Why is the time interval between the events in frame S larger than in frame S'?

[Benzoate]

Homework Statement

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

Homework Equations

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)

 

[learningphysics]

Homework Statement

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

Homework Equations

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)