[ D.C. Champeney, G.R. Isaak, A.M. Khan, Phys. Lett. 7 (1963) 241 ]
: I do agree with you that mechanical vibrations result in radial
: oscillations of the source and the absorber and that (ua - us).m is
: therefore not zero. The typical frequency of this oscillation is
: directly related to the elasticity of the material used for the rotor
: and the Mossbauer crystal and it is several order of magnitude higher
: than the rotation frequencies of the rotor (see below). Since one
: considers the average of delta nu/nu in at least a quadrant in this
: kind of experiment (this is what was done by Turner et al; Champeney et
: al use two quadrants), (ua-us).m oscillates many times for such
: periods. So even if the instantaneous value of this quantity can be
: very high, its average value is much much smaller because the bumps of
: (ua-us).m compensates its drops. Moreover it will give the same
: contribution in every quadrant, resulting in an uniform background. On
: the contrary the term (ua-us).v is different in different quadrant if
: one postulates a Galilean.
It seems to me that you misunderstand a basic principle of the
Mössbauer effect. This effect works only because unlike as in the
ordinary case, the Doppler broadening does not depend on thermal
motion of the absorbing (or emitting) atom but on the movement of
the whole crystal. Even a temperature as low as 3 degrees Kelvin
would 'normally' still be responsible for a Doppler broadening
resulting in a frequency width of the order of Df/f = 10^-8.
A Doppler broadening of Dv/c leads to frequency broadening of the
same size: Df/f = Dv/c. Dv is the range of the radial velocities
from the emitting crystals to the absorbing ones.
The experiment is based on the logic of a Mössbauer effect with a
frequency width of Df/f = 2 * 10^-12. A prerequisite of such a low
frequency width is therefore a (distance) velocity range between
emitters and absorbers of around Dv = 0.6 mm/s.
Oscillations in the rotor leading to radial velocities do NOT AVERAGE
OUT. Instead, they broaden the Mössbauer frequency width.
Now let us assume that in the rotor emerge oscillations with a
frequency of f = 10^6 Hertz (as you suggest) and then ask the
question: what is the swing amplitude r of a harmonic oscillation
with a frequency f = 10^6 Hz whose maximal velocity is v = 0.6 mm/s?
r = v / (f * 2 pi) = 6*10^-4 m / 10^6 * 2 pi) ~= 10^-10 m.
That's in the order of atom sizes! Let us assume that there are no
other causes for distance changes between source and absorber (e.g.
acoustic vibrations) than such 10^6 Hz oscillations of source and
absorber with each a swing amplitde only 10^-10 m. Not even in this
case the subsequent reasonings of the experimenters would be justified.
:: The centripetal acceleration of both source and detector is
:: a = v^2 / r = (313 m/s)^2 / 0.0405 m = 2.42 * 10^6 m/s^2
:: That is around 250 thousand times the acceleration caused by the
:: earth! And only 1 nanosecond of this acceleration leads to a velocity
:: of 2.42 mm/s.
: ... and this attempt of yours is not correct. Indeed the centrifugal
: force and the elastic stresses in the apparatus cancel each others and
: what remains in a permanent regime are only oscillations driven by
: elastic forces.
Only for comparison: oscillations with a velocity amplitude
of v = 0.6 mm/s (f = 10^6 Hz, r = 10^-10 m) lead to a maximal
a = v^2 / r = v * f * 2 pi ~= 360 m/s^2
This is four orders of magnitude smaller than the centripetal
acceleration of source and detector due to the 1230 Hz rotation.
: Finally Champeney et al. wrote that they have tested the influence of
: these effects (end of p. 242)
: <<Using an unshifted source-absorber combination at opposite tips
: (Co57 in Fe56 source, 81% enriched Fe57 absorber), a combination less
: sensitive to aether drift but more sensitive to vibrations than the
: shifted pair, we were able to deduce that vibrations could have had no
: significant effect on our results.>>
What is "less sensitive to aether drift than" 'not sensitive at all'?
In this respect the experiment is quite typical. Despite being well done
in general, the whole thing depends on a crucial premise whose validity
has not or only superficially been verified.
To sum up:
1) The experimenters use a Mössbauer absorber whose typical absorption
spectrum under normal conditions (e.g. without relevant accelerations)
is known to have a width of around df/f = 2*10^-12.
2) They conclude from their formula (1) (i.e. Jackson's 11.12) that this
absorption spectrum and an ether drift of around 200 m/s (in the right
direction) would lead to a frequency shift of around the Mössbauer
frequency width when changing the rotation speed of their rotor from
200 Hz to 1230 Hz and the other way around.
3) No systematic correlations in the statistical data with such changes
in the rotor frequency can be detected.
4) They conclude [V = ether drift]:
"We may place a limit on the value of V by searching for any diurnal
periodicity. By performing a least squares analysis in comparing the
weighted observations with cosine curves of various amplitudes and
phases we obtain the values V = 1.6 m/s /+- 2.8 m/s. phi = 5.2 rad."
Nowhere in the paper do Champeney at al. show that are aware of how
sensitive the Mössbauer absorption spectrum is to smallest radial
Wolfgang Gottfried G.