Möte med S: Matematikutbildning för IT-Samhället

PM inför Möte med Socialdemokraterna i Riksdagens Utbildningsutskott 30/11

S har inbjudit mig till möte om matematikutbildning med följande utgångspunkt:

• Socialdemokraterna stödjer en investering i matematik men vi vet ännu inte hur regeringen vill lägga upp programmet och kommer självklart ha synpunkter på hur så bör ske.
• Vad gäller en modernisering av skolan för att passa it-samhället så har vi har under flera års tid kritiserat regeringen för att inte ta informationsteknologin på allvar, vi vet att detta skulle kunna ha stor betydelse för t ex undervisningen i matematik.
• Vi skulle gärna ta del mer av hur du tycker att matematikundervisningen och it i skolan bör utvecklas.

Inför mötet hoppas jag att Mikael Damberg/S vill ta del av:

• Changing Education Paradigms (Sir Ken Robinson)
• Skolan Dödar Motivationen (svensk gymnasielev)
• How to Fix Math Education (New York Times 24/9 2011)

mina debattinlägg på Newsmill och Teknikdebatt:

• Katederundervisning Förbereder Inte för IT-Samhället
• Mattelyftet: Ge Alla Barn en iPad
• Juholt Kan Vinna Valet med Krav på Framtidsinriktad Skola
• Mattelyft Utan IT Faller Platt

inlägg på min blogg om Matematik-IT och Mathematics Education, artiklar på Google Knol

om Mathematics/Science Education, samt följande debattartikel som kommer att publiceras i Ny Teknik:

Om ett par år kommer alla elever att ha en egen laptop eller iPad från skolstart, som ett naturligt uttryck för att skolan är en del av IT-samhället med alla dess möjligheter till aktivt lärande i nya former.

Detta ställer nya krav på skolan och lärarutbildningen måste nu reformeras så att alla elever kan ges en god förberedelse för liv och arbete i IT-samhället. Detta gäller alla ämnen men särskilt i IT-intensiva tekniska ämnen av avgörande betydelse för Sveriges konkurrenskraft.

Detta har oppositionen med sin utbildningspolitiske talesman Mikael Damberg (S) förstått, som framgår av hans artikel på SKLs Blogg om eSamhället. Men det har inte utbildningsminister Jan Björklund, som i sitt nya initiativ Mattelyftet beordrat Skolverket att utarbeta en plan för att omskola alla mattelärare till mer av "traditionell katederundervisning", till en kostnad av 2.6 miljarder.

Björklund motiverar sitt direkta statliga ingripande med en minskning enligt PISA från 510 år 2000 till 494 år 2009, dvs en minskning med 3%. Björklund beskriver minskningen om 3% som så alarmerande att staten "inte stillatigande kan titta på" utan måste diktera undervisningen, som i ett totalitärt samhälle.

Skolverket tar i sin plan dock avstånd från "en dominerande traditionell skol- och undervisningskultur", dvs Björklunds "katederundervisning". Resultatet är en statlig förvaltning i kramp, en lärarutbildning i paraplys och en skola utan framtidshopp. Björklunds miljarder skulle kunna användes för att leda skolan in i IT-samhället, inte minst genom en reformerad skolmatematik eftersom datorn är en matematikmaskin, men stora resurser kommer nu istället att förödas på meningslös revision utan IT.

Björklund kör över hela svenska folket, inklusive elever, föräldrar, lärare, lärareutbildare, fack och statlig förvaltning, med ett meningslöst kostsamt statligt diktat, men kritiken av Mattelyftet har hittills varit svag och splittrad. Skolverket försöker lamt att obstruera men alla lärarutbildare med ansvar för skolans undervisning säger ingeting. Det är inte lätt att säga nej till 2.6 miljarder, även om ändamålet är tveksamt och PISA-resultaten bara kommer att fortsätta att sjunka.

Men skattebetalarna vill inte att miljarder förslösas på ett meningslöst illa genomtänkt statligt diktat. Detta ger oppositionen en lysande möjlighet att ta initiativet i skolpolitiken med en offensiv framtidsinriktad skolpolitik där resurser istället används för leda skolan in i IT-samhället.

Mikael Damberg förstår vad Björklund inte förstår, och det skall bli mycket intressant att se vad ett kommande möte med Damberg kan leda till. Jag har förgäves sökt få tala med Björklund men hans dörr är stängd. På en direkt fråga om de växande digitala klyftorna och bristen på moderna datorer i svenska skolor från Damberg svarar Björklund att "det är inget som han ligger sömnlös över". Nej, Björklund sover tungt och drömlöst och det är inte bra för svensk skola.

Min blogg ger mer information om matematik och matematikundervisning i IT-samhället. När alla barn om ett par år kommer att ha en laptop eller iPad i skolväskan kommer skolans arbete att förändras. Vi är snart där och måste förbereda oss.

Sammanfattning:

• Skolan måste reformeras för att passa det nya IT-samhället
• IT = ord, bild, ljud, siffror, diagram... i digital form: ettor och nollor
• IT bygger på matematik: logik, geometri, algebra, Calculus, beräkning
• Matematikämnet ger grunden för IT i skolan
• Matematikämnet förändras med IT: Från formler till beräkningsalgoritmer
• IT-Matematik: logik, programmering, beräkning, simulering
• Genomgripande reform av mål, innehåll och form från åk 1
• Nya läroplaner, nya läromedel
• Ny lärarutbildning i matematik med IT
• Prototyp: Body and Soul, Mathematical Simulation Technology

Mål för S-Matematik:

• ge alla redskap för att klara sig i IT-samhället: ord, bild, matematik, simulering
• kombination av manuell/praktisk och språklig/teoretisk kunskap
• matematik grunden för IT
• logik, orsak-verkan, korrekthet
• ABF tradition i modern tappning: ge arbetaren IT-redskap
• att kunna styra sitt liv
• att kunna uttrycka sig
• att kunna förstå text, bild, diagram, formler
• att förstå logik
• att kunna styra datorn: bildbehandling Photoshop
• textbehandling
• att kunna göra film, presentation, analys.

Viktiga S-aspekter:

• individualiserad undervisning
• interaktivt lärande: feed-back
• läraren frigörs från rutinuppgifter
• elevers särskilda behov kan tillfredställas
• fler elever kan engageras
• utbredd matematikskräck kan motverkas
• matematik en ges annan mening än prestige och gradering.

Möjlighet för S att vinna nästa val:

Björklund tittar defensivt bakåt mot 1950-talets realskola för de få och ger därmed S en enastående möjlighet att ta initiativet med en offensiv skolpolitik för de många för dagens och morgondagens samhälle. S söker ett vinnande valprogram. (S)kolfrågan kan vara svaret.

