The Postulates — Question 10

Question 10

Changing source velocity does not change a vacuum flight time

Two sources cross the same laboratory point at $t=0$ with different velocities and each emits a pulse toward a fixed detector at $x=D$. The pulses travel through vacuum. A competing emission model proposes laboratory speeds $c+v_1$ and $c+v_2$.

1. Predict the detection-time difference using the light postulate.

2. For $v_1=0.20c$, $v_2=-0.20c$, find the difference predicted by the competing model, expressed in units of $D/c$.

Question 10 - Solution

Changing source velocity does not change a vacuum flight time

(a) Method and calculation

$$x_1=ct,\quad x_2=ct\quad\Rightarrow\quad t_1=t_2=D/c.$$$$\boxed{\Delta t=t_2-t_1=0}.$$

(b) Interpretation and further calculation

$$t_1^{\mathrm{model}}=\frac{5D}{6c},\qquad t_2^{\mathrm{model}}=\frac{5D}{4c}.$$$$\boxed{\Delta t_{\mathrm{model}}=\frac{5D}{12c}}.$$

Physical check

The emissions are colocated and simultaneous in the laboratory, so no remote synchronization ambiguity enters the comparison at one detector.