(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

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