- #1
stunner5000pt
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- 2
Homework Statement
Let P be the 4 momentum
u be the 4 velocity
a) Evaluate the Lorentz invariant [itex]P^2[/itex]
b)Differentiate [itex]P^2=P_{\mu}P_{\mu}[/itex] and show that
[tex]\vec{u}\cdot\frac{d}{dt}\left(\frac{m_{0}\vec{u}}{\sqrt{1-u^2/c^2}}\right)=m_{0}c^2\frac{d}{dt}\left(\frac{1}{\sqrt{1-u^2/c^2}}\right)[/tex]
2. The attempt at a solution
The first part yields an answer of [tex]E^2 -p^2 c^2=m^2 c^4[/tex]
Now for part b. Does the P^2 have anything to do with the equality that needs to be proven? Do i need to differentiate P^2 with respect to time? Do i hav to differentiate
[tex]E^2 -p^2 c^2=m^2 c^4[/tex] with respect to time?
Please help!
Thanks