Free particle in Minkowski spacetime

[coopre]

Homework Statement

A free particle is moving in the x direction through Minkowski spacetime,
and has velocity V as measured by a stationary observer at x = 0; t = 0. Express
the particle's world-line parametrically in terms of V , parametrized by the particle's
proper time 

Homework Equations

unknown

The Attempt at a Solution

Help I have been stuck on this problem for hours now, and what I keep getting is wrong so idk where to start now please help!

 

[tiny-tim]

welcome to pf!

hi coopre! welcome to pf!

you're looking for a parametrisation (x,t) = (x(τ),t(τ)), where τ is the proper time of the particle

(y and z will be constant)

you know (x,t) = (Vt,t) …

so find τ as a function of t (and V), then invert it to get t as a function of τ (and V) …

what do you get? ​

 

[camron_m21]

I was getting confused on this one as well; it seemed too easy. My solution turned out to be:

t = τγ, and x = Vτ/γ, by using dx/dt = γ dx/dτ.

Hopefully this is correct, helpful, or both.

 

[tiny-tim]

hi camron_m21!

t = τγ, and x = Vτ/γ,

one of them is right!