Physics Help Forum relativistic timing

 Special and General Relativity Special and General Relativity Physics Help Forum

 Sep 8th 2008, 07:09 PM #1 Junior Member   Join Date: Aug 2008 Posts: 9 relativistic timing 1. The problem statement, all variables and given/known data A member of a colony on Jupiter is required to salute the UN flag at the same time as it is being done on Earth at noon in New York. If observers in all inertial frames(i.e. any observer traveling at any arbitrary velocity) are to agree that he has performed his duty, how long must he solute for(i.e. seeing you don't know how fast the observer is traveling, what time iterval ensures that the rising of the falg and the saluting are simultaneous for all possible speeds of the observer)? (Distance between the planets is approximately 8 x10^6 km, ignore any relative motion of the planets) 2. Relevant equations Lorentz Transformation 3. The attempt at a solution I need help getting started on this. I have no idea what to do at all(partly because of not understanding what the question wants) I'm not sure if I'm suppose to derive an equation, or there is a number answer to this. I'm totally stuck on the thought process portion and cannot/don't know how to translate anything onto paper. I know that the arbitrary observer can have velocity from the range of -c to c but I don't know if that means I should end up with two solutions which will give us the time interval. So any advice on how to begin this would be greatly appreciated. Thanks
Sep 9th 2008, 07:34 AM   #2

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,856
 Originally Posted by jianxu 1. The problem statement, all variables and given/known data A member of a colony on Jupiter is required to salute the UN flag at the same time as it is being done on Earth at noon in New York. If observers in all inertial frames(i.e. any observer traveling at any arbitrary velocity) are to agree that he has performed his duty, how long must he solute for(i.e. seeing you don't know how fast the observer is traveling, what time iterval ensures that the rising of the falg and the saluting are simultaneous for all possible speeds of the observer)? (Distance between the planets is approximately 8 x10^6 km, ignore any relative motion of the planets) 2. Relevant equations Lorentz Transformation 3. The attempt at a solution I need help getting started on this. I have no idea what to do at all(partly because of not understanding what the question wants) I'm not sure if I'm suppose to derive an equation, or there is a number answer to this. I'm totally stuck on the thought process portion and cannot/don't know how to translate anything onto paper. I know that the arbitrary observer can have velocity from the range of -c to c but I don't know if that means I should end up with two solutions which will give us the time interval. So any advice on how to begin this would be greatly appreciated. Thanks
I'm off by a negative sign and I'm not sure why. But here it goes.

I'm going to make the simplifying assumption that the observers' origin is at the Earth at the time that the salute is supposed to be given. Let's synchronize all the observers' clocks with the Earth clock and let t = 0 be when the salute is supposed to be performed. The saluter has to salute somewhat before this time in order for the signal to be received at t = 0 on Earth, so he/she has to salute at t = -L/c where L is the Earth-Jupiter distance. Now an observer moving at speed v sees the salute at:
$\displaystyle t' = \gamma \left ( -\frac{L}{c} - \frac{Lv}{c^2} \right )$

$\displaystyle t' = -\frac{L}{c} \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}} = -\frac{L}{c} \sqrt{\frac{c + v}{c - v}}$
So as v goes from 0 to c the time t' goes from -L/c to (ahem) minus infinity.

Given the result I strongly suspect our poor saluter is going to have to salute forever (and we can logic that out.) I just can't find a way to get rid of the pesky negative sign.

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Sep 9th 2008, 09:48 AM #3 Junior Member   Join Date: Aug 2008 Posts: 9 thank you for your help. I actually understand what I should be looking for now
Sep 9th 2008, 11:06 AM   #4

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,856
 Originally Posted by jianxu thank you for your help. I actually understand what I should be looking for now
I'd be interested in how you get the final answer, once you figure it out. That negative sign is driving me crazy!

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Sep 10th 2008, 01:40 PM #5 Junior Member   Join Date: Aug 2008 Posts: 9 yep so we use initial t' = gamma(t - vx/c^2) what we're suppose to assume is that t' = 0 because all observers have to see the event simultaneously. At this point we know the range of speed an observer can have ranges from -c to c so we just plug that in and solve for t for the two different velocities
Sep 10th 2008, 01:45 PM   #6

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,856
 Originally Posted by jianxu yep so we use initial t' = gamma(t - vx/c^2) what we're suppose to assume is that t' = 0 because all observers have to see the event simultaneously. At this point we know the range of speed an observer can have ranges from -c to c so we just plug that in and solve for t for the two different velocities
Ah. Working backward. I like it. Thank you for sharing.

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Tags relativistic, timing

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post helpmeout Kinematics and Dynamics 1 Oct 10th 2015 06:46 AM MMM Kinematics and Dynamics 0 May 4th 2015 07:34 AM nathanzzf Quantum Physics 4 Jan 4th 2010 04:07 AM Pmb Special and General Relativity 28 Aug 1st 2009 02:02 PM physicsquest Special and General Relativity 2 May 26th 2009 11:58 AM