## reference frames

1. The problem statement, all variables and given/known data

Two events happen at the same point x'(0) in frame S' at t(1)' and t(2)'

a) Use equations x=gamma*(x'+vt') and t=gamma*(t'+vx'/c^2) to show in frame S the time interval between the events is greater than t(2)'-t(1)' by a factor of gamma

2. Relevant equations

3. The attempt at a solution

x=gamma*(x'+vt')
t=gamma*(t'+vx'/c^2)

t(2)=gamma*(t(2)'-vx'(2)/c^2) and t(1)=gamma*(t(1)'-vx'(1)/c^2)
x'(2)=x'(1)=x'(0)
t(2)-t(1)= gamma*(t'(2)-t'(1))-gamma*v/c^2(-v*x'(0)+v*x'(0))
t(2)-t(1)=gamma*(t(2)'-t'(1))

from the reference frame of S' the two events that were at the same reference point in the S prame with not be at the same reference point in the S' frame. hence, x'(1) will not equal x'(2)

t'(2)= gamma*(t(2)-v*x(2)/c^2)
t'(1)=gamma*(t(1)-v*x(2)/c^2)
t'(2)-t'(1)=gamma*(t(2)-t(1))-gamma*v/(c^2)*(x(2)-x(1))

hence , t(2)-t(1) is large than t'(2)-t'(1)

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Recognitions:
Homework Help
 Quote by Benzoate 1. The problem statement, all variables and given/known data Two events happen at the same point x'(0) in frame S' at t(1)' and t(2)' a) Use equations x=gamma*(x'+vt') and t=gamma*(t'+vx'/c^2) to show in frame S the time interval between the events is greater than t(2)'-t(1)' by a factor of gamma 2. Relevant equations 3. The attempt at a solution x=gamma*(x'+vt') t=gamma*(t'+vx'/c^2) t(2)=gamma*(t(2)'-vx'(2)/c^2) and t(1)=gamma*(t(1)'-vx'(1)/c^2)
Shouldn't you be using +vx'(2)/c^2 etc...

 x'(2)=x'(1)=x'(0) t(2)-t(1)= gamma*(t'(2)-t'(1))-gamma*v/c^2(-v*x'(0)+v*x'(0)) t(2)-t(1)=gamma*(t(2)'-t'(1))
You've proven your result above. I don't understand the purpose of the part below.

 from the reference frame of S' the two events that were at the same reference point in the S prame with not be at the same reference point in the S' frame. hence, x'(1) will not equal x'(2) t'(2)= gamma*(t(2)-v*x(2)/c^2) t'(1)=gamma*(t(1)-v*x(2)/c^2) t'(2)-t'(1)=gamma*(t(2)-t(1))-gamma*v/(c^2)*(x(2)-x(1)) hence , t(2)-t(1) is large than t'(2)-t'(1)