Why APS Supports CO2 Alarmism

What would the physicists of the 1927 Solway conference (with Planck 3rd left-first row with hat) have said about CMB and DLR and related global warming?

This is a continuation of the previous post The Fiction of Heating of CMB.

The American Physical Society APS gives crucial scientific support to the CO2 alarmism of IPCC by its (famous) Statement on Climate Change:

• The evidence is incontrovertible: Global warming is occurring.
• If no mitigating actions are taken, significant disruptions in the Earth’s physical and ecological systems, social systems, security and human health are likely to occur.
• We must reduce emissions of greenhouse gases beginning now.

I have asked physicists why they support CO2 alarmism and here is the argument that emerges:

1. Stefan-Boltzmann's law (SB) reads $R = \sigma T^4$, where $R$ is the radiance in W/m2 from a blackbody of temperature $T$ and $\sigma$ is SB's constant.
2. Cosmic Microwave Background Radiation (CMB) is a "faint glow" of empty space with heating effect according to SB with $T\approx 3\, K$.
3. Downwelling Longwave Radiation (DLR) is a similar "glow" of the atmosphere at $T\approx 255\, K$ heating the Earth surface at $T\approx 288\, K $, about 100 million times stronger than CMB.
4. Since the heating of DLR is so much stronger than that of CMB, and CMB is incontrovertible, global warming is incontrovertible.

When I inform a physicist that this argument uses Stefan-Boltzmann in a wrong way (False-SB discussed in previous posts), he/she stares at me as if he cannot believe what is being said.

I then carefully explain that the true Stefan-Boltzmann's Law (True-SB) concerns radiation from a blackbody of temperature $T>0$ into a background at $0\, K$, that is more generally, True-SB expresses radiation into a background of lower temperature. I carefully explain that the above argument speaks about radiation from a blackbody of a low temperature into a background of higher temperature, that is a False-SB is used.

The physicist then stares at me angrily, and says that I am wrong, that he is in charge of SB and that he is a student to a student to a student of Planck and that the SB is derived from Planck's law and thus neither he nor the SB can be wrong.

When I carefully explain that Planck's law concerns radiation into a background of lower temperature (o K), and not the other way around as expressed by False-SB, the physicist gets really angry and says that only physicists can understand Planck's law, because only physicists can understand the proof of Planck's law, which was given by Planck himself, and because they are all students of Planck and I am not.

When I then point out that Planck's proof concerns radiation into a background of lower temperature (o K), the physicist says that I must be mistaken and anyway the proof is not so relevant, and therefore is certainly not remembered by todays physicists because it is now so old and in fact so difficult that it can no longer be taught, and the only thing that counts is Planck's law, and Planck's law has been verified by infinitely many experiments.

So there we stand:

• I claim that physicists are using a False-SB and that a True-SB does not give support to the idea that CMB is a "faint glow" from empty space which together with a "glow" from the atmosphere is contributing to global warming.
• A physicist is not willing to give up CMB as a "faint glow" from empty space and thus certainly not DLR as a "glow" from the atmosphere adding to global warming.

But the scientific question remains: Is False-SB true? Or is False-SB false?

If Planck was alive, we could have asked him about his proof of his law. To help the discussion I have formulated a new proof of Planck's law presented in Computational Blackbody Radiation.

Mathematics of Financial Crisis, and Climate Crisis

In Climate Crisis vs Financial Crisis I identified a common root of a (i) global financial crisis and (ii) global climate crisis as an instability from a two-way flow of (i) money between banks and loan takers and (ii) heat energy between atmosphere and Earth.

In the case (i) this is illustrated by an entrepreneur with an idea (e.g. solar panels) but no money (=0) who gets a loan X when signing a debt contract of X, according to the equation

• 0 = X - X

with the loan X exactly balanced by a corresponding debt X. This gives the entrepreneur the possibility to start a company for production of solar panels. If the interest rate is close to zero (as in Japan and the US) and there are no restrictions on the size of the loan, then the entrepreneur will be able to realize the idea on any scale.

But some ideas are not so good and the company will go bankrupt (e.g. Solyndra) leaving the contradictory equation 0 = - X , which will ask for new even bigger loans, et cet. This is how the financial crisis is now escalating with central banks feeding fresh X into the market without limit on X, and - X going to minus infinity, like in Greece right now.

In the case (ii) of climate crisis X is about 350 W/m2 according to the Kiel-Trenberth energy budget, about the same as the total insolation from the Sun.

