No Sir, I did Not Run the Red Light!

twin paradox


Once upon a time, there was a physicist (named Albert) who got stopped by a policeman at an intersection. The policeman said hello and started to write a ticket (as is usual). Albert was surprised and asked what he had done wrong. The policeman said,

"Albert, you violated Section 9-8-020 (c) (i) when you disobeyed red steady circular light!" ( In English, he ran a red light.) Albert politely argued, "I am sorry officer, but the light was green. Here, take a look at this, please, I can prove it to you." Then he explained.

In Einstein's theory of relativity, because of time dilation, there is a phenomena called the Doppler effect or, the Doppler shift. Suppose you have a light (or any electromagnetic wave) source, which moves with a speed v either toward the observer or away from the observer. Suppose the light emitted by the source has a frequency as the source sees it. Then, according to the theory of relativity, the frequency of the light that a stationary observer will see is DIFFERENT from the actual emitted frequency.

The observed frequency depends on whether the source is moving toward the observer or away from him.

If the source and the observer are getting closer and closer, the observed light frequency is higher than the emitted one by a constant shift. The magnitude of the shift depends on the magnitude of the relative speed of the observer and the source.

If the source and the observer are moving away from each other, the observed light frequency will be smaller, again by a constant shift depending on the magnitude of the relative speed. Since the frequency of the light determines its color (see page entitled "Visible spectrum)", the color of the observed light will be different from the emitted color.

To express these qualitative words quantitatively, I show the formulae which allow you to calculate the observed frequency nu(obser) from the knowledge of the emitted frequency nu(emmi) and from the knowledge of their relative speed V.

To illustrate, I show (see table below) what an observer would see a red emitted light, depending on his speed.

Red color seen as Red Yellow Green Blue Violet
Albert's speed (in % of c) 0 11 17 29 45

How did the story end with Albert and the physicist? See the next page.

twin paradox


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Last updated: June 18, 1999 AP