Ahmad Hadeed Blog

The Green Red Light !

Just imagine saying that to your local police officer :P
A question in my modern physics book (Relativity Chapter) says:

“A physics professor claims in court that the reason he went through the red light was due to his motion, that is was Doppler shifted to green”

Now some may not know what is the meaning of Doppler effect, so I'll explain that briefly.
You sure do remember standing on the sidewalk where someone angry is passing by you in his car with his hands on the horn, or maybe an ambulance or a fire truck where passing by.
The sound is always with a higher pitch when the sound generator is approaching while at lower pitch when leaving. This is called the Doppler effect, it's basically depending on the speed of motion of the object, speed of sound in the medium (in the case of sound) & the initial frequency (the sound of the source).

Now in the case of light, things gets a bit more complicated, since light moves at the speed of... (well, light of course). The relativistic effect should be included.

The relativistic Doppler effect is indicated by the law:

Where:
c = Speed of light = 3*10^8
Lambda = wavelength
For the red light = 650 nm
For the green light = 550 nm
u = The speed of motion.
Note that: u = -u in case of approaching.

Doing the math to get u, we discover that based on the professor's claims, he was driving with a speed of (5*10^7 m/s), a more convenient unit (180*10^6 km/h) or (112.5*10^6 miles/h).

Well, if it was me, I'd pay the fine for crossing the red light rather than that cosmic over speeding! :P