http://www.astro.ucla.edu/~wright/kierein.html

Kierein's Erroneous Compton Model for the Redshift

Kierein proposes that the Compton shift causes the redshift. To do this he needs to invoke new physics to:

increase the electron scattering cross-section by a wavelength dependent factor that is as large as 1 trillion for VHF radio waves,
imagine that Compton scattering can change the wavelength of radiation without changing its direction, even though the both the standard formula and Kierein's modified formula give zero wavelength change for zero scattering angle,
increase the density of ordinary matter in the Universe by a factor of 1 thousand,
and require that only 0.01% of this matter can be in the form of stars.

Let us now examine whether these new physical laws are consistent with experimental data.

Kierein adds a nonstandard factor of (wavelength)/(Compton wavelength) to the Thomson scattering cross-section, and thus gets a wavelength shift that is proportional to wavelength as required by the observations of redshifted spectra. However, this nonstandard factor is not allowed by observations. Consider VHF radio waves of wavelength 1 meter passing through the Earth's ionosphere which has number densities of electrons of about 10⁶ per cubic centimeter over distances of 3*10⁷ cm. The Thomson scattering cross-section is 6.7*10⁻²⁵ square cm so the optical depth of the ionosphere in the standard model is (number density)*(path length)*(cross section) = 10⁶*3*10⁷*6.7*10⁻²⁵ = 2*10⁻¹¹ which is very small. The Compton wavelength of the electron is h/mc = 2.4*10⁻¹⁰ cm so if Kierein were correct the optical depth of the ionosphere to Compton scattering for 1 meter radio waves would be increased by a factor of (100 cm)/(2.4*10⁻¹⁰) = 4.1*10¹¹ to 8. So if Kierein were correct radio waves at 300 MHz could not penetrate the ionosphere, which would be a big surprise to radio astronomers who observe at these wavelengths. Amateur radio operators who do EME (moonbounce) work in the 2 meter band would be surprised too: an extra 140 db of path loss would certainly be noticeable!

The solar wind has an electron density of about 5 per cc over path lengths of about 150 million km giving an even greater optical depth. This would not affect moonbounce work but would make VHF radio astronomy impossible.

So the enhanced scattering proposed by Kierein does not occur in nature. The Thomson cross-section gives the correct scattering rate, and it is not increased by a factor of trillions for radio waves as proposed by Kierein. The wavelength shift per scattering is the Compton wavelength times (1-cos(theta)), which is only a small fraction of an Angstrom. This shift is a significant fraction of the wavelength for X-rays but only a small fraction for optical light and is negligible for radio waves. Thus the Compton effect cannot explain the cosmological redshift which gives the same fractional change in wavelength at all wavelengths.

Kierein requires n_e = (H/c)/sigma_T/<1-cos(theta)> = 10⁻⁴ per cc which is 1000 times higher than the value predicted by the standard Big Bang nucleosynthesis model. I have assumed <1-cos(theta)> = 1 - which is the value for Rayleigh scattering - so the required density would be higher if the scattering angles really were smaller as Kierein requires. But even using large scattering angles gives a minimum density 40 times greater than the critical density for H_o = 65. At most 0.01% of this baryonic matter can be in the form of stars. The gravitational collapse time for matter at this density is only 2 billion years so this model does not give a static Universe with an age of 12 billion years.

Kierein justifies his model using the limb effect in solar spectral lines, which is normally attributed to convection: hot material rises and is brighter than the cool falling material, so the net effect is a blueshift at the center of the solar disk which vanishes at the limb. But if we do attribute this effect, which is about 300 m/sec, to electrons then the shift per electron must be much less than Kierein's assumption which then requires even more electrons in the Universe to produce the observed redshift. The number of electrons along the line-of-sight to the photosphere at the disk center is N_e = 3*10²⁰ per sq. cm, and if this column density produces a redshift of dz = 0.000001, then the electron density in the Universe must be

n_e = N_e/(c*dz/H_o) = 0.02 per cc

This density is 4000 times the critical density, so the gravitational collapse time is even shorter.

The wavelength shift per scattering is proportional to <1-cos(theta)> which is about 0.5*theta². Thus there can be no redshift due to the Compton effect unless there is a change in the direction of propagation. The change in angle per scattering could be less if there were more electrons (but Kierein already needs 1000 times too many electrons), but this would lead to more scatterings, and with more scattering the variances of the angles would add up to the same smearing. This would result in smearing out point sources into smooth blobs of light at large redshifts, an effect that is not seen out to z = 4.92. Kierein's model requires a smearing of about 1 radian at redshift z = 1. The actual smearing is less than 10⁻⁶ radians from HST observations of the most distant object at z = 4.92. Since the frequency shift is proportional to the square of theta, Kierein's model fails by a factor of more than a trillion, even if all the other problems could be solved.

Finally, the statistical variation in the number of scatterings will lead to a broadening of spectral lines at high redshift which is not seen. Songaila et al. (1994, Nature, 371, 43) show an iron line with observed wavelength 433.37 nm, a redshift of 0.74462, and a FWHM of 0.01 nm. If the total wavelength change of 185 nm is produced in steps of the Compton wavelength = 0.0024 nm, then 77,000 scatterings are needed and one would expect a standard deviation of sqrt(77,000) = 278 leading to a FWHM of sqrt(8*ln2)*278*0.0024 = 1.6 nm. The observed line is 160 times narrower than this, so the required shift per scattering must be 25,000 times smaller than the Compton wavelength.

Kierein offers the example of light traveling through a dielectric: slowing down as it enters the medium, without changing direction, in order to justify his assumption that Compton scattering can change the wavelength of light without changing its direction. This of course is nonsense. The frequency of light in a dielectric never changes, and the wavelength gets shorter (a blueshift?) — but once the light leaves the medium the wavelength returns to exactly the same value it had before. This is required by the conservation of energy and momentum! Passing through a transparent medium gives no redshift at all, and certainly not one proportional to the path length.

Conclusion

Kierein needs to drastically change the properties of the Compton effect to make his model for the redshift. He increases the cross-section by a factor of up to one trillion and decreases the scattering angle by a factor of one million. The mean wavelength shift per scattering must be at least 25,000 times smaller than the Compton wavelength. The result is nothing like the known Compton effect, so Kierein is really invoking a unknown physical effect and not the Compton effect. The other objections to tired light models also apply. This model is not acceptable.

Kierein's Erroneous Dark Matter Model

Kierein proposes that dispersion due to electrons on the line of sight to gamma ray bursts causes the optical light to peak a "couple days later" than the GRB itself. Now this time delay is given by

    [e^2 \int n_e ds]
										t = -----------------
										[2\pi m_e c f^2]

With t = 2*86400 sec and f = 5E14 Hz, I get \int n_e ds = 3E37 per sq. cm. For a typical cosmological distance of ds = 2E28 cm, this requires an electron density of 1.5 billion per cc, which is more than 1,000 times larger than the electron density in the Earth's ionosphere! This is certainly a lot of dark matter!

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