Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: paul.fr on 15/11/2007 16:23:21
-
Please forgive me if i am wrong, but if two cars crash and both ar travelling at 60mph then the combined speed of the crash is 120mph...yes?
so what if the same two cars (or rockets...) were travelling at 0.6 the speed of light, would their combined speed be faster than the speed of light?
-
Although it cannot be done with cars it is commonly done with Electrons and Positrons in particle accelerators travelling at 99.9999% the speed of light.
I some sense the collision could be said to occur at 2c but of course each particle exist in its own reference frame so special relativity survives
-
If I'm driving car A at 60 mph, and you're driving car B at 60 mph, and you crash into me head on, then it could look to me as if you're approaching me at 120 mph before the crash. This is called a "Galilean" addition of velocities (they just add together).
If you try to do the same thing at close to the speed of light, since nothing can move faster than the speed of light, you get an extra factor in the equation, so you can't just add velocities, since, as you point out, that would lead to velocities faster than the speed of light. The actual equation to correctly add really fast velocities together is here: http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_Theory_of_Relativity
Of course, if you're going slow enough, then the extra factor that appears because of special relativity is negligible, and you can just add velocities together.
Finally, to answer your question, if two rockets slammed into each other, and each had a speedometer that said "0.6 times the speed of light," rocket pilot A would say that rocket B is coming at him at a speed of around 0.88 times the speed of light.
-
Please forgive me if i am wrong, but if two cars crash and both ar travelling at 60mph then the combined speed of the crash is 120mph...yes?
so what if the same two cars (or rockets...) were travelling at 0.6 the speed of light, would their combined speed be faster than the speed of light?
The correct formula, valid at *every* speeds is not V = v1 + v2 but, instead:
V = (v1 + v2)/(1 + v1•v2/c2)
let's try with 60mph:
V = (60 + 60)/(1 + 60•60/675,000,0002) = 120/(1 + 7.9*10-15) ≈ 120( 1 - 7.9*10-15) =
= 120 - 0.000000000000948 = 119,999999999999052 mph
So, the combined speed of the crash is NOT 120mph actually; but the difference is not measurable with common instruments.
Now let's try with 0.6c:
V = (0.6c + 0.6c)/(1 + 0.6c•0.6c/c2) = c(0.6 + 0.6)/(1 + 0.36) = 1.2c/1.36 ≈ 0.88c
-
Although it cannot be done with cars it is commonly done with Electrons and Positrons in particle accelerators travelling at 99.9999% the speed of light.
I some sense the collision could be said to occur at 2c but of course each particle exist in its own reference frame so special relativity survives
No. See up.
-
Yep I knew you had to do something like a Lorentz transform but I thought I would just start the ball rolling