The Secret of Radiative Heat Transfer vs CMB and Big Bang

A main challenge to physicists at the turn to modernity 1900 was to explain radiative heat transfer as the process of emission, transfer and absorption of heat energy by electromagnetic waves described by Maxwell's equations. The challenge was to explain why real physics avoids an ultra-violet catastrophe with radiation intensity going to infinity with increasing frequency beyond the visible spectrum. 

More precisely, the challenge was to uncover the physics of a blackbody spectrum with radiation intensity scaling with $T\nu^2$ with $T$ temperature and frequency $\nu\le\nu_{max}$ with $\nu_{max}$ a cut-off frequency scaling with $T$, and intensity quickly falling to zero above cut-off. 

Planck as leading physicist of the German Empire took on the challenge and after much struggle came up with an explanation based on statistics of energy taking the above form as Planck's Law, which has served into our time as a cover up a failure to explain a basic phenomenon in physical terms. 

Computational Blackbody Radiation offers an explanation in terms of finite precision physics setting a cut-off (scaling with temperature) on the frequency of emission from coordinated oscillations of an atomic lattice, with uncoordinated atomic motion stored as heat energy.

In this analysis heat is transferred from a body of higher temperature  to a body of lower temperature through a resonance phenomenon analogous to the resonance between two tuning forks. The essence can be described in terms of a  forced acoustically weakly damped harmonic oscillator:

• $\dot v(t)+\nu^2u(t)+\gamma v(t)=f(t)=sin(\bar\nu t)$ for $t>0$                    (1)

where $u(t)$ is displacement at time $t$, $v(t)=\dot u(t)$ is velocity, the dot represents derivative with respect to time $t$, $\nu$ is the frequency of the harmonic oscillator and $\bar\nu\approx\nu$ that of the forcing. For radiation the damping term takes the form $\gamma\ddot v(t)$. 

Mathematical analysis shows assuming small damping with $\gamma << 1$ and near resonance with $\nu\approx\bar\nu$ and integration over a period:

• $Output = \gamma \int v^2(t)dt \approx \int f^2(t)dt = Input$         (2)
• Velocity $v(t)$ out-of-phase with $f(t)$.                                                                (3)

Even if it looks innocent, (2) represents the essence of Planck's Law with (3) expressing basic physics: Out-of-phase means that the interacting between forcing and oscillator corresponds to a "pumping motion" with the forcing balanced mainly by the harmonic oscillator itself and not the damping. In the acoustic case $T=\int v^2(t)dt$ and thus $Output =\gamma T$, which in the case of radiation takes the form $Output = \gamma T\nu^2$ or Planck's Law. 

Sum up:

• Radiative balance between two bodies of equal temperature is expressed by (2).
• Heating of a body B1 with lower temperature from body B2 of higher temperature from frequencies above cut-off for B1.  
• High frequency cut-off effect of finite precision physics and not statistics.
• Blackbody spectrum is continuous (all frequencies) and requires atomic lattice. 
• A gas ha a line spectrum with selected frequencies, which is not a blackbody spectrum.
• Cosmic Microwave Background radiation as a perfect blackbody spectrum of an after-glow of Big Bang without atomic lattice appears as very speculative, with Big Bang itself as even more speculative beyond experimental confirmation.  

Temperature or Radiative Flux? Pressure or Convective Flux?

The prime evidence put forward to support global warming alarmism is a measurement of the spectrum of  Outgoing Longwave Radiation OLR from the Earth into cold empty space showing that total OLR is 1% less than total incoming short wave radiation from the Sun with the message that the Earth is heating up. 

The measurement is done from satellites (AIRS and ISIS) looking down on the atmosphere using instruments in the form of spectrometers supposedly measuring radiative fluxes over a range of infrared frequencies forming the spectrum, see previous posts on OLR.  The instruments use bolometers based on thermopiles sensitive to temperature and compute radiative fluxes using complex software for radiative heat transfer such as Modtran. The instruments thus directly measure temperature and then report radiative flux after postprocessing. To confirm global warming,  better accuracy than 1% is required for total OLR and also of course for total incoming radiation. Is this possible?

To compute radiative flux from input of temperature using software for radiative heat transfer requires input of coefficients of emissivity, absorptivity and transmissivity, and so has serious issues as concerns accuracy. 

To see a basic issue, let us compare with a more familiar setting of seeking to compute the fluid flux in a pipe or around an object from reading pressure. We then recall that pressure can be read by a pitot tube:

where the left open end is inserted into the fluid and so takes on the stagnation pressure or total pressure in the fluid passing by and then is read by a nanometer to the right. We understand that measuring pressure can be done with high precision, but if we now ask about the total convective fluid flux, we will have to supply additional information about the nature of the flow. If the flow is steady, inviscid, incompressible and irrotational, then Bernouilli's  Law can be used to compute fluid velocity and so convective flux, but that is a very special case. 

We thus see that reading temperature by a thermopile or pressure by a Pitot tube can be done directly by an instrument for which the physics is transparent. 

On the other hand, to report radiative/convective flux from reading of temperature/pressure is a complicated issue requiring detailed additional information, which may not be available. 

Direct measurement of total flux by some form of capturing technique like that in an anemometer, also is subject to very big uncertainties.  

Supporting global warming on an assessment of OLR measured to less 1% precision lacks credibility. 

How to Generate Heat Energy

We recall from a previous post:

• Heat energy can be generated from large scale kinetic energy by compression. 
• Kinetic energy can be generated from heat energy by expansion.

More precisely, we saw in the previous saw that heat energy at high temperature can generate useful mechanical work. Heat energy at high temperature can be created by nuclear/chemical reactions. 

Heat energy typically at lower temperatures also appears as losses from electrical currents subject to resistance, fluid motion subject to turbulent/laminar viscosity and friction between solid bodies. These losses appear as substantial, unavoidable and irreversible as expressions of a 2nd Law.

We have seen that heat energy $\sim T\nu^2$ of frequency $\nu$ carried by an atomic lattice of temperature $T$ subject to high-frequency cut-off $\nu <\frac{T}{h}$ expressing ordered synchronised atomic oscillation or kinetic motion, can be radiated. Here $h$ is a constant. 

We can view turbulent dissipation in fluid flow as a form of high-frequency forcing above present cut-off which cannot be reradiated and so is absorbed as internal energy in the form of unordered small scale kinetic energy. We can similarly view viscosity and friction as forms of high-frequency forcing supplying internal energy. 

The contribution to internal energy increases the temperature and so allows unordered small scale motion to be synchronised to higher frequency and then radiated.  

The key is thus that turbulent, viscous and frictional dissipation all represent high-frequency forcing above   present cut-off, which cannot be represented and reradiated and so shows up as internal energy as small scale kinetic energy. 

Rubbing hands is one way to transform large scale kinetic motion into small scale kinetic motion as heat energy. The brakes on your car work the same way. 

Exergy as Energy Quality

Kinetic energy, electrical energy, chemical and nuclear energy can all be converted fully into heat energy, while heat energy can only be partially converted back again. This is captured in the 2nd Law of Thermodynamics. We can thus say that heat energy is of lower quality compared with the other forms. More generally, the term exergy is used as a measure of quality of energy of fundamental importance for all forms of life and society as ability to do work.

