\subsection{The greenhouse effect hypothesis}
%
Among climatologists, 
in particular those who are 
affiliated with the Intergovernmental
Panel of Climate Change (IPCC)%
%
\footnote{The IPCC was created in 1988 
          by the World Meteorological Organization (WHO)
          and the United Nations Environmental Programme (UNEP).}%
%          
, there is a \lq\lq scientific consensus\rq\rq\TschSpace%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\cite{AAAS2006}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
, that the relevant mechanism is the 
atmospheric greenhouse effect,
a mechanism heavily relying on
the assumption, that  
radiative heat transfer 
clearly dominates over the other forms
of heat transfer such as thermal conductivity, 
convection, condensation \textit{et cetera}\TschSpace%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
\cite{%
IPCC1990,%
IPCC1990SummaryForPolicymakers,%
IPCC1992,%
IPCC1994,%
IPCC1994RadiativeForcing,%
IPCC1996,%
IPCC2000,%
IPCC2001%
}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
%

In all past IPCC reports and 
other such scientific summaries 
the following point evocated 
in 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
\ifthenelse{\equal{IJMPB}{\TschStyle}}
           {Ref.~\refcite{IPCC1990SummaryForPolicymakers}, p.\,5,}
           {}%
\ifthenelse{\equal{arXiv}{\TschStyle}}
           {Ref.~\cite{IPCC1990SummaryForPolicymakers}, p.\,5,}
           {}
\ifthenelse{\equal{TeX4ht}{\TschStyle}}
           {Ref.~\cite{IPCC1990SummaryForPolicymakers}, p.\,5,}
           {}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
is central to the discussion:
%
\begin{quote}
\lq\lq 
One of the most important factors is the
\textbf{greenhouse effect}; 
a simplified explanation of which is as follows. 
Short-wave solar radiation can pass 
through the clear atmosphere relatively 
unimpeded.
But long-wave terrestrial radiation emitted 
by the warm surface of the Earth is partially 
absorbed and then re-emitted by a number of 
trace gases in the cooler atmosphere above. 
Since, on average, the outgoing long-wave 
radiation balances the incoming solar radiation, 
both the atmosphere and the surface 
will be warmer than they would be 
without the greenhouse gases
$\dots$
The greenhouse effect is real;
it is a well understood effect,
based on established scientific 
principles.\rq\rq
\end{quote}
%
To make things more precise, supposedly,     
the notion of 
\textit{radiative forcing} 
was introduced by the IPCC 
and related to the assumption of 
\textit{radiative equilibrium}.
In
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
\ifthenelse{\equal{IJMPB}{\TschStyle}}
           {Ref.~\refcite{IPCC1994RadiativeForcing}, pp.\,7-6,} 
           {}%
\ifthenelse{\equal{arXiv}{\TschStyle}}
           {Ref.~\cite{IPCC1994RadiativeForcing}, pp.\,7-6,}
           {}%
\ifthenelse{\equal{TeX4ht}{\TschStyle}}
           {Ref.~\cite{IPCC1994RadiativeForcing}, pp.\,7-6,}
           {}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
one finds the statement:
%
\begin{quote}
\lq\lq
\textit{A change} 
in average net radiation
at the top of the troposphere 
(known as the tropopause), 
because of a change in either
solar or infrared radiation, 
is defined for the purpose of this report 
as a 
\textit{radiative forcing}. 
A radiative forcing perturbs the balance 
between incoming and outgoing radiation.
Over time climate responds to the perturbation
to re-establish the radiative balance.
A positive radiative forcing tends on average 
to warm the surface;
a negative radiative forcing on average
tends to cool the surface.
As defined here, the incoming solar
radiation is not considered a radiative forcing,
but a change in the amount of incoming solar radiation
would be a radiative forcing
$\dots$
For example, an increase in atmospheric 
${\rm CO}_2$ concentration leads to a
reduction in outgoing infrared radiation
and a positive radiative forcing.%
\rq\rq  
\end{quote}