The equation 0 = X - X has a special property, which underlies the instability, namely that X is arbitrary. If there is no interest are no restrictions the loan X can be take any size, and if X is large then instability results: If X is large then a loss of even a small portion of X may be large and a financial crisis will result.

The Kiehl-Trenberth energy budget has the same property: X = 350 W/m2 is supposedly being motivated by a Stefan-Boltzmann law, but the motivation is weak being based on a False-SB:

The exchange X in the Kiehl-Trenberth is fictitious and could be anything, and if it is chosen to be large (= total insolation), then climate crisis results: With X = 350 W/m2 an alarming climate sensitivity of 3 C is claimed by CO2 alarmists.

Conclusion: The financial crisis is real because the equation 0 = X - X with large X is real and unstable, while the climate crisis is fictitious because the equation 0 = X - X in climate science with X large is unreal, in fact only valid for X = 0 and then not unstable.

If you are unsure of the meaning of the equation 0 = X - X, assume that you have no money (=0)

and then as compensation you go to the bank and borrow X = $1 billion. Would you then say that you suddenly have become a billionaire?

Climate Crisis vs Financial Crisis?

CO2 alarmism is based on the Kiel-Trenberth global energy budget with massive two-way transfer of heat energy between the atmosphere and the Earth of the order of 350 W/m2 as Downwelling/Upwelling Longwave Radiation (DLR/ULR), about the same as the total input from the Sun.

There is an analogy in global economy as a massive two-way transfer of money between state and people, or between central banks and commercial banks. The financial crisis can be seen as an expression of the instability arising from such a massive two-way transfer, which appears to create heaps of money out of nothing, like writing 0 = 100 - 100 and seeing 100s appearing from 0.

DLR/ULR similarly represents an instability of global climate, which by CO2 alarmists is being used to sell a climate crisis.

The financial crisis is real, because there is an unstable two-way flow of money between state and people. The question is now if the climate crisis is real, because there is an unstable two-way flow of heat energy between the atmosphere and the Earth as DLR/ULR?

In short: Is DLR/ULR reality or fiction? Does Nature have a central bank which can issue energy bonds and supply a global climate market with energy capital, out of nothing?

No, there is no direct evidence that Nature has such a central bank. There is no direct evidence that DLR/ULR is real, and thus there is no direct evidence of a climate crisis.

GWPF reports Europe Reconsidering Its Unilateral Climate Policy. It is clear that Europe cannot handle both a financial crisis and a climate crisis. If there is no climate crisis after all, then the financial crisis may be possible to resolve by limiting the unstable two-way transfer of money, following what Mother Earth is doing with the flow of energy to keep a stable climate.

Evidence that DLR is Fiction?

The evidence of Downwelling Longwave Radiation put forward by CO2 alarmists is that an IR-detector of some sort when pointed to the sky gives a reading which is not zero, and the non-zero reading is used as evidence that something has been recorded, which is then interpreted as DLR or backradiation from the cold sky to the warmer surface of the Earth.

The evidence of DLR is thus a non-zero reading of an IR-detector.

Suppose now, to turn the argument around, that the reading of the IR-detector is zero. That would be the case if the IR-detector works by detecting a temperature difference and if the temperature difference happens to be zero. This would be the case if the temperature of the Earth is equal to the temperature of the sky. The IR-detector working on a principle of

temperature difference, like a thermocouple, would then record zero, as if nothing was recorded.

The following questions present themselves:

• What could be concluded from a zero reading of an IR-detector?
• That there is positive DLR?
• That there is positive DLR precisely balanced by Upwelling Longwave Radiation?
• Or can nothing positive be concluded from a zero reading?

IR Detectors and True-SB

In the previous post From Correct Planck Law to True-SB and False-SB I derived the following Stefan-Boltzmann Law based on the new proof of Planck's radiation law presented in Computational Blackbody Radiation in Slaying the Skydragon:

(True-SB) $R(T,T_b) =\int_{T_b}^{T}\gamma T f^2 df + \int_0^{T_b}\gamma (T - T_b) f^2df \equiv I_1 + I_2$,

where $R(T,T_b)$ is the radiance from a blackbody of temperature $T$ into a blackbody background of temperature $T_b < T$.

Here the first integral $I_1$ is the radiance from the blackbody absorbed as heat by the background above the cut-off of the background and $I_2$ the net heat absorbed below cut-off as the difference between absorbed and emitted radiation.

Let us see what (True-SB) can tell us about the possible design of IR detectors, where $T$ is the temperature of the object to be detected and $T_b$ that of the detector. There are two types of detectors to consider (see here):

1. cooled with $T_b < T$
2. un-cooled with possibly $T_b > T$.

