Claes Johnson on Mathematics and Science

Questioning Relativity

2012-01-17T23:36:00.000-08:00

There is a new sequence of posts on World As Computation questioning Einstein's special and general theory of relativity through the following themes:

Lennart Bengtssons Dubbla Budskap 3

2012-01-12T00:15:00.000-08:00

Lennart Bengtsson tuggar oförtrutet vidare med förnyat dubbelt budskap i SvD som både klimatalarmist och skeptiker:

Modellberäkningar av jordens klimat, som till sin natur är osäkra, indikerar risker för en förhöjd temperatur under detta sekel kanske på så mycket som ytterligare 2–3 grader. För att reducera denna risk måste givetvis växthusgasutsläppen på sikt minska och detta inte bara i västvärlden.
Det finns dock ingen anledning att framhäva extrema oväder då detta inte blir en följd av ett varmare klimat. Detta skulle Wijkman och Rockström säkert begripa om det hade studerat meteorologi och inte som nu prata i nattmössan.

LB är ytterst vetenskaplig garant för svensk klimatpolitik genom KVAs uttalande om den vetenskapliga grunded för klimatförändringar som han så klart uttrycker i 1.

Genom 2. vill nu LB nu uppenbarligen backa från den alarmism han uttrycker i 1. Detta tillnyktrande är bara att välkomna, men då måste också KVAs uttalande skrivas om.

Direkt fråga till LB: När kommer denna revision? Eller blir det inget?

Lennart Bengtssons Dubbla Budskap 2

2012-01-09T23:22:00.000-08:00

Min analys att Lennart Bengtsson far med dubbla budskap vad gäller farligheten av mänskliga utsläpp av koldioxid, får idag stöd av Johan Rockström och Anders Wijkman i SvD Klimatutsläppen bör inte bagatelliseras:

Å ena sidan bejakar Bengtsson den av människan orsakade klimatförändringen.
Å andra sidan hävdar han att utsläppen inte bidrar nämnvärt till extrema väderhändelser.
Bengtsson avrundar med att raljera över förslag att minska koldioxidutsläppen.
I stället vill han fälla ”litet mera skog längs vägar, järnvägar och högspänningsledningar för att minska skadorna för trafik och elförsörjning”.
Det är djupt olyckligt när en ledande forskare som Lennart Bengtsson bagatelliserar utsläppen av växthusgaser.

Ja, det är djupt olyckligt när den forskare som ytterst ansvarar för svensk klimatpolitik genom att ha skrivit KVAs yttrande om den vetenskapliga grunden för klimatförändringar, kommer med två motstridiga budskap:

Koldioxidutsläpp är farligt, i enlighet med IPCC.
Koldioxidutsläpp är inte farligt, i motsats till IPCC.

KVA måste nu komma ut ur garderoben och bekänna färg: 1 eller 2? När detta är gjort kommer svensk klimatpolitik att skrivas om.

No Solutions to New Years Puzzle

2012-01-02T11:37:00.000-08:00

The New Year Puzzle has not received any convincing solutions and therefore additional clues are offered in new posts on The World As Computation:

Utsätt Svensk Klimatpolitik för Riksdagens Hearing

2012-01-02T03:13:00.000-08:00

Svensk klimatpolitik grundar sig på KVAs uttalande Den Vetenskapliga Grunden för Klimatförändringar som ansluter sig till FNs klimatpanel med begränsning av koldioxidutsläpp som främsta mål och medel.

Kanada har nu insett att denna politik har nått vägs ände och lämnar Kyoto överenskommelsen om utsläppsbegränsning. Även svensk klimatpolitik måste nu revideras.

För att ge underlag bör Riksdagen genomföra en hearing om klimatvetenskap med deltagande av såväl företrädare som kritiker till nuvarande dogma.

Jämför med den hearing som Kanadas senat nyligen genomförde med skeptiker inkl Ross McKitrick.