We can make this more precise by recalling that the quality of heat energy comes to expression in radiative and conductive heat transfer from a body B1 of temperature $T_1$ to a neighbouring body B2 of lower  temperature $T_2<T_1$ in basic cases according to Stefan-Boltzmann's Law or Fourier's Law:

• $Q = (T_1^4-T_2^4)$            (SB)
• $Q = (T_1-T_2)$                    (F)

with $Q$ heat energy per time unit. Heat energy of higher temperature thus can be considered to have higher quality than heat energy of lower temperature, which of course also plays role in conversion of heat energy to other forms of energy. The maximal efficiency of a heat engine operating between $T_1$ and $T_2$ and transforming heat energy to mechanical work, is equal to $\frac{T_1-T_2}{T_1}$ displaying the higher quality of $T_1$.

Heat energy at high temperature is the major source for useful mechanical work supporting human civilisation, while heat energy at lower temperatures appears as a useless loss e g in the cooling of a gasoline engine.

But what is the real physics behind (SB) and (F)? This question was addressed in a previous post viewing (F) to be a special case of (SB) with the physics behind (SB) displayed in the analysis of Computational Blackbody Radiation. 

The essence of this analysis is a high-frequency cut-off $\frac{T}{h}$ allowing a body of temperature $T$ to only emit frequencies $\nu <\frac{T}{h}$, where $h$ is a constant. This allows a body B1 of temperature $T_1$ to transfer heat energy to a body B2 of lower temperature $T_2$ via frequencies $\frac{T_2}{h}<\nu <\frac{T_1}{h}$, which cannot be balanced by emission from B2.  

High frequency cut-off increasing linearly with temperature represents Wien's displacement law (W), giving improved exergy with increasing temperature.

The high-frequency cut-off can be seen as an expression of finite precision limiting the frequency being carried and emitted by an oscillating atomic lattice in coordinated motion, with frequencies above cut-off being carried internally as heat energy as uncoordinated motion. 

Higher temperature thus connects to higher quality heat energy or better exergy. The standard explanation of this basic fact is based on statistical mechanics, which is not physical mechanics. 

PS Radiative heat transfer without high-frequency cut-off would boil down to (F), while (SB) is what is observed, which gives support to (W).

Secret of Conductive and Radiative Heat Transfer

This is a continuation of the previous post on Heat Conduction in Solids as Radiative Heat Transfer with  clarifying analysis from Mathematical Physics of Blackbody Radiation and Computational Blackbody Radiation.

The key aspect of both conductive and radiative heat transfer is interaction in a coupled system of weakly damped oscillators of different frequencies tending to an equilibrium with all oscillators having the same temperature as the system temperature. The damping can be frictional (1st order time derivative) or radiative (3rd order time derivative) 

There are two main questions: (i) Why do different systems take on the same temperature? (ii) Why do oscillators with different frequencies in a system take on the same temperature?  

The answer is hidden in the interaction between incoming radiation, oscillator and outgoing radiation in a weakly radiatively damped oscillator analysed in detail in the above texts. The essence is that under near resonance between incoming frequency and oscillator frequency,  

• incoming radiation is balanced by outgoing radiation plus internal heating. 

This is a non-trivial basic fact reflecting that the forcing and oscillator are out-of-phase with a shift of half a period as a consequence of small radiative damping and near resonance. 

Two coupled oscillators thus interact with outgoing from one oscillator acting as incoming for the other and vice versa and so are led to take on the same temperature, which is then spread over the oscillators of a system and also over systems. 

The essential components in this equilibration process are thus

• weakly damped oscillators generating outgoing radiation and internal heating 
• out-of-phase balance between forcing and damping from near resonance
• high-frequency cut-off increasing with temperature from finite precision computation.  

This analysis connects to Planck's derivation of his law of radiation with statistics replaced by finite precision thus replacing non-physics by physics. 

Heat Conduction in Solids as Radiative Heat Transfer

What is the physics of heat conduction in a solid like a metal? The trivial story is that "heat flows from warm to cold" or "there is a flux of heat from warm to cold" which scales with the temperature difference or gradient. 

But heat is not a substance like water in a river flowing from high-altitude/warm to low-altitude/cold, which connects to the caloric theory and also to phlogiston theory presenting fire as form of substance, both debunked at the end of the 18th century. 

In any case there is a law of physics named Fourier's Law:

• $q =- \nabla u$          (F)

which combined with a law of conservation 

• $\nabla\cdot q = f$

leads to the following heat equation (here in stationary state for simplicity) in the form of Poisson's equation

• $-\Delta u = f$.                    (H)

where $u(x)$ is temperature and $f(x)$ heat source depending on a space variable $x$, and $q(x)$ is named "heat flux" although it has no physical meaning; heat is not any substance which flows or is in a state of flux. 

Let us now seek the physics of (F) in the case of metallic body as a lattice of atoms, and so seek an explanation of the observation that the temperature distribution $u(x)$ of the body tends to an equilibrium state with $u(x)=U$ with $U$ a constant (assuming no interaction with the surrounding and no internal heating for simplicity). 

We thus ask: 

• What is the physics of the process towards equilibrium with constant temperature?
• How is heat transferred from warm to cold?
• Why is (F) valid?

We then recall our analysis of radiative transfer of energy at distance in a system of bodies/parts separated in space which (without external forcing) leads to an equilibrium state with all bodies having the same temperature, based on the following physical model:

• Each body is a vibrating lattice of atoms described by a wave equation with small radiative damping. 
• The bodies interact by electromagnetic waves through resonance. 
• There is a high-frequency cut-off increasing linearly with temperature with the effect that heat transfer mediated by electromagnetic waves between two bodies, is one-way from high temperature to low temperature. 

The key is here the high-frequency cut-off increasing with temperature, which makes heat transfer one-way. The cut-off can be seen as a form of finite precision threshold allowing coordinated lattice vibration only below cut-off, thus allowing a high temperature lattice to carry higher frequencies. It is like a warmed-up opera soprano being able to reach higher frequencies.

We can view metallic body as a system composed of parts/atoms interacting by 

electromagnetic waves at small distance. 

Heat conduction will then come out as a special case of electromagnetic heat transfer 

between atoms of different temperature with high-frequency cut-off guaranteeing one-way transport as expressed by (F) and exposed above. 

Note that the reference text Conduction of Heat in Solids by Carslaw and Jaeger presents (F) as an ad hoc physical law without physics.

Recall that the standard explanation of radiative heat transfer from warm to cold is based on statistics without physics, which if used to explain heat conduction would again invoke statistics without physics thus not very convincing. 

Also note that the standard explanation of heat transfer in a gas involves collisions of molecules of different kinetic energy, which is not applicable to a metal with atoms in a lattice.

PS1 Fluid flow in a river from higher to lower altitude is driven by pressure. "Heat flow" from warm to cold is not driven by pressure and so the physics is different. 

PS2 Also compare with one-way osmotic transport of material driven by pressure. 

2nd Law or 2-way Radiative Heat Transfer?

In the present discussion of the 2nd Law of Thermodynamics let us go back to this post from 2011 exposing the 19th century battle between 1-way transfer (Pictet) vs 2-way transfer (Prevost) of heat energy by radiation playing a central role in climate science today. 

