Special Relativity with 2 light beams moving towards each other

[Felipe Doria]

1. The problem statement, all variables and given/known data

If one light beam is heading toward you from the right, and another is heading toward you from the left, how quickly from the perspective of the right-moving beam is the left-moving beam approaching it?

1) 0

2) c

3) 1.5c

4) 2c

2. Relevant equations

(v+w) / (1 + cw/c2)

3. The attempt at a solution

I tried plugging in c into the equation for both v and w but it gives me (c + c) / (1 + c2/c2) which equals 2c. It is one of the possible answers but I know nothing can go faster than c so I'm thinking the answer is probably c. Am I right? If so, why? If not, what am I doing wrong? Thank you very much for your help!

[ACG52]

(c + c) / (1 + c2/c2) which equals 2c.

 

2c/(1 + 1) equals c.

[Felipe Doria]

2c/(1 + 1) equals c.

I'm so dumb, I forgot the second 1 in the equation. Thank you!

[swansont]

I know nothing can go faster than c so I'm thinking the answer is probably c.

 

No single object with mass can travel at (or faster) than c as measured by an observer. There are phenomena such as closing speed which are not in this category (regardless of whether it's a photon or not)

 

In a sense this is a trick question, because the photon is not in an inertial frame and the physics of special relativity only applies to inertial frames. There is no real way for us to know the perspective of either beam. As a limit, though for any two objects traveling close to c, the speed one sees the other approach at will approach c.

 

The fact that you saw an answer and it didn't make sense show good instincts.

[Felipe Doria]

 

No single object with mass can travel at (or faster) than c as measured by an observer. There are phenomena such as closing speed which are not in this category (regardless of whether it's a photon or not)

 

In a sense this is a trick question, because the photon is not in an inertial frame and the physics of special relativity only applies to inertial frames. There is no real way for us to know the perspective of either beam. As a limit, though for any two objects traveling close to c, the speed one sees the other approach at will approach c.

 

The fact that you saw an answer and it didn't make sense show good instincts.

Thank you for your help! I had just forgotten to add the second 1 and done 2c/1 instead of 2c/2 as dumb as that might sound.

[davidivad]

this is a funny little scenario.

the problem here stems from the fact that nothing can travel faster than the speed of light.

therefore the measurement cannot be physically made. it would require faster than light transmission to measure.

the speed of the opposing beam is unmeasureable from the measuring beam so this is no more than an excercise in math.

Edited March 16, 2014 by davidivad