Appendix
G: Causes of Redshift
This appendix
discusses issues that relate to spectral redshift. Section G.1 examines the
concept that gravitational redshift may explain the extreme redshift of the
quasar. Section G.2 discusses the spectral redshift theory of Paul Marmet, which
indicates that collisions of photons with hydrogen atoms can produce spectral
redshift. The Marmet redshift effect gives a promising explanation for the
intrinsic redshifts of quasars and some galaxies. Paul Marmet also proposes his
redshift effect as an explanation for the Hubble redshift.
G.1:
Cause of Quasar Redshift
When the extreme quasar redshift was discovered in 1963, two concepts
were considered to explain it: (a) redshift due to the Doppler velocity effect,
and (b) gravitational redshift. The gravitational redshift possibility was
quickly dismissed for reasons that we will now discuss, and this left the
Doppler velocity explanation. It was concluded that quasars must be receding at
extremely high velocities, and so must be billions of light years away. There
were two reasons for rejecting gravitational redshift, which are:
(1)
Analyses based on the Einstein theory indicated that a star would become
unstable if it has a sufficient mass-to-radius ratio to achieve a large
gravitational redshift.
(2)
The spectra of quasars display "forbidden" spectral lines of oxygen
and other elements. Forbidden spectral lines are not seen on earth, and have
only been observed in the radiation from a hot gaseous nebula, which has a gas
density very much lower than can be achieved on earth. At this low density, an
enormous volume of gas is required to generate appreciable power. It was
concluded that the volume of an atmosphere of a star exhibiting large
gravitational redshift would be far too small to radiate the energy that is
observed in the forbidden spectral lines of quasars.
The
following discussion shows that these reasons do not invalidate the
gravitational redshift possibility. Consequently, gravitational redshift remains
a strong candidate for explaining the very large redshift of the quasar.
G.1.1
Instability of Stars with Large Mass-to-Radius Ratios
The normalized mass m of a star is defined as MG/c2, where M
is the star mass in conventional units, G is the gravitational constant of
Newton's theory, and c is the speed of light. Normalized mass has the units of
distance. The normalized mass m of our sun is 1.475 kilometers. The m/r ratio at
the surface of our sun is 2.12x10-6, where r is the radius to the sun
surface.
The Einstein Schwartzschild solution indicates that the density of matter
should be infinite at certain points within a star if the m/r ratio at its
surface exceeds 4/9. Therefore it was concluded that a star would become
unstable and collapse into a black hole if its m/r ratio is greater than 4/9.
According to the Einstein theory, a star with an m/r ratio of 4/9 would exhibit
a gravitational redshift of 2.
S. Chandrasekhar [12]
extended this concept by showing with analysis of the Einstein theory that a
star should exhibit strong radial oscillations unless its m/r ratio is much
smaller than 4/9. This indicates that the maximum gravitational redshift that
can be displayed by a stable star should be much less than 2. Under this
constraint, the quasar redshift cannot be explained as a gravitational effect.
These arguments against the gravitational explanation for the quasar
redshift are refuted by the Yilmaz theory. The stability problems exhibited by
the Einstein theory are related to the black hole singularity, which is merely a
mathematical flaw of the Einstein theory. As shown in Fig. 1.3-2 of the Summary
portion of this website (Section 1.3), the slopes of spatial contraction and
clock rate for the Einstein theory are extremely steep for large values of the
m/r ratio, and this property suggests instability. The slope for the Yilmaz
theory is gradual, and so the Yilmaz theory does not exhibit instability at
large values of the m/r ratio.
Therefore, we conclude that the analysis by Chandrasekhar
[12] does not apply to the Yilmaz theory. The Yilmaz theory predicts that a
stable star can exhibit sufficient gravitational redshift to explain the
redshifts of all quasars.
G.1.2
Analysis of Quasar Spectra by Greenstein and Schmidt
In Feb. 1963, Maarten Schmidt and Jesse Greenstein discovered that
quasars exhibit extreme redshift. The first quasars that they studied were 3C48
(with a redshift of 0.367) and 3C273 (with a redshift of 0.158). Their analyses
of these quasars were reported in their classic 1964 paper in the Astrophysical
Journal [13].
Greenstein and Schmidt [13] observed "forbidden" spectral lines
of oxygen and neon in the quasar spectra. These forbidden lines are never
experienced on earth, and are observed only in the radiation from gaseous
nebula, which are extremely thin clouds of ionized gas. Gas density in these
nebulae is usually less than 105 electrons per cubic centimeter,
whereas the density of a high vacuum on earth is about 1015 electrons
per cubic centimeter. To generate these forbidden lines, it is believed that an
enormous volume of hot gas of very low density is required. Gaseous nebulae are heated
to a temperature of about 10,000 degrees Kelvin by the radiation from
stars.
