Time difference between two moving inertial frames of reference

1,616

You should be using Lorentz transformations to change from spacetime coordinates in one frame to the other $$t'=\gamma(t-\frac{vx}{c^2})$$ So for the case above $\gamma=\frac{5}{4}$ $v=0.6c$ and the time and space coordinates in the unprimed frame you have stated gives the correct result. Your method does not work as you need to treat time and space on equal footing in special relativity. The equation for time dilation tells you the time between two events depending on the speed of your reference frame. Have a look at this http://en.wikipedia.org/wiki/Lorentz_transformation

Share:
1,616
Mohideen Imran Khan
Author by

Mohideen Imran Khan

Updated on September 22, 2022

Comments

  • Mohideen Imran Khan
    Mohideen Imran Khan about 1 year

    This is a question I am trying to solve:

    Let S and S' be two inertial frames of reference and S' is moving relative to S at a velocity of 0.6c.

    When x = x' = 0, t = t' = 0.

    At t = 2 x 10-7 s, an event occurs at frame S for which x = 50m. When does the event occur with respect to S' ?

    And I tried the following solution:

    Taking t' to be the proper time, t = γ t'

    where t is 2 x 10-7 s and γ is the lorenz factor.

    I got t' = 1.6 x 10-7 s. However, the correct solution is indicated as 1.25 x 10-7 s. What am I doing wrong?