In 1-way transfer a warm body heats a colder body in accordance with the 2nd Law. 

In 2-way heat transfer both warm and cold bodies are viewed to heat each other, but the warm heats more and so there is a net transfer of heat energy from warm to cold. But a cold body heating a warm body violates the 2nd Law of thermodynamics, and so there is something fishy here. 

Yet the basic mathematical model of radiative heat transfer in the form of Schwarzschild's equation involve 2-way transfer of heat energy, in apparent violation of the 2nd Law. 

I have discussed this situation at length on this blog with tags such as 2nd law of thermodynamics and radiative heat transfer with more on Computational Blackbody Radiation.

If you worry about the 2nd Law, you can ask yourself how 2-way radiative heat transfer is physically possible, when it appears to violate the 2nd Law? What is false here: 2nd Law or 2-way heat transfer?

What is your verdict? 

The 2nd Law as Radiative Heat Transfer

The 2nd Law of Thermodynamics states that heat energy $Q$ without forcing, is transferred from a body of temperature $T_1$ to a body of temperature $T_2$ with $T_1>T_2$ by conduction according to Fourier's Law if the bodies are in contact: 

• $Q =\gamma (T_1-T_2)$ 

and/or by radiation according Stephan-Boltzmann-Planck's Law if the bodies are not in contact as radiative heat transfer: 

• $Q=\gamma (T_1^4-T_2^4)$        (SBP)

where $\gamma > 0$.

The energy transfer is irreversible since it has a direction from warm to cold with $T_1>T_2$. It is here possible to view conduction as radiation at close distance and thus reduce the discussion to radiation. 

We can thus view the 2nd Law to be a consequence of (SBP), at least in the case of two bodies of different temperature: There is an irreversible transfer of heat energy from warm to cold. 

To prove 2nd Law for radiation thus can be seen to boil down to prove (SBF). This was the task taken on by the young Max Planck, who after a long tough struggle presented a proof in 1900, which he however was very unhappy with, since it like Boltzmann's H-theorem from 1872 was based on statistical mechanics and not classical deterministic physical mechanics.

But it is possible to prove (SBF) by replacing statistics with an assumption of finite precision computation in the form of  Computational Blackbody Radiation. Radiative heat transfer is here seen to be geared as a deterministic threshold phenomenon like a semi-conductor allowing heat transfer only one-way from warm to cold. 

Another aspect of radiation is that it is impossible to completely turn off or block by shielding of some sort. It connects to the universality of blackbody radiation taking the same form independent of material matter as shown here. 

We are thus led to the following form of the 2nd Law without any statistics:

• Radiative heat transfer from warm to cold is unstoppable and irreversible. 

The finite precision aspect here takes the form of a threshold, thus different from that operational in the case of turbulent dissipation into heat energy connecting to complexity with sharp gradients as discussed in recent posts.

PS To learn how statistical mechanics is taught at Stanford University by a world-leading physicist, listen to Lecture 1 and ask yourself if you get illuminated:

• Statistical mechanics is useful for predictions in cases when you do not know the initial conditions nor the laws of physics.

2nd Law for Radiative Heat Transfer as Finite Precision Physics

Transfer of heat energy from warm to cold by electromagnetic waves.

This is a continuation of recent posts on the 2nd Law of Thermodynamics.

There is a 2nd Law for radiative heat transfer expressing:  

• Heat energy is transferred by electromagnetic waves from a body with higher temperature to a body with lower temperature, not the other way.  (*) 

Why is that? Standard physics states that it is a consequence of Plank's law of radiation based on statistics of energy quanta, as an analog of Boltzmann's proof of a 2nd Law based on statistical mechanics. The objections raised to Boltzmann's proof carry over to that of  Planck, who was very unhappy with his proof but not as unhappy as Boltzmann with his. 

An approach without statistics is presented on Computational Blackbody Radiation where (*) appears as a high frequency cut-off increasing with temperature. The effect is that only frequencies above cut-off for the body with lower temperature have a heating effect resulting in one-way transfer of heat from warm to cold. For more details check-out this presentation. 

The high-frequency cut-off can be seen as an expression of finite precision increasing with temperature of atomic oscillation as heat energy. One-way heat transfer is thus a threshold phenomenon connected to finite precision.

Similarly, the photoelectric effect can be explained as a threshold phenomenon connected to finite precision, where only light of sufficiently high frequency can produce electrons. 

A 2nd Law based on finite precision physics thus can serve a role both in both fluid mechanics, and electromagnetics,  and also quantum mechanics as discussed in this post.  

In other words, finite precision physics in analog or digital form appears as the crucial aspect giving  meaning to a universal 2nd Law, which is missing in standard physics with infinite precision. 

The general idea is to replace statistical physics, which is not real physics, by finite precision computation, which can be both analog and digital physics. 

Of course, this idea will not be embraced by analytical mathematicians or theoretical physicists working with infinite precision...

Unphysical Schwarzschild Equation for Heat Transfer by Conduction

Schwarzschild's equation for heat transfer by radiation through the atmosphere is a two-stream upwelling-downwelling heat transfer model with the net heat transfer expressed as the difference between upwelling and downwelling streams. It is the basic model for radiative heat transfer used in climate models.

To get perspective on this two-stream model, let us see what a two-stream model for heat transfer by conduction instead of radiation would look like. We shall then compare with the standard one-stream model for vertical heat conduction through a horisontal layer, which is Fourier's Law:

• $q(x) = -\gamma\frac{T(x+dx)-T(x)}{dx}$   or $q(x) = -\gamma\frac{dT}{dx}$,    (1)

where $q(x)$ is net heat transfer/flow, $\gamma$ is a heat conductivity coefficient, $T(x)$ is temperature, $x$ is a vertical coordinate and $dx$ a small increment.

A two-way version of Fourier's Law takes the form

• $q(x) =\gamma\frac{T(x)}{dx} - \gamma\frac{T(x+dx)}{dx}$   (2) 

where the net heat transfer $q(x)$ is expressed as the difference of two gross streams  $\gamma\frac{T(x)}{dx}$ and $\gamma\frac{T(x+dx)}{dx}$ in opposite directions. But this two-way version is unstable because you are dividing temperatures $T(x)$ and $T(x+dx)$ by the small quantity $dx$, and so it is both uncomputable (by dividing by small $dx$) and unphysical since an unstable system does not have permanence over time. Note that the derivative $\frac{dT}{dx}$ does not suffer from the same instability since $dT$ is small.

We conclude that a Schwarzschild two-stream model for heat transfer by conduction is unstable, uncomputable and unphysical. Can we expect that Schwarzschild's two-stream model for heat transfer by radiation does not suffer from the same deficiency?  

It remains to formulate a stable one-stream model for heat transfer by radiation through an absorbing/emitting gas. An interesting such model is presented here, to which I will return.  

