"Max Keon" skrev i melding ...
Paul B. Andersen wrote:
"Max Keon" skrev i melding ...
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?
Why is this so hard to get?
dW/df is energy per frequency unit.
That is, it is how much energy there is in the part of the spectrum
that has frequencies between f and f+1.
dW/dt is energy per wavelength unit
That is, it is how much energy there is in the part of the spectrum
that has wavelengths between b and b+1.
Since f = c/b, it means that the bandwidth df = -c/b^2*db
Thus the energy dW/df in the bandwidth 1 Hz,
it is equal to the energy dW/db in the bandwidth c/b^2 metres.
Thus dB/df = (c/b^2)*dB/db
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.
Oh, my dear.
You really are a crank, aren't you? :-)
This is a case of simple ignorance of elementary math and physics.
If you don't believe me, why don't you look up "black body radiation" in
an elementary physics textbook and learn it in stead of all this nonsense?
In most books you will find both spectra side by side, and how
you derive the one from the other.
Or you can see:
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html
Why you bother to make so much fuss about something which
can be cleared up by half an hour reading, beats me.
I "make so much fuss" because the problem for me had not yet been
satisfactorily resolved. I had not imagined for a second that the
CMBR graph plot would follow a curve shape that was so obviously
different to that plotted according to wavelength, without
justification? Do you really believe that I think you folk are
complete idiots?
Yes.
Max Keon wrote in June 2002
| Since all inflation based theories
| have been soundly demolished by the CMBR's non compliance with an
| appropriate black body curve, and by the necessarily enormous
| magnitude of that background radiation, what are the implications
| for GR?
As you say, I could have cleared this up some time ago with half an
hour of reading. But why couldn't this have been cleared up on a
newsgroup for all to see, a long time ago?
I did. In June 2002
http://www.google.com/groups?q=g:thl...lly.uninett.no
And considering that you in your reply wrote:
| I am gratefully enlightened by your reply, as perhaps are others who
| are following this thread. This is how I learn what goes on in your
| world.
| It seems that I am once again in your debt.
I thought you had got it.
To me, your clarification
prior to your last reply fell a long way short of identifying the
problem. It's an elementary problem, but you didn't explain it in
an elementary fashion. But then, why should you?
A couple of lines simple math is as elementary as I can make it.
Of the two options, "ask for clarification" or "make outlandish
comments", I chose the latter because option (1) would probably
have resulted in the same type of derogatory comments, but would
not necessarily achieve anything more than I already had. Option (2)
offsets the them/me credibility balance in favor of the them, which
opens the door for the same comments to be thrown, but it also opens
the door for better clarification.
Thanks for the excellent link.
Anyway, have you had any thoughts on what was obviously part 2 of
the original post? i.e. the enormous shortfall in the spectral
energy density of the microwave background?
I did,
http://www.google.com/groups?hl=no&l...lly.uninett.no
You wouldn't listen.
Paul