1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simultaneity of lasers homework

  1. Jun 7, 2010 #1
    1. The problem statement, all variables and given/known data

    A spaceship (SH) moves with speed v=0.6c relative to a space station (SS) (sic!). Two lasers, A and B, on the SS are 5.00m apart as measured by the SS observers. The gamma factor for a speed v=0.6c is 1.25.

    The lasers are fired simultaneously acc. to the SS observers. Light from each laser makes a mark on the SH. The SH observers measure the distance between the two marks to be 6.25m.
    We are to calculate the difference in time between the firings of the two lasers acc. to the SH observers.


    2. Relevant equations

    I'm taking the equation 'for' simultaneity from http://en.wikipedia.org/wiki/Special_relativity


    3. The attempt at a solution

    \Delta t' = \gamma \left( \Delta t - \frac{v \Delta x}{c^2} \right),
    where in our case:
    \Delta t = 0s (events are simultaneous in S frame), \gamma = 0.6c, \Delta x = 6.25m.
    It results in 15.6ns.

    Please tell whether I'm correct with my attempt.
     
  2. jcsd
  3. Jun 7, 2010 #2
    Re: simultaneity

    I would use a relativistic invariant. [tex]r^{\mu}r_{\mu}=(c \Delta t)^{2}-{\Delta r}^{2}[/tex]. This quantity is the inner product of two four vectors so it is invariant under Lorentz transformation. In this case, it would be equal both in the SH frame and the SS frame. Just set it equal for the two frames, plug in what you know, and solve for the unknown.
     
  4. Jun 7, 2010 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Re: simultaneity

    The unprimed quantities are measurements in the SS frame, so [itex]\Delta x\ne 6.25~\textrm{m}[/itex].
     
  5. Jun 7, 2010 #4
    Re: simultaneity


    To americanforest: I forgot to add that it should be solved with high school physics tools, therefore we mustn't use the invariant.

    To vela: I agree. We should thus divide the 6.25m by gamma factor, right?
     
  6. Jun 8, 2010 #5

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Re: simultaneity

    No, not quite. Δt is the temporal difference between two events, right? Δx is the spatial distance between those same two events. What are the two events and how far apart in space are they?
     
  7. Jun 8, 2010 #6
    Re: simultaneity


    The two events are the firings. Since they are simultaneous in SS frame, dt=0. We also know that in SS frame their spatial separation is dx=5m.
     
  8. Jun 8, 2010 #7

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Re: simultaneity

    Yup, you got it.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook