Physics Van 3-site Navigational Menu

Physics Van Navigational Menu

Q & A: Adding relativistic velocities

Learn more physics!

Most recent answer: 07/17/2010
Q:
Here's a scenario: You are traveling at 0.95c in one direction, and a fellow "traveler" is traveling at the same speed in the opposite direction. Relative to your motion, the fellow traveler is moving, seemingly impossibly, at a speed of 1.9c. We know that the speed of light is always constant at c, so what would you see with regards to the fellow traveler?
- Harry (age 26)
Australia
A:
Hello Harry,
Your question is frequently asked in different guises.  Your particular scenario is a bit tricky "You are traveling at 0.95c in one direction, and a fellow 'traveler' is traveling at the same speed in the opposite direction."  The frame of reference is not specified but let's assume it is with respect to an observer on earth.  Sure enough, the earth observer would claim that your relative velocity is 1.9 c.  There is no problem with that.   However in the reference frame of the first traveler it's a different matter.   In order to solve the problem you need to understand and use the Lorentz Transformation.  See: http://en.wikipedia.org/wiki/Lorentz_transformation .   The method I used was to Lorentz transform an earth observer to the frame of reference of traveler A and then ask the question "What Lorentz transformation would be necessary to transform traveler B's ship into his reference frame?   After a whole bunch of algebra I got VAB = (VA+VB)/(1 + VAVB). (I set c = 1 for convenience).  In your scenario the relative velocity would be  VAB = 0.9987    This could be checked by traveler A using an advanced radar speed gun.


LeeH

(published on 07/17/2010)

Follow-up on this answer.