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On the previous page, I described the phenomena called relativistic Doppler shift ( also called the redshift): if a light source and an observer move closer and closer, the observed light frequency is shifted toward the blue end of the visible spectrum, and, if they move away from each other, toward the red end of the spectrum.
Now back to Albert and the policeman. Albert just finished his story with words: "... and since I was approaching the intersection, I was moving toward the traffic light, in which case the Doppler formula must be used. I am not arguing. The light may have been red for you, officer, but I saw it GREEN, so I proceeded. Therefore, I am not responsible for this violation." The policeman heard the story presented by Albert, took a look at the formulae Albert showed him, and said: "Yes, Sir, I understand what you are saying, you are not guilty of violating Section 98020 (c) (i) disobeying red steady circular light. But please give me your driver's license, and step out of your car. I am taking you to jail for disobeying the 55 mi/h speed limit . Since you saw a green light you were traveling at 31,875 mi/sec  about 114 million mi/h above the speed limit!" This Doppler shift phenomenon is useful in determining the speed of celestial objects. Astronomers measure the Doppler shift of light emitted by those objects and then, like our policeman, are able to calculate its speed. As soon as they have the speed, astronomers use the general theory of relativity to calculate the distance to those objects. In the previous couple of pages we discussed the implications of Einstein's theory of special relativity. We have already talked about the relativistic addition of speeds, Cerenkov radiation, E=mc^2, time dilation and Doppler shift.
There is one more very important consequence of the theory of relativity, which seems to contradict with our everyday experience: the simultaneity of events in different frames of reference. Please turn to next page. 

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last modified 1/5/2001 email Fermilab 
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