Understanding Speed in an A,B,C Situation

[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?

 

[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:

$$s = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}$$


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

= .92

 

[jtbell]

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.

 

[DaveC426913]

&%$@$! latex...

 

[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 ;))?

 

[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.

 

[Monkfish]

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

 

[dx]

Chapter one is free: http://www.eftaylor.com/download.html#special_relativity

Discussion of the spacetime diagram starts on page 26.

 

[Monkfish]

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

 

[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 can't be greater than c if one is stationary, but I am not sure about this one.

 

[jtbell]

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.

 

[Idyllic]

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.

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