Answer to Question #142336 in Mechanics | Relativity for ALEX

Question

Stanley, who works for the rail system shown in Fig. 1, has carefully synchronized the clocks at all of the rail stations. At the moment that Stanley measures all of the clocks striking noon, Mavis is on a high-speed passenger car traveling from Ogdenville toward North Haverbrook. According to Mavis, when the Ogdenville clock strikes noon, what time is it in North Haverbrook? (i) Noon; (ii) before noon; (iii) after noon.

Answer 1

As stanley is at rest , And the train is moving at very high speed with respect to ground.

So There will be the time dilation under lorentz transformation. Mavis clock is on the train,

According to time dilation formula,

$\Delta t=\dfrac{\Delta t'}{\sqrt{1-\dfrac{v^2}{c^2}}}$

As it is seen from the above formula that Dilated time$(\Delta t')$ is always greater than the proper time$(\Delta t)$ .

So with respect to stanley Mavis clock is running slow.

Hence there is before noon in the mavis clock according to stanley.