Lennart Bengtssons Dubbla Budskap

2011-12-30T07:01:00.000-08:00

Vem är LB? Varför så glad?

Lennart Bengtsson, prof i meteorologi och ledamot av Kungliga Vetenskapsakademien (KVA), är huvudansvarig för KVAs uttalande Den Vetenskapliga Grunden för Klimatförändringar. KVA slår fast följande vetenskapliga grund för svensk klimatpolitik:

FN:s klimatpanel IPCC har gjort en bred och systematisk sammanfattning av den vetenskapliga litteratur som behandlar klimatförändringen.
Gruppen har dragit slutsatsen att antropogena utsläpp av växthusgaser har lett till en ökning av temperaturen vid jordens yta.
Medan effekten av växthusgaser är väletablerad, är förståelsen för effekten av aerosoler (vilka huvudsakligen orsakar en kompenserande nedkylning) mycket mindre.
En ökning av koldioxidhalten i atomsfären orsakar också en försurning av haven, vilket kan få mycket allvarliga effekter på marina ekosystem.
Samtidigt som en mindre uppvärmning kan vara acceptabel, åtminstone i vissa regioner, kommer en högre grad av uppvärmning sannolikt orsaka mycket allvarliga problem världen över.
Det finns också en möjlighet, även om den troligen är liten, att stabiliteten hos vissa landisar kommer att minska vilket kan leda till en snabbare höjning av havsnivåerna.
För det första förväntas den långa uppehållstiden av CO2 i atmosfären påverka atmosfärens sammansättning under flera hundra år, förmodligen med oåterkalleliga konsekvenser för jorden under för människan överskådliga tidsrymder.
För det andra finns det en möjlighet, om än liten, för extrema och snabba svängningar i klimatsystemet, vilket kan resultera i en snabb höjning av havsnivån eller långvariga perioder av torka i utbredda områden som är viktiga för matproduktion.
Omfattande åtgärder mot klimatförändringarna måste därför innehålla både
ett vetenskapligt förhållningssätt, med huvudmålet att åstadkomma en bättre kvantifiering av allvarliga och oacceptabla risker,
och ett samhälleligt förhållningssätt med målet att, baserat på det rådande kunskapsläget, begränsa riskerna.

Vi ser att KVAs uttalande är helt i linje med den koldioxidalarmism som IPCC propagerar över världen.

LB har skrivit KVAs uttalande, men frågan är om LB står bakom vad han låtit KVA uttala?

Det verkar inte så om man läser LBs debattartikel i SvD med rubriken Att Minska Utsläpp Löser Inte Problemen där LB tar avstånd från koldioxidalarmism.

Det är nu dags att visa Dina kort Lennart Bengtsson!

När Du så gjort kommer svensk klimatpolitik att skrivas om.

Go ahead! Svenska folket väntar på besked!

Följ den spännande upplösningen i direktsändning från The Climate Scam.

Lennart Bengtssons Svenska Klimatpolitik

2011-12-28T23:47:00.000-08:00

Lennart Bengtsson: Meningslöst att minska utsläppen av koldoxid.

Lennart Bengtsson är ansvarig för KVAs uttalande Den Vetenskapliga Grunden för Klimatförändringar med stöd till FNs och IPCCs koldioxidalarmism.

Lennart Bengtsson är därmed vetenskaplig garant för svensk klimatpolitik med radikala utsläppsbegränsningar som mål.

Men Lennart Bengtsson är en dubbelnatur, som både säger A och icke-A: I dagens SvD Brännpunkt sågar Bengtsson samma svenska klimatpolitik under titeln Att minska utsläpp löser inte problemen:

Al Gore och många klimataktivister menar att om vi bara kan få stopp på växthusgasutsläppen kommer situationen att förbättras. Tyvärr är det inte så enkelt.
Extrema väderhändelser är allvarliga och allt bör göras för att minska risk för liv och egendom...Men att föreställa sig att skadeökningarna främst beror på koldioxidutsläppens ökning är naivt och missledande.
Det saknar dessutom vetenskaplig substans.
I många länder är extrem kyla faktiskt värre än extrem värme och ger upphov till större förlust i människoliv.

