Simple question from a newbie

1. Oct 15, 2009

Monkfish

Can someone with a bigger brain than me please explain this situation:

You've got 3 people A, B, & C. B is in the middle and A & C move away from him in opposite directions at 2/3 the speed of light as seen by B. What speed is C going from the perspective of A and why?

2. Oct 15, 2009

DaveC426913

C and A will be moving at approx .92c wrt each other

Relativistic velocities do not add the way we expect. When two relativistic velocities are "added", the answer will always be less than c. This is the formula:

[TEX]s = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}[/TEX]

= .666 + .666 / (1 + .4435 / 1^2)

= .92

Last edited: Oct 15, 2009
3. Oct 15, 2009

Staff: Mentor

I won't give you the exact answer because it is instructive for you to try to calculate it yourself using the relativistic "velocity addition" formula:

http://hyperphysics.phy-astr.gsu.edu/hbasees/Relativ/einvel.html

Nevertheless, I can tell you that the answer must be less than the speed of light, so if you get a larger number you've made a mistake somewhere.

4. Oct 15, 2009

DaveC426913

&%$@$! latex...

5. Oct 16, 2009

Monkfish

Thanks for the equation. Is there a way to visualize this using a 3D space-time diagram (as opposed to a 4D diagram which would a little difficult to draw ;))?

6. Oct 16, 2009

dx

You can visualize it using just a 2D spacetime diagram (1 space + 1 time). Unfortunately there is no easy way for me to draw it for you, so I refer you to the excellent textbook Spacetime Physics by Taylor and Wheeler.

7. Oct 16, 2009

Monkfish

Thanks. It must be a good book because it's bloody expensive!

8. Oct 16, 2009

dx

9. Oct 16, 2009

Monkfish

Thanks, I'll give it a read and if my puny brain can cope, I'll start saving up my pennies. :)

10. Oct 17, 2009

Idyllic

I would also like to know the answer to this question. Can it be figured out just using einsteins two posulatees? I proved that the relative velocities cant be greater than c if one is stationary, but im not sure about this one.

11. Oct 17, 2009

Staff: Mentor

The relativistic "velocity addition" equation is normally derived from the Lorentz transformation equations, which can in turn be derived from Einstein's postulates. I've never seen it derived "directly" from the postulates.

12. Oct 19, 2009

Idyllic

thanks were about to learn about it at uni. This stuff is so damn exciting.