\noindent%
However, in general \lq\lq scientific consensus\rq\rq\ 
is not related whatsoever to scientific truth 
as countless examples in history have shown. 
\lq\lq Consensus\rq\rq\ is a political term, 
not a scientific term.
In particular, from the viewpoint 
of theoretical physics the radiative approach, 
which uses physical laws
such as Planck's law and Stefan-Boltzmann's law
that only have a limited range of validity
that definitely does not cover the atmospheric 
problem, must be highly questioned\TschSpace%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
\cite{Stefan1879,Boltzmann1884,Planck1900,Planck1901,Rybicki1979}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
For instance in many calculations 
climatologists perform calculations 
where idealized black surfaces 
e.g.\ representing 
a ${\rm CO}_2$ layer and
the ground, respectively, radiate
against each other. In reality, we must
consider a bulk problem, in which 
at concentrations of 300~ppmv
at normal state still 
%
\begin{eqnarray}
N 
&\approx&
3 \cdot 10^{-4} 
\,\cdot\,
V
\,\cdot\,
N_L
\nonumber \\
&\approx&
3 \cdot 10^{-4} 
\,\cdot\,
(10 \cdot 10^{-6}) ^3
\,\cdot\,
2.687 \cdot 10^{25}
\nonumber \\
&\approx&
3 \cdot 10^{-4} 
\,\cdot\,
10^{-15}
\,\cdot\,
2.687 \cdot 10^{25}
\nonumber \\
&\approx&
8 \cdot 10^{6}
\end{eqnarray}
%
${\rm CO}_2$ molecules are distributed within a cube $V$
with edge length $10\,\mu m$, 
a typical wavelength 
of the relevant infrared radiation.%
%
\footnote{$N_L$ is determined by the well-known Loschmidt number\TschSpace%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{Virgo1933}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
.}
%
In this context an application of the formulas
of cavity radiation is sheer nonsense.

It cannot be overemphasized that 
a microscopic theory providing the base 
for a derivation of macroscopic quantities 
like thermal or electrical transport coefficients 
must be a highly involved many-body theory. 
Of course, heat transfer is due to interatomic 
electromagnetic interactions mediated 
by the electromagnetic field. 
But it is misleading to visualize a photon as 
a simple particle or wave packet travelling 
from one atom to another for example. 
Things are pretty much more complex and cannot be 
understood even in a (one-)particle-wave duality 
or Feynman graph picture.

On the other hand, the macroscopic thermodynamical 
quantities contain a lot of information and can be 
measured directly and accurately in the physics lab.
It is an interesting point that the thermal conductivity
of ${\rm CO}_2$ is only one half of that of nitrogen
or oxygen. In a 100 percent ${\rm CO}_2$ atmosphere
a conventional light bulb shines brighter
than in a nitrogen-oxygen atmosphere due to
the lowered thermal conductivity of its environment. 
But this has nothing to do 
with the supposed ${\rm CO}_2$ 
greenhouse effect which refers
to trace gas concentrations. Global climatologists
claim that the Earth's natural greenhouse effect 
keeps the Earth 33~$^\circ{\rm C}$ warmer than it 
would be without the trace gases in the atmosphere. 
80 percent of this warming is attributed to water vapor 
and 20 percent to the 0.03 volume percent ${\rm CO}_2$. 
If such an extreme effect existed, it would show up even in a
laboratory experiment involving concentrated ${\rm CO}_2$    
as a thermal conductivity anomaly. It would be manifest itself 
as a new kind of \lq superinsulation\rq\
violating the conventional heat conduction equation.
However, for ${\rm CO}_2$  such anomalous heat transport
properties never have been observed.

