Free particle in Minkowski spacetime

  • Thread starter coopre
  • Start date
  • #1
2
0

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!
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
welcome to pf!

hi coopre! welcome to pf! :wink:

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? :smile:
 
  • #3
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.
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
251
hi camron_m21! :smile:
t = τγ, and x = Vτ/γ,

one of them is right! :wink:
 

Related Threads on Free particle in Minkowski spacetime

Replies
3
Views
1K
  • Last Post
Replies
1
Views
156
E
Replies
7
Views
785
Replies
2
Views
106
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
840
Top