Difference Between Emission and Absorption of Radiation

In a sequence of posts on radiative heat transfer and DLR/backradiation I have studied a wave model of the form:

• $U_{tt} - U_{xx} - \gamma U_{ttt} - \delta^2U_{xxt} = f $

where the subindices indicate differentiation with respect to space $x$ and time $t$, and

1. $U_{tt} - U_{xx}$ represents a vibrating string with U displacement
2. $- \gamma U_{ttt}$ is a dissipative term modeling outgoing radiation = emission
3. $- \delta^2U_{xxt}$ is a dissipative modeling internal heating = absorption
4. $f$ is incoming forcing/microwaves,

where $\gamma$ and $\delta^2$ are positive constants connected to dissipative losses as outgoing radiation = emission and internal heating = absorption.

We see emission represented by $-\gamma U_{ttt}$ and absorption by $-\delta^2U_{xxt}$. We now ask:

1. How is the distinction between emission and absorption expressed in this model?
2. Is Helmholtz Reciprocity valid (emission and absorption are reverse processes)?
3. Is Kirchhoff's Radiation Law (emissivity = absorptivity) valid?

Before seeking answers let us recall the basic energy balance between incoming forcing $f$ measured as

• $F = \int f^2(x,t)\, dxdt$

assuming periodicity in space and time and integrating over periods, and (rate of) outgoing radiation = emission $R$ measured by

• $R = \int \gamma U_{tt}^2\, dxdt$,

the oscillator energy $OE$ measured by

• $OE =\frac{1}{2}\int (U_t^2 + U_x^2)\, dxdt$

and (rate of) internal energy = absorption measured by

• $IE = \int \delta^2U_{xt}^2\, dxdt$

with the energy balance in stationary state expressed as

• $F = R + IE$
• incoming energy = emission + absorption.

The model has a frequency switch switching from emission to absorption as the frequency increases beyond a certain threshold proportional to temperature in accordance with Wien's displacement law.

We now return to questions 1 - 3.

Both terms generate dissipative effects when multiplied with $U_t$ as $R = \int \gamma U_{tt}^2\, dxdt$ and $IE = \int \delta^2U_{xt}^2\, dxdt$, but the terms involve different derivatives with $U_{tt}$ acting only in time and $U_{xt}$ acting also in space.

The absorption $U_{xt}^2$ represents a smoothing effect in space, which is irreversible and thus cannot be reversed into emission as reversed absorption.

The emission $U_{tt}^2$ represents a smoothing effect in time, which is irreversible and thus cannot be reversed into absorption as reversed emission.

In other words, in the model both absorption and emission are time irreversible and thus cannot be reversed into each other.

We conclude that the model does not satisfy Helmholtz reciprocity.

Nevertheless, the model satisfies Kirchhoff's law as shown in a previous post.

Conclusion:

The space derivative in $U_{xt}$ models absorption as process of smoothing in space with irreversible transformation of high frequencies in space into low frequencies with a corresponding increase of internal energy as heat energy.

Absorbed high frequencies can with increasing temperature be rebuilt through (resonance in) the wave equation into high frequency emission.

Absorption and emission are not reverse processes, but my be transformed into each other

through (resonance in) the wave equation and the switch.

We may compare absorption with a catabolic process of destroying (space-time) structure and emission with an anabolic process of building structure, with the wave equation as a transformer.

For more details see Mathematical Physics of Blackbody Radiation and The Clock and the Arrow.

Why Judy Curry Has Given Up CO2 Alarmism

When Judy Curry on August 13 2011 gave up the idea of DLR/backradition after a long debate on my article on blackbody radiation in Slaying the Sky Dragon, she did not understand that this effectively meant that she gave up CO2 climate alarmism, as is now evidenced by her criticism of her former alarmist buddy Richard Muller and his BEST data.

But real science is logical. If you say A then you have to say B.

PS Two days later Curry again agrees with Muller and the criticism has faded, probably because of heavy backradiation.

Helmholtz Reciprocity and DLR/Backradiation

Helmholtz Reciprocity Principle (HRP) states that absorption and emission of light can be viewed as reversed processes arising by reversal of time. Absorption of a light ray by a (black) body is simply emission of a light ray running backwards in time, or the other way around.

Downwelling Longwave Radiation (DLR) and backradiation seek justification by HRP. Kirchhoff's Radiation Law stating that emissivity and absorptivity of a radiating body are equal,

was justified by Planck with reference to HRP.

But is HRP a valid physical principle? What is the relation between HRP and the 2nd Law?

HRP describes reversible physics while the 2nd Law described irreversible physics, and so HRP and the 2nd Law describe different physics.

Is the real physics of absorption and emission the time reversal of each other? Probably not.

The process of absorption is like reading and the process of emission like writing. To state

that reading and writing are the reverse of each other would miss the difference between the active constructive aspect of reading and the passive consumption aspect of reading.

The analysis in Mathematical Physics of Blackbody Radiation shows that absorption and emission are different processes satisfying a 2nd law which does not allow time reversal, and thus indicates that HRP is not valid.

Without HRP the support of DLR/backradiation evaporates.

Note that HRP conforms to a corpuscular theory of light as photon particles for which time reversal is no problem. But such a theory is capable of describing only simple ray tracing physics and not real physics.

Reality and Fiction of Stefan-Boltzmann's Radiation Law

Human accountant in charge of a non-physical fictional Stefan-Boltzmann Law.

In previous posts on radiative heat transfer I have compared two different formulations of Stefan-Boltzmann's Radiation Law (SB) for the radiative exchange of heat energy between two blackbodies of different temperatures:

1. one-way transfer from hot to cold,
2. two-way transfer with net transfer from hot to cold.

To see which formulation best represents physics, recall the wave equation model of a blackbody as a vibrating string with displacement $U$ subject to radiative damping:

• $U_{tt} - U_{xx} = f - (-\gamma U_{ttt})= f + \gamma U_{ttt}$,

which expresses a balance between the string force $U_{tt} - U_{xx}$ and the net force $f+\gamma U_{ttt}$ from the radiation pressure $-\gamma U_{ttt}$ and the exterior forcing $f$. For details see Mathematical Physics of Blackbody Radiation.

The essential aspect is now the interplay between the internal energy (density) $IE$ of the vibrating string

• $IE=\frac{1}{2}(U_t^2 + U_x^2)$

and the net forcing $f +\gamma U_{ttt}$, which is expressed in the following energy balance obtained by multiplying the force balance by $U_t$ and integrating in space and time to get

• $\int \frac{dIE}{dt}dxdt = \int (f +\gamma U_{ttt})U_tdxdt$.

