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Transverse Doppler Shift & Gravitational Frequency Shift



 
 
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  #1  
Old July 27th 04 posted to sci.physics.relativity
Australopithecus Afarensis
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Default Transverse Doppler Shift & Gravitational Frequency Shift

On a first glance, we all expect the transverse Doppler shift and
gravitational frequency shift to be in red. That is observed to have longer
wavelength than the origination. This also means the observed photon has a
lower energy. However, according to Lorentz Transform, we have

E' = (E + B * P c) / sqrt(1 - B^2), where

** E' = observed energy
** E = energy of the source
** B c = speed of the platform when this photon left (vector)
** P = momentum of the photon at the source (vector)

In a transverse condition, there are 90 degrees separating the dot product.
Thus,

B * P = 0

Thus, we are left with

E' = E / sqrt(1 - B^2)

Since

** E' = h f'
** E = h f, where

** f' = observed frequency
** f = frequency at the source
** h = Planck's constant

Then, we have

f' = f / sqrt(1 - B^2)

Which means the observed transverse Doppler frequency is BLUE shifted
despite an observed time dilation of

dt'/dt = 1 / sqrt(1 - B^2)

Now, since GR does not dwell on Newtonian explanation of gravity, the only
way GR can explain a gravitational red shift is through time dilation.
However, the transverse Doppler shift tells us that despite a time dilation,
the observed blue shift is due to the increase in relativistic mass of the
photon. Appling the same concept of time dilation actually gives an
increase in relativistic mass, we should expect GR to predict a
gravitational BLUE shift instead.


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  #2  
Old July 27th 04 posted to sci.physics.relativity
Dirk Van de moortel
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Posts: 15,355
Default Transverse Doppler Shift & Gravitational Frequency Shift


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