Wednesday, August 13, 2008

Should you Brake, Slow Down or Go?

How fast would you need to be traveling towards a red traffic light to see it appear as green?


  1. You're a little rusty on physics, and then you pull this question out?? Well, you asked for it...

    The wavelength of green light is around 530 nm, yielding a frequency of 5.66*10^14 Hz (566 THz). Red light has an average wavelength of 685 nm, with a frequency of 438 THz. According to my graduate E&M book, the relativistic Doppler shift (different from the classical Doppler shift, since light travels the same speed in all inertial reference frames) is given by:

    w' = gamma * w * (1-Beta*cos(theta))

    w' = new frequency
    w = old frequency
    gamma = 1 / sqrt(1-Beta^2)
    Beta = v/c
    v = your velocity
    c = velocity of light
    theta = angle between your velocity vector and that of the light (0 degrees in this case, assuming you're headed straight at the traffic light)

    Plugging everything in:

    566 = 438/sqrt(1-Beta^2)*(1-Beta)

    and solving, yields:

    Beta = -0.25

    Therefore, you need to go 1/4 the speed of light, and the negative means you need to go the opposite direction of the light.

    So you must go 1/4 the speed of light (about 75,000,000 m/s, or about 671,000,000 mph) toward the traffic light. I know my car can't go that fast ;-)

  2. Abe -
    I love reading your answers to these questions. Between you and Mike I am learning something everyday that I wouldn't have the opportunity to learn in my normal day to day.
    Thanks guys!

  3. As always abe, your answer is so much better than I could have said it.


  4. I would just wait until it turns green ;)

  5. Just watch out for those cameras!


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