CO2 Alarmism Collapses under False SB Law

The basic picture of climate alarmism with $\epsilon\sigma T_a^4$ = Downwelling Longwave Radiation DLR from the atmosphere to the Earth, according to a False Stefan-Boltzmann law.

In recent posts on Downwelling Longwave Radiation DLR I have compared two versions of Stefan-Boltzmann's radiation law, one named False-SB:

• $R = \sigma T^4 - \sigma T_b^4$

and one named True-SB:

• $R = \sigma (T^4 - T_b^4)$

where $R$ is the radiance from a blackbody at temperature $T$ into a background at temperature $T > T_b$ and $\sigma$ is Stefan-Boltzmann's constant.

Although False-SB and True-SB look algebraically very similar, they describe very different physics: False-SB describes the radiative transfer R as the difference of two-way gross flows

$\sigma T^4$ (from the blackbody to the background) and $\sigma T_b^4$ (from the background to the blackbody). True-SB describes only one-way (net) flow from the blackbody to the background, assuming that $T > T_b$.

The physics of False-SB is thus two-way flow, while the physics of True-SB is one-way flow.

False-SB can be seen as a violation of the 2nd law of thermodynamics with $\sigma T_b^4$ transfer of heat from a colder background to a warmer body.

True-SB follows in the case $T_b = 0$ by integration over frequencies of Planck's radiation law, and in the case $T > T_b > 0$ by a direct extension of Planck's law.

But False-SB does not follow the same way, because there is no two-way Planck law to integrate. So how is then False-SB proved in the scientific literature? Which scientist is responsible for the False-SB?

The answer is that the proof of False-SB is considered to be so trivial that nobody has cared to write down the proof. The proof of False-SB is considered so self-evident that nobody claims to have given a proof. Remember that Planck got the Nobel Prize for his radiation law which proved True-SB, and thus a proof of False-SB could also be worth a prize, unless the proof is so trivial that anybody can do it.

So what is then the (trivial) proof of False-SB? There are two proofs in the literature:

1. Application of True-SB twice:

• Apply True-SB first with $T_b = 0$ and then with $T = 0$, and add up the results.
• Alternatively, apply twice switching the roles of radiator and background.

2. Distributive law of algebra:

• $\sigma (T^4 - T_b^4)= \sigma T^4 - \sigma T_b^4$.

Both 1. and 2. look so trivial that nobody would care to claim priority and thus carry responsibility.

But both 1 and 2 are incorrect, and accordingly lack correct justification, because

• Setting $T = 0$ violates the the assumption of True-SB that $T > T_b$.
• Switching roles changes the physics and does not describe a uniqe situation.
• The physical meaning of the algebraic law is missing.

We thus have a situation where a physical law, which lacks support in physics literature (False-SB), is taken for granted because it is viewed to be so obvious, and then is used by climate scientists to sell AGW alarm, while there is no climate scientist responsible for presenting the false law.

False-SB can be used to sell alarm because it deals with the difference of two gross flows, which is unstable in the sense that a small relative change of any of the gross flows can cause a big relative change of the net flow, which allows inflation of a small cause (doubled CO2) into a big effect (global warming of 3 C).

But True-SB cannot be used to sell alarm, and therefore it is crucial in climate alarmism to use False-SB.

This suggests the following strategy when debating with a CO2 alarmist:

1. Ask which SB law supports CO2 alarmism.
2. At the answer that it is the False-SB, ask for a proof.
3. At the answer that the proof is trivial, ask about the details of the proof.
4. At the answer that it directly follows by application twice of True-SB, ask how.
5. At the answer, first $T_b=0$ and then $T=0$, tell that $T=0$ is not allowed in True-SB.
6. At the answer that the proof anyway is trivial, go back to 4 and repeat.

I recently tried this with Prof Grant W Petty, and noticed that it works very efficiently: Prof Petty got angry and slammed the door.

Try it yourself, and see how it works. To get more arguments, take a look at CO2 Alarmism Debunked by Mathematics.

Since nobody claims priority and thus responsibilty of False-SB, it becomes the responsibility of anyone using it, that is the responsiblity any climate alarmist.