För mera i samma kritiska anda, se Bengtsson sågar IPCCs Klimatmodellering.

Bengtsson säger alltså

A = begränsa utsläppen av koldioxid (KVA)
icke-A = begränsa inte utsläppen eftersom det är meningslöst (SvD).

Men man kan inte säga både A och icke-A om man via KVA skall vara vetenskaplig garant för svensk klimatpolitik.

Vad som nu behövs är att KVA reviderar sitt uttalande och tar avstånd från IPCC. När kommer det Lennart Bengtsson?

Bengtsson's eget förslag till lösning av klimatfrågan är enkelt och klart genomförbart:

föreslår jag som en praktisk åtgärd att man fäller litet mer skog längs vägar, järnvägar och högspänningsledningar...

PS Bengtsson har också offentligt uttalat att min klimatmatematik är "rappakalja". Kanske även detta behöver revideras?

Clue to Puzzle: God's Equation

2011-12-28T00:57:00.001-08:00

There is a new post on The World As Computation about about the connection between matter/antimatter/dark-matter and gravitation/dark-energy.

Christmas and New Year Puzzle

2011-12-24T01:02:00.000-08:00

The World as Computation presents a Christmas and New Year Puzzle.

Many thanks to the Readers of this blog for this year!

Dark Energy: Repulsion by Implosion?

2011-12-20T11:22:00.000-08:00

There is a new post on The World as Computation about dark energy.

Dark Age of Physics: Parallel Universes

2011-12-19T06:44:00.000-08:00

There is a new post on The World as Computation:

Dark Age of Physics: Parallel Universes.

Skitskola: Vem Bär Ansvaret?

2011-12-17T01:42:00.000-08:00

I SVT URs Världens Bästa Skitskola får vi veta att svenska elevers kunskaper i matematik är dåliga: Att dividera 800 med 100 visar sig vara för svårt för de flesta, något som kinesiska barn i tredje klass visas gapskratta åt.

En lektor på KTH meddelar svenska folket:

Tillståndet i matteundervisningen Sverige är sämre än i en del U-länder.
Helt bedrövligt att elever går genom grundskola och gymnasium utan att lära sig de enklaste basgrejer.
Sverige ligger efter, har stoppat huvet i sanden under lång tid.

Katastrof alltså. Men finns det ansvariga för sakernas tillstånd? Vi borde kunna hitta ansvariga bland

professorer och lektorer i matematik
lärarutbildare
lärare
politiker.

SVT UR ställer inte frågan om ansvar. Jag har själv sökt hitta ansvariga men bland Bockarna Bruse bara blivit hänvisad uppåt eller neråt utan att vara sig hitta Stora eller Lilla Bocken Bruse med ansvar. Är inte detta konstigt?

Är det inte konstigt att min debattartikel som nu ligger uppe på Ny Teknik tigs ihjäl av alla Bockarna Bruse?

Redan nu kan elever med dyskalkyli få använda dator för att bättre klara skolan och skolmatematiken. Enligt SVT UR verkar det som om de flesta svenska elever har detta syndrom och alltså skulle kunna få en iPad.

Vad gäller s k u-länder så får nu alla elever i Rwanda en laptop vid skolstart och många länder är på väg att följa. Så småningom kommer även Sveriges skola att gå in i dataåldern, men är det verkligen så begåvat att bli sist? Det är väl egentligen inte så svårt att räkna ut att det är korkat och helt onödigt?

How to Get a Nobel Prize

2011-12-16T07:47:00.000-08:00

There is a new post on The World as Computation presenting a scientific method of How to Get a Nobel Prize.

Keep confidential. Do not spread!

Is the Cosmological Principle Valid?

2011-12-16T03:53:00.001-08:00

I have written a new post on The World as Computation:

Is the Cosmological Principle Valid?

The answer is: No.