We can take the argument one step further by expressing conservation of heat energy in the form 

• $\frac{q(x)-q(x-dx)}{dx} = f(x)$  (3)

where $f(x)$ is a heat source. Combined with (2) this gives the model (with $\gamma =1$)

• $\frac{T(x)}{dx^2} - \frac{T(x+dx)}{dx^2} - \frac{T(x-dx)}{dx^2} +\frac{T(x)}{dx^2}=f(x)$  (4) 

which in the spirit of Schwarzschild splitting the source $f(x)$ into a contribution to "upwelling heat flux" $q_{up}$ and "downwelling heat flux" $q_{down}$, we can write as  

• $q_{up}(x)\equiv\frac{2T(x)}{dx^2} =\frac{f(x)}{2}$                                                   
• $q_{down}(x)\equiv\frac{T(x+dx)}{dx^2} + \frac{T(x-dx)}{dx^2}=-\frac{f(x)}{2}$ 

with net flow $q(x)=q_{up}(x)-q_{down}(x)$ balancing $f(x)$ according to (4). These are unstable unphysical equations that do not make sense. We compare with combining (3) with (1) into the standard heat equation 

•  $-\frac{d^2T}{dx^2} \approx -\frac{T(x+dx)-2T(x)+T(x-dx)}{dx^2}=f(x)$

which makes perfect sense as a differential equation allowing stable solution. We understand that Schwarzschild's two-stream model for heat transfer by conduction is no good. Is it then no good also for heat transfer by radiation?

Finite Precision Computation/Physics and Heat Energy

Euler CFD as a parameter free Theory of Everything ToE for slightly viscous incompressible fluid flow is a prime example of the idea of finite precision digital computation capable of simulating physics as a form of finite precision analog computation. Euler CFD captures turbulent flow from a principle of best possible digital solution of Euler's equations in a situation where exact (laminar) solutions are all unstable without permanence over time and so are unphysical and cannot be observed. 

The essence of turbulent flow captured by Euler CFD is the production of heat energy in turbulent dissipation from residual stabilisation in a situation where Euler residuals can be made small only in a weak mean value sense, but blow up in a strong pointwise sense. The dissipative mechanism thus expresses an impossibility to computationally resolve the flow because of finite precision, which in physical terms means production of heat energy as small scale unordered motion. 

Radiative heat transfer also involves an aspect of finite precision in the sense that a body viewed as a set of oscillators is capable of radiating only frequencies below a certain cut-off frequency scaling with temperature because synchronisation of the oscillators necessary for radiation is in finite precision impossible above cut-off. 

There is connection between turbulent flow and radiative heat transfer in that the heat energy generated in turbulent dissipation ultimately is released in radiation, and so gives a meaning to heat energy as unordered motion as unsynchronised oscillatory motion.  

Recall from the blog post 2nd Coming of the 2nd Law that finite precision computation/physics explains why certain processes are irreversible as processes where large scale kinetic energy/ordered motion is transformed into small scale kinetic energy/disordered motion, which cannot be reversed because the precision required to restore large scale order from small scale disorder is not there. This is like restoring all your manuscripts after a tornado has swept them into little pieces, or your hard disk has collapsed. 

Finite precision computation open an approach to the 2nd Law which is different from the standard based on statistics. Small scale disorder is the result of turbulent dissipation as a finite precision resolution of increasingly complex flow arising from flow instability, a resolution which cannot be reversed in finite precision.  It is like necessary (because storage is limited) chopping digits/details, which cannot be retrieved.

Heat energy as internal energy as small scale disordered motion is low quality energy in the sense that transformation to other forms of energy such as large scale motion comes with severe losses.  This puts limits to the efficiency of steam and combustion engines transforming heat energy into piston motion. On the other hand electric energy is high quality energy typically generated from large scale motion in generators allowing efficient electrical motors returning large scale motion. Heating by electricity is thus involves a form of quality degradation, which can be expensive, while heating by burning fossil fuels is efficient and cheap.    

What Is Heat Energy?

Heat energy is a central element in both thermodynamics and radiative heat transfer. But what is in fact heat energy?

The 1st Law of Thermodynamics states that the total energy as kinetic energy plus (internal) heat energy remains constant in a system (without chemistry/fission/fusion) with no energy exchange with its surrounding. The 2nd Law of Thermodynamics states that transformation of kinetic energy into heat energy is irreversible. 

The Planck-Stefan-Boltzman Law (PSB Law) expresses that the transfer of heat energy by electromagnetic radiation from a warmer body of temperature $T_w$ to a colder body of temperature $T_c<T_w$ scales with $T_w^4 -T_c^4$. 

Computational Thermodynamics and Computational BlackBody Radiation present a new approach to uncover the mysteries of both the 2nd Law of Thermodynamics and the PSB Law based on a principle of finite precision computation/physics. In  this setting heat energy takes the form of small scale unordered kinetic motion.

In thermodynamics kinetic energy thus takes the form of large scale ordered motion and small scale unordered motion which is the result of turbulent dissipation into heat energy. The 2nd Law expresses that the process of turbulent dissipation is irreversible because in finite precision unordered small scale motion cannot be coordinated into large scale ordered motion. Heat energy here appears as "internal energy" with limits set by the 2nd Law as concerns transformation to "external energy" as large scale kinetic motion.

In radiative heat transfer the temperature of a body determines a cut-off frequency scaling with temperature with heat energy as atomic vibrations with only frequencies below cut-off appearing in synchronized ordered form capable to generating outgoing radiation. Here the finite precision limit thus scales with the inverse of the temperature and the heat transfer from a warm to a cold body consist only of the frequencies above cut-off for the colder and below cut-off for the warmer. 

In both cases heat energy is a result of an impossibility arising from finite precision computation. In thermodynamics heat energy is unresolvable unordered small scale kinetic motion. In thermodynamics a body absorbs heat energy as unordered kinetic motion for frequencies above cut-off. 

In short, heat energy emerges as a rest product of finite precision computation/physics meeting unresolvable scales of motion. 

Even if now heat energy is a form of rest product, it does not mean that it cannot be recycled into useful energy to some extent. In thermodynamics a gas expanding into a larger volume creates turbulence which is turned into heat energy, which can be used to do work when expanding into an even bigger volume. In radiative heat transfer a colder body when heating up by absorbing heat in unordered form from a warmer body, increases its cut-off and so can radiate higher frequencies in synchronised ordered form.   

CO2 Global Warming Alarmism: Hour of Reckoning

Driving in the wrong direction on a one-way street, firmly believing it to be a two-way street, is stupid and potentially deadly hazardous for other people.

The US Environmental Protection Agency EPA has now cleansed its web page from CO2 global warming alarmism and US Energy Sec. Perry declares

• We should ‘renegotiate’ the Paris Climate Change Agreement,

This signals the beginning of the end of the CO2 alarmism driven by EU politicians and US Democrats:

• Trump may pull US out of Paris agreement within two weeks. 
• White House leaning toward exiting Paris climate pact

This is a victory for rational science showing that the "CO2 greenhouse effect" has been artificially

boosted to seemingly dangerous levels without proper scientific evidence, only in order to fit a certain political agenda. 

I feel happy to have contributed to this insight through an analysis of the unphysical nature of the concept of "back radiation" which is central to the proclaimed alarmingly big "CO2 greenhouse effect". 

You find "back radiation" in many books on atmospheric physics as one part of a "two-stream" radiative transfer model originally proposed by Schwarzschild in 1905 with net heat transfer warm-to-cold as the difference of two gross heat transfers warm-to-cold and cold-to-warm. See also History of Radiative Heat Transfer.

