It's not possible for me to explain the contents of this post
without including fairly detailed images. I've included the links
to these images, but it's far easier to pay a visit to this web
page. http://www.ozemail.com.au/~mkeon/cmbonly.html

B.Y.O.
---------

Cosmic Microwave Background Radiation (3)

My earliest attempt at properly justifying the zero origin universe
within the microwave background data failed because I failed to
recognize a flaw in my reasoning at the time. Attempt no.2 was
fairly well demolished in a rather lengthy debate over the way in
which I had combined blackbody curves, and how those curves came
to be. I was thus forced to go back to square one and do it all
over again. The flaw in my original reasoning, which should have
correctly described how the CMBR came to be in the zero origin
universe, quickly became apparent. My graph plot of the CMBR
spectrum was based on emissive power per wavelength, where the CMBR
spectrum is normally displayed as spectral energy density, which is
power according to frequency. I was attempting to fit my curve to
the wrong curve shape.
-------------------

The CMBR monopole spectrum graph is supposedly the expanded
blackbody temperature plot of the early universe after it had
evolved for 300,000 or 10 million years (the goal posts keep
changing), at which time it had cooled to 4000 degrees K, being
the temperature threshold where hydrogen was no longer ionized.
The universe became fairly abruptly transparent and all of the
previously entrapped radiation was released into the universe from
everywhere to travel the universe to everywhere.

A background radiation is also expected in a zero origin universe,
but certainly not for the same reasons. The temperature of that
universe would range from absolute zero at the origin to its current
temperature. And because the universe has evolved from nothing,
there can be no doubt that it will continue to evolve. The rate of
that evolution is clearly demonstrated in the red shifting of the
characteristic spectral lines of atoms per increasing distance into
the past.

The very early universe would have remained relatively unchanged
for a very long time (relative to the current time rate) and the
temperature of the entire universe could be summed up as a general
heat source (but not a blackbody) and averaged to give a temperature
that represents the heat of the universe at the time, and whatever
curve shape the combined temperatures generate, the power curve will
peak at a specific wavelength. That wavelength can represent the
entire spectrum for that era in the evolution of the universe, which
should be quite valid because the relationship between the curve
peak and the rest of the spectrum would remain consistent as the
universe evolves. i.e. Double the temperature and every wavelength
in the spectrum halves.

The purpose of the next image is only to graphically demonstrate
that all wavelengths halve if the temperature is doubled. Each
curve in the graph was computer generated using Planck's blackbody
equation for emissive power per wavelength. The power spectrums have
been brought into an alignment using multipliers so that they can
be directly compared.

http://www.ozemail.com.au/~mkeon/compare2.jpg

Notice that the curve shape is always exactly proportional no matter
what temperature it's plotted for? Those proportions never change.
The power peak of any blackbody spectrum can be adjusted with a
multiplier so that it peaks at the same level as a curve who's shape
is to be tested against a blackbody spectrum, and then a multiplier
sets the peak of the spectrums to align at the same wavelength, and
it always tells the same story. The fit with the blackbody curve
will never vary, no matter what radiator temperature is used in
the test. Or, the test curve itself can be varied with a simple
multiplier so that it can be compared with a specific blackbody
radiator temperature, and exactly the same story unfolds. The test
spectrum also never changes. The asymmetry in the curve shapes of
the spectrums plotted for energy density per frequency and emissive
power per wavelength can be deemed to be always exactly the same,
no matter what the temperature difference is between the two.

The set of black curves in this image are extensions of the 8 K
curve, created with appropriate wavelength multipliers. i.e. # * 1,
# * 32, # * 32^2 and # * 32^3. The green curve is the spectral
energy density spectrum for 2 K. The two curves can't be directly
compared of course, but the point I'm trying to make should be
obvious.

http://www.ozemail.com.au/~mkeon/compare3.jpg

Since the evolution of the universe is dependent on interactions
between existing matter, the more advanced the stage of evolution
the faster will be its development. Even though the universe is
heating up at a squaring rate, the time that the temperature stays
current is changing at an inverse squaring rate. Neither the origin
nor the present will contribute to the background. Background
radiation curves can then be plotted within the parameters of,
infinite background emissions of zero energy (1 x 0), and zero
background emission in the present (0 x 1).