Debatt Ny Teknik: Ipad åt Alla

2011-12-14T00:38:00.000-08:00

I Rwanda får nu alla elever en laptop från 9 års ålder.

Min debattartikel om Matematik-IT som nytt kärnämne i skolan har nu publicerats i Ny Teknik.

Som vanligt tiger de som har ansvar för att skolmatematiken idag är en katastrof, professorer,

lärarutbildare och pedagoger, med Jan Björklund överst.

Som vanligt finns det många kommentatorer som inte har förstått att IT och matematik hör ihop.

Men det finns också positiva röster, som vittnar om att iPad i förskolan funkar bra.

Matematik-IT med Ipad åt Alla kommer att bli ett effektivt konkurrensmedel i jakten på elever där friskolorna nu kommer att ta täten och kommunala skolor snart måste följa.

Proppen är Jan Björklund, och hoppet går till Mikael Damberg: En lysande chans för S att komma ur sin förlamning med en framtidsinriktad skolpolitik.

From Google Knol to Annotum

2011-12-12T23:11:00.000-08:00

Google Knol launched in 2009 as a challenge to Wikipedia, is now being discontinued and transformed into Annotum at Wordpress with the following motivation:

Google is prioritizing our product efforts so we can make things much simpler for our users and devote more resources to high impact products.

Evidently knowledge was not viewed to be simple enough for Google users and therefore not a "high impact product".

In any case I have as suggested by Google transferred my knols to Annotum under the name The World as Computation, which thus collects my knol articles and also serves as a blog.

The transfer has not been seamless and has given me incentive to update the articles to keep them alive, a work which will take some time.

As of now I will thus run two overlapping blogs and hope readers will find both.

Dark Age of Physics?

2011-12-10T04:57:00.000-08:00

To celebrate the 2011 Nobel Prize in Physics I have written the post Accelerating Expansion Without Dark Energy? on the new home at The World as Computation of My Book of Knols.

More about the dark age of physics as presented by the Nobel Laureates here.

Missing Physics of Sailing

2011-12-07T00:39:00.000-08:00

In The Secret of Sailing a new explanation of the physics of sailing is presented based on the new analysis of the generation of lift and drag of a wing in The Mathematical Secret of Flight and The Secret of Flight summarized in a talk.

Let us compare with current state-of-the-art:

School of Physics U of New South Wales: Newton's old theory (incorrect)
physicstoday : Bernoulli or Newton? (both incorrect or empty)
Wikipedia: Like an airplane wing (empty)
U of Alaska-Fairbanks: Bernoulli (incorrect or empty)
Real World Physics Problems: Newton (incorrect)
Teacher's Domain: Like an airplane wing (empty), Bernoulli (incorrect or empty)
U of North Carolina: Bernoulli (incorrect or empty)
howstuffworks: Bernoulli (incorrect or empty)
The Physics of Sailing Explained: Bernoulli (incorrect or empty)

The most ambitious treatment is given in Physics of Sailing by J. Kimball, where both Bernoulli and Kutta-Zhukovsky's circulation theory are presented, but with a disappointing sum-up on p 163:

The sail experiences lift because the sail deflects the wind. Equal and opposite forces mean that is the sail pushes the wind in one direction, the wind pushes the sail the other way. This explanation, which relies only on the rule of equal and opposite forces, is surely correct.

Yes, it is surely correct, as any empty theory which explains nothing, as illustrated in the above picture.

We see that there is surely a great need for a correct theory which explains the physics of sailing and that there is no such theory as state-of-the-art.

Our work fills this gap in physics theory and in particular shows that the state-of-the-art explanations represented by Newton, Bernoulli or Kutta-Zhukovsky are all incorrect.

Of course, the physics of flying and sailing is not of any interest to physicists of today paralyzed by string theory, but it is an interesting problem of physics of importance to many.

