Pentcho Valev
2015-03-22 09:23:35 UTC
When an observer starts moving towards a light source with (small) speed v, the frequency he measures shifts from f=c/λ to f'=(c+v)/λ, where c is the speed of the waves relative to a stationary observer and λ is the wavelength.
Question: Why does the frequency shift from f=c/λ to f'=(c+v)/λ?
Answer 1 (fatal for Einstein's relativity): Because the speed of the waves relative to the observer shifts from c to c'=c+v (that is, relative to the observer, the speed of the light is now greater than c).
Answer 2 (possibly saving Einstein's relativity): Because...
There is no reasonable statement that could become Answer 2:
"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://farside.ph.utexas.edu/teaching/315/Waveshtml/node41.html
"Thus, the moving observer sees a wave possessing the same wavelength (...) but a different frequency (...) to that seen by the stationary observer."
http://physics.bu.edu/~redner/211-sp06/class19/class19_doppler.html
"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'/λ=(v+vO)/λ."
Clever Einsteinians have always known that the speed of light varies with the speed of the observer. Here is an implicit confession:
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:
Loading Image...
(stationary receiver)
Loading Image...
(moving receiver)
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."
_______________________________________
[end of quotation]
Since "the distances between subsequent pulses are not affected", and since "four pulses are received in the time it takes the source to emit three pulses", the speed of the light as measured by the receiver (observer) is:
c' = 4d/t = (4/3)(3d/t) = (4/3)c
where d is the distance between subsequent pulses, t is "the time it takes the source to emit three pulses", and c=3d/t is the initial speed of the light (as measured by the source).
Clearly the speed of light (relative to the observer) varies with the speed of the observer, as predicted by Newton's emission theory of light and in violation of Einstein's relativity.
Pentcho Valev
Question: Why does the frequency shift from f=c/λ to f'=(c+v)/λ?
Answer 1 (fatal for Einstein's relativity): Because the speed of the waves relative to the observer shifts from c to c'=c+v (that is, relative to the observer, the speed of the light is now greater than c).
Answer 2 (possibly saving Einstein's relativity): Because...
There is no reasonable statement that could become Answer 2:
"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://farside.ph.utexas.edu/teaching/315/Waveshtml/node41.html
"Thus, the moving observer sees a wave possessing the same wavelength (...) but a different frequency (...) to that seen by the stationary observer."
http://physics.bu.edu/~redner/211-sp06/class19/class19_doppler.html
"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'/λ=(v+vO)/λ."
Clever Einsteinians have always known that the speed of light varies with the speed of the observer. Here is an implicit confession:
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:
Loading Image...
(stationary receiver)Loading Image...
(moving receiver)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."
_______________________________________
[end of quotation]
Since "the distances between subsequent pulses are not affected", and since "four pulses are received in the time it takes the source to emit three pulses", the speed of the light as measured by the receiver (observer) is:
c' = 4d/t = (4/3)(3d/t) = (4/3)c
where d is the distance between subsequent pulses, t is "the time it takes the source to emit three pulses", and c=3d/t is the initial speed of the light (as measured by the source).
Clearly the speed of light (relative to the observer) varies with the speed of the observer, as predicted by Newton's emission theory of light and in violation of Einstein's relativity.
Pentcho Valev