But what you find in many physics books is not necessarily true physics, and this is the case with two-stream radiative heat transfer, which is fake-science. This is because heat transfer cold-to-warm violates the 2nd law of thermodynamics. In the two-stream Schwarzschild equations this is present as an effect of unphysical absorption from unphysical back radiation. Schwarzschild formulated his model to allow analytical solution as first priority and did not worry about unphysical aspects. 

Two-stream radiative transfer is based on a mis-interpretation of Stefan-Boltzmann-Planck's Law $\sigma T^4$ as the radiative heat energy emitted by a black body of temperature $T$ Kelvin independent of the temperature of the environment of the body, while the physically correct interpretation is  radiative energy emitted into a background of temperature zero Kelvin. 

The radiative heat energy emitted by a black body of temperature $T$ in an environment of temperature $T_0$ is thus given by $\sigma (T^4-T_0^4)$ if $T_0\le T$. If $T_0>T$ then the body absorbs energy from the environment and emits no energy. 

The mis-interpretation of SBP law is widely spread and apparently accepted by many more or less prominent physicists. This is made possible by the fact that the standard derivation of the SBP law is based on statistics obscuring real physics. I have given an alternative derivation based on transparent physics exhibiting the mis-interpretation.  

CO2 alarmists like two-stream gross flow because small changes of gross flow can be big and support alarmism, while small changes of net flow will remain small and give no reason for alarm. And true radiative heat transfer is one-stream warm-to-cold. 

In short, the CO2 swindle is based on unphysical two-stream radiative heat transfer between the Earth surface and the atmosphere of size 300 W/m2 claimed to suggest a global warming alarm of 3 C, while the true net transfer is 10 times smaller about 30 W/m2, which can only suggest a harmless warming of 0.3 C. 

There is much evidence that CO2 alarmism is scientific swindle, a basic element being the unphysical idea of two-stream radiative transfer connected to a mis-interpretation of the SBP law. To be ignorant of physics may be inconvenient but to make a mis-interpretation of a physical law believing it to be true physics can be very dangerous; for example believing that a one-way street is a two-way street can be lethal...and the more convinced you are the more dangerous...

It is the responsibility of physicists to gard that basic physics of radiative heat transfer is correctly described in the physics literature.  Apparently physicists today have other priorities (like string theory and multiversa) and so the mis-interpretation of the SBP law as a basis for CO2 alarm has been able to survive under the wings of physics, but now the time of reckoning is here...as evidenced by EPA...

Murry Salby is today a leading skeptic to CO2 alarmism, but the mis-conception of two-stream radiative heat transfer was present in his 1996 book Fundamentals of Atmospheric Physics as a result of mis-management of fundamental physics in modern times allowing violation of the 2nd law of thermodynamics as the cornerstone of classical physics.

PS1 Schwarzschild's two-stream model for radiative heat transfer takes the following form for a horisontal slab atmosphere, with vertical coordinate $x$ with $x=0$ at the Earth surface and $x=X$ at the top of the atmosphere, in terms of a gross upward heat flux $F^+(x)$ and a gross downward heat flux  $F^-(x)$ satisfying the following advection-absorption equations for $0\lt x\lt X$:

• $\frac{dF^+}{dx} + F^+ = Q$               (1)
• $-\frac{dF^-}{dx} + F^- = Q$               (2) 

where $Q(x) =\sigma T(x)^4$ is supposed to express the SBP law with $T(x)$ the temperature at $x$ and $\sigma$ Stefan-Boltzmann's constant, and $x$ serves as an optical coordinate normalizing absorption. The atmosphere is supposed to be heated from below at $x=0$ by a heat source $H$, and the heat is radiatively transported to the top of the atmosphere from where it is radiated into outer space at 0 K. Conservation of heat energy gives the additional equation

• $F^+-F^- = H$,                                      (3)

from which follows by adding/subtracting (2) from (1) that $F^+ + F^-=2Q$ and $\frac{d(F^++F^-)}{dx}=-H$ and thus:

• $2Q(x) = H(X-x)+H$,                          (4)
• $F^+ =\frac{H}{2}(X-x)+H$
• $F^-=\frac{H}{2}(X-x)$                        

which determines the temperature profile $T(x)$. Schwarzschild's model resulting in linear $Q(x)$, is very simplistic. Only a model with $Q(x)$ constant could be more simplistic.

Schwarzschild's model (1-2) expresses conservation of upward and downward heat fluxes through a thin atmospheric layer radiating both upward and downward according to SBP in the form $Q(x) =\sigma T(x)^4$.

The model is unphysical because it is based on mis-interpretation of SBP and through the equation
$-\frac{dF^-}{dx} + F^- = Q$ introduces spurious absorption.

In a following post I will consider one-stream models for radiative transport based on real physics.

PS2 I have over the years had heated debates about back radiation and two-stream radiative with many people including Roy Spencer and Judy Curry and I have met the strong grip physics books, right or wrong, can have on peoples minds. Planck is primarily to be blamed because of his unphysical proof of the law of black body radiation using statistical arguments, which he himself did not believe in and was very unhappy with, but also secondarly all the leading physicists after Planck who uncritically have accepted what cannot be true physics.

I have many times met the reaction, when I express my view that two-stream radiative heat transfer to be unphysical, that people get upset and in anger block further communication. Thus the idea of two-stream radiative heat transfer has been protected from scrutiny allowing it to serve as a corner-stone of the "greenhouse effect" invented to serve CO2 global warming alarmism. 

        

Unphysical Basis of CO2 Alarmism = Hoax

CO2 alarmism is based on an unphysical version of Stefan-Boltzmann's Law and associated Schwarzschild equations for radiative heat transfer stating a two-way radiative heat transfer from-warm-to-cold and from-cold-to-warm with net transfer as the difference between the two-way transfers.

This is expressed as "back radiation" from a colder atmosphere to warmer Earth surface in Kiehl-Trenberth's Global energy budget (above) and in Pierrehumbert's Infrafred radiation and planetary temperature based on Schwarzschild's equations, presented as the physical basis of CO2 alarmism.

In extended writing I have exposed the unphysical nature of radiative heat transfer from-cold-to-warm as violation of the 2nd law of thermodynamics, see e.g.

• Mathematical Physics of Blackbody Radiation
• Unphysical Schwarzschild vs Physical Model for Radiative Transfer

Massive two-way radiative heat transfer between two bodies is unphysical because it is unstable, with the net transfer arising from the difference between two gross quantities, and the 2nd law says that Nature cannot work that way: There is only transfer from-warm-to-cold and there can be no transfer from-cold-to-warm. Radiative heat transfer is always one-way from-warm-to-cold.

CO2 alarmism is thus based on a picture of massive radiative heat transfer back-and-forth between atmosphere and Earth surface (see above picture), as an unstable system threatening to go into "run-away-global-warming" at slightest perturbation.  But there is no true physics behind this picture, only alarmist fiction. 

Real physics indicates that global climate is stable rather than unstable, and as such insensitive to a very small change of the composition of the atmosphere upon doubling of CO2. There is little/no scientific evidence indicating that the effect could be measurable, that is be bigger than 0.5 C.

Note that climate models use Schwarzschild's equations to describe radiative heat transfer and the fact that these equations do not describe true physics is a death-blow to the current practice of climate simulation used to sell CO2 alarmism.