Nytt Kärnämne: Matematik-IT

2011-12-06T05:30:00.000-08:00

Här är en ny version av en kommande debattartikel i Ny Teknik med hänsyn tagen till mitt möte med S om Matematik-IT den 30/11:

Om bara ett par år kommer alla elever att ha en egen iPad (eller motsvarande) 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. Var och en som sett en 3-åring hantera en iPad förstår potentialen.

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, med matematikämnet som grund.

Det naturliga är att introducera IT som en del av skolmatematiken från första klass, eftersom datorn är en matematikmaskin, i ett nytt kärnämne Matematik-IT som ersätter det gamla matematikämnet, och som kan beskrivas som: Matematik för IT + Matematik med IT.

Att IT kommer att förändra skolans arbete 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 paralys och en skola utan framtidshopp.

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.

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 väl kanske inte så 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. S skulle kunna ta initiativet i skolpolitiken med följande program:

Ge alla elever en iPad (eller motsvarande) vid skolstart.
Skapa ett nytt ämne Matematik-IT, som lär ut:
IT som del av Matematik + Matematik med IT.
Stöd med utbildning/fortbildning i Matematik-IT.

Programmet är konkret, realiserbart utan miljarder och ger stor hävstång för satsade resurser, till skillnad från Björklunds som bara förstör resurser. S skulle med detta program visa initiativkraft och framtidstro och därmed både kunna ta sig ur sin egen förlamning och göra någonting bra för Sverige. Jag presenterade förslaget för Damberg den 30/11 och väntar nu på reaktion.

Will KTH Simulation Technology Start 2012?

2011-12-06T01:08:00.000-08:00

The KTH Bachelor program in Simulation Technology based on BodyandSoul scheduled to start in the Fall 2011 was stopped because of opposition to BodyandSoul at KTH.

The program is now scheduled to start in the Fall 2012 with BodyandSoul replaced by new material to be developed by people without connection to BodyandSoul. The "new material" is described as a "new view of mathematics" =

combination of analysis, computation and application = BodyandSoul.

This leads to the contradiction of both using BS and not using BS. The program will thus both start and not start in the Fall 2012. The program is described in the program catalog as follows:

In education and entertainment the development of simulators, games and animation for film, web and mobiles, is based on increasingly advanced technology.

But contradictions are not allowed in mathematics, nor in reality.

The Secret of Sailing

2011-12-04T07:10:00.000-08:00

I have updated the upcoming book The Secret of Sailing in accordance with the update of The Secret of Flying with the computational results in the 2009 article The Mathematical Secret of Flight confirmed with better resolution.

Altogether we presents the first scientifically correct explanation of the generation of lift L and drag D of a wing or sail with L/D > 10, which is needed to make both flying and sailing possible in practice.

It is expected that the new explanation will open to improved designs of both sails and keels.

Notice that the new Americas Cup design AC45 (preparing for the AC72 in 2013 match) has a main sail in the form of a wing.

Rapport från Möte med S om Matematik-IT

2011-11-30T09:00:00.000-08:00

Mötet med Socialdemokraterna i Riksdagens Utbildningsutskott om Matematik och IT resulterade i följande konkreta förslag:

Ge alla elever en iPad vid skolstart.
Skapa ett nytt ämne Matematik-IT, som lär:
IT som del av Matematik +
Matematik med IT.
Stöd med utbildning/fortbildning i Matematik-IT.

Återstår att se om S vill göra detta till en del av sitt utbildningsprogram. Inte omöjligt.

Forts följer...

PS. En iPad som kostar 4000 kr och används under 4 år ger en kostnad av 1000 kr/år och elev.

iPaden ersätter vanliga böcker som kostar minst dubbelt. Lärandet ökar och kostnaden minskar.

Sammanfattning PM Matematik-IT: Möte med S

2011-11-28T23:16:00.000-08:00

Sammanfattning av PM inför Möte med S om Matematik-IT 30/11:

MIKAEL DAMBERG:

Vi behöver metoder som förbereder för arbete och medborgarskap i ett kunskapsintensivt och högteknologiskt samhälle.
Sverige halkat efter när det gäller utvecklandet av lärandet med stöd av digital teknik, att utveckla lärararbetet med IKT och att utveckla skolan med samma verktyg.
Sverige måste utarbeta en nationell strategi för digital kompetens i skolan.
Skola fokuserad på framtidens kunskaper i stället för gårdagens typ.