The black curve in the next graph was generated according to those
conditions. The yellow curve was generated likewise, but the whole
x-scale is shifted so that the zero mark aligns with the .34mm
wavelength mark. The reason for this is that the entire spectrum
of the *obviously* visible universe is not represented in the CMBR.
The 13E+9 light year chunk of the past since the big bang universe
became transparent can't be included as a component of the
background radiation in that universe, and since the zero origin
curve is compelled to obey big bang's rules, the present for that
curve is necessarily set in the past by 13E+9 years, when the zero
origin universe was in a lesser evolved state. However, the curve
shape will never change, no matter what stage of evolution it's
plotted to. The .34mm x-scale offset was chosen because it was the
best fit, I certainly couldn't predict it. But this time it should
help to determine how far and how fast the universe is evolving.

No part of the black curve would fall below the yellow curve if
the true relationship between the power spectrums was shown.

http://www.ozemail.com.au/~mkeon/cmbzro.jpg

The zero origin curve is not a particularly good fit with the 2.73
blackbody curve, but I now find that it doesn't need to be. There
is now one major difference in that the power attributed to a
representative wavelength for a stage of evolution is raised to
the fifth power instead of the fourth, as it was before. That is
of course the normal relationship between wavelength and power, as
specified in Planck's blackbody radiation equation. Exactly the same
wavelength-power relationship will prevail regardless of what kind
of spectrum a wavelength belongs in, so long as the conditions that
create the spectrum shape don't change. Double the temperature and
the power received from any equivalent wavelength (halved wavelength)
in the newly generated spectrum will have increased 32 fold. And it
doesn't have to be an enclosure in thermal equilibrium either. The
only significance of that, is that it produces a specific spectrum
shape.

The following is extracted from the program that plotted the curves
for the zero origin universe. It will make a lot more sense as it
is than if I try developing any sort of formula from it.

a = a + .005
' "a" are stages of evolution in steps
' from 0 to 1 in increments of .005

IF a 1 THEN END

b = 1 - a ^ 2
' "b" stores the power ratio per time rate
' of evolution at each step of "a".

wl = (1 / a) - 1
' The initial time zone wavelength on the graph plot is 199mm.
' That's the first step recorded from infinity, and the universe
' had then already existed for an eternity. That wavelength
' bridges the infinite gap to zero, and blends in with the next
' evolution stage. There are of course no discrete stages.

zl = (b * a) ^ 5 * 28000
' "b * a" sets the power for the stage of evolution. That result
' is now raised to the fifth power because that's the rate at which
' each wavelength of a power spectrum increases per temperature
' increase. That rule applies for every object in the universe.
' Double its temperature and the emissive power at each halved
' (equivalent) wavelength increases 32 fold.

' "28000" is obviously a multiplier for curve comparison. Such
' a multiplier sets the power peak, and will not change the curve
' shape one bit.
' ---------------------------

The Qbasic program that generated the curves can be found here
http://www.ozemail.com.au/~mkeon/cmbbas.exe as a self extracting
zip file.

Something that has concerned me for some time is the fact that even
at the peak of the hype for an expanded blackbody explanation for
the CMBR, the raw monopole spectrum data was conspicuously absent,
while the dipole data was clearly set out for all to see. Since
I've never come across any raw data for the monopole, I've had to
improvise by using the raw dipole spectrum data.

Because the dipole is taking the same picture of the cosmic
background as the monopole, by default it has the same spectrum as
the monopole. Apart from its power peak falling a long way short
of the all sky spectrum, the only difference is that the entire
spectrum has been slightly red or blue shifted depending on which
way the dipole is being measured. What I can't understand though
is why the following dipole graph, which was plotted with the raw
dipole data set, shows such an enormous blue shift. The peak of
its spectrum has been shifted to that of a 3.4 K radiator. That
represents a substantial velocity relative to the cosmic
background.

