Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: AllenG on 20/07/2009 01:04:53

Title: Can two objects move apart at faster than the speed of light?
Post by: AllenG on 20/07/2009 01:04:53
If two objects are launched in opposite directions from a central point and they are traveling from the point of origin at 3/4C how fast are they traveling away from one another?
Title: Re: Can two objects move apart at faster than the speed of light?
Post by: Ethos on 20/07/2009 01:08:33
Quote from: AllenG on 20/07/2009 01:04:53
If two objects are launched in opposite directions from a central point and they are traveling from the point of origin at 3/4C how fast are they traveling away from one another?
If I'm not mistaken, their relative speed would be 186,282 miles/sec.
Title: Re: Can two objects move apart at faster than the speed of light?
Post by: lightarrow on 20/07/2009 11:33:55
Quote from: AllenG on 20/07/2009 01:04:53
If two objects are launched in opposite directions from a central point and they are traveling from the point of origin at 3/4C how fast are they traveling away from one another?
In relativity velocities don't add, you can't write V = v1 + v2. The correct formula instead is:

V = (v1 + v2)/(1 + v1*v2/c2)

So, if  v1 = v2 = (3/4)c, for example, you have:

[(3/4)c + (3/4)c]/[1 + (9/16)] = (3/2)c/(25/16) = (24/25)c = 0.96c
Title: Re: Can two objects move apart at faster than the speed of light?
Post by: Stefanb on 22/07/2009 07:31:39
Quote from: lightarrow on 20/07/2009 11:33:55
Quote from: AllenG on 20/07/2009 01:04:53
If two objects are launched in opposite directions from a central point and they are traveling from the point of origin at 3/4C how fast are they traveling away from one another?
In relativity velocities don't add, you can't write V = v1 + v2. The correct formula instead is:

V = (v1 + v2)/(1 + v1*v2/c2)

So, if  v1 = v2 = (3/4)c, for example, you have:

[(3/4)c + (3/4)c]/[1 + (9/16)] = (3/2)c/(25/16) = (24/25)c = 0.96c
Can you explain how you got that formula? Or why that is the case in relativity? I would like to know [:)]
Title: Re: Can two objects move apart at faster than the speed of light?
Post by: lyner on 22/07/2009 13:13:29
If you start with the premise that the speed of light appears to be the same for all observers then the Lorentz formula applies for all measurements of relative velocities. The basis for relativity is that there is no 'preferred frame of reference'. We don't exist on a piece of 3D graph paper which defines where we are, how fast we're going and in what direction. All motion and position is relative to the observer.
Look at this link if you want the details; it tells you 'why'. Otherwise you just have to accept what lightarrow was telling you.
http://en.wikipedia.org/wiki/Special_relativity (http://en.wikipedia.org/wiki/Special_relativity)
Title: Re: Can two objects move apart at faster than the speed of light?
Post by: lightarrow on 23/07/2009 10:03:24
Quote from: Stefanb on 22/07/2009 07:31:39
Can you explain how you got that formula? Or why that is the case in relativity? I would like to know [:)]
As sophiecentaur implicitly wrote, it's not so immediate, if you don't know relativity very much. From the two postulates of relativity (1. light' speed doesn't depend on the light source's speed; 2. the laws of physics are the same in all inertial frames of reference) you can get the lorentz equations for a boost (= rectilinear movement) along the x direction:

x' = γ(x-v*t)
y' = y
z' = z
t' = γ(t-x*v/c2)

then you derive x' with respect to t' and find the velocity of the object in the prime frame of reference and then you relate dx/dt to that velocity.

If you are interested in the detailed computations...when I come back home, after my holidays [:)]