We se that the rate of change $\frac{dIE}{dt}$ of internal energy $IE$ is balanced by a net force $f + \gamma U_{ttt}$ scaled with $U_t$. We can interpret $E=\int IE\, dx$ as an accumulator recording the net effect of the forcing and radiation, with $E$ proportional to $T_U^2$ with $T_U$ the temperature of the blackbody (with displacement) $U$.

In the case the forcing $f$ is delivered by another blackbody with displacement $V$ and temperature $T_V> T_U$, the energy balance takes the form

(1) $\int\frac{dE}{dt}dt= \int (\gamma V_{tt}^2 -\gamma U_{tt}^2)dxdt$,

where $\frac{dE}{dt}$ thus is the rate of heating of blackbody $U$ by the radiation from the hooter blackbody $V$ expressed as an integral of net forcing.

The right hand side of (1) can formally be rewritten as

$\int\frac{dE}{dt} dt= \int \gamma V_{tt}^2dx dt - \int\gamma U_{tt}^2dxdt$

from which follows by performing the integration with respect to $x$, and cancelling the integration with respect to $t$ (see Mathematical Physics of Blackbody Radiation for details):

(2) $\frac{dE}{dt} = \sigma T_V^4 - \sigma T_U^4$.

This is the version of Stefan-Boltzmann's Radiation Law (SB) cherished in climate science describing the heating $\frac{dE}{dt}$ as the difference of two gross flows of incoming radiation $\sigma T_V^2$ and outgoing radiation $\sigma T_U^4$.

We thus have two forms of SB:

1. (1) with one-way heat transfer from integration of net forcing,
2. (2) with two-way heat transfer as difference of integrated gross forcings.

I argue that (1) is physical since the internal energy $E$ acts as an accumulator of net forcing,

while (2) is unphysical because the accumulated quantities $\sigma T_V^4$ and $\sigma T_U^4$ lack physical realization.

The account of heat transfer expressed in (2) can formally be made by a human accountant on a piece of paper, but not by the blackbodies themselves and thus (2) lacks physical correspondence.

The conclusion is that one-way transfer of net flow is physics while two-way transfer of gross flows is fiction. In other words, DLR/backradiation is fiction.

Who Proved of Kirchhoff's Law of Radiation?

Kirchhoff's Radiation Law stating that the emissivity of a radiating body is equal to its absorptivity presented in 1859, initiated an intense study of blackbody radiation by Rayleigh, Jeans, Wien and others leading into Planck's proof of his radiation law opening to the quantum mechanics of modern physics.

Kirchhoff's Law can be seen as a triviality stating that emission equals absorption as an expression of energy balance. But Kirchhoff's Law concerns emissivity and absorptivity as emission and absorption per unit time, and in this setting it is not at all trivial. The question is why a body capable of absorbing radiation and emitting radiation, must absorb and emit at the same rate? Is it because emission and absorption are simply the reverse of each other with emission simply absorption backwards in time?

No, it is not so trivial, because emission and absorption are different physical processes both with an arrow of time which cannot be reversed. Emission and absorption are not the reverse of each other.

In a previous post I sketched a proof of Kirchhoff's Law based on a wave model with radiative damping analyzed in more detail in Mathematical Physics of Blackbody Radiation.

Let us trace the history of the proof of Kirchhoff's Law with Experimenting theory: The proofs of Kirchhoff's Radiation Law before and after Planck by A. Schirrmacher presenting the following story:

1. Kirchhoff (1859): Thought experiments with mirrors, basic thermodynamics.
2. Planck (1906); Heat rays, basic thermodynamics.
3. Hilbert (1912-14): Integral equation, axiomatic method.

The debate about the proof was intense and no winner was elected. Further studies were made by Dirac and Heitler based on quantum mechanics.

In the modern textbook Radiative Heat Transfer by M. Modest, Kirchhoff's law is presented as a triviality:

• It is easy to show that a black surface also emits a maximum amount of radiative energy, i.e., more than any other body at the same temperature. To show this, we use one of the many variations of Kirchhoff's law: Consider two identical black-walled enclosures, thermally insulated on the outside, with each containing a small object—one black and the other one not. After a long time, in accordance with the Second Law of Thermodynamics, both entire enclosures and the objects within them will be at a single uniform temperature.
• This characteristic implies that every part of the surface (of enclosure as well as objects) emits precisely as much energy as it absorbs. Both objects in the different enclosures receive exactly the same amount of radiative energy. But since the black object absorbs more energy (i.e., the maximum possible), it must also emit more energy than the nonblack object (i.e., also the maximum possible).
• By the same reasoning it is easy to show that a black surface is a perfect absorber and emitter at every wavelength.

We see here an example of a common feature of modern science: A question which once caused a heated debate between the giants of science of the time without ever being settled including

• interpretation of quantum mechanics
• d'Alembert's paradox
• Loschmidt's paradox
• 2nd Law of Thermodynamics

eventually is being put aside as being trivial or a no-issue of little interest.

But Kirchhoff's law is not a triviality and it is a fundamental part of the theory of radiation, and therefore a proof is of considerable interest.

PS To the students at MIT Kirchhoff's Law is presented as trivial energy balance.

Two-Way Transfer of Heat as OLR/DLR Violates the 2nd Law

In a sequence of posts on radiative heat transfer between two bodies of different temperature, I have compared two views with deep historical roots:

1. One-way transfer from hot body to cold body (Pictet)
2. Two-way transfer with net transfer from hot to cold (Prevost),

where 2. is used to support CO2 alarmism in the form of DLR/backradiation.

1. satisfies the 2nd law of thermodynamics, but what about 2.?

Well, two-way transfer is commonly viewed as two opposite streams of photons, which are not considered to interfere with each other, and thus must viewed to be independent. But this means that one of these independent streams of photons concerns transfer from cold to hot and thus violates the 2nd law.

This is a simple argument showing that the mantra of DLR/backradiation lacks rationale, by violating the 2nd law.

The argument can be dressed up in more precise mathematical form, as shown in Computational Thermodynamics and Mathematical Physics of Blackbody Radiation.

Radiative Heat Transfer: Kirchhoff's Law in New Light

Kirchhoff's Law of Thermal Radiation: 150 Years starts off by:

• Kirchhoff’s law is one of the simplest and most misunderstood in thermodynamics.

