VARIABLE SPEED OF SOUND AND LIGHT

If the observer starts moving towards/away from the sound or light source, the speed of the waves relative to him increases/decreases (in violation of special relativity); accordingly, the wavecrests start hitting him more/less frequently:

http://www.youtube.com/watch?v=bg7O4rtlwEE
"Doppler effect - when an observer moves towards a stationary source. ...the velocity of the wave relative to the observer is faster than that when it is still."

http://www.youtube.com/watch?v=SC0Q6-xt-Xs
"Doppler effect - when an observer moves away from a stationary source. ....the velocity of the wave relative to the observer is slower than that when it is still."

The only way to avoid the collapse of Einstein's relativity is to assume that the motion of the observer somehow changes the wavelength; then this change in wavelengh, in the absence of any change in the speed of the waves relative to the observer, produces the Doppler frequency shift:

http://lewebpedagogique.com/physique...8doppler_p.gif

Pentcho Valev

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 (...) 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 time t, ct/lambda waves pass a fixed point. A moving point adds another vt/lambda."

That is, in time t, N=(c+v)t/lambda waves pass the moving point, and the speed of the waves relative to the moving point is:

c' = N(lambda)/t = c+v, in violation of special relativity.

If v is smaller than (1/3)c, the relativistic corrections are negligible (for v=(1/3)c gamma is 1.05) and both c'=c+v and f'=c'/lambda are virtually exact formulas no matter whether the classical or the relativistic Doppler effect is considered.

Pentcho Valev

On Sunday, May 18, 2014 10:06:13 AM UTC-7, Pentcho Valev wrote:
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 (...) 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 time t, ct/lambda waves pass a fixed point. A moving point adds another vt/lambda."



That is, in time t, N=(c+v)t/lambda waves pass the moving point, and the speed of the waves relative to the moving point is:



c' = N(lambda)/t = c+v, in violation of special relativity.


If v is smaller than (1/3)c, the relativistic corrections are negligible (for v=(1/3)c gamma is 1.05) and both c'=c+v and f'=c'/lambda are virtually exact formulas no matter whether the classical or the relativistic Doppler effect is considered.

Pentcho Valev

Do individual photons actually move?

http://www.youtube.com/watch?feature...&v=EVzUyE2oD1w
Dr Ricardo Eusebi: "f'=f(1+v/c). Light frequency is relative to the observer. The velocity is not though. The velocity is the same in all the reference frames."

The video shows a light source and an (initially) stationary observer measuring the frequency to be f=c/d, where d is the distance between the wavecrests.

When the observer starts moving with speed v away from the light source, the videowatcher clearly sees that the speed of the wavecrests relative to the observer shifts from c to c'=c-v, and that this causes the frequency the observer measures to shift from f=c/d to f'=(c-v)/d=f(1-v/c).

Yet Dr. Ricardo Eusebi explains that the shift from c to c'=c-v, although clearly seen in the animation, is not there - rather, the speed of the wavecrests relative to the observer remains unchanged (c'=c):

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."

Needless to say, not all scientists suffer from the above schizophrenia. Many admit, explicitly or implicitly, that the speed of the light waves relative to the observer does vary with the speed of the observer:

http://physics.bu.edu/~redner/211-sp...9_doppler.html
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)."

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."

Tony Harker: "In a time t the number of waves which reach the observer are those in a distance (c-Vo)t."

Consequence: The speed of the light waves relative to the moving observer is:

c' = distance/time = (c - Vo)t/t = c - Vo,

in violation of Einstein's relativity.

Pentcho Valev