In a cooled detector with $T_b < T$ both $I_1$ and $I_2$ are positive and $R(T,T_b)$ can

be directly recorded as heating transferred into an electric signal by a thermocouple. (For a star a large distance only $I_1$ is recorded, with the help of optical magnification of the input,

but this is not IR.)

In an un-cooled detector the heat transfer would be away from the detector if $T_b>T$, and

in principle the object could be detected from recording the cooling of the detector. But this is

a form of negative detection which may be difficult to get to work in practice.

More interesting is to explore what (True-SB) suggests for the design by heating in the case the object has lower temperature than the detector:

In this case the signal from the object does not contain frequencies above the cut-off of the detector and so $I_1=0$, but by magnifying the signal optically (by a lense) the radiation below cut-off can be changed into

• $I_2(M)= \int_0^{T_b}\gamma (MT - T_b) f^2df$

where $M>1$ is a magnification factor and $I_2(M)$ may thus become positive even if $T_b > T$.

We sum up the experience from (True-SB):

1. If the temperature of the detector is lower than the object, then direct recording of heating is possible (with $I_1>0$ and possibly also $I_2>0$ ).
2. If the temperature of the detector is higher than that of the object, then heating may be recorded after optical input magnification (with $I_2>0$).

Note added: I made a mistake believing that a lens can magnify radiance, which I correct in Learning by Seeing.

From Correct Planck Law to True-SB and False-SB

In recent posts I have exhibited a version of Stefan-Boltzmann's radiation law referred to as False-SB which is used by climate scientists to support CO2 alarm, and I have shown that False-SB is the result of an incorrect application of Planck's radiation law. Let me here again show the incorrect argument leading to False-SB, and the correct argument leading to

True-SB.

Stefan-Boltzmann's radiation law in its original form (SB) expressing the total radiance from a blackbody of temperature T into a background at 0 K, is obtained by integration/summation over frequencies of Planck's radiation law expressing the radiation intensity $I(f,T)$ emitted by a blackbody as a function of frequency $f$ and temperature $T$, per unit frequency, surface area, viewing solid angle and time:

• $I(f,T)=\gamma Tf^2\theta (\nu, T),\quad \gamma =\frac{2k}{c^2}$

with the high-frequency cut-off factor

• $\theta (f, T)=\frac{\frac{hf}{kT}}{e^\frac{hf}{kT}-1}$,

where $c$ is the speed of light in vacuum, $k$ is Boltzmann's constant, with $\theta (\nu ,T)\approx 0$ for $\frac{hf}{kT}>10$ say and $\theta (f ,T)\approx 1$ for $\frac{hf}{kT}<1$. Since $h/k\approx 10^{-10}$, this effectively means that only frequencies $\nu\le T 10^{11} $ will be emitted, which fits with the common experience that a black surface heated by the high-frequency light from the Sun, will not itself shine like the Sun, but radiate only lower frequencies.

We refer to $\frac{kT}{h}$ as the cut-off frequency because frequencies $f>\frac{kT}{h}$ will be radiated subject to strong damping. We see that the cut-off frequency scales with $T$, which is Wien's Displacement Law.

Normalizing and simplifying the exponential cut-off, Planck's law can be written in the form

• $I(f ,T) =\gamma Tf^2$ for $f\le T$
• $I(f,T) = 0$ for $f > T$.

The idea is now that SB is obtained from Planck's law by summation/integration over frequencies. The basic form of SB expresses the total radiance $R(T,0)$ of a blackbody of temperature $T$ radiating into a background at 0 K as

• $R(T,0)=\gamma T\int_0^{T}f^2df = \sigma T^4$

where $\sigma =\frac{\gamma}{3}$.

We next seek the radiance $R(T,T_b)$ when the background is a blackbody of temperature $T_b > 0$. Planck proved his law in the case $T_b=0$ by using an argument based on statistics of quanta and it is not clear how to extend this argument to $T > T_b > 0$. Accordingly, a derivation of $R(T,T_b)$ from Planck law in the case $T_b > 0$, appears to be missing in physics literature.

To be able to compute $R(T,T_b)$ a new proof of Planck's law was given in Computational Blackbody Radiation in Slaying the Skydragon, a proof which allows direct generalization to $T_b>0$ with (compare with previous post):

• $R_{True}\equiv R(T,T_b) =\int_{T_b}^{T}\gamma T f^2 df + \int_0^{T_b}\gamma (T - T_b) f^2df \equiv I_1 + I_2$,

where the first integral $I_1$ is the radiance from the body into the background above the cut-off of the background and the second integral the net radiance below cut-off. Notice that if $T\approx T_b$, then $I_1\approx 3 I_2$ and so the above cut-off contribution $I_1$ dominates the radiance.