So, when you meet the argument that Pierrehumbert is an authority on infrared radiation and planetary temperature, you can say that this is not convincing because Pierrehumbert is using incorrect physics (which also comes out by the fact that he forgets gravitation as the true origin of the very high temperature on the surface of Venus and not radiation).

If now CO2 alarmism is based on incorrect physics or non-physics, then it may be fair to describe it as "hoax".

Think of it: Suppose that "scientific consensus" through MSM is bombarding you with a message that the Earth has to be evacuated because there is imminent fear that the "sky is going to fall down" because Newton's law of gravitation says that "everything is pulled down". Would you then say that "since it is said so it must be so" or would you say that this is a non-physical misinterpretation of Newton's law?  Think of it!

The edX course Making Sense of Climate Science Denial is a typical example of the CO2 alarmism  based on the incorrect physics of "back radiation", which is forcefully trumpeted by the educational system,  as illustrated in the following key picture of the course:

Secret of Laser vs Secret of Piano

There is a connection between the action of a piano as presented in the sequence of posts The Secret of the Piano  and a laser (Light Amplification by Stimulated Emission of Radiation), which is remarkable as an expression of a fundamental resonance phenomenon.

To see the connection we start with the following quote from Principles of Lasers by Orazio Svelto:

• There is a fundamental difference between spontaneous and stimulated emission processes. 
• In the case of spontaneous emission, the atoms emit e.m waves that has no definite phase relation with that emitted by another atom... 
• In the case of stimulated emission, since the process is forced by the incident e.m. wave, the emission of any atom adds in phase to that of the incoming wave...

A laser hus emits coherent light as electromagnetic waves all in-phase, and thereby can transmit intense energy over distance. 

The question is how the emission/radiation can be coordinated so that the e.m. waves from many/all atoms are kept in-phase. Without coordination the emission will become more or less out-of-phase resulting in weak radiation. 

The Secret of the Piano reveals that the emission from the three strings for each note in the middle register, which may have a frequency spread of about half a Herz, are kept in phase by interacting with a common soundboard through a common bridge in a "breathing mode" with the soundboard/bridge vibrating with half a period phase lag with respect to the strings. The breathing mode is initiated when the hammer feeds energy into the strings by a hard hit.

In the breathing mode strings and soundboard act together to generate an outgoing sound from the soundboard fed by energy from the strings, which has a long sustain/duration in time, as the miracle of the piano. 

If we translate the experience from the piano to the laser, we understand that laser emission/radiation is (probably) kept in phase by interaction with a stabilising half a period out-of-phase forcing corresponding to the soundboard, while leaving part of the emission to strong in-phase action on a target.

An alternative to quick hammer initiation is in-phase forcing over time, which requires a switch from input to output by half a period shift of the forcing. 

We are also led to the idea that black body radiation, which is partially coherent, is kept in phase by interaction with a receiver/soundboard. Without receiver/soundboard there will be no radiation. It is thus meaningless to speak about black body radiation into some vacuous nothingness, which is often done based on a fiction of "photon" particles being spitted out from a body even without receiver, as physically meaningless as speaking into the desert.    

Does an Undetectable "Greenhouse Effect" Exist?

Vincent Gray seeks to clarify the physics of the "greenhouse effect" in a new blog post at 

The Australian Climate Sceptics - Exposing the flaws in the greatest hoax inflicted on the human race:

1. Greenhouse gases, predominantly water vapour, do absorb infra red radiation from the earth, radiate the additional energy in all directions, including downwards and so warm the earth. 
2. So the greenhouse effect does exist. 
3. This effect must be very small as it has not been detected, despite the enormous effort that has been applied to try and find it.

We read that Vincent here puts forward the idea that the atmosphere by radiating heat energy downwards causes warming of the Earth surface in a process of two-way radiative heat transfer between the atmosphere and surface including "back radiation" from a cold atmosphere to a warm surface. Vincent thus accepts the picture painted by CO2 alarmism based on a "greenhouse effect" and thereby gives it a free ride. Vincent shares this view with many "skeptics".

At the same time as Vincents claims that "the greenhouse effect exists", he informs us that it has not been detected, presumably then because "it must be very small". 

All this is unfortunate because the two-way heat transfer including back radiation which Vincent describes, is not true physics but fake physics, as I have argued in extended writing. 

Vincent defends his position with a direct attack on my position with the following argument (in bold):

• Radiation energy is converted to heat if it is absorbed by any suitable object. 
• The temperature of that object is quite irrelevant. 
• The speculation by some that radiation cannot be absorbed by an object whose temperature is bigger than that of the radiant emitter requires the absurd assumption that radiation, is capable of detecting the temperature of distant objects before deciding whether they are fit to receive absorption. 
• Such an assumption restores the need for a belief in the existence of an ether.

But is it absurd that an absorber can detect if the temperature of an emitter is bigger than its own temperature? Not at all! That information is encoded in the spectrum of the emission as the high-frequency cut-off described in Wien's displacement law with the cut-off increasing linearly with temperature. The result is that emission from a certain temperature cannot be re-emitted by an absorber at lower temperature and thus must be absorbed and turned into heat causing warming. 

A stone put in the sun light, can thus very well detect that the sun light falling upon itself was emitted at a temperature higher than its own, because sun light contains frequencies above the cut-off frequency of the stone.  The stone detects this by finding itself being unable to re-emit these frequencies and thus cannot prevent getting heated by the Sun. This is nothing the absorber "decides" to do in Vincent's vocabulary, because atoms have no free will "to decide",  but simply something the absorber is unable to do, which involves no "decision" and thus can be physics.

 So in conclusion I pose the following question to Vincent (and other "skeptics"):  Since the "greenhouse effect" cannot be detected experimentally and your theoretical argument in support of its existence has shown to be incorrect, wouldn't it be more rational to give up arguing that the "greenhouse effect exists" because there is "back radiation",  thus giving support to CO2 alarmism?

I have asked Vincent to respond to this post, but it may well be be that Vincent, like some other "skeptics", simply hides (and warms up) after making an attack on a skeptic position of a frequency above his own cut-off.

PS Vincent's claim of existence of a phenomenon that is not detectable, connects to an (unfortunate) aspect of modern physics, as opposed to classical physics, rooted in the Bohr Copenhagen interpretation of quantum mechanics, where the wave function is not viewed to represent real physics independent of human observation, but instead represents human understanding in statistical terms limited to what can be observed by humans. Modern physicists following Bohr are thus allowed to speak about only physics which is observable and then in statistical terms. But this is too narrow, and has opened the possibility of a vast physical landscape beyond observation, which physicists are now eagerly exploring in the extreme forms of string theory and multiversa. The (unfortunate) result is that speaking about phenomena of physics which cannot be detected, which in the view of classical physics is nonsense,  has now become mainstream modern physics. 

