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Brightness detected based on direction of travel relative to source

  1. Nov 21, 2007 #1
    I don’t see that this question has been asked before and I am hoping the generous moderators of this forum will be able to answer it.

    Suppose you have the “standard” situation with the man M on the embankment and the woman W in the center of the moving train car. (The train has lots of windows enabling M to see in.) W strikes a match (it’s a special kind of match that has a constant luminosity, L). The distance between W (and the match) and the front of the car is D1; the distance between W and the back of the car is D2. Since we assume W is in the exact middle, D1=D2.

    At each end of the car is a brightness detector with a digital LCD readout. Brightness is equal to L/4[pi]r, I believe, where L is luminosity and r is the distance from the light source to the detector. The distance that the light travels from the match to the front detector is r1; the distance that the light travels from the match to the rear detector is r2.

    Because the train is moving toward the front, r1 > r2. This should mean that the rear detector measures a level of brightness that is greater than that measured by the front detector. Thus the rear detector would display a number that is greater than the number displayed by the front detector.

    Wouldn’t M and W see the same numbers? In the same train car going in the opposite direction, wouldn’t the rear detector display a number that is less than the number displayed by the front detector?
  2. jcsd
  3. Nov 21, 2007 #2


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    Science Advisor

    You forgot the Headlight Effect. (I found this site independently :wink: ).
    Quick explanation: There are many effects you have to consider, all of which conspire to make the Lorentz Transformations valid. However, if you look at it differently: The LT are indeed valid (or, at least, self-consistent), and all those effects are simply derived from it. So it is no miracle that all works out self-consistently.
  4. Nov 21, 2007 #3


    Staff: Mentor

    Energy is a frame-variant quantity so luminosity (energy/time) and brightness (luminosity/area) are also frame variant. A detector moving away from a source will generally detect lower energy than one moving towards a source as the Doppler red-shift lowers the energy of the detected photons, but does not change the number of photons.
  5. Nov 21, 2007 #4
    Thanks very much! I wasn't aware of the headlight effect.
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