We see that $R(T,T_b}$ is the sum of two integrals with positive integrands both expressing radiance from the warm body into the colder background. We should now stop here having reached an expression for $R_{True}=R(T,T_b)$ correctly derived from a correct Planck law.

However, climate scientists have introduced an incorrect version of SB named False-SB, obtained by rewriting $I_1$ as follows:

• $I_1 = \int_0^{T}\gamma Tf^2df - \int_0^{T_b}\gamma Tf^2df =\sigma T^4 - \sigma TT_b^3$

which since $I_2 = \sigma (T-T_b)T_b^3$ gives False-SB on the (seductively simple) form

• $R_{False} = \sigma T^4 - \sigma T_b^4$

expressing the transfer of energy from the body to the background as the difference of two gross flows in opposite directions. We see that False-SB arises by rewriting an integral with positive integrand as the difference of two integrals with positive integrands as follows:

• $\int_{T_b}^{T} f^2 df = \int_0^{T}f^2df - \int_0^{T_b}f^2df$,

where the lower integration limit $0$ could be replaced by any positive number smaller than $T_b$. False-SB arises when giving this formal mathematical manipulation a physical meaning stating that one-way net flow is the difference of two-way gross flows, with the flow from the background in violating with the 2nd law of thermodynamics.

We see that False-SB arises by writing the correct $R(T,T_b)$ as

• $R_{False} = (R(T,T_b) + C) - C$,

where $C$ is an arbitrary positive constant, and then assigning the arbitrary constant $C$ a definite physical meaning as the transfer of heat from the colder background to the warmer body, in violation of the 2nd law of thermodynamics. The only correct choice is $C=0$ which gives the correct net flow $R(T,T_b)$ as stated above.

False-SB is thus obtained by an ad hoc generalization of SB for $T_b=0$ in the form $R(T,0)=\sigma T^4$, to the incorrect form $R_{False} = \sigma T^4 - \sigma T_b^4$ in striking violation of the 2nd law.

Note that the seduction of $R_{False}$ is enhanced by the fact that $R_{False}$ gives the

correct net flow $R(T,T_b)$, which by proponents of the correctness of $R_{False}$ is used as evidence that $R_{False}$ is correct. But this only shows that there is an aspect (one-way net flow) of $R_{False}$ which is correct, while the two-way gross flow suggested by $R_{False}$ is grossly incorrect.

If the only meaning of $R_{False}$ is net flow equal to $R(T,T_b)$, then $R_{False}$ should better be eliminated from the discussion altogether by replacing it with the correct $R(T,T_b)$. DLR should thus be eliminated as fictitious pseudo-physics.

Finally, the difference between $R_{True}$ and $R_{False}$ comes out as different stability

properties of one-way net flow and two-way gross flow, with $R_{False}$ supporting the idea of high climate sensitivity behind CO2 alarmism. If $R_{False}$ and DLR is eliminated from the discussion, then CO2 alarmism crumbles.

False-SB Violates the 2nd Law

To understand the difference between the two versions of Stefan-Boltzmann's radiation law (SB) under discussion, True-SB and False-SB, let us inspect the proof of SB from Planck's radiation law in its normalized form presented in Computational Blackbody Radiation:

• $R(f ,T) =\gamma Tf^2$ for $f\le T$
• $R(f,T) = 0$ for $f > T$

where $R(f ,T)$ is the radiance of frequency $f$ from a blackbody of temperature $T$, $\sigma$ is a constant and a simplified high-frequency cut-off is used (as compared to Planck's exponential cut-off).

The total radiative transfer $R_{True}$ to a blackbody 1 of temperature $T_1$ from a blackbody 2 of temperature $T_2>T_1$ is given by integration over frequencies as follows:

• $R_{True} =\int_{T_1}^{T_2}\gamma T_2 f^2 df + \int_0^{T_1}\gamma (T_2 - T_1) f^2df \equiv I_1 + I_2$,

where the first integral $I_1$ is the heating effect from 2 above the cut-off of 1 and the second integral the net heating from 2 below cut-off.

We see that $R_{True}$ expressing True-SB is the sum of two integrals with positive integrands, that is, $R_{True}$ is the sum of many small positive contributions all with transfer of heat from 2 to 1.