An extensive theory of the processes involved in the generation of
forbidden spectral lines has been developed from observations of gaseous nebula,
combined with theoretical analyses. Greenstein and Schmidt [13] applied this
theory to the lines they observed in the spectra of quasars 3C48 and 3C273. They
concluded that the forbidden spectral lines of these quasars cannot be explained
by a viable stellar model that has a large gravitational redshift, and so the
redshifts of these quasars must be Doppler effects produced by extremely high
velocities. With such high velocities, the quasars must be at enormous
distances, and must radiate enormous amounts of power.
Let us examine the findings that Greenstein and Schmidt [13] derived from
their studies of the spectra of quasar 3C48, which has the larger redshift of
the two quasars. We will see that the physical model of 3C48 that they predicted
is inconsistent with the observed time variation of the radiation from this
quasar.
The theory of forbidden spectral lines evolved from observations of
spectra radiated from gaseous nebulae. Most of the observed nebulae have
electron densities less than 105 electrons per cubic centimeter.
Seaton and Osterbrock [16] studied some gaseous nebulae that may have electron
densities as large as 7x106 electrons pet cubic centimeter, which
appears to be the upper limit to the observed values of electron density. The
ratios of the intensities of different spectral lines were found to give
indications of the density of the nebulae atmospheres.
Based on the presence of forbidden spectral lines and the ratios of the line
intensities, Greenstein and Schmidt [13] estimated the electron density Ne
of the atmosphere of quasar 3C48 to be 3x104 electrons per cubic
centimeter. In their Eq. 3b, they estimated .that the power radiated in the
hydrogen spectral line Hb
per unit volume of gas should be 10-25 Ne2
erg/sec per cubic centimeter, where Ne is the number of electrons per
cubic centimeter. Since 1 watt is 107 erg/sec, this can be expressed
as
P/v =
10-32 Ne2 watt/cm3
(Hb
line) (G.1-1)
where
P is the power radiated within a volume v of the gas.
Setting Ne equal to 3x104 electrons gives the
following for the power per unit volume radiated by 3C48 in the Hb
spectral line:
P/v =
0.9x10-23 watt/cm3
(Hb
line, 3C48)
(G.1-2)
The redshift Dl/l
of 3C48 is 0.367. For small Doppler redshifts, the velocity ratio V/c is
approximately equal to the redshift 0.367, where V is the galaxy velocity. With
this approximation, Greenstein and Schmidt calculated the velocity V of 3C48 to
be 0.367c, which is 110,000 km/sec. They assumed a Hubble constant of 100 km/sec
per Mpc (megaparsec). This gave a distance of 1100 megaparsecs. Since one parsec
is 3.26 light years, this represents 3.6 million light years.
In the Special Relativity theory published in 1905, Einstein showed
that the exact formula for the velocity ratio corresponding to a given Dl/l
spectral redshift is
V/c
= [(1 + Dl/l)2
- 1]/[(1 + Dl/l)2
+ 1] (G.1-3)
Applying
this formula to the 0.367 redshift value for 3C48 gives a V/c ratio of 0.3028,
which represents a quasar velocity of 90.8 km/sec. The best average value for
the Hubble rate today is about 65 km/sec per magaparsec, which is equivalent to
20 km/sec per million light years. With this Hubble
constant, the calculated distance of 3C48 is 1400 megaparsecs. However, there is
still appreciable uncertainty in the value of the Hubble constant. The 3C48
distance of 1100 megaparsecs calculated by Greenstein and Schmidt is consistent
with our present knowledge of the Hubble constant.
Based on the measured values of spectral lines of 3C48, Greenstein and
Schmidt calculated the power levels that must be radiated in the observed
spectral lines of 3C48 assuming that 3C48 is at a distance of 1100 megaparsec,
or 3.6 million light years. These are given in Table G-1. The intensity of
spectral line [OIII] was too small to be measured accurately, and so its
calculate emitted power is indicated as "present". The lines in
brackets [] are forbidden spectral lines, which are not observed on earth. Lines
[O II] and [O III] are spectral lines of oxygen, and [Ne V] is a spectral line
of neon.
Based on the expression in Eq. G.1-2, a volume of 7.11x1058 cm3
is required to generate the power of 6.4x1035 watts given for the Hb
line in Table G-1. Since there are 105 centimeters per kilometer,
there are 1015 cubic centimeters per cubic kilometer. Hence this
volume is 7.11x1043 km3. One light year (Lyr) is 9.47x1012
km, and so the gas volume in cubic light years is
v =
7.11x1043 km3
= 83,700
Lyr3 (G.1-4)
This
is equivalent to the volume of a sphere with a radius of 27 light years, or 8.3
parsecs. Greenstein and Schmidt
[13] (p. 1) estimated the gas volume for 3C48 to have a radius of about 10
parsecs, which is consistent with our calculation.
