SPECIAL RELATIVITY INCOMPATIBLE WITH DOPPLER EFFECT

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."

http://www-cosmosaf.iap.fr/RELATIVIT...20Thibault.htm
Thibault Damour: "Or, en relativité restreinte, les fréquences mesurées par deux observateurs en mouvement relatif sont différentes (effet Doppler-Fizeau). Pour une vitesse relative faible, l'effet (f'-f)/f est égal à v/c."

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 (variable) speed of the light waves relative to the moving observer. Special relativity is violated.

Einsteinians' only objection is that the formula f'=f(1+v/c) is an approximation - the relativistic corrections (time dilation) are not taken into account. However, if v is small enough ("pour une vitesse relative faible"), the relativistic corrections "are negligible here", which means that both f'=f(1+v/c) and c'=c+v are virtually exact. 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. If v is small enough, we have c'=c+v with or without the relativistic corrections, and the violation of special relativity is more than obvious.

The Albert Einstein Institute clarifies the effects by analysing a scenario where the wavelength is replaced by the distance between subsequent light pulses:

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.

Again, 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 Newton's emission theory of light and in violation of special relativity.

That the speed of the light waves (relative to the observer/receiver) varies with the speed of the observer/receiver is clearly seen in this video (although Eusebi obeys Ignatius of Loyola's principle and says the velocity remains the same):

http://www.youtube.com/watch?feature...&v=EVzUyE2oD1w
Dr Ricardo Eusebi: "Light frequency is relative to the observer. The velocity is not though. The velocity is the same in all the reference frames."

Ignatius of Loyola: "That we may be altogether of the same mind and in conformity with the Church herself, if she shall have defined anything to be black which appears to our eyes to be white, we ought in like manner to pronounce it to be black."

Pentcho Valev

http://physics.bu.edu/~redner/211-sp...9_doppler.html
Professor Sidney Redner: "The Doppler effect is the shift in frequency of a wave that occurs when the wave source, or the detector of the wave, is moving. Applications of the Doppler effect range from medical tests using ultrasound to radar detectors and astronomy (with electromagnetic waves). (...) We will focus on sound waves in describing the Doppler effect, but it works for other waves too. (...) Let's say you, the observer, now move toward the source with velocity vO. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vO. The frequency of the waves you detect is higher, and is given by: f'=v'/(lambda)=(v+vO)/(lambda)."

For light waves v=c and we have:

f' = c'/L = (c+vO)/L

where L=(lambda) and c'=c+vO is the speed of light relative to the observer. Clearly special relativity is violated.

The relativistic corrections add a factor of gamma but this does not save special relativity:

f' = (gamma)c'/L = (gamma)(c+vO)/L

Even if one advances the absurd assumption that gamma somehow changes the wavelength (L'=L/(gamma)), the formula f'=c'/L' still gives a speed of light relative to the observer, c', different from c. If vO is small enough, gamma can be omitted and the formula c'=c+vO is virtually exact.

Special relativity is incompatible with both non-relativistic and relativistic Doppler effect.

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..."

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 a small (so that the relativistic corrections are negligible) 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.

In this scenario the wavelength of light is replaced by "the distance between subsequent pulses", and the Albert Einstein Institute clearly states that this distance is not affected by the motion of the receiver (it would be too idiotic to state the opposite). That is, if L' is the distance as measured in the moving receiver's frame, and L is the distance as measured in the stationary receiver's frame, we have L'=L. By combining this with f'=c'/L' we come to the conclusion that "the speed of the light waves relative to the moving receiver" is the only possible interpretation of c'=c+v.

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: 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."

That is, the motion of the receiver obviously cannot change "the distances between subsequent pulses" and accordingly the speed of light as measured by the receiver is (4/3)c, in violation of special relativity.

This conclusion is consistent with the classical Doppler effect but one can easily see that the relativistic corrections change essentially nothing - the speed of light relative to the receiver remains different from c.

Pentcho Valev

http://www.cmmp.ucl.ac.uk/~ahh/teach...24n/lect19.pdf
Tony Harker, University College London: "The Doppler Effect: Moving sources and receivers. The phenomena which occur when a source of sound is in motion are well known. The example which is usually cited is the change in pitch of the engine of a moving vehicle as it approaches. In our treatment we shall not specify the type of wave motion involved, and our results will be applicable to sound or to light. (...) Now suppose that the observer is moving with a velocity Vo away from the source. (....) If the observer moves with a speed Vo away from the source (...), then in a time t the number of waves which reach the observer are those in a distance (c-Vo)t, so the number of waves observed is (c-Vo)t/lambda, giving an observed frequency f'=f(1-Vo/c) when the observer is moving away from the source at a speed Vo."

If "in a time t the number of waves which reach the observer are those in a distance (c-Vo)t", then the speed of the light waves relative to the observer is:

c' = ((c - Vo)t)/t = c - Vo

in violation of special relativity. The relativistic corrections do not change essentially this conclusion - c' remains different from c. If Vo is small enough, the relativistic corrections are negligible and both f'=f(1-Vo/c) and c'=c-Vo are virtually exact formulas.

Pentcho Valev