We shall now see that False-SB arises by rewriting $I_1$ as follows:

• $I_1 = \int_0^{T_2}\gamma T_2f^2df - \int_0^{T_1}\gamma T_2f^2df =\sigma T_2^4 - \sigma T_2T_1^3$

where $\sigma =\frac{\gamma}{3}$, which since $I_2 = \sigma (T_2-T_1)T_1^3$ gives False-SB on the form

• $R_{False} = \sigma T_2^4 - \sigma T_1^4$

expressing the transfer of energy from 2 to 1 as the difference of two gross flows with different signs. We see that False-SB arises by rewriting an integral with positive integrand as the difference of two integrals of different signs as follows:

• $\int_{T_1}^{T_2} f^2 df = \int_0^{T_2}f^2df - \int_0^{T_1}f^2df$,

where the lower integration limit $0$ could be replaced by any positive number smaller than $T_1$. False-SB arises when giving this formal mathematical manipulation a physical meaning stating that one-way net flow is the difference of two-way gross flows, with the flow from 1 to 2 violating the 2nd law of thermodynamics and involving an arbitrary constant.

False-SB thus arises by an ad hoc translation to physics of a mathematical operation which results in a violation of the 2nd law of thermodynamics.

Accordingly False-SB is not found in physics literature, but has appeared outside physics as an ad hoc free invention by climate scientists for the purpose of selling CO2 alarm.

Stability of True-SB vs False-SB

The different stability properties of the two versions discussed in recent posts of Stefan-Boltzmann's radiation law, True-SB and False-SB, can be exhibited by comparing the stability of the following simplified SBs:

1. $R = T_1 - T_2$
2. $R = T_3$ where $T_3 = T_1 - T_2$,

where $R$ is the heat flow between two bodies of temperature $T_1$ and $T_2$, expressed in two different forms: 1. as the difference of two-way gross flows and 2. as one-way net flow.

Stability concerns the effect on the output $R$ from perturbations of input ($T_1$, $T_2$ and $T_3$). Denoting the perturbation of $T_i$ by $dT_i$ for $i=1,2,3$, it is natural to assume a bound $E$ on relative perturbation of the form

• $\frac{\vert dT_i\vert}{T_i}\le E$ for $i=1,2,3$.

Estimating the effect $dR$ on the output $R$ from the $dT_i$, we have

$\vert dR\vert \le \vert dT_1\vert +\vert dT_2\vert = \frac{\vert dT_1\vert}{T_1} T_1 + \frac{\vert dT_2\vert}{T_2} T_2 \le ET_1 + ET_2=E(T_1+T_2)$,

which is to be compared with

$\vert dR\vert \le \frac{\vert dT_3\vert}{T_3}T_3 \le E T_3$.

If $T_3$ is much smaller than $T_1+ T_2$, then the second bound is much smaller which expresses that 2. is more stable than 1. or that 1. is more unstable than 2.

A particular case is given by $T_1=T_2$ with $T_3 =0$. This is the case of two blackbodies of equal temperature which according to 2. is very stable, but according to 1. much less stable.

The different stability gets expressed in different assessments of climate sensitivity, from 1. unstable with alarm to 2. stable without alarm.

Question to Curry about Stefan-Boltzmann and DLR

In a recent post Judy Curry lets Grant W Petty speak out with reference the ongoing discussion on my blog with Petty. Curry assists Petty with:

• I will continue to (barely) follow Claes Johnson’s work to see if he is able to come with anything interesting or publishable.

Here is something interesting Judy of main importance to CO2 alarmism: In recent posts on Downwelling Longwave Radiation DLR and Stefan-Boltzmann's radiation law (SB) I have shown that CO2 alarmism is based on a version of SB without support in physics literature, a version I have referred to as False-SB, and I have compared False-SB with a correct version named True-SB.

Since you take up my work on your blog in critical terms, I think I have reason to ask you to articulate your critique of my work and in particular state if you consider False-SB to be true with a solid support in theoretical physics and experiment. Is it so? Or do consider my critique to be well founded?

