Brightness detected based on direction of travel relative to source

[wsellers]

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?

 

[Ich]

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.

You forgot the http://www.anu.edu.au/Physics/Searle/Obsolete/Seminar.html" (I found this site independently ).
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.

 

[Dale]

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.

 

[wsellers]

Thanks very much! I wasn't aware of the headlight effect.