Our calculated diameter of this gas sphere is 54 light years.
Table
G-1: Power in spectral lines emitted from 3C48, assuming it is at a distance of 1100
megaparsecs, or 3.6 million light years.
spectral
line power in watts
Hb
6.4x1035
Mg II
3.1x1035
[Ne V]
1.7x1035
[O II]
3.3x1035
[O III]
present
Greenstein and Schmidt [13] (p. 19) state that the absolute visual
magnitude of 3C48 is about -25. Absolute visual magnitude is the magnitude that
an object would have if it were viewed at a distance of 10 parsecs (32.6 light
years). The absolute visual magnitude of our sun is 4.85. The difference in
absolute visual magnitude of 3C48 and our sun is therefore about 29.9. A
magnitude difference is defined as 2.5 times the logarithm. Hence the logarithm
of the power ratio is 11.96, which represents a power ratio of 9.1x1011.
Thus the optical power radiated from 3C48 (assuming it is at its redshift
distance of 1100 megaparsecs) is 910 billion (9.1x1011) times the
power radiated from our sun.
Thus, Greenstein and Schmidt [13] calculated that quasar 3C48 is
radiating a power level equivalent to 910 billion suns. To generate the
forbidden spectral lines, this power is illuminating a cloud of thin gas
equivalent in volume to a sphere with a diameter of 54 light years.
A serious problem with this quasar model is that the brightness of 3C48
varies with time. Greenstein and Schmidt [13] (p. 16) report that the optical
flux from 3C48 "has changed by a factor of 1.4, apparently independently of
wavelength, over a period of 600 days". This implies that the amplitudes of
the forbidden spectral lines vary in this manner. To achieve this rapid
variation, the gas cloud should have a diameter of about 5 light years, not 50
light years. Hence the study predicted a gas volume that is too large by about a
factor of 1000.
G.1.3
Implications of Rapid Variations of Quasar Brightness
After this early study of quasars, many more quasars were rapidly
discovered. Redshift values increased from 0.367, for 3C48, to over 5. Many
quasars vary greatly in brightness over periods of months, weeks, days, and
even hours. This indicates that
some quasars are no larger than our solar system.
Greenstein and Schmidt deduced from the presence of forbidden spectral
lines in the quasar spectra that these lines are generated within an enormous
volume of very thin gas. However, even for the 3C48 quasar that they studied,
their predicted gas volume was 1000 timers greater than is allowed by the time
variation of the quasar brightness. When we consider the much more rapid
brightness variations observed in quasars discovered since that time, the
predictions derived from forbidden spectral line theory become completely
meaningless.
Therefore, it is clear that the forbidden lines observed in quasar
spectra cannot be explained even in a crude sense by the theory that evolved
from the study of forbidden lines in gaseous nebulae. A quasar definitely does
not behave in any sense like a huge gaseous nebula containing very thin gases.
How can we explain the forbidden spectral lines in the quasar spectra?
Let us reconsider the possibility that the quasar redshift is caused by an
intense gravitational field. Gasses in an intense gravitational field probably
behave quite differently than they do in a weak gravitational field.
Consequently forbidden spectral lines may be generated in an intense
gravitational field at much higher gas densities. Besides, an extremely compact
star should have a very large magnetic field, which would induce enormous
currents in the ionized stellar atmosphere. These currents may strongly affect
the generation of forbidden spectral lines.
An atom emits a photon when an electron drops from one state to a lower
state. An emitted photon can be readily absorbed if it strikes a similar atom,
which is tuned to its wavelength. However, in the presence of a strong
gravitational gradient, the wavelength of an emitted photon decreases rapidly
with radial distance from the center of the star. Therefore a photon moving away
from the center of the star soon encounters atoms tuned to a shorter wavelength,
which do not readily absorb the photon. Thus the absorption of photons can be
much less in an intense gravitational field.
Considerations such as these suggest that the generation of forbidden
spectral lines should be radically different in the presence of a very large
gravitational field. This possibility offers a promising explanation for the
forbidden spectral lines in quasar spectra.
If we assume that intense gravitational fields are not involved in
generating forbidden spectral lines in quasar spectra, we are left with an
enigma. The theory of forbidden spectral lines that has evolved from studies of
gaseous nebulae is not even remotely adequate to explain the forbidden spectral
lines in quasar spectra, when we consider the rapid variation of brightness
displayed by many quasars.
