If say you have some scalar field, θ(x^u), where x^u represents the 4-vector coordinates of spacetime, and then the typical classical equation of motion, a = -∇θ, how would one go about 'generalizing' this to a relativistic version? Since F = ma, would you have to write it as d/dt (P^u) where P^u is the relativistic 4-momentum? But since P^0 = m, this means that the 0 component of the 4-vector simply vanishes, and this seems unsatisfactory to me since you're essentially just keeping everything Newtonian. Can anybody shed some light on this?(adsbygoogle = window.adsbygoogle || []).push({});

(sorry for the bad notation)

Thanks in advance

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# A Relativistic generalization of Newton’s equation

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