Measuring an Event — Question 2

Question 2

Unequal arrival times can correspond to simultaneous emissions

Flashes at $x_A=-600\,\mathrm m$ and $x_B=900\,\mathrm m$ reach the origin at $5.0\,\mu\mathrm s$ and $6.0\,\mu\mathrm s$, respectively. Use $c=3.00\times10^8\,\mathrm{m/s}$ and Einstein-synchronized laboratory clocks.

1. Reconstruct both emission times.

2. Determine the detector position that would receive these flashes simultaneously.

Question 2 - Solution

Unequal arrival times can correspond to simultaneous emissions

(a) Method and calculation

$$t_A=5.0-600/c=3.0\,\mu\mathrm s,\quad t_B=6.0-900/c=3.0\,\mu\mathrm s.$$$$\boxed{\Delta t_{\mathrm{emission}}=0}.$$

(b) Interpretation and further calculation

$$|x+600|=|900-x|\quad\Rightarrow\quad\boxed{x=150\,\mathrm m}.$$$$t_R=3.0\,\mu\mathrm s+750/c=\boxed{5.5\,\mu\mathrm s}.$$

Physical check

Equal reception requires equal path lengths only because the reconstructed emissions are simultaneous.