Let us see what we can say about Kirchhoff's Radiation Law stating that the emissivity and absorptivity of a radiating body are equal, in the setting of the wave model with damping presented in Computational Blackbody Radiation and Mathematical Physics of Blackbody Radiation:

(1) $U_{tt} - U_{xx} - \gamma U_{ttt} - \delta^2U_{xxt} = f $

where the subindices indicate differentiation with respect to space $x$ and time $t$, and

1. $U_{tt} - U_{xx}$ models a vibrating material string with $U$ displacement
2. $- \gamma U_{ttt}$ is a dissipative term modeling outgoing radiation
3. $- \delta^2U_{xxt}$ is a dissipative term modeling internal heating by friction
4. $f$ is the amplitude of the incoming forcing,
5. $T$ is temperature with $T^2=\int\frac{1}{2}(\vert U_t^2+U_x^2)dxdt$,
6. (1) expresses a balance of forces,

where $\gamma$ and $\delta^2$ are certain small damping coefficients defined by spectral decomposition as follows in a model case:

• $\gamma = 0$ if the frequency $\nu >\frac{1}{\delta}$
• $\delta = 0 $ if the frequency $\nu < \frac{1}{\delta}$,

where $\delta = \frac{h}{T}$ represents a "smallest coordination length" depending on temperature $T$ and $h$ is a fixed smallest mesh size (representing some atomic dimension).

This represents a switch from outgoing radiation to internal heating as the frequency $\nu$ passes the threshold $\frac{T}{h}$, with the threshold increasing linearly with $T$.

The idea is that a hotter vibrating string is capable of radiating higher frequencies as coherent outgoing radiation. The switch acts as a band filter with frequencies outside the band being stored as internal heat instead of being radiated: The radiator is then muted and heats up internally instead of delivering outgoing radiating.

A spectral analysis, assuming that all frequencies share a common temperature, shows an energy balance between incoming forcing $f$ measured as

• $F = \int f^2(x,t)\, dxdt$

assuming periodicity in space and time and integrating over periods, and (rate of) outgoing radiation $R$ measured by

• $R = \int \gamma U_{tt}^2\, dxdt$,

and (rate of) internal energy measured by

• $IE = \int \delta^2U_{xt}^2\, dxdt$,

together with the oscillator energy

• $OE =T^2 = \frac{1}{2}\int (U_t^2 + U_x^2)\, dxdt$

with the energy balance in stationary state with $OE$ constant taking the form

• $F = \kappa (R + IE)$

with $\kappa\lessapprox 1$ is a constant independent of $T$, $\gamma$, $\delta$ and $\nu$. In other words,

• incoming energy = $\kappa\times$ outgoing radiation energy for $\nu <\frac{1}{\delta}$
• incoming energy = $\kappa\times$ stored internal energy for $\nu > \frac{1}{\delta}$,

which can be viewed as an expression of Kirchhoffs' law that emissivity equals absorptivity.

The equality results from the independence of the coefficient $\kappa$ of the damping coefficients $\gamma$ and $\delta^2$, and frequency.

Summary: The energy of damping from outgoing radiation or internal heating is the same even if the damping terms represent different physics (emission and absorption) and have different coefficients ($\gamma$ and $\delta^2$).

PS: Note that internal heat energy accumulating under (high-frequency) forcing above cut-off eventually will be transformed into low-frequency outgoing radiation, but this transformation is not part of the above model.

Radiative Heat Transfer: Resonance

In a sequence of posts I have compared a wave model and a particle model for radiative heat transfer, which can be illustrated in the interaction between the two partners of a marriage:

Wave model:

• Interchange of energy by a phenomenon of resonance.
• The wiser partner transfers energy to the less wise by resonance.
• Happy educated marriage.

Particle model:

• Interchange of energy by invectives.
• The partner with the stronger invectives wins the battle.
• Unhappy primitive marriage.

Let us now add some mathematics to this picture:

Wave model:

The model for radiative exchange of heat energy between two blackbodies 1 and 2 analyzed in Mathematical Physics of Blackbody Radiation, satisfies the following energy balance for each frequency $\nu$:

• $\frac{dOE_1}{dt} + R_1 + IE_1 = F^2 = \frac{dOE_2}{dt} + R_2+ IE_2$

where each blackbody consists of an oscillator with energy $OE$ subject to damping from outgoing radiation of energy $R$ per unit time and damping from internal heating (friction)

of energy $IE$, with the subindex indicating the energy for each body, and $F^2$ representing

the common shared energy.

The damping mechanisms are subject to the following cut-off rule depending on frequency $\nu$ and temperature $T$, assuming a principal form:

• if $\nu > T $ then $R(\nu ) =0$
• if $\nu < T $ then $IE(\nu ) =0$.

The cut-off rule expresses that the outgoing radiation is replaced by internal heating as the frequency passes a threshold proportional to temperature.

We consider a stationary state with $OE_1$ and $OE_2$ constant, in which case the energy balance takes the form

• $R_1 + IE_1 = F^2 = R_2+ IE_2$.

By the cut-off rule it follows that if $T_1>T_2$ then

• R_1 = IE_2

which expresses that the radiation from 1 is stored in 2 as heat, that is radiative transfer from hot to cold in accordance with the 2nd law of thermodynamics.

This model for radiative transfer can be illustrated in the above picture of two harmonic oscillators (blackbodies) connected by a spring (radiation) as a transfer of energy between the oscillators by the connecting spring.

Particle model:

In a particle model of radiative transfer each blackbody is supposed to both emit and absorb photons with the hotter body emitting more than absorbing and thus losing heat and the colder body absorbing more than emitting and thus heating up. This is a primitive model without the physics of resonance.

A model is primitive if the essential physics is missing. A primitive model does not help understanding and has little predictive capability. Primitive is not the same as simple.

A simple model describing essential physics (e.g. Newton's 2nd law) is not primitive and thus may be useful.

CO2 alarmism is based on a particle model for radiative heat transfer supposed supporting

an idea of DLR/backradiation. This is primitive.

Science Collapse from Wave-Particle Duality

Physics books generally propagate a concept of wave-particle duality expressing that matter and light on atomic scales can exhibit both wave and particle properties. In particular, the old wave-particle controversy on the nature of light going back to Huygens-Newton, which was revived with the introduction of quantum mechanics, is presented as a Solomonic compromise that light is both particle and wave.

Newton's particle theory of light was replaced by a wave theory expressed by Maxwell's equations in the late 19th century, but particles were reintroduced in the early 20th century by Planck to explain blackbody radiation and by Einstein to explain the photoelectric effect. Light was here seen as a stream of light particles later named photons.

Wave-particle duality was then in the hands of Bohr and his Copenhagen interpretation described as wave-function collapse expressing that Schrödinger's distributed continuous wave function "collapsed" into a singular point/delta function upon observation.

