The Relativity of Simultaneity — Question 5

Question 5

A moving clock array has a spatial offset at one laboratory instant

Clocks fixed at positions $x\prime=0$ and $x\prime=L_0=600\,\mathrm m$ are synchronized in their own frame. At a fixed laboratory time, use the inverse relation $t=\gamma(t\prime+vx\prime/c^2)$, with $v=0.60c$.

1. Find the difference in displayed readings of the front and rear clocks at that laboratory instant.

2. At laboratory time $t=0$, when the rear clock reads zero, find the front reading.

Question 5 - Solution

A moving clock array has a spatial offset at one laboratory instant

(a) Method and calculation

$$0=\Delta t=\gamma(\Delta t\prime+vL_0/c^2).$$$$\boxed{\Delta t\prime=-vL_0/c^2=-1.20\,\mu\mathrm s}.$$

(b) Interpretation and further calculation

$$t\prime_{\mathrm{rear}}=0,\qquad t\prime_{\mathrm{front}}=t\prime_{\mathrm{rear}}+\Delta t\prime.$$$$\boxed{t\prime_{\mathrm{front}}=-1.20\,\mu\mathrm s}.$$

Physical check

This compares two distinct clocks on a laboratory simultaneity slice; it does not compare successive ticks of a single clock.