Pound Rebka redshift-a rational explanation

On May 29, 9:36 am, John Polasek wrote:
On 24 May 2012 22:09:23 +0100 (BST), Tom Roberts wrote:

when the Mossbauer source is at the
bottom of the tower and the absorber is at the top, the frequencies
are related by
f_T = f_B(1 - gH/c^2), (1)

This is the frequency _measured_ in the experiment and
it differs from the frequency _predicted_ by the theory.

How is the measured frequency reconciled with the predicted
one despite the sign difference between equations (1) and (9)?

Somewhere you made a sign error. There is no doubt that the frequency
measured at the top is lower (smaller) than that measured at the bottom..
We know this because the detector at the top must be moving upward, away
from the source, to maximize detection of the gammas; the Doppler shift
from such motion reduces the measured frequency of the gammas.

To understand the possibilities of predicting both the red and blue
shifts at the same time, look no further than the Lorentz transform.
Its time transformation is given as follows.

** dt1 = (dt3 – [v31] * d[s32] / c^2) / sqrt(1 – v31^2 / c^2) ... (1)

Where

** dt1 = Time flow rate at #1
** dt3 = Time flow rate at #3
** [v31] = Velocity of #1 as observed by #3
** d[s32] = Spatial geometry (a vector) at #2 as observed by #3
** [] * [] = Dot product of two vectors

Or you can condense all the equations of the Lorentz transform into a
concise, single equation as follows.

** c^2 dt1^2 – ds12^2 = c^2 dt3^2 – ds32^2 = c^2 dt2^2

Then, you can derive the following equation using the Lagrangian
method. Physicists interpret it as the relativistic momentum of #2 as
observed by #1, #3, or anyone to be invariant.

** v12 / sqrt(1 – v12^2 / c^2) = Cosntant
** v32 / sqrt(1 – v32^2 / c^2) = Constant

Where

** v12 = ds12/dt1
** v32 = ds32/dt3
** sqrt(1 – v12^2 / c^2) = Lagrangian that min elapsed time at #2
** sqrt(1 – v32^2 / c^2) = Lagrangian that min elapsed time at #2

From the above equation, it should not be too difficult to derive the
transformation of energy as follows.

** E12 = (E32 – [v31] * [p32]) / sqrt(1 – v31^2 / c^2) ... (2)

Where

** E12 = Energy of #2 as observed by #1
** E32 = Energy of #2 as observed by #3
** [p32] = Momentum of #2 as observed by #3

From equation (1) describing the transformation of time, the
transformation of frequency can be stated as follows.

** f12 = f32 sqrt(1 – v31^2 / c^2) / (1 – [v31] * [v32] / c^2) ...
(3)

Where

** f12 = 1 / dt1
** f32 = 1 / dt3
** [v32] = d[s32]/dt3

Similarly, from equation (2) describing the transformation of energy,
the transformation of frequency can be derived as follows.

** f12 = f32 (1 – [v31] * [v32] / c^2) / sqrt(1 – v31^2 / c^2) ...
(4)

Where

** E12 = h f12, Planck’s law
** E32 = h f32
** [p32] = E32 [v32] / c^2

Notice equation (3) and (4) are exactly the opposite of the other.
This allows self-styled physicists to claim either blue or red shift
depending on what is expected. For example, under longitudinal
Doppler effect, equation (4) is claimed to support the classical
Doppler result. On the other hand, under longitudinal Doppler effect,
equation (3) is applied. This is another example that SR and GR can
explain all experimental results since both faiths have all the bases
covered as their predictions. shrug

The Pound-Rebka result is another example with the two dual equations:

** dTau^2 = c^2 (1 – 2 U) dt^2
** Etau^2 = (1 – 2 U) E^2

It depends on how one wishes to fudge it. Anything can be shown
mathematically possible under SR and GR from loads of contradictions
within. Fvcking sad, no? shrug

yes, and you don't seem to be able
to make a simple, qualitative expression
of your quadratic manipulations;
did you complete the second-power?

why did you use "longitudinal" twice,
in your "on the other hand" -- what does it mean,
as opposed to "lattitudinal?"

Anything can be shown
mathematically possible under SR and GR from loads of contradictions
within.