But to be both particle and wave is a logical contradiction like being both square and circular at the same time, and logical contradictions in science are catastrophic. From a contradiction anything can follow and the crisis of physics of today can be seen as a result of this contradiction. The fiction of "wave-function collapse" of Bohr designed to handle the contradiction prepared for the real collapse of physics of today. Wave-particle duality is double-speak and double-speak in science is catastrophical.

Is there then any way of avoiding the collapse? Is it possible to throw out particles once and for all and be happy with only waves in a consistent wave theory? A number of physicists say yes, see Are There Any Photons at All? and Collective Electrodynamics by Carver Mead. It is further possible to describe both blackbody radiation and the photoelectric effect using wave theory.

The evidence for waves is massive while the evidence for particles is almost nil. In particular, wave theory has a mathematical expression in the form of Maxwell's equations and Schrödinger's wave equation as compact general descriptions of electro-magnetics and quantum mechanics. Particle theory has a trivial mathematical expression as straight lines traced by rays of photons. Particle theory is bogged down by infinities from singularities of

point/delta functions.

A physical theory with a non-trivial mathematical expression is very useful. This is wave theory.

A physical theory with a trivial mathematical dress is not useful. This is particle theory.

Recall the late Einstein did not believe in the light quanta or photons he had happened to let in to the inner room of science, as he confessed shortly before his death (1954):

• 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.

Particle theory is behind the idea of DLR/backradition playing a key role in CO2 climate alarmism expressing a collapse of climate science.

What do physicists of today say about the collapse from wave-particle duality? Nothing it seems. Because physics has collapsed?

Radiative Heat Transfer: Phlogistons and Photons

I will now argue that phlogiston theory has similarities with photon theory of light in the case of infrared radiation of global climate.

Phlogiston theory says that all combustible resources contain particles named phlogistons without colour, odor, taste or mass, which are liberated in burning.

Photon theory says that light consists of particles named photons without mass and charge carrying energy along straight lines at a constant speed of light. Photons have different frequencies and and energy proportional to frequency.

Photon theory describes radiative heat transfer between two bodies as a two-way stream of photons emitted/absorbed by the bodies, with the hotter body emitting photons of higher frequency and in higher numbers as compared to the colder body, which results in a net transfer of heat energy from hot to cold.

Photon theory is a particle theory of light going back to Newton's corpuscular theory of light,

and is to be compared with the wave theory of light as electromagnetic waves described by Maxwell's equations. The wave theory of light describes almost all observed phenomena of light.

The wave theory of light replaced the particle theory in the late 19th century, but was revived in the early 20th century by Planck to describe blackbody radiation and by Einstein to describe the photoelectric effect.

Phlogiston theory is no longer taught, but the photon theory of light is still used to explain certain phenomena believed to be difficult to explain by a wave model, typically related to the

phenomena of emission and absorption involving interaction between matter and electromagnetic waves. In photon theory emission is seen as ejection of photon particles and

absorption as the opposite.

For visible light, emission of photons as finite quanta of energy can be associated with discrete changes of atomic electronic structure. For infrared radiation with much larger wave lengths than atomic dimensions, the interaction between matter and waves must involve collective motion of many atoms and the photon theory does not seem to be applicable.

This mean that photon theory cannot be used to describe blackbody radiation at the modest temperatures of global climate. In this case the photon theory is similar to the phlogiston theory as a very simplistic theory with little predictive capability, and a wave theory based on Maxwell's equations can be preferable, as shown in Mathematical Physics of Blackbody Radiation.

The fact that photon theory can be useful for certain applications at high-energy short wave-lenghts, does not mean that it is also uselful for completely different applications at low-energy long wave-lengths.

Nevertheless, the photon theory serves as support of the propaganda of CO2 alarm based on

the idea that streams of photons from the atmosphere contribute to global warming as DLR/backradiation, which rather represents phlogiston theory than real physics.

Radiative Heat Transfer: History

Radiative heat transfer is described in two different ways, as:

1. One-way net transfer from hot to cold.
2. Two-way transfer between hot and cold with net transfer from hot to cold.

I argue that 1. is physical obeying the 2nd law of thermodynamics, while 2. is unphysical violating the 2nd law.

The origin of 1. and 2. is traced in The Laws of Radiation and Absorption and Pictet's Experiment back to

1. Pictet:

• two-way wave theory
• one-way transfer of heat energy from hot to cold.

2. Rumford (Benjamin Thompson):

• wave theory
• radiant heat as an analog to sound
• higher frequencies excite lower frequencies: heating.

3. Prevost:

• particle theory, corpuscular fluid caloric
• matter of heat or fire
• quanta of energy
• two-way transfer with hot winning over cold.

The difference between 1. + 2. and 3 is expressed clearly in different views on the case with two bodies of equal temperature:

• Pictet/Rumford: no exchange of heat energy because of a "balance of power" as standing wave.
• Prevost: exchange of equal quanta of energy.

The difference can also be seen in the experiment by Pictet illustrated above, with an object and a thermometer placed in the foci of two concave mirrors:

Pictet observed that if the body was chilled by ice, then the thermometer initially at room temperature showed cooling, as if coldness or cold was transferred from the ice to the thermometer. If the body or thermometer was out of focus nothing happened, apparently because the radiative contact disappeared.

The experiment was initially met with surprise suggesting an exchange of something like "quanta of cold" transferred by "frigorific rays" as an analog to exchange of quanta of heat

by a stream of photons.

Pictet gave the natural explanation based on 1. that what happens is that the warm thermometer heats the ice and thus looses heat showing cooling.

Prevost gave a different explanation based on 2. as an imbalance of exchange of "fire particles"

with the effect that the warmer thermometer loses more particles than it receives and thus cools off.

Notice that 3. is similar to the phlogiston theory about a fire-like element released during combustion. Phlogiston theory is no longer part of science, but surprisingly 2. has survived with support of the idea of radiative heat transfer as streams of energy quanta or photons coming from quantum mechanics.

3. thus represents a strange mix of old phlogiston theory and modern physics, and this mix is used by CO2 alarmists to sell the idea of DLR/backradiation.

It is now time to once and for all finish the debate between 1. + 2. and 3. and put 3. into the wardrobe together with phlogiston theory.

3. violates the 2nd law by allowing transfer of heat from cold to warm and 2. serves no other role than supporting CO2 alarmism.

