Authors: Henok Tadesse
The Special Theory of Relativity ( STR ) provides a formula for the Doppler effect of light that differs from conventional formulas based on ether theory and emission theory. The relativistic Doppler effect formula becomes undefined for source-observer relative velocities greater than the speed of light. Since STR asserts that no ( relative ) velocity can ever reach or exceed the speed of light, this has never been seen as a problem. However, it will be shown in this paper that relative velocities greater than the speed of light can be attained even within the framework of STR, i.e. without violating the universal light speed limit. Imagine a light source and an observer at rest relative to each other and located close to each other. Light emitted by the source travels to a distant mirror and reflects back to the observer, while the mirror is moving towards the observer and the source with velocity equal to ( close to ) the speed of light. In this case the relative velocity between the mirror image of the source and the observer is equal to twice the speed of light, 2c. Since it is the relative velocity of the mirror image of the source and the observer that determines the Doppler effect, which is equal to 2c in this case, the relativistic Doppler effect formula becomes undefined because β = V/c = 2c/c = 2, which is greater than 1, resulting in a square root of negative number in the relativistic Doppler effect formula. This disproves relativistic Doppler effect, and hence the Special Theory of Relativity. According to STR the usual analysis is that the mirror image of the source never attains the speed of light because of the relativistic velocity addition formula. Since STR has been disproved logically, experimentally and theoretically, this assertion is not valid.
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