Therefore, in this paper, the popular greenhouse 
ideas entertained by the global climatology 
community are reconsidered within the limits 
of theoretical and experimental physics. 
Authors trace back their origins  
to the works of Fourier\TschSpace%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{Fourier1824a,Fourier1824b}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
(1824), 
%
Tyndall\TschSpace%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{Tyndall1861,Tyndall1863a,Tyndall1863b,Tyndall1873a,Tyndall1873b}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% 
(1861)
%
and 
Arrhenius\TschSpace%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{Arrhenius1896,Arrhenius1901,Arrhenius1906}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% 
(1896). 
%
A careful analysis of the original papers shows
that Fourier's and Tyndall's works did not really 
include the concept of the atmospheric greenhouse 
effect, whereas Arrhenius's work fundamentally 
differs from the versions of today.
%
With exception of
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\ifthenelse{\equal{IJMPB}{\TschStyle}}
           {Ref.~\refcite{Arrhenius1906},}
           {}%
\ifthenelse{\equal{arXiv}{\TschStyle}}
           {Ref.~\cite{Arrhenius1906},}
           {}
\ifthenelse{\equal{TeX4ht}{\TschStyle}}
           {Ref.~\cite{Arrhenius1906},}
           {}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
the traditional works precede the 
seminal papers of modern physics,
such as Planck's work on the radiation
of a black body\TschSpace%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{Planck1900,Planck1901}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
Although the arguments of Arrhenius were falsified 
by his contemporaries they were picked up by 
Callendar\TschSpace%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{%
Callendar1938,%
Callendar1939,%
Callendar1940,%
Callendar1941,%
Callendar1949,%
Callendar1958,%
Callendar1961%
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% 
and Keeling\TschSpace%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
\cite{%
Keeling1960,%
Keeling1973,%
Keeling1976,%
Keeling1978,%
Keeling1989,%
Keeling1996,%
Keeling1998%
}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
, the founders of the modern 
greenhouse hypothesis.%
%
\footnote{%
Recently, von\,Storch critized 
the anthropogenic global warming scepticism
by characterizing the discussion as 
\lq\lq a discussion of yesterday and the day before 
yesterday\rq\rq\TschSpace%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{Stockholm2006}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
Ironically, it was Calendar and Keeling 
who once reactivated \lq\lq a discussion
of yesterday and the day before yesterday\rq\rq\
based on \textit{already falsified} arguments.
}
%
Interestingly, 
this hypothesis has been vague
ever since it has been used.
Even Keeling stated 1978\TschSpace%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{Keeling1978}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{quote}
\lq\lq 
The idea that ${\rm CO}_2$ from fossil fuel burning 
might accumulate in air and cause warming of the 
lower atmosphere was speculated upon as early as the latter
the nineteenth century (Arrhenius, 1903). 
At that time the use of fossil fuel was
slight to expect a rise in atmospheric 
${\rm CO}_2$ to be detectable. The idea was
convincingly expressed by Callendar (1938, 1940) 
but still without solid evidence
rise in ${\rm CO}_2$.\rq\rq\
\end{quote} 
%
The influence of 
${\rm CO}_2$
on the climate was also discussed thoroughly 
in a number of publications that appeared
between 1909 and 1980, 
mainly in Germany\TschSpace% 
%
\cite{%
Albrecht1933,%
Albrecht1935,%
Albrecht1951,%
Barker1933,%
Baur1934,%
Baur1935,%
Cess1990,%
Curtis1956,%
deBary1954,%
Gold1909,%
Gribbin1978,%
Hofmann1955,%
Manabe1964,%
Manabe1967,%
Manabe1969a,%
Manabe1969b,%
Manabe1980,%
Martin1932,%
Mecke1921,%
Moeller1933,%
Moeller1943a,%
Moeller1943b,%
Moeller1954,%
Moeller1959,%
Moeller1961,%
Muegge1932,%
Schaefer1926,%
Wimmer1926}.
% 
The most influential authors were
M\"oller\TschSpace% 
%
\cite{%
deBary1954,%
Moeller1933,%
Moeller1943a,%
Moeller1943b,%
Moeller1954,%
Moeller1959,%
Moeller1961,%
Muegge1932},
%
who also wrote a textbook on
meteorology\TschSpace% 
%
%
\cite{%
Moeller1973a,%
Moeller1973b},
% 
and Manabe\TschSpace% 
%
%
\cite{%
Manabe1964,%
Manabe1967,%
Manabe1969a,%
Manabe1969b,%
Manabe1980,%
Moeller1961}. 
%
It seems, that the joint work of 
M\"oller and Manabe 
%
\cite{%
Moeller1961}
%
has had a significant influence 
on the formulation of the modern 
atmospheric ${\rm CO}_2$ 
Greenhouse conjectures and hypotheses,
respectively.
% 
 
In a very comprehensive report
of the US Department of Energy (DOE),
which appeared in 1985\TschSpace% 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{DOE1985},
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
the atmospheric greenhouse hypothesis
had been cast into its final form
and became the cornerstone in all
subsequent IPCC publications\TschSpace%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\cite{%
IPCC1990,%
IPCC1990SummaryForPolicymakers,%
IPCC1992,%
IPCC1994,%
IPCC1994RadiativeForcing,%
IPCC1996,%
IPCC2001,%
IPCC2000%
}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%

Of course, it may be, 
that even if the oversimplified picture
entertained in IPCC global climatology
is physically incorrect, a thorough discussion may
reveal a non-neglible influence of certain radiative
effects (apart from sunlight) on the weather, and hence 
on its local averages, the climates, which may be dubbed 
the ${\rm CO}_2$ greenhouse effect.
But then three key questions will remain, 
even if the effect is claimed to serve 
only as a genuine trigger of a network 
of complex reactions:

\begin{enumerate} 
\item Is there a fundamental ${\rm CO}_2$ 
      greenhouse effect in physics?
\item If so, what is the fundamental physical principle  
      behind this ${\rm CO}_2$ greenhouse effect?
\item Is it physically correct to consider 
      radiative heat transfer as the fundamental
      mechanism controlling the weather setting
      thermal conductivity and friction to zero?
\end{enumerate}        

The aim of this paper is to give an 
affirmative \textit{negative} answer 
to all of these questions rendering 
them rhetoric.  
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%          {}
%\ifthenelse{\equal{arXiv}{\TschStyle}}
%           {\pagebreak}
%          {}
%\ifthenelse{\equal{TeX4ht}{\TschStyle}}
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%  