Petty on DLR 4

Here is a reaction by Prof Petty on my question True-SB or False-SB by Experiment:

1. If you're going to publicly blog about what I have said in a non-public email exchange, at least do both me and your readers the courtesy of honestly representing what I said.
2. You wrote "The argument of Prof Petty is now the following: If there is no experiment in sight capable of making a distinction between True-SB and False-SB, it must mean that if True-SB is true then False-SB is equally true. Is this a correct scientific argument?"What I in fact said was quite different, as anyone who actually read my message will agree. I said that if the difference can't be detected experimentally, then "it matters not a whit for climate."
3. You argue in your blog that the difference does matter for "stability aspects." And I return to my original claim, which is that if it matters in any way for the response of the climate system, it must also be experimentally detectable.
4. Again, please describe a realizable experiment in which a measurement of X yields an outcome of Y according to one theory and an outcome of Z according to the other. If you cannot, then I claim you are engaging in mere sophistry.

My answer:

• It is not up to me to prove that your False-SB is not true.
• It is up to you to prove that the False-SB you are using is true.
• You have given a proof of False-SB consisting of applying True-SB twice, and I have shown that you cannot do that because you are using True-SB in way which is not consistent with the proof of True-SB. Your proof of False-SB is incorrect.
• It is up to you to give an experiment recording a difference between False-SB and True-SB. If you cannot do that it means that your False-SB is identical with the True-SB and then False-SB can be removed from the discussion completely, unless you insist on mere sophistry.
• Do you see what I am saying?

Here is the response from Prof Petty:

• Claes, It's hard enough for me to find the time (and justification) to engage in one online debate. I'd be a fool to open a second front.
• I plan to spend this nice Fall weekend with my neglected family and, maybe, raking leaves. I'd like to cordially invite everyone else to do the same. Grant

Well, well, maybe raking leaves is the best thing to do, but as a proof of False-SB it is not so convincing, I believe.

How to Measure Downwelling Longwave Radiation

Experimental setup for direct measurement of Downwelling Longwave Radiation DLR.

True-SB or False-SB by Experiment?

In recent posts I have compared a true form of Stefan-Boltzmann's radiation law describing one-way net radiative heat transfer between bodies of different temperature, named True-SB, and an incorrect form not described in physics literature describing net flow as the difference between two-way gross flows, named False-SB, in communication with Prof Grant W. Petty claiming that False-SB is true.

Prof Petty asks if it possible to set up an experiment showing that False-SB is false? Maybe, but since False-SB describes a fictitious non-physical two-way flow, the experiment would amount to prove the non-existence of a certain phenomenon, and proving non-existence is in general much more difficult than proving existence. Existence is proved by exhibiting the object claimed to exist, while non-existence requires a search through all possibilities which may well be impossible.

Further, any test observing the net flow, which is the only flow which can be observed directly, will not be a disproof of False-SB.

The argument of Prof Petty is now the following: If there is no experiment in sight capable of making a distinction between True-SB and False-SB, it must mean that if True-SB is true then False-SB is equally true. Is this a correct scientific argument?

No, it is not correct, because even if the two versions give the same net flow, they have fundamentally different stability aspects, and stability is essential in the basic applications of SB in climate science concerning climate sensitivity, which is global warming under a small

perturbation of radiative forcing. The different stability is displayed in comparing net with the difference of gross quantities in an equality such as

• 0 = 100 - 100.

Here the net (flow) is 0 (two bodies of equal temperature), while gross flow is 100. The net flow on the left hand side remains small under small perturbations, while a small relative perturbation of gross flow (small relative change of the temperature of one of the bodies), may turn the right hand side into 1, which is an infinite inflation of 0.

True-SB and False-SB describe vastly different physics (one-way vs two-way heat transfer) and

the fact the the net flow of False-SB is the same as in True-SB, is not evidence that False-SB is true.

What is required by any scientist claiming that False-SB is true, like Prof Petty, is direct theoretical and experimental verification that False-SB is true, but both are missing. It is not enough to say that since the net flow is the same as in True-SB, also False-SB must be true. This is not science, only pseudo-science.

The following question presents itself: If now True-SB and False-SB describe the same net flow, and the only thing that matters is net flow, why cannot climate scientists like Prof Petty be content with the True-SB but instead so ardently have to insist that False-SB is true?

Yes. you are right: The stability aspect of False-SB serves the purpose of selling CO2 alarmism

by inflating something neglible to something alarming. But alarm based on pseudo-science is pseudo-alarm.

Is CMB Heating the Earth?

The Cosmic Microwave Background Radiation (CMB) is thermal radiation in the radio spectrum filling the observable universe with an almost uniform glow at 2.75 K as a relic of Big Bang.

Is CMB a form of Downwelling Longwave Radiation (DLR) to be added to the incoming radiation from the Sun in an energy budget for the Earth with atmosphere?

