- #1
latentcorpse
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I found a question in one of my past papers that I was unsure about:
Show by explicit solution x(t) that the equation
[itex]\frac{d^2 \xi^\alpha}{d \tau^2}=0[/itex]
where [itex]\xi^\alpha=(ct, \vec{x})[/itex] and [itex]\tau[/itex] is proper time, represents a straight world line for a massive particle.
My initial thoughts were just to integrate twice with respect to tau but it's worth 4 marks and so i think it must be a bit more involved than that. Besides if we integrated wrt tau then our answer would be in terms of tau and I think (but not 100%) that we are looking to imply that [itex]\xi^i(t)=A_it+B_i[/itex].
Also, what does [itex]\xi^\alpha=(ct, \vec{x})[/itex] actually mean?
thanks.
Show by explicit solution x(t) that the equation
[itex]\frac{d^2 \xi^\alpha}{d \tau^2}=0[/itex]
where [itex]\xi^\alpha=(ct, \vec{x})[/itex] and [itex]\tau[/itex] is proper time, represents a straight world line for a massive particle.
My initial thoughts were just to integrate twice with respect to tau but it's worth 4 marks and so i think it must be a bit more involved than that. Besides if we integrated wrt tau then our answer would be in terms of tau and I think (but not 100%) that we are looking to imply that [itex]\xi^i(t)=A_it+B_i[/itex].
Also, what does [itex]\xi^\alpha=(ct, \vec{x})[/itex] actually mean?
thanks.