G.1.3
Summary of Arguments against Quasar Gravitational Redshift
When quasars were first discovered, the evidence against gravitational
redshift seemed to be overwhelming. Analyses of stellar instability appeared to
eliminate this possibility, and the presence of forbidden spectral lines in the
quasar spectra also appeared to eliminate it.
However,
we have seen that the predictions of stellar instability at large mass-to-radius
ratios, which are derived from the Einstein theory, are definitely refuted by
the Yilmaz theory. This leaves the issue of forbidden spectral lines.
When we consider the variation of radiation power displayed by many
quasars, which are extremely rapid in some quasars, the explanations of
forbidden spectral lines, based on present forbidden line theory, are not even
remotely adequate. Therefore, analyses based on this theory cannot be used to
dismiss the possibility that the quasar redshift is produced by gravity. In
fact, there does not appear to be any viable explanations for quasar spectral
lines unless we assume that the quasar has an intense gravitational field.
G.2
Marmet
Analysis of Redshift Caused by Cloud of Hydrogen
The following analysis is based on an article by Paul
Marmet [17].
Equation 12 of Reference [17] gives the following formula for the redshift
produced by one collision of a photon with a hydrogen molecule:
Df/f
= R
= MT2 (G.2-1).
I have substituted the symbol f to represent frequency, instead of n. The following value is given
for the constant M:
M =
2.73x10-21 K-2
(G.2-2)
In the discussion following Eq. 19 of
Reference [17], the following value is
given for the assumed blackbody temperature T of the radiation:
T =
50,000 K
(G.2-3)
The Doppler redshift Df/f
produced by a receding velocity V is approximately equal to V/c. Hence this
redshift Df/f is equivalent to the
following velocity V:
V =
(Df/f)c
= cMT2
(G.2-4)
Substitute Eqs. G.2-2, -3 into Eq. G.2-4, and
set c equal to 3x108 meter/sec.
This yields the following
V =
2.05x10-3 m/sec =
2.05 mm/sec. »
2 mm/sec
(G.2-5)
Thus, the theory predicts a Doppler
shift of approximately 2 mm/sec per photon collision.
Let us determine the number of photon collisions during a path length L
of one light year. By Eq. 14 of Reference [17], the number of collisions N is
equal to
N =
DLs
(G.2-6)
where D is the density of hydrogen
molecules, L is the length of one light year, and s
is the effective cross section of the hydrogen molecule. The values for L
and s are
L =
1 light year = 9.47x1015 meter
(G.2-7)
s
= 3.14x10-20
meter2
(G.2-8)
The value for s
is given in Appendix B, Eq. B8 of reference [17]. Let us assume a density of hydrogen molecules equal to 1
molecule per cubic centimeter, or 1 million molecules per cubic meter:
D =
1 cm-3 =
106 meter -3
(G.2-9)
Substituting Eqs. G.2-7 to -9 into Eq.
G.2-6
gives the following number of photon collisions per light year of path length:
N/L =
297 »
300 collisions per light year
(G.2-10)
Multiplying Eqs. G.2-5 and G.2-10 gives the
following effective Doppler velocity corresponding to the redshift produced by a
path length of one light year
For density of 1 H molecule per cm3:
V/L =
60 (cm/sec) per light year
(G.2-11)
Section 3.10 of Reference [17] shows that clouds of molecular hydrogen have been measured with densities of 200 hydrogen molecules per cubic centimeter, or 200 million hydrogen atoms per cubic meter. Assuming this density, there are 60,000 photon collisions per light year. Hence the effective Doppler velocity corresponding to the redshift produced by a path length of one light year is 200 times the value of Eq. G.2-11, which gives
V/L =
120 (meter/sec) per light year.
(G.2-12)
Paul Marmet has postulated that this effect can explain the Hubble
redshift. Recent studies have yielded an average Hubble expansion rate of about
20 km/sec per million light years, which is equivalent to 65 km/sec per
megaparsec. This expansion rate is equivalent to 2 cm/sec per light year.
Comparing this rate with Eq. G.2-11 (which corresponds to a density of 1 hydrogen
atom per cm3}, shows that the Hubble redshift could be explained by
an average concentration of 1/30 hydrogen atom per cubic centimeter throughout
the universe. This is equivalent to 33,000 hydrogen atoms per cubic meter.
Paul Marmet
[18] gives information that relates to this redshift effect. This article shows that there is at least 10 times as much molecular
hydrogen in our universe as atomic hydrogen. There is probably very much more,
because molecular hydrogen (H2) is extremely stable.
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