Unphysical Schwarzschild vs Physical Model for Radiative Transfer

The basic model for radiative heat transfer in a horisontal slab atmosphere, with vertical coordinate $x$ with $x=0$ at the Earth surface and $x=X$ at the top of the atmosphere, was formulated by Schwarzschild in 1906 as a two-stream  gross-flow model in terms of a gross upward heat flux $F^+(x)$ and a gross downward heat flux  $F^-(x)$ satisfying the following advection-absorption equations for $0\lt x\lt X$:

• $\frac{dF^+}{dx} + F^+ = Q$               (1)
• $-\frac{dF^-}{dx} + F^- = Q$               (2) 

where $Q(x) =\sigma T(x)^4$ is supposed to express Stefan-Boltzmann's law with $T(x)$ the temperature at $x$ and $\sigma$ Stefan-Boltzmann's constant, and $x$ serves as an optical coordinate normalizing absorption. The atmosphere is supposed to be heated from below at $x=0$ by a heat source $H$, and the heat is radiatively transported to the top of the atmosphere from where it is radiated into outer space at 0 K. Conservation of heat energy gives the additional equation

• $F^+-F^- = H$,                                      (3)

from which follows by adding/subtracting (2) from (1) that $F^+ + F^-=2Q$ and $\frac{d(F^++F^-)}{dx}=-H$ and thus:

• $2Q(x) = H(X-x)+H$,                          (4)
• $F^+ =\frac{H}{2}(X-x)+H$
• $F^-=\frac{H}{2}(X-x)$                        

which determines the temperature profile $T(x)$. We note that Schwarzschild's model with linear $Q(x)$, is very simplistic. Only a model with $Q(x)$ constant could be more simplistic.

Schwarzschild's equations (1-2) are supposed to express conservation of upward and downward heat fluxes through a thin atmospheric layer radiating both upward and downward according to Stefan-Boltzmann in the form $Q(x) =\sigma T(x)^4$.

Schwarzschild's two-stream model is unphysical in the sense that the gross downward flux $F^-$ is directed against the temperature gradient and thus violates the 2nd law of thermodynamics. Further, the two sided radiation up/down according to $Q(x) =\sigma T(x)^4$ in (1-2) is also unphysical, because  $Q(x) =\sigma T(x)^4$ is the blackbody radiation into a background at 0 K, which is not the case. Scwarzschild's model is thus doubly unphysical and we shall now see that the unphysical aspects do not cancel to give a physical model.

Let us thus compare Schwarschild's unphysical two-stream gross-flow model with a one-stream net-flow model based on Stefan-Boltzmann's law in its correct physical form

• $Q=\sigma (T_2^4-T_1^4)$                     (5)

as the net radiative heat transfer radiative between two blackbodies of temperature $T_1$ and $T_2$ with $T_2>T_1$, in accordance with the 2nd law with heat transfer from warm to cold (but not the other way).

We then start from the following balance equation expressing that the total inflow of heat at a thin layer at level $0\lt x\lt X$ from layers at levels $y$ with $0\le y\lt x$, equals the total outflow into levels $x\lt y\le X$:

• $\int_0^x\sigma (T(y)^4-T(x)^4)\exp(-\alpha (x-y))dy = \int_x^X\sigma (T(x)^4-T(y)^4)\exp(-\alpha (y-x))dy$
• $+H\exp(-\alpha x)$                                                         (6)

with the exponential factor $\exp(-\alpha\vert x-y\vert )$ accounting for the absorption between levels $x$ and $y$ with a non-negative absorption coefficient $\alpha$, and the term $H\exp(-\alpha x)$ accounts for the effect of the heat source $H$ at $x=0$, and $\sigma T(X)^4 = H$.

Reshuffling terms in (6), we obtain the following integral equation in $Q(x)=\sigma T(x)^4$ for $0\le x\le X$

• $ \int_0^xQ(y)\exp(-\alpha (x-y))dy+ \int_x^XQ(y)\exp(-\alpha (y-x))dy$
• $= Q(x)(\int_0^x\exp(-\alpha (x-y))dy+ \int_x^X\exp(-\alpha (y-x))dy)+H\exp(-\alpha x)$,

which can be written

•  $Q(x)-c(x)\int_0^XQ(y)\exp(-\alpha\vert x-y\vert )dy =-c(x)H\exp(-\alpha x)$   (7)

for $0\le x\le X$ with $c(x) = 1/(2-\exp(-\alpha x)-\exp(-\alpha (X-x)),$ which together with the outflow condition $Q(1) = H$ determines $Q(x)$ uniquely as the solution of a Fredholm integral equation of the 2nd kind.

To compare with the two-stream model, let us formally split Stefan-Boltzmann's equation (5) algebraically into the (unphysical) form

• $Q=\sigma T_2^4-\sigma T_1^4$                   (8)  

and rewrite (6) accordingly collecting positive terms and writing $Q(x)=\sigma T(x)^4$ as above, into

• $A+B = C+D+E$                                                  (9)
• $A(x)= \int_0^xQ(y)\exp(-(x-y))dy$
• $B(x)= \int_x^XQ(y)\exp(-(y-x))dy$
• $C(x)=Q(x)(1-\exp(-x))$
• $D(x)=Q(x)(1-\exp(-(X-x))$
• $E(x) = H\exp(-\alpha x)$. 

To compare the models we observe that by the definitions of $A$ and $B$:

• $\frac{dA}{dx}+A = Q$
• $-\frac{dB}{dx}+B = Q$

which shows that $A$ corresponds to $F^+$ and $B$ to $F^-$.  We recall that

• $F^+ + F^-=2Q$ 

which we we compare with (9):

• $A+B=C+D+E=Q(2-\exp(-x)-\exp(X-x))+H\exp(-\alpha x)$,

to conclude that the two models are not identical, and so the models give different temperature distributions. 

The lesson is that radiative heat transfer should better be modeled using the physical one-stream net-flow correct form of Stefan-Boltzmann's law (5). Using the unphysical two-stream gross-flow form (1-2) can lead to unphysical results.

It is possible that an unphysical gross-flow model can give a physically meaningful result by happy cancellation of unphysical gross-flow aspects. But to rely on an unphysical model to derive conclusions about real physics is risky because the happy cancellation may not be granted, in particular not if the question concerns the effect of perturbations, as is the case in global warming modeling.

The unphysical aspects of Schwarzschild's model are:

1. The downward flux $F^-$ violates the 2nd law.
2. The downward flux $F^-$ generates unphysical absorption in (2).
3. The basic equations (1) and (2) do not represent correct physics. 

Despite these shortcomings, Schwarzschild's model has come to serve as the basic model of atmospheric radiation supporting CO2 alarmism.  The unphysical of nature of this basic model gives one reason to view also CO2 alarmism to be unphysical.

In a following post we will solve the integral equation (7) and compare with Schwarzschild's solution. To start with we note that for $\alpha$ large (7) approaches $\frac{d^2Q}{dx^2}=0$ resulting in a linear $Q(x)$ as in Schwarzschilds model. More generally, the physical model (7) is close to Schwrzschilds model in the trivial cases of a nearly opaque and transparent atmosphere, but not so in the more relevant case in between.

The integral equation (7) can by differentiation be turned into a (diffusion-advection-absorption) ordinary linear differential equation.

