4

$A$ and $B$ are two stationary points on a line $30,000,000$ km apart.

A light flashes at $B$, and at that precise moment a rocket takes off at $A$ at $180,000$ km/second.

The rocket is considered stationary relative to itself, and thus Point $B$ is approaching the rocket at $180,000$ km/second. This reduces the distance from the rocket to $B$ by $0.8$ to $24,000,000$ km. The light travels at $300,000$ km/second, therefore the rocket will see the flash after $80$ seconds ($240,000,000/300,000$).

Is this calculation correct?

If it is not correct, could you please explain why.

Thank you very much!

JohnColtraneisJC
  • 1,965
Leibel
  • 41
  • Yes, that looks correct. You could work it out in another way too - rather than looking at length contraction, by looking at time dilation. You should get the same answer. – John Doe Jan 29 '18 at 19:12
  • Thank you! I have had a rather talented physicist claim that the correct time is 50 seconds (180,000 km/second + 300,000 km/second). He insists that I am missing a subtle point, but I can't make out what it is... – Leibel Jan 29 '18 at 20:50
  • The correct answer seems should be 50 seconds instead of 80 seconds. The point is (1) the distance between the rocket and $B$ has been reduced, and (2) the time that the rocket saw the light flashing at $B$ has also changed. For (2), what I mean is, if you (at $A$ in the rest frame with respect to $A$ and $B$) see the light flashes at $t_{\text{you}}=0$, the rocket would find the same light flashing at $t_{\text{rocket}}=-30$ seconds (suppose $t_{\text{you}}=t_{\text{rocket}}=0$ at $A$). Basically, the moment that you see the light flashes would differ from the moment that the rocket sees so. – hypernova Apr 09 '18 at 18:09
  • I would recommend to use Lorentz transformation. Let $K_1(t_1,x_1)$ be the rest frame you adopted, and $K_2(t_2,x_2)$ the stationary frame of the rocket. On the one hand, in your $K_1$, set $t_1$ as when you see the rocket meets the light, and $x_1$ as where you see their meet. On the other hand, Lorentz transformation tells you the relation between $\left(t_1,x_1\right)$ and $\left(t_2,x_2\right)$. And $t_2$, the moment when the rocket finds itself meeting the light, is exactly the expected answer. – hypernova Apr 09 '18 at 18:18
  • In addition, the question might be less ambiguous if it reads how long it would take for the rocket to see the light after it finds itself passing through point $A$. – hypernova Apr 09 '18 at 18:21

0 Answers0