CO2 alarmists believing in a False Stefan-Boltzmann Law (False-SB) with two-way radiative transfer of heat energy between bodies of different temperature, would say Yes: CMB is a form of DLR which heats the Earth. The weak glow at 2.75 K is heating the globe.

Scientists using a True-SB, with only one-way transfer from hot to cold, would say No: There is only transfer of heat from the Earth to the cosmic background at 2.75 K.

What do you say? Yes or No? Is the colored picture of CMB a proof that CMB heats the Earth?

False SB Not Part of Physics Literature

The scientific explanation of the greenhouse effect of climate science.

Making a little field study to see how text books present (Yes) or not present (No) the False-SB (False-Stefan-Boltzmann Law) discussed in previous posts, we find:

• Atmospheric Radiation: Theoretical Basis by Goody and Yung: No
• Radiative Heat Transfer by Modest: No
• Radiative Transfer by Chandrasekhar: No
• 3D Radiative Transfer in Cloudy Atmospheres by Marshak-Davis: No
• An Introduction to Radiative Transferby Peraiah: No
• Radiative Transfer in the Atmosphere and Ocean by Thomas-Stamnes: Yes
• An Introduction to Atmospheric Physic by Andrews: Yes
• Fundamentals of atmospheric radiation by Bohren-Clothiaux: Yes
• A First Course in Atmospheric Radiation by Petty: Yes
• An Introduction to Atmospheric Radiation by Liou: Yes
• An Introduction to Atmospheric Physics by Fleagle-Businger: Yes
• Assessing Climate Change by Rapp: Yes
• UN Climate Change Science Compendium 2009: Yes
• Advancing the Science of Climate Change 2010, NRC: Yes
• The Greenhouse Effect by Lindzen: Yes
• IPCC TAR 2007: Yes.

The result can be generalized as follows:

1. In a general basic physics texts on radiative transfer not connected to climate science, there is no reason to introduce the False-SB, because radiative transfer is one-way and False-SB is two-way. Accordingly, physics literature on radiative transfer does not mention False-SB.

2. Most texts on climate science including atmospheric radiation present False-SB, because most texts connect to CO2 alarmism and False-SB serves as the scientific basis of alarmism by suggesting that global climate is sensitive to small perturbations of radiative forcing.

In short: False-SB is a free invention of CO2 alarmism, and is not part of basic physics literature. False-SB is thus pseudo-science. Probably the biggest scientific fraud all times.

For an list of the use of False-SB in academic teaching see Consensus Science compiled by Alan Siddons.

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.

Climate Alarmism Based on False Stefan-Boltzmann Law

The recent posts on Downwelling Longwave Radiation DLR give strong evidence, kindly supplied by Prof Grant W Petty, that climate alarmism of global warming is based on a false version of Stefan-Boltzmann's radiation law (SB), a version which lacks support in physics literature.

The original true-SB reads:

• R = sigma (T^4 - T_b^4)

where R is the radiance from a blackbody at temperature T into a background at temperature T_b < T and sigma is Stefan-Boltzmann's (positive) constant.

The false-SB reads:

• R =R_out - R_in,
• where R_out = sigma T^4 and R_in = sigma T_b^4.

Prof Petty claims that false-SB is obtained by formally applying true-SB with T_b = 0 and with T = 0, and then adding up the results. This is the same as formally rewriting true-SB in the form

• R = sigma T^4 - sigma T_b^4,

using formally the distributive law of algebra:

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

According to Prof Petty, the false-SB is obtained by applying true-SB twice, or by using the distributive law. Prof Petty then expresses a consensus of (alarmist) climate scientists.

What Prof Petty is doing seems like a trivial operation, under the assumption that the trivial operation is permissible from physics point of view, or that it is permissible to use the distributive law from physics point of view. Prof Petty shows that he is firmly convinced that the trivial operation is permissible, because it is so trivial.

But triviality is not a sufficient condition for truth. The truth is that the operation, as trivial it may be, is not permissible:

It is not permissible to formally apply true-SB twice with T_b = 0 and with T = 0, because the assumption of true-SB is that T > T_b and this assumption is violated in the case T = 0.

It is not permissible to attribute to the distributive a physical meaning, unless this meaning is specified, and it is not.

The conclusion is that climate alarmists regularly, apparently without thinking, are using a false-SB.

Even worse, climate alarmists use the false-SB as the scientific evidence that the trace gas CO2 can cause dangerous global warming. The false-SB serves alarmism by offering the instability

required to make it credible that a small cause (trace gas) can have a big effect (dangerous global warming). It is like writing

• R = 10 = 100 - 90 = R_out - R_in

and then talking about perturbations, of say 1%. A 1% perturbation of net flow R (= 0.1) can then be turned into 1% perturbation of gross flow R_out (= 1), with an inflation factor of 10.