JAN BJÖRKLUND:

1 miljard för fortbildning för att utveckla undervisningen.
I klartext, mer katederundervisning:
Lärare skall förklara, berätta, instruera och repetera i helklass och dessutom leda diskussion och samtal i helklass för att säkerställa att eleverna förstår det matematiska tänkandet och matematiska begreppen.
Mindre av eget arbete mer av katederundervisning.
Sanningen är att katederundervisning är väl beprövad och väl fungerande.
Växande digitala klyftorna och bristen på moderna datorer i svenska skolor inget jag ligger sömnlös över.

VERKLIGHTEN:

Om 2 år har alla elever en iPad (eller liknande)
iPad Appar förändrar skolans arbete radikalt från åk 1:
Läsa-Skriva-Räkna-IT: Kunskap, Samhälle, Teknologi, Arbete, Liv...
IT = Matematik + Logik + Programmering + Data
IT = Beräkning + Data (Google sökmotor)
Matematik för/med IT
Reform av Skolans Matematik
Nytt: Mål, Innehåll, Form
VAD, VARFÖR, HUR? Gamla svar gäller inte längre.
Reform av Skolan

MATEMATIK I PARALYS (pga datorn):

Hierarki: universitet-gymnasium-grundskola-förskola
Kardinal = Professor i Matematik vid Universitet
Splittring-Misstro: Matematiker - Didaktiker
Alla: Skolmatematiken Funkar Inte! Katastrof!!
2011 = 1950 (Björklund) = 1900
Kardinal säger inte: IT-Reform.
Kardinal säger: Didaktiker, lärare och elever är korkade
Kardinal säger: Ingenting kan och därför inte bör förändras
Didaktiker kan bara gå runt i cirkel.
PARALYS (inte bara i Sverige)
INGEN BÄR ANSVARET: Alla lägger skulden på tidigare skola
Vem är PÅVE?
Nationalkommitten för Matematik (KVA)??
Matematikersamfundet??
Påven har abdikerat, Kyrkan står kvar, men är tom.

MISSION för S:

Initiera reform av lärarutbildning - fortbildning: Matematik-IT
Låt PÅVEN visa sig och bära sitt ansvar.
Unik chans för S att Ta Initiativet
Unik chans för S att Rädda Sveriges Konkurrenskraft
Skola med/för IT = Skola för Alla = (S)KOLA

VÄRLDEN:

Oslo Univ, Simula Research Lab
Rwanda: Alla elever laptop från 9 år
Nya Världen: Kina, Indien, Brasilien, Afrika,...
Gamla Världen: Kris: Finans: Klimat...

Renormalization in QED, Blackbody Radiation and Turbulence

2011-11-28T00:26:00.000-08:00

There is a connection between the cut-off in Computational Blackbody Radiation and the cut-off in Renormalization of QED, namely

avoiding an ultraviolet catastrophe of infinite energy
by transforming high-frequency waves into low-frequency waves
in a form of reinvestment.

In the case of blackbody radiation with an absorbing body with a cut-off proportional to temperature subject to forcing from incident waves, the reinvestment comes out as heating (increasing temperature) from incident wave frequencies above the current cut-off.

There is also a connection to turbulent dissipation with high-frequency kinetic energy being transformed into low frequency internal/heat energy. The total energy as the sum of kinetic and internal energy collects the reinvestment and is thus conserved.

Renormalization thus concerns reinvestment of what is cut off, like collecting the branches cut off from a tree and using them together with the trunk of the tree so that nothing is lost.

The basic question concerns partition of energy between the trunk and branches (on branches)

and its dependence on the size of the cut-off length.

In turbulