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Demonstrate that the quantity E^2-p^2c^2 for a particle is an invariant, i.e. it has the same magnitude in all inertial reference frames. What is the magnitude of this invariant? |
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Answer» Solution :As before `E=m_0c^3(dt)/(DS)`, `p_x=m_0c(DX)/(ds)`. Similarly `p_y=m_0c(dy)/(ds)`, `p_z=m_0c(DZ)/(ds)` Then `E^2-c^2p^2=E^2-c^2(p_x^2+p_y^2+p_x^2)` `=m_0^2c^4((c^2dt^2-dx^2-dy^2-dz^2))/(ds^2)=m_0^2c^4` is invariant |
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