The discussion focuses on proving the Lorentz invariance of the momentum 4-vector equation $$\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}$$. Participants emphasize that demonstrating Lorentz invariance requires showing the equation holds true across all inertial reference frames, specifically through Lorentz transformations. The equation involves the tensor of rank two, ##F^{\mu\nu}##, and the transformation must validate both the original and transformed forms of the equation. This foundational concept is crucial for understanding relativistic physics.
PREREQUISITESThis discussion is beneficial for physics students, particularly those studying special relativity, as well as educators and researchers focused on the mathematical foundations of relativistic mechanics.
Well then why not try it? When we say that an equation is Lorentz invariant, what we mean is that it holds true in all (inertial) reference frames accessible via a Lorentz transformation. So, that means that you have to show that ifflintbox said:I was thinking about doing a Lorentz transformation to this four vector, but I don't know what this would yield.
You're right! Thank you so much.Fightfish said:Well then why not try it? When we say that an equation is Lorentz invariant, what we mean is that it holds true in all (inertial) reference frames accessible via a Lorentz transformation. So, that means that you have to show that if
\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}
then
\frac{dp^{\mu'}}{d\tau}=\frac{q}{mc}F^{\mu'\nu'}p_{\nu'}
is also true.