Radiative Heat Transfer: Theory

In a couple of posts I will seek to summarize experience on radiative heat transfer between two bodies of different (or equal) temperature. We will see that there are two models with deep historical roots:

1. One-way net transfer from hot to cold.
2. Two-way transfer between hot and cold with net transfer from hot to cold.

I argue that 1. is physical obeying the 2nd law of thgermodynamics, while 2. is unphysical violating the 2nd law.

2. represents the model underlying CO2 alarmism with DLR/backradiation from a cold atmosphere to a warm Earth.

I will first consider 1. as expressed in the model studied in Computational Blackbody Radiation

and Mathematical Physics of Blackbody Radiation.

This model is based on a frequency cut-off increasing with temperature, which means that a radiating body is only able to absorb and re-radiate frequencies below cut-off, while frequencies above cut-off are absorbed and stored as internal heat energy. The result is that a body can radiatively transfer heat energy to a body of lower temperature with lower cut-off, but not the other way around. In other words, the model satisfies a 2nd law of thermodynamics.

We thus consider the following wave model for radiation as a continuum of oscillators with damping of the form:

(1) $U_{tt} - U_{xx} - \gamma U_{ttt} - h^2U_{xxt} = f $

where the subindices indicate differentiation with respect to space $x$ and time $t$, and

1. $U_{tt} - U_{xx}$ represents the oscillators in a wave model with U displacement
2. $- \gamma U_{ttt}$ is a dissipative term modeling outgoing radiation
3. $- h^2U_{xxt}$ is a dissipative modeling internal heating
4. $f$ is incoming forcing/microwaves,

where $\gamma$ represents the constant in Planck's radiation law and $h$ represents a smallest mesh size, connected to dissipative losses as outgoing radiation and internal heating, respectively. The model establishes an energy balance between incoming forcing $f$ measured as

• $F = \int f^2(x,t)\, dxdt$

assuming periodicity in space and time and integrating over periods, and (rate of) outgoing radiation $R$ measured by

• $R = \int \gamma U_{tt}^2\, dxdt$,

oscillator energy $OE$ measured by

• $OE =\frac{1}{2}\int (U_t^2 + U_x^2)\, dxdt$

(rate of) internal energy measured by

• $IE = \int h^2U_{xt}^2\, dxdt$

with the energy balance in stationary state expressed as

• $F = R + IE$
• incoming energy = outgoing radiation energy + stored internal energy.

Assuming that all frequencies have the same temperature, a common temperature $T$ can be defined by $OE$ and $IE$.

The model has temperature dependent frequency cut-off which effectively means that for frequencies $\nu$ below cut-off $IE_{\nu}=0$ and for frequencies above cut-off $R_{\nu}=0$ with $IE_{\nu}$ and $R_{\nu}$ the contribution to $IE$ and $R$ from frequency $\nu$.

The model can be used to describe radiative heat transfer between two bodies in radiative contact established by sharing the forcing $f$, with the first body satisfying (1) and the second body satisfying a similar wave equation with displacement $V$:

(2) $V_{tt} - {V}_{xx} - \gamma {V}_{ttt} - h^2{V}_{xxt} = f$

The model (1) + (2) can now be used to describe the heat transfer between a body 1. with temperature $T_1$ described by (1) and a body 2. with temperature $T_2$ described by (2). Assuming that $T_1>T_2$, we have for frequencies below cut-off for 1. and above cut-off for 2. (leaving out a frequency subindex) in stationary state:

• $F = R_1 = IE_2$

which effectively expresses transfer of heat from the hotter 1. to the colder 2. For frequencies

below the cut-off of 2. (with $R_1=R_2$) and above the cut-off of 1. (with $IE_1=IE_2$) there is no heat transfer.

The above model thus describes one-way radiative heat transfer from hot to cold with the radiation $R_1$ from 1. being transfered into heating $IE_2$ of 2. in the frequency range between the respective cut-offs. The 2nd law of thermodynamics is thus enforced by a temperature-dependent cut-off shifting outgoing radiation to internal heating for frequencies above cut-off.

The above description covers the basic one-way aspect of the heat exchange between the two bodies, assuming oscillator energy to be stationary.

Transfer of $IE$ into $OE$ requires separate modeling. One can think of the internal energy $IE$ as incoherent high frequency energy which can be organized into coherent oscillator motion stored as $OE$, which can be emitted as coherent radiation $R$.

Radiation Double-Speak

In politics it is necessary to use words with multiple meaning to allow different people to make different interpretations of words like "equality", "liberty" and "justice". The society of Orwell's 1984 can only exist with doublespeak.

Doublespeak is also used in science, although in principle scientific terms are supposed to be well defined. An example of a term with double meaning is "radiation" which is used in two different ways:

1. as immaterial electromagnetic wave
2. as transfer of heat energy between material bodies.

In a wave model it is possible to make a distinction between 1. an electromagnetic wave as an immaterial carrier or medium for the 2. transfer of heat energy between material bodies. An essential scientific question the concerns the interaction of emission and absorption between the immaterial wave and the material body as the heat energy is transferred.

It is possible to allow the waves to be two-way, while the transfer of heat energy is one-way from warm to cold, as shown in Computational Blackbody Radiation and Mathematical Physics of Blackbody Radiation.

This distinction is however not possible if a particle model is used, if radiation is viewed as a stream of "energy quanta" or photon particles, since then the carrier is the same as the carried energy (in analogy with Marshall Macluhans "the medium is the message").

In a particle model the processes of emission and absorption are viewed as as a "spitting out" and "swallowing" of photons or "packets of heat energy" or "quanta", in a primitive line of thought. The transfer of heat energy like particle motion becomes two-way, with the body spitting the most winning a game of heat transfer.

The confusion in the debate on DLR/backradiation as the basis of the greenhouse effect of CO2 alarmism, comes from the doublespeak of radiation as both 1. and 2. This makes it possible to speak about "radiation from the colder atmosphere to the warmer Earth surface" as "Downwelling Longwave Radiation" even if such a transfer would violate the 2nd law.

The particle model of light introduced by Newton was replaced by Maxwell's wave model in the late 19th century, but was then surprisingly reintroduced by the early Einstein and Planck while the late Einstein did not accept that idea of light as a stream of particle quanta.

A particle model of light is indeed very primitive and lacks in particular for IR or microwaves, all rationale because the wave length is millions of times larger than the atomic dimensions.

A primitive particle model allows doublespeak flipping back and forth between 1. and 2.

and this is cleverly used by CO2 alarmists to meet critique that DLR/backradiation

violates the 2nd law. But this is primitive and is no longer possible if a less primitive wave model is used.

Note that Planck in the Faustian deal of previous post made in the preface to his Theory of Heat Radiation, struggles to explain why he has given up a wave model of radiation, in order to give the impression that he is not using doublespeak of both particle and wave.

