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)

 

[m2003]

by a factor of gamma

The time interval between events is relative and can be perceived differently depending on the reference frame. In frame S, the time interval between the events is greater because of the factor of gamma in the equations for time dilation. This factor takes into account the relative speed between the two frames and causes a difference in the perception of time. In frame S', the events may seem to occur closer together because the frame is moving at a different velocity compared to frame S. This difference in perception of time is a result of the theory of relativity and helps to explain the concept of time dilation.