This is precisely the argument used to produce the climate sensitivity of 3 C upon doubling of CO2 of IPCC alarmism , which is 10 times too big. It is illustrated in the Kiel-Trenberth energy budget with its backradiation/DLR and

• R_out = 339/392 and R_in = 321 = DLR with R_out - R_in much smaller than R_out.

In short, climate alarmism is based on a false SB law, which allows a false 10-fold inflation of effects of doubled CO2.

For a more detailed presentation, take a look at my recent talk:

• CO2 Alarmism Debunked by Mathematics

and the upcoming book Mathematical Physics of Blackbody Radiation based on the article

Computational Blackbody Radiation in the book Slaying the Sky Dragon.

The use of false-SB is illustrated e.g. in

• Idealized Greenhouse Model
• The Global Energy Balance
• The Greenhouse Effect

and many other sources presenting the so-called greenhouse effect.

Of course, it is natural to pose the following questions:

• Is it really possible that a false-SB is used by so many climate scientists?
• What are physicists saying? After all, physicists are responsible for SB.
• If many scientists agree, then they must be correct?

I will report if some answers come in...

Petty on DLR 3: Incorrect Science Exposed

Here is the response by Prof Petty on the previous post Petty on DLR 2 with my question

• Who proved that (SB-invented) is a consequence of (SB-original)?

Prof Petty writes:

• First, tell me who told you could apply Newton's 2nd law of motion to your car? Newton didn't know about cars. And cars carry passengers -- - who told you can apply F=ma to a loose collection of several bodies simultaneously? What kind of free invention is it to use a physical law on a system it wasn't derived for?
• And how about the law of conservation of energy? Are you sure energy conservation applies to EVERY system, including those it was never empirically tested on? Give me an original source that proves that energy is conserved in the orbit of a satellite. I can't personally build and launch a satellite, so I don't believe satellites exist.
• Yes, let's see how far your science gets without the ability to actually APPLY the universal laws that have been established. Your science is a sterile one of naked laws lacking in any legitimate application to any situation other than the specific ones envisaged by their namesakes. Only falling apples experience gravity. Only trains can be used to observed relativity.
• Thanks for confirming what I had suspected but refused to completely accept until now -- that your concept of physics is so far removed from mine that further dialogue is hopeless.
• I'm seriously sorry for the time I've wasted on the lot of you.
• Any more messages from anyone in this list get filtered.

What to say? Well, Prof Petty shows a common trait of climate scientists, to get upset and scream instead of discussing science.

Prof Petty illustrates how important it is to understand the proof of a mathematical theorem, to be able to correctly apply the theorem. If the proof is not understood, then it there is a high risk that the theorem will be applied in a way that is not allowed by the proof.

The SB law here named (SB-invented) used in climate science is supposed to be the result of applying an original SB law named (SB-original) twice. But the proof of (SB-original) does not allow a blind application twice. The proof only covers applying the law once to a specific situation. If double application was allowed, then it would be able to modify the proof of (SB-original) into a direct proof of (SB-invented). But this proof is missing in the literature.

I have given a new proof of (SB-original) (in the Skydragon book, see also the upcoming book Mathematical Physics of Blackbody Radiation) which can be extended to a proof of a SB law of the form:

• R = sigma (T^4 - T_b^4)

but not to a proof of (SB-invented). In this form there is no difference of gross flows, only net flow. This is highly important when considering perturbations in connection to assessment of climate sensitivity.

It would be good for the discussion if Prof Petty was willing to read my proof and reflect about

the potential danger of blindly applying a physical law without proper understanding of the conditions for the validity of the law, without understanding the rationale of its justification.

Prof Petty shows his lack of understanding fundamentals of science by exclaiming:

• What kind of free invention is it to use a physical law on a system it wasn't derived for?

This is precisely what I am talking about: You are not as a scientist allowed to apply a law to a situation for which it is not intended/derived for. If you do that, you may cause great damage and you may be responsible.

If a bridge engineer applies a formula to a case for which it is not intended and the bridge falls down, then the engineer may face a legal process. If a scientist applies a law to a case for which it is not intended (not covered by its proof) and the result is false global warming alarm,

then the scientist may face a legal process. To send a false alarm about a fire to the fire station by interpreting the setting Sun as a great fire, will not be appreciated.

In any case the discussion with Prof Petty has been illuminating and I thank him for that.