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DOPPLER EFFECT MEANS VARIABLE SPEED OF LIGHT
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." Since, in a time t, "the number of waves observed is (c-Vo)t/lambda", the speed of the waves relative to the observer is c'=((c-Vo)t/lambda)(lambda/t)=c-Vo, in violation of special relativity. 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.usna.edu/Users/physics/mu...plerEffect.pdf Carl Mungan: "Consider the case where the observer moves toward the source. In this case, the observer is rushing head-long into the wavefronts, so that we expect v'v. In fact, the wave speed is simply increased by the observer speed, as we can see by jumping into the observer's frame of reference. Thus, v'=v+v_o=v(1+v_o/v). Finally, the frequency must increase by exactly the same factor as the wave speed increased, in order to ensure that L'=L - v'/f'=v/f. Putting everything together, we thus have: OBSERVER MOVING TOWARD SOURCE: L'=L; f'=f(1+v_o/v); v'=v+v_o." 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." It is explicit in Sidney Redner's and Carl Mungan's texts and implicit in Paul Fendley's text that the frequency shift from f to f'=f(1+v/c) can only be caused by a shift in the speed of light (relative to the observer) from c to c'=c+v, in violation of special relativity. See more he http://fqxi.org/data/essay-contest-f...equency_Im.pdf Shift in Frequency Implies Shift in Speed of Light Pentcho Valev |
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DOPPLER EFFECT MEANS VARIABLE SPEED OF LIGHT
THEOREM: The speed of light varies with the speed of the observer (c'=c+v) if and only if it varies with the gravitational potential (c'=c(1+gh/c^2)).
The top of a tower of height h shoots a bullet downwards with initial speed u. As the bullet reaches the ground, its speed (relative to the ground) is: u' = u(1 + gh/u^2) The top of a tower of height h emits a light pulse downwards with initial speed c. As the pulse reaches the ground, its speed (relative to the ground) is: c' = c(1 + gh/c^2) Einsteinians admit the validity of and sometimes even deduce the above result: http://www.youtube.com/watch?v=ixhczNygcWo "The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c." Integrating dc/dh=g/c gives: c' = c(1 + gh/c^2) Equivalently, in gravitation-free space where a rocket of length h accelerates with acceleration g, a light signal emitted by the front end will be perceived by an observer at the back end to have a speed: c' = c(1 + gh/c^2) = c + v where v is the speed the observer has at the moment of reception of the light relative to the emitter at the moment of emission. Clearly, the speed of light varies with the speed of the observer, in violation of special relativity. Pentcho Valev |
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DOPPLER EFFECT MEANS VARIABLE SPEED OF LIGHT
In a gravitational field, the speed of light varies exactly as the speed of cannonballs does. Accordingly, by measuring the gravitational redshift of light coming from astronomical objects we in fact measure THE DECREASE IN THE SPEED OF LIGHT (generally, any frequency shift is a measure of a shift in the speed of light):
http://www.einstein-online.info/spot...t_white_dwarfs Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..." http://courses.physics.illinois.edu/...ctures/l13.pdf University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light." In the absence of a gravitational field, the analogy between photons and cannonballs remains valid: the speed of light relative to the observer varies with the speed of the observer: 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 observer cannot change the wavelength ("the distances between subsequent pulses are not affected") and accordingly the speed of light as measured by the receiver is (4/3)c. Pentcho Valev |
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DOPPLER EFFECT MEANS VARIABLE SPEED OF LIGHT
On Mar 18, 10:41*am, Pentcho Valev wrote:
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." Since, in a time t, "the number of waves observed is (c-Vo)t/lambda", the speed of the waves relative to the observer is c'=((c-Vo)t/lambda)(lambda/t)=c-Vo, in violation of special relativity. 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.usna.edu/Users/physics/mu...plerEffect.pdf Carl Mungan: "Consider the case where the observer moves toward the source. In this case, the observer is rushing head-long into the wavefronts, so that we expect v'v. In fact, the wave speed is simply increased by the observer speed, as we can see by jumping into the observer's frame of reference. Thus, v'=v+v_o=v(1+v_o/v). Finally, the frequency must increase by exactly the same factor as the wave speed increased, in order to ensure that L'=L - v'/f'=v/f. Putting everything together, we thus have: OBSERVER MOVING TOWARD SOURCE: L'=L; f'=f(1+v_o/v); v'=v+v_o." 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." It is explicit in Sidney Redner's and Carl Mungan's texts and implicit in Paul Fendley's text that the frequency shift from f to f'=f(1+v/c) can only be caused by a shift in the speed of light (relative to the observer) from c to c'=c+v, in violation of special relativity. See more he http://fqxi.org/data/essay-contest-f...equency_Im.pdf Shift in Frequency Implies Shift in Speed of Light Pentcho Valev Sound(phonon waves) have a velocity limit due to the atmosphere or whatever physical medium (such as Earth), and photon waves have their speed/velocity limited by aether, whereas graviton waves seem to have at least 2c to work with, perhaps because their half wavelength is worth 13.75e9 ly. |
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