I have put up an new version of my upcoming talk at
Climate Sense 2018 with the title:
Of particular focus is the Fundamental Theorem of Calculus stating that if $F(x)$ is a primitive function of $f(x)$, that is $\frac{dF}{dx}=f$, then
- $\int_a^bf(x)\, dx = F(b) - F(a)$.
For example, if $f(x)=1$, then $F(x)=x$, and so we can formally write
- $1 = \int_{100}^{101} f(x)\, dx = F(101)-F(100)=101 - 100$
expressing the positive quantity $\int_{100}^{101} f(x) dx = 1$ as the difference between the two (large) numbers 101 and 100. This is mathematics and not yet physics.
The radiative flux of heat energy $Q$ from a warm body of temperature $T_2$ to a colder body of temperature $T_1 < T_2$ is (essentially) given by the integral
- $Q = \int_{T_1}^{T_2}f(\nu )\,d\nu$
where $f(\nu )$ is the Planck spectrum with $\nu$ frequency. Here the limits of the integral scale with temperature reflecting the cut-off in frequency expressed by Wien's displacement law giving the
warm body the "overkill" spectrum $f(\nu )$ above the cut-off $T_1$ for the cold body, with the overkill effectively causing the heating while the shared spectrum below cut-off has no heating effect, as explained in more detail
here.
With $F(T)=\sigma T^4$ and $F$ acting as a primitive function of the Planck function $f$, the radiative flux $Q$ can now according to the Fundamental Theorem formally be expressed in the form of the Stefan-Boltzmann Law
- $Q = \sigma T_2^4 - \sigma T_1^4$
thus formally expressing the positive quantity $Q$ as the difference between two (large) numbers $\sigma T_2^4$ and $\sigma T_1^4$.
The Voodoo Physics of the Greenhouse Effect is the result of giving the mathematical identity
- $\int_{T_1}^{T_2}f(\nu )\,d\nu = \sigma T_2^4 - \sigma T_1^4$
a physical meaning with the physical one-way flux $Q=\int_{T_1}^{T_2}f(\nu )\,d\nu$ expressed as the difference between the entities $F(T_2)=\sigma T_2^4$ and $F(T_1)=\sigma T_1^4$, now freely invented to be forms of two-way "radiative fluxes" back-and-forth between the bodies. From one-way physical flux are thus created two-way fluxes from a mathematical identity without any proper physical correspondence. Note in particular that $F$ as primitive function of $f$ is undetermined up to a constant, thus allowing fictitious back-and-forth fluxes of any magnitude.
Note that $F(T)=\sigma T^4$ can be interpreted physically as the one-way radiative flux from a body of temperature $T$ into a background at 0 K. But the physics is missing of viewing the one-way radiative flux between two bodies as a difference between two separate fluxes into a background at 0 K.
A property (identity) of a mathematical model is thus freely interpreted to be real physics, in the same way as an operation of a voodoo doll is believed to be able to have a real effect on a real person.
This is nothing but Voodoo Physics, and this is the nature of the Greenhouse Effect based on Back Radiation from cold to warm underlying the CO2-alarmism so forcefully preached by IPCC with now Macron as ardent follower.
Macron, despite (or maybe thanks to) his education in French elite schools with all its mathematics, thus appears to be overwhelmed by the Fundamental Theorem of Calculus and cannot separate model from reality.
Voodoo = operation on model believed to have real effect on real person.
PS The Pyrgeometer is a perfect example of a voodoo doll, reporting (non-physical) back radiation $\sigma T_1^4$ from a cold atmosphere at $T_1$ to warmer Earth surface at $T_2$, by measuring $Q$ and (erroneously) viewing $\sigma T_2^4$ to be radiation from the Earth surface, as
if the Earth surface was radiating directly to surrounding space at 0 K and not to the atmosphere at $T_1$ K.
You can buy a
pyrgeometer from Kipp and Zonen and play with it as a voodoo doll believing it reports real physics if you want to sell CO2-alarmism. From the above analysis you may understand that in fact it represents a symbiosis of science and commercial industry serving CO2-alarmism by supplying fictional physics.
