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.