frac {v^{2}}{c^{2}}}-1]}{1-{\frac {v^{2}}{c^{2}}}}}={\frac {m_{0}^{2}c^{4}}{1-{\frac {v^{2}}{c^{2}}}}}=-m_{0}^{2}c^{4}+m^{2}c^{4}=(mc^{2})^{2}\Rightarrow E=pc}