EVEN RELATIVISTIC DOPPLER EFFECT TOPPLES RELATIVITY

http://www.hep.man.ac.uk/u/roger/PHY.../lecture18.pdf
Roger Barlow, Professor of Particle Physics: "The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. (...) Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/lambda waves pass a fixed point. A moving point adds another vt/lambda. So f'=(c+v)/lambda. (...) Relativistic Doppler Effect: These results depend on the absolute velocities of the source and observer, not just on the relative velocity of the two. That seems odd, but is allowable as sound waves are waves in a medium, and motion relative to the medium may legitimately matter. But for light (or EM radiation in general) there is no medium, and this must be wrong. This needs relativity. (...) If the source is regarded as fixed and the observer is moving, then the observer's clock runs slow. They will measure time intervals as being shorter than they are in the rest frame of the source, and so they will measure frequencies as being higher, again by a gamma factor: f'=(1+v/c)(gamma)f..."

In the non-relativistic case (light waves are considered but time dilation is ignored), as the observer starts moving towards the light source with speed v, the speed of the light waves relative to him shifts from c to c'=c+v, and this causes the frequency he measures to shift from f=c/lambda to f'=c'/lambda=(c+v)/lambda=(1+v/c)f. Special relativity is violated - the speed of light relative to the observer varies with the speed of the observer.

In the relativistic case, as the observer starts moving towards the light source with speed v, the speed of the light waves relative to him shifts from c to c'=(c+v)(gamma), and this causes the frequency he measures to shift from f=c/lambda to f'=c'/lambda=(c+v)(gamma)/(lambda)=(1+v/c)(gamma)f. Special relativity is violated again. If v is small enough, in both the non-relativistic and relativistic case we have c'=c+v, which means that the speed of light relative to the observer varies with the speed of the observer as predicted by both Newton's emission theory of light and Maxwell's 19th century electromagnetic theory.

http://fr.wikipedia.org/wiki/Effet_Doppler_relativiste
"Effet Doppler relativiste (...) Supposons que l'observateur et la source s'éloignent l'un de l'autre à une vitesse relative de v (v est négative si l'observateur et la source se déplacent l'un vers l'autre). Analysons ce problème depuis le référentiel de la source en supposant qu'un front d'onde arrive à l'observateur. Le prochain front d'onde est donc à la distance L=c/Fs de lui (où L est la longueur d'onde, Fs est la fréquence de l'onde au moment de son émission et c la vitesse de la lumière). Puisque le front d'onde se déplace à la vitesse c et que l'observateur se déplace à la vitesse v, la durée (telle que mesurée dans le référentiel de la source) entre les crêtes à l'arrivée est donnée par t=L/(c-v)... (...) À cause de la dilatation du temps (relativiste), l'observateur va mesurer cette durée comme étant to=t/gamma...."

Dans le cas non-relativiste (la dilatation du temps est ignorée), la vitesse des crêtes par rapport à l'observateur est c'=L/t=c-v, en violation de la relativité restreinte.

Dans le cas relativiste, la vitesse des crêtes par rapport à l'observateur est c'=(L/to)=(c-v)(gamma), toujours en violation de la relativité restreinte. Si v est petite, on a c'=c-v dans le cas relativiste aussi.

Pentcho Valev

http://rockpile.phys.virginia.edu/mod04/mod34.pdf
Paul Fendley: "Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) (it goes up heading toward you, down away from you). There are relativistic corrections, but these are negligible here."

That is, if the frequency measured by the stationary observer is f=c/L (L is the wavelength), the frequency measured by an observer moving towards the light source with speed v is:

f' = f(1+v/c) = (c+v)/L = c'/L

where c'=c+v has a definite physical meaning: it is the speed of the light waves relative to the moving observer. The formula f'=f(1+v/c) is an approximation (the relativistic corrections are not taken into account) and so is c'=c+v. However Paul Fendley explains that the relativistic corrections "are negligible here", which means that both f'=f(1+v/c) and c'=c+v are virtually exact. Special relativity is violated.

Let us still add the relativistic corrections (time dilation is taken into account):

f' = f(1+v/c)(gamma) = (c+v)(gamma)/L = c'/L

where c'=(c+v)(gamma) is the speed of the light waves relative to the moving observer. Clearly both the non-relativistic and relativistic Doppler effect violate special relativity. If v is small enough, we have c'=c+v in both cases, which means that the speed of light relative to the observer varies with the speed of the observer as predicted by both Newton's emission theory of light and Maxwell's 19th century electromagnetic theory.

Pentcho Valev

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. (...) 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..."

That is, if the frequency measured by the stationary receiver is f=c/L (L is the distance between subsequent pulses), the frequency measured by a receiver moving towards the light source with speed v is:

f' = f(1+v/c) = (c+v)/L = c'/L

where c'=c+v is the speed of the light waves relative to the moving receiver. Special relativity is violated.

The relativistic corrections (time dilation is taken into account) add a factor of gamma:

f' = f(1+v/c)(gamma) = (c+v)(gamma)/L = c'/L

where c'=(c+v)(gamma) is the speed of the light waves relative to the moving receiver. Clearly both the non-relativistic and relativistic Doppler effect violate special relativity. If v is small enough, we have c'=c+v in both cases, which means that the speed of light relative to the receiver varies with the speed of the receiver as predicted by both Newton's emission theory of light and Maxwell's 19th century electromagnetic theory.

Pentcho Valev