Mer "Korrespondens" med Lennart Bengtsson om Radiative Heat Transfer

Brev till mig från LB 5/4:

Eftersom jag råkade ha ett exemplar av Elsassers monografi sänder jag den här. Den är lite gammaldags (1942) med en av de bättre sammanställningarna. Den var min lärobok i strålning när jag studerade för Bert Bolin 1961-62. Kanske Claes Johnson eller eller C-G Ribbing som framstående svenska fysiker kunde låta mig veta vad som är fel i denna framställning.PS bifogar en biografi över Walter M Elsasser http://en.wikipedia.org/wiki/Walter_M._Elsasser#Publications

Mitt svar 5/4:

Tack för detta Lennart:

Noterar att Elsasser på sid 77 säger att koldioxidens möjliga stora inverkan på klimatet enl Arrhenius är en "untenable speculation".

Vidare,  grundfelet i framställningen är att Elsasser i  formuleringen av Plancks inte anger att lagen beskriver utstrålningen mot en bakgrund av 0 K, vilket är den rätta fysikaliska innebörden. Utgående från denna oklarhet har sedan en föreställning växt fram om existensen av "two-stream radiative transfer", trots att överföringen kall-till-varm står i strid med 2a lagen, uttryckt i tex Schwarzschilds ekvationer. Dessa ekvationer har formell karaktär och motsvaras inte av reell fysik (spec eftersom 2a lagen överträds). Om ekvationerna ges fysikalisk innebörd kan felaktiga slutsatser följa, som tex i Kiehl-Trenberths energibudget med ett brutto energiutbyte via strålning om 300 W/m2 mellan jordyta och atmosfär, detta utan fysikalisk motsvarighet.

Grundfrågan är alltså tolkningen av Plancks lag, och denna måste utgå från bevis av lagen
där premisserna anges. Om dessa premisser inte innehåller någonting om "återstrålning", så kan inte något sådant senare införas med åberopande av Plancks lag. Om så görs, innebär det att Plancks lag misstolkas, vilket inte är korrekt vetenskap.

Eller hur ser Du på denna fråga om den fysikaliska innebörden av Plancks lag? Utstrålning mot en bakgrund av 0 K? Eller något annat?

Vänliga påskhälsningar, Claes

Mitt brev till LB med förnyad begäran om svar 7/4:

Hej Lennart:

Jag har inte fått någon respons från Dig på mitt svar på Din fråga till mig om vad som är icke-fysik i Elsassers framställning. Jag har utvecklat mitt svar en analys av Schwarzschilds ekvationer som jag ber Dig ta ställning till och ge feedback på:

http://claesjohnson.blogspot.se/2015/04/unphysical-schwarzschild-radiative.html

Det är alldeles uppenbart att det finns ett klart behov av det seminarium om fysiken bakom "återstrålning" som jag begärt att KVA skall arrangera. Vill Du nu arbeta för att detta seminarium kommer till stånd? 

Frågan kommer att ligga kvar till dess den blir besvarad. Om den inte blir besvarad innan KVA presenterar sitt nya uttalande, så minskar det uttalandets värde för sitt avsedda syfte att tjäna som vetenskapligt underlag för svensk klimatpolitik fram till 2050.   

Vänligen, Claes

LBs svar: TBA

Min kommentar: 

Korrespondensen med LB är hela tiden sporadisk med olika utspel som inte följs upp och brev som inte besvaras, som en form av krypskytte. Vad gäller "återstrålning" kan vi förvänta oss att LB (på samma sätt som Henning Rodhe) efter att först ha försvarat "återstrålning" såsom varande själva grunden för AGW, så kommer LB snart att säga att när allt kommer omkring så är inte "återstrålning" så vidare värst viktigt, utan det är istället att "den effektiva utstrålningsnivån" kommer att höjas med mera CO2 från mänskliga utsläpp, och det är detta som är själva kärnan i CO2 alarmismen. Hur lång tid behöver LB för att komma fram till detta? Och vad säger då sakkunskapen om fysiken hos "den effektiva utstrålningsnivån"??

PS Vad vi kan vänta oss från KVA är detsamma som det uttalande av APS som sågats av Judith Curry.

Earth's Energy Budget With and Without Back Radiation

The above diagram is supposed to capture the essence of the science of CO2 global warming alarmism. We see massive "Back Radiation" of 324 W/m2 hitting the Earth's surface from the "Greenhouse Gases" below the Top of Atmosphere TOA, while the net radiative transfer from the surface to TOA is 26 W/m2, about 10 times as small.

The main "greenhouse gas" is water vapor with CO2 contributing maybe 10% to the total "greenhouse effect" of 33 C as the difference between the surface temperature and that of TOA.

 To estimate the effect of a doubling of CO2, one can argue as follows: The total "back radiation" from "greenhouse gases" is about 300 W/m2 and so the total effect of CO2 can be estimated to 30 W/m2, which according to Stefan-Boltzmann may correspond to a global warming of 7 C, which is the upper limit of CO2 alarmism, without taking any saturation reduction effect into account.

On the other hand, using instead of a nominal 300 W/m2, a net of 30 W/m2, we end up with 0.7 C as the upper limit, without saturation effect.

We thus have the following two estimates for global warming upon doubled CO2 to compare:

1. With "back radiation": 7 C
2. Without "back radiation": 0.7 C 

Here 1. is catastrophical, while 2. is harmless. 

We see the critical role of "back radiation" for CO2 alarmism.

But "back radiation" is fiction without physical reality, and so is then also CO2 alarmism. 

Of all scientific bluffs through the history of science, "back radiation" will be described as the biggest, as the bluff with potentially biggest effects for human civilization.

For a deeper analysis of "back radiation" see earlier posts in categories "radiative heat transfer" and "myth of back radiation".

Physics Illusion 2: Photons as Light Particles

Computational Blackbody Radiation describes radiative energy transfer as a resonance phenomenon between resonators connected by standing electromagnetic waves in a vacuum between the resonators. The acoustic analog is depicted above: Energy is transferred from one tuning fork to another by standing acoustic waves as pressure variations in still air.

In this model the finite speed of electromagnetic (or acoustic) waves only influences the energy transfer in a start up phase, while in a stationary state of standing waves the energy transfer can be viewed to be instantaneous without time delay, or to be without time aspect. The transfer of energy is one-way from hot (high frequency) to cold (low frequency).

In this view there is no need to introduce particles named photons carrying energy packets at finite speed back and forth between the resonators, as if the resonators were connected by a two-way highway with trucks transporting energy in both directions. There is no experimental evidence of the existence of such a two-way stream of light quanta. Einstein introduced light quanta in his annus mirablis 1905, but changed mind before passing away:

• All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)

The lights we see in the sky thus result from resonance by standing electromagnetic waves in the vacuum between our eyes and a distant star, and not by light particles having traveled for billions of years before hitting the retina of an eye. Energy is transferred from one tuning fork to the other by acoustic standing waves but there are no phonon particles carrying the energy by flying like a swarm of wasps between the forks.

The idea of a photon as an elementary particle acting as force carrier of the electromagnetic force, is a basic element of the standard model. No wonder that physicists are not happy with this model. The photon as carrier of the electromagnetic force like the graviton as carrier of the gravitational force, is probably Einstein's biggest mistake, far bigger than the cosmological fudge constant in Einstein's equations, and a return to the primitive corpuscular theory of light of Thomas Hobbes (1644), which was superseeded by Huygen's wave theory (1678), once Newton was dead, but then surprisingly popped up again in Einstein's 1905 article on the photoelectric effect.