But Planck did not save modern physics from doublespeak, with the wave-particle duality as

the ultimate expression of doublespeak, elevated to virtue in modern physics.

Notice that an electromagnetic wave cannot store energy, while a material body can store energy as heat: As soon as the light emission form a material body is turned off, the light goes off, and there is no light to be absorbed. This shows that the electromagnetic wave is a carrier of energy without capacity to store energy itself. An electrical circuit with capacitor and inductor can store energy, but not a light wave.

In a particle model the stream of particles as energy quanta represent stored energy, and again the distinction between the immaterial transmitter of energy and and material energy becomes muddled.

The Faustian Deal of DLR/Backradiation by Planck

Max Planck just after having made the deal with statistics of quanta in 1900.

In our search for the origin of the idea of DLR or backradiation, let us see what Planck says

in the Preface to the 2nd edition of his Theory of Heat Radiation from 1914 when explaining the difference as compared to the 1st edition from 1907:

• The main fault of the original treatment was that it began with the classical electrodynamical laws of emission and absorption, whereas later on it became evident that, in order to meet the demand of experimental measurements, the assumption of finite energy elements must be introduced, an assumption which is in direct contradiction to the fundamental ideas of classical electrodynamics.
• It is true that this inconsistency is greatly reduced by the fact that, in reality, only mean values of energy are taken from classical electrodynamics, while, for the statistical calculation, the real values are used; nevertheless the treatment must, on the whole, have left the reader with the unsatisfactory feeling that it was not clearly to be seen, which of the assumptions made in the beginning could, and which could not, be finally retained.
• In contrast thereto I have now attempted to treat the subject from the very outset in such a way that none of the laws stated need, later on, be restricted or modified. This presents the advantage that the theory, so far as it is treated here, shows no contradiction in itself, though certainly I do not mean that it does not seem to call for improvements in many respects, as regards both its internal structure and its external form. To treat of the numerous applications, many of them .very important, which the hypothesis of quanta has already found in other parts of physics, I have not regarded as part of my task, still less to discuss all differing opinions.

In short, what Planck does here is to give up his analysis of blackbody radiation based on a classical deterministic continuum physics wave model in the form of Maxwell's equations (classical electrodynamics) for an analysis based on statistical particle physics model borrowed from thermodynamics.

Planck thus replaces deterministic continuum mechanics by statistical mechanics of quanta, an thus finally gives up his long struggle to save his rational soul from the statistics of quanta he had introduced in 1900 with the words:...

• ...the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be

but which had propelled him to become the father of modern physics. Planck thus made a true Faustian deal, which is described in the upcoming book Dr Faustus of Modern Physics.

As concerns DLR/backradiation Planck states on page 1 of his 1914 book:

• All heat rays which at a given instant pass through
  the same point of the medium are perfectly independent of one
  another, and in order to specify completely the state of the
  radiation the intensity of radiation must be known in all the
  directions, infinite in number, which pass through the point in
  question; for this purpose two opposite directions must be
  considered as distinct, because the radiation in one of them is
  quite independent of the radiation in the other.
• ...heat rays are identical
  with light rays of the same wave length. The term "heat
  radiation" then, will be applied to all physical phenomena of the
  same nature as light rays.
• Every light ray is simultaneously a
  heat ray.
• As a further consequence of this law we shall
  apply to the radiation of heat all the well-known laws of
  experimental optics, especially those of reflection and refraction, as
  well as those relating to the propagation of light.

Planck speaks about "heat rays" as streams of "heat particles", in analogy with "light rays" as streams of "light particles" or "photons", in opposition to light as wave phenomenon.

Newton proposed a particle theory of light which was abandoned when Maxwell showed that light is an electromagnetic wave phenomenon. Planck and Einstein reintroduced the old particle theory because of certain perceived difficulties with Maxwell's wave model.

In Mathematical Physics of Blackbody Radiation I propose a way out of these difficulties

based on a new concept of finite precision computation within Maxwell's wave model and without any particle statistics.

A particle model of light must viewed as primitive, and as a primitive model it is misleading, in particular misleading into an unphysical concept of a two-way transfer of heat energy between bodies of different (or equal) temperature carried by "heat rays" traveling back and forth. Very primitive, indeed. But very popular among CO2 alarmists.

If Planck would have been alive today, we could have asked him about the rationality of his "heat rays" supporting CO2 alarmism. Since this is not the case we have to ask living physicists but they say nothing,

just refer to Planck in his grave.

Do Living Physicists Support DLR/Backradiation?

The inventor of the idea of DLR/backradiation supporting CO2 alarmism: Pierre Provost, 1791.

In Section 5.2 of Mathematical Physics of Blackbody Radiation I recall the following statement from Planck's The Theory of Heat Radiation:

• We shall assume that the radiation in one direction is completely independent of the radiation in a different direction, even opposite.
• But the empirical principal law that the emission of any volume-element depends entirely on what takes places inside of this element holds true in all cases (Prevost's principle). A body A at $100^{\circ} C$ emits toward a body B at $0^{\circ} C$ exactly the same amount of radiation as toward an equally large and similarly situated body B' at $1000^{\circ} C$. The fact that the body A is cooled by B and heated by B' is due entirely to the fact that B is weaker, B' stronger emitter than A.

This statement can be seen as the origin of the idea underlying CMB and DLR that the radiation from a blackbody is independent of the temperature the environment or background. Planck refers as support to Prevost's exchange principle from 1791:

• Absolute equilibrium of free heat is the state of this fluid in a portion of space which receives as much of it as it lets escape. Relative equilibrium of free heat is the state of this fluid in two portions of space which receive from each other equal quantities of heat, and which moreover are in absolute equilibrium, or experience precisely equal changes.
• The heat of several portions of space at the same temperature, and next to one another, is at the same time in the two species of equilibrium.

Mathematical Physics of Blackbody Radiation I give a new analysis of blackbody radiation challenging the idea of Provost/Plank of two-way radiative exchange of heat between two bodies with the hotter winning the game of net heat transfer as a stronger emitter.

So what is true physics:

1. Is radiative heat transfer one-way from hot to cold, as my analysis suggests?
2. Is radiative heat transfer two-way with the hotter being the stronger, as Provost claimed in 1791?

Does it matter? I say yes, because the stability properties can be vastly different in one-way and two-way transfer. It can be the difference between a harmless climate sensitivity of 0.3 C and and alarming of 3 C.

To empirically distinguish between 1. and 2. is difficult since only net heat transfer is directly observable. To refer to two-way transfer as an empirical principal law, as Planck does, is questionable.

