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Since nobody cares whether Einstein's relativity is correct or not (it is a money-spinner anyway), the Albert Einstein Institute can safely explain the Doppler effect by implicitly assuming that the speed of light as measured by the observer varies with the speed of the observer:
http://www.einstein-online.info/spotlights/doppler
Albert Einstein Institute: "The frequency of a wave-like signal - such as sound or light - depends on the movement of the sender and of the receiver. This is known as the Doppler effect. (...) In the above paragraphs, we have only considered moving sources. In fact, a closer look at cases where it is the receiver that is in motion will show that this kind of motion leads to a very similar kind of Doppler effect. Here is an animation of the receiver moving towards the source: (...) By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, the distances between subsequent pulses are not affected, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses."
Let the distance between subsequent pulses (which is not affected by the motion of the receiver) be L and the time it takes the source to emit three pulses be t. The speed of the pulses a fixed receiver measures is 3L/t = c. Accordingly, the speed of the pulses the moving receiver measures is 4L/t = (4/3)c.
Pentcho Valev pvalev@yahoo.com