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Topic: SPECIAL RELATIVITY INCOMPATIBLE WITH DOPPLER EFFECT
Replies: 4   Last Post: Sep 26, 2013 12:58 AM

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 Pentcho Valev Posts: 2,843 Registered: 12/13/04
SPECIAL RELATIVITY INCOMPATIBLE WITH DOPPLER EFFECT
Posted: Sep 17, 2013 2:31 AM

http://www.hep.man.ac.uk/u/roger/PHYS10302/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%C3%89%20par%20DAMOUR%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):

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

Date Subject Author
9/17/13 Pentcho Valev
9/20/13 Pentcho Valev
9/22/13 Pentcho Valev
9/25/13 Pentcho Valev
9/26/13 Pentcho Valev