The question is open. It would be interesting to see new independent support of 2. from active physicists living today. One can argue that the 2nd law of thermodynamics supports 1. but not 2. The 2nd law was unknown to Provost.

A scientist putting forward a certain statement as true often refers to some other scientist as being the responsible, typically the scientist who first gave the evidence of the truth. If that

first scientist is dead and cannot answer questions, which is often the case (as in Planck's reference to Provost), a scientific controversy may arise from different interpretations of what the now dead scientist actually meant or did. Therefore science should be carried by living scientists who carry the responsibility and are willing to answer questions.

In the present case there is a confusion between

• radiation as electromagnetic wave,
• radiation as heat transfer,

which makes the debate confusing, but there seems to be no living physicist willing to answer the questions and carry the responsibility.

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.

The Fiction of Heating by DLR and CMB

The Holmdal Horn Antenna used by Penzias and Wilson to first discover CMB.

This is a continuation of the post Picture of CMB from Resonance, Not Radiative Heating.

Cosmic Microwave Background Radiation (CMB) is supposed to be a "faint glow" at 3 K of thermal radiation filling the empty space of the Universe as relic of Big Bang and Downwelling Longwave Radiation (DLR) is similarly supposed to be a "glow" of the atmosphere with the effect of heating the Earth surface.

DLR is supposed to be very substantial, of the same size as the insolation, about 300 W/m2, while CMB is indeed very faint about 100 million times smaller, in accordance with Stefan-Boltzmann's radiation law (SB) stating that radiance scales like $T^4$ with $T$ temperature in Kelvin K and the temperature of the atmosphere is about $100\times 3$ K.

Measurements of CMB by the COBE gave the Nobel Prize in Physics in 2006 to Georg Smooth and John Mather for discovering CMB. Similarly, measurements of DLR are presented as evidence of DLR supporting CO2 alarmism.

The existence of both CMB and DLR is thus manifested by certain instrument readings and to understand the nature of CMB and DLR, we have to ask what in fact the instrument or detector, is recording.

The detector of CMB is a radio-telescope, which like a radio tuner tunes in different resonance frequencies of an antenna which produces an electrical signal, which is amplified into a recording over frequency or a spectrum.

The recorded spectrum is matched with a black-body spectrum according to Planck's law,

where the peak of the recorded spectrum determines the temperature (3 K) from which a radiance can be computed by Planck's law. The recorded spectrum is thus translated by using Planck's law into a radiance measured in W/m2, which is perceived as a "faint glow".

Does this mean that the faint glow of CMB is heating the Earth? There are two answers, depending on which form of Stefan-Boltzmann's radiation law (sum over frequencies of Planck's law) we are willing to use: False-SB or True-SB.

False-SB says that the faint glow of CMB heats the Earth with $\sigma T_b^4$ W/m2 where $\sigma$ is Stefan-Boltzmann's constant and $T_b$ is the temperature computed from the spectrum. False-SB states that there is a flow of heat energy from empty space to the Earth of size $\sigma T_b^4$ (with $T_b = 3$ K).

True-SB states that there is a transfer of heat energy from the Earth(+atmosphere) to space of size $\sigma (T^4 - T_b^4)$ where $T > T_b$ is the temperature of the Earth, but no transfer from space to the Earth.

False-SB is false in the sense that it lacks description/justification in physics literature.

True-SB has massive theoretical and experimental support.

We sum up our experience of CMB:

1. CMB is measured by radio resonance into a spectrum without physical scale because of signal amplification.
2. The recorded spectrum is matched with Planck's law to give a temperature $T_b$.
3. False-SB is used to compute a radiance $R =\sigma T_b^4$ as a faint glow of CMB heating the Earth.

A similar procedure is used to record a spectrum of DLR, and from the spectrum compute

DLR as heat transfer/radiance from the atmosphere to the Earth.

We see that in both cases, a spectrum is recorded, and from the spectrum a radiance is computed by a False-SB. We understand that an instrument recording of CMB/DLR is one thing, and radiance of CMB/DLR is something different: It is not recorded but computed using a False-SB without physical justification.

We conclude that the interpretation of CMB/DLR as radiance expressed in W/m2, lacks rationale. CMB should not be described as a "faint glow". DLR should not be viewed as heating the Earth surface.

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?

Picture of CMB from Resonance, not Radiative Heating

The Cosmic Microwave Radiation (CMB) shows a blackbody spectrum of temperature 2.725 K

peaking at a wave length of about 0.2 cm beyond the far infrared spectrum. CMB is detected by radio-telescopes by resonance like radio antennas resonating with incoming radio waves thus generating a weak electrical signal which can be amplified into detection.

It would be difficult to detect CMB by thermal IR-imaging since the signal is very weak and thermal detection would require a detector at lower temperature than 2.725 K.

The concept of Downwelling Longwave Radiation DLR from the cold atmosphere to the warm Earth surface plays a key role in CO2 alarmism. CMB is here presented as an ultimate form of DLR with the argument that a picture of CMB shows that DLR is real. If even the cold dark space is contributing to global warming, then global warming must be real, right?

Let us now scrutinize this argument in the setting of mathematical model of blackbody radiation studied in Computational Blackbody Radiation, in the case of a radio-telescope as CMB-detector. The model takes the form of set oscillators with damping (see here for some more details)

• $U_{tt} - U_{xx} - \gamma U_{ttt} - h^2U_{xxt} = f$

where the subindices indicate differentiation with respect to space $x$ and time $t$, and

1. $U_{tt} - U_{xx}$ represents the oscillators in a wave model
2. $- \gamma U_{ttt}$ is a dissipative term modeling outgoing radiation
3. $- h^2U_{xxt}$ is a dissipative modeling internal heating
4. $f$ is incoming forcing/microwaves,

where $\gamma$ represents the constant in Planck's radiation law and $h$ represents a smallest mesh size, connected to dissipative losses as outgoing radiation and internal heating, respectively.

Microwaves are characterized by low frequency and long wave length (compared to visible and

infrared light) and in this case the dissipative loss of internal heating is small and is not detectable while the resonance can be detected after amplification just like a radio antenna is capable of detecting a weak radio wave by resonance followed by amplification.

Pictures of CMB are thus produced by an IR-camera in the form of a radio-telescope which works by resonance and not radiative heating. A CMB picture can therefore not be used as evidence that the weak glow of CMB acts as in a weak form of radiative heating named DLR or backradiation. This is because the CMB picture is not obtained from detection of radiative heating, but from resonance and amplification.

We conclude that a CMB picture is not any evidence of DLR, because no DLR is detected.