Paul B. Andersen wrote:

"Max Keon" skrev i melding
...
CMBR? Not in the Big Bang Universe.
-----

For some time I've been trying to understand why the spectral
energy density graph plot of the 2.73 K CMBR, per formula [1]
(2 * pi * f^3) / (c^2 * (exp(h * f / (k * T)) - 1)), is nothing
like a 2.73 K blackbody radiator plot according to formula [2]
(2 * pi * h * c^2) / (b^5 * ((exp((h * f) / (k * T))) - 1))
(b is wavelength)

And why is that?
I have shown you this before, it is quite simple:
dW/df = (2 *pi *h* f^3) / (c^2 * (exp(h * f / (k * T)) - 1)),
f = c/b, df/db = -c/b^2
dW/db = (dW/df)*(df/db)
dW/db = -(2*pi*h*c^2) / (b^5*((exp((h*c)/ k*T*b))) - 1))

The graph plot of intensity per frequency unit along a scale of
frequencies can be easily converted for direct comparison with
formula [2] by converting frequency to wavelength with (c / f) and
plotting the curve on the same graph scale as for formula [2].

No, you cannot.
If you insert f = c/b in [1], it is still dW/df, which is different
from dW/db.

Whatever shape the curves may follow, 5.35 cycles per cm is the peak
point along the emissive power curve for a 2.73 K radiator according
to formula [1], and that is found to be 1 / 5.35 = .187 cm
wavelength. But this is not so according to formula [2], which
gives the peak wavelength as .106 cm.

dW/db = -c/b^2* dW/df
so it is quite obvious that they don't peak at the same
frequency/wavelength.

I'm trying to picture what you are describing, but it just doesn't
add up. You are saying that the wavelength that emits the greatest
energy quantity from a blackbody radiator is dependent on which
formula is used? That can't possibly be. If a .106 cm wavelength
carries the greatest energy quantity, then it carries the greatest
energy quantity. How can a .187 cm wavelength also claim to carry
the greatest energy quantity, from the same radiator temperature?

I'll try a more hands on approach.
From a graph of the CMBR, plotted according to formula [1] above,
I note that the frequency of oscillation which carries the greatest
energy quantity is roughly 5.3 cycles per cm. I record that
information and, with a simple calculation, I determine that the
wavelength at that frequency is 1 / 5.3 = .188 cm. I can now use
this data for a comparison with the peak of the power curve plotted
for a 2.73 K radiator according to formula [2] above, which peaks
at roughly .11 cm. I then use an appropriate multiplier for spectral
energy density per [1], or the emissive power per [2] to bring
either into an alignment with the other, for a direct comparison.

But no amount of juggling can make the wavelengths attributed to
the two peak power points coincide.

Unfortunately you haven't discovered a way to bend the rules of the
Universe, you've merely shown that the curve shape to which the CMBR
was made to align was based on a flawed formula. And if you genuinely
believe in what you are saying, you have also demonstrated that maths
can befuddle the minds of even the best.


--
Max Keon