The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Replies: 6   Last Post: Mar 31, 2013 2:59 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Pentcho Valev

Posts: 5,009
Registered: 12/13/04
Posted: Mar 31, 2013 2:59 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
John Stachel: "But here he ran into the most blatant-seeming contradiction, which I mentioned earlier when first discussing the two principles. As noted then, the Maxwell-Lorentz equations imply that there exists (at least) one inertial frame in which the speed of light is a constant regardless of the motion of the light source. Einstein's version of the relativity principle (minus the ether) requires that, if this is true for one inertial frame, it must be true for all inertial frames. But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair. We have no details of this struggle, unfortunately. Finally, after a day spent wrestling once more with the problem in the company of his friend and patent office colleague Michele Besso, the only person thanked in the 1905 SRT paper, there came a moment of crucial insight. In all of his struggles with the emission theory as well as with Lorentz's theory, he had been assuming that the ordinary Newtonian law of addition of velocities was unproblematic. It is this law of addition of velocities that allows one to "prove" that, if the velocity of light is constant with respect to one inertial frame, it cannot be constant with respect to any other inertial frame moving with respect to the first. It suddenly dawned on Einstein that this "obvious" law was based on certain assumptions about the nature of time..."

Einstein reconstructed space and time - the centaur he created, spacetime, was able to neutralize any variation of the speed of light relative to the moving observer. However Einstein forgot to procrusteanize the wavelength - it remained (and still is) insensitive to the motion of the observer. Given the formula:

(frequency) = (speed of light)/(wavelength)

the insensitiveness of the wavelength to variations in the speed of the observer implies that both the frequency AND THE SPEED OF LIGHT vary with the speed of the observer, in violation of special relativity:
"vO is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c + vO. (...) The motion of an observer does not alter the wavelength. The increase in frequency is a result of the observer encountering more wavelengths in a given time."
"La variation de la fréquence observée lorsqu'il y a mouvement relatif entre la source et l'observateur est appelée effet Doppler. (...) 6. Source immobile - Observateur en mouvement: La distance entre les crêtes, la longueur d'onde lambda ne change pas. Mais la vitesse des crêtes par rapport à l'observateur change ! Lobservateur se rapproche de la source: f'=V'/(lambda)=f(1+Vo/V). (...) L'effet Doppler peut se produire pour toutes les sortes d'ondes."
"L'effet Doppler est le décalage de fréquence d'une onde acoustique ou électromagnétique entre la mesure à l'émission et la mesure à la réception lorsque la distance entre l'émetteur et le récepteur varie au cours du temps. (...) Pour comprendre ce phénomène, il s'agit de penser à une onde à une fréquence donnée qui est émise vers un observateur en mouvement, ou vis-versa. LA LONGUEUR D'ONDE DU SIGNAL EST CONSTANTE mais si l'observateur se rapproche de la source, il se déplace vers les fronts d'ondes successifs et perçoit donc plus d'ondes par seconde que s'il était resté stationnaire, donc une augmentation de la fréquence. De la même manière, s'il s'éloigne de la source, les fronts d'onde l'atteindront avec un retard qui dépend de sa vitesse d'éloignement, donc une diminution de la fréquence. Dans le cas sonore, cela se traduit par un son plus aigu lors d'un rapprochement de la source et un son plus grave en s'éloignant de celle-ci. Dans le domaine de la lumière visible, on parle de décalage vers le bleu pour un rapprochement et vers le rouge dans le cas d'éloignement en se référant au spectre lumineux. La même chose s'applique à toutes les gammes d'ondes électromagnétiques dont les ondes utilisées par les radars."

Pentcho Valev

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.