Ray Tomes wrote [on 4/25/97]:
>
> (1.1*10^25 m)/(3.086 m/pc)*(100 km/s)/(299,800 km/s)=.119
>
> I calculate z=.119 for a full rotation or .0595 for a half rotation
> (which is when the light looks the same again). This compares with the
> Harmonics theory strong 12th harmonic which is 2^(1/12)=1.0595 or
> exactly the same! The z=.0595 quantum is one of the two strongest ones
> predicted by the Harmonics theory at large scales and this value is also
> found as one of the major galaxy supercluster redshift quanta.
>
Ray Tomes seems to be pleased that the Nodland and Ralston "screwy"
scale, Lambda_s = 1.1E25 m, agrees with one of his harmonics. This
scale converts into z = H_o*Lambda_s/c = 0.119. Tomes then states that
since the polarization comes back to the same orientation after only
half a turn, the real spacing is at dz = 0.119/2 = 0.0595. But Tomes
is making a big error here, because Lambda_s is the distance for the
polarization to rotate by one half radian! Nodland and Ralston's Eq(1)
is
beta = (0.5/Lambda_s)*r*cos(gamma)
with beta in radians. Thus the true spacing for full turns is
4*pi*Lambda_s, and the half-turn distance is 2*pi*Lambda_s.
Thus the actual value is 12.6 times higher than the one Tomes liked! I
would hope that a factor 12.6 error in predicting a quantity "measured"
to an "accuracy" of 7% like the "screwy" scale would be enough to kill
a theory, but I am not holding my breath. After all, the dz = 0.0595
is the 12th "harmonic" in Tomes's theory.
This new distance is large enough so that the non-linear terms in r(z)
should be used, and we see from Nodland and Ralston's equation
r(z) = (c/H_o)*(2/3)*[1-(1+z)^{-3/2}]
(actually their equation is much more confused and confusing than this,
but the above is correct) that it is IMPOSSIBLE to get an r as large as
2*pi*Lambda_s, even for z -> infinity! A quick look at Figs 1c and 1d
in Nodland and Ralston shows that the largest r is 6.8E25 m which is
almost but not quite 2*pi*Lambda_s. [Actually 6.8E25 m is bigger than
r(infinity) indicating that Nodland and Ralston made arithmetic or
plotting errors in addition to a major statistical error.]
So galaxies can't be placed on a lattice with a spacing given by the
half-turn distance because that would require z's greater than
infinity. If I take Tomes's fundamental harmonic with z = 1 instead,
this gives r = 1300/h Mpc and beta = 1.8 radians, which doesn't seem
to be anything special. Thus Nodland and Ralston's erroneous
interpretation of observational data does not in any way support Ray
Tomes's harmonic theory.