In trying to compare curves in the graph, I found it easier to shift
the monopole curve to align with the dipole than vice versa. The
monopole is shifted to the right with a multiplier based from the
zero mark on the graph scale. And that adjustment is quite valid
for the purpose of the comparison. As you can see, the monopole
was certainly no exact match with the raw dipole data, and as a
consequence would be no better a match with the raw monopole data,
if it could be found.

http://www.ozemail.com.au/~mkeon/cmb5-05.jpg

I've also included the trailing end of a 13 degree K plot, which
only indicates the presence of the galaxy. The galaxy power spectrum
is not in proportion of course, but the curve mismatch on the hotter
side of the graph could be adjusted all over the place by making
different assumptions regarding dust and thermal contributions to
the data from the galaxy.

The CMBR graph for the zero origin universe was plotted along a line
between the origin and the present and is therefore plotted on
intensity per wavelength. It can of course also be plotted according
to spectral energy density. Or I can simply convert the intensity
per wavelength to spectral energy density. The conversion is very
simple. c/(w*pi^.5) does the x-scale conversion. Then the power
attributed to each wavelength on the intensity per wavelength scale
is raised to power^.5 which converts the emissive power curve to
the realm of spectral energy density. The entire power spectrum of
the blackbody enclosure can be elevated to the scale of the spectral
energy density realm and the curve shape can, with an appropriate
power multiplier, be directly compared with anything else plotted
in that realm, but not outside that realm.

For the sole purpose of comparing curve shapes, there is nothing
whatever wrong with converting between emissive power per wavelength
and energy density per frequency, nothing at all. Swapping between
frequency and wavelength doesn't alter anything because the two
properties of the single entity are inseparable. And I can choose
any graph scale I like for the energy density per frequency, even
if the x-scale happens to coincidentally align with a linear
wavelength scale.

The curves in the two frames of this animation were plotted
accordingly. They compare the elevated zero origin curve and the
monopole with the graph plotted from the raw dipole data, which
has been shifted to the colder end with a multiplier so that it
can be directly compared after the power spectrums of each are set
to peak at the same height. Once again, that method of adjustment
is quite valid. Notice how close a fit the zero origin curve is?

http://www.ozemail.com.au/~mkeon/cmbcom.gif

Using an x-scale where frequency is linear hides a substantial curve
misalignment between the raw dipole data and the monopole on the
lower frequency end of the graph, doesn't it. I've often wondered
why the CMBR was invariably depicted using a linear frequency scale.

-----

Max Keon

I wrote:
My earliest attempt at properly justifying the zero origin universe
within the microwave background data failed because I failed to
recognize a flaw in my reasoning at the time. Attempt no.2 was
fairly well demolished in a rather lengthy debate over the way in
which I had combined blackbody curves, and how those curves came
to be. I was thus forced to go back to square one and do it all over
again. The flaw in my original reasoning, which should have
correctly described how the CMBR came to be in the zero origin
universe, quickly became apparent. My graph plot of the CMBR
spectrum was based on emissive power per wavelength, where the CMBR
spectrum is normally displayed as spectral energy density, which
is power according to frequency. I was attempting to fit my curve
to the wrong curve shape.

It's probably doesn't make much difference, but after some
fossicking around in some old files, I found that paragraph was
not correct. It should more appropriately read;
My earliest attempt at properly justifying the zero origin universe
within the microwave background data failed because I failed to
recognize *many* flaws in my reasoning at the time. Attempt no.2 was
fairly well demolished in a rather lengthy debate over the way in
which I had combined blackbody curves, and how those curves came
to be. I was thus forced to go back to square one and do it all over
again. It seems I might have it right this time.

But my main concern was the wording in this later paragraph;
The set of black curves in this image are extensions of the 8 K
curve, created with appropriate wavelength multipliers. i.e. # * 1,
# * 32, # * 32^2 and # * 32^3. The green curve is the spectral
energy density spectrum for 2 K. The two curves can't be directly
compared of course, but the point I'm trying to make should be
obvious.

This may better convey what I was trying to say;
The set of black curves in this image are extensions of the 8 K
curve, created with appropriate power multipliers for each doubling
wavelength step. i.e. # * 1, # * 32, # * 32^2 and # * 32^3. The
green curve is the spectral energy density spectrum for 2 K. The
two curves can't be directly compared of course, but the point I'm
trying to make should be obvious.

http://www.ozemail.com.au/~mkeon/compare3.jpg

The updated web version is stored at
http://www.ozemail.com.au/~mkeon/cmbonly.html

These little problems seem to appear within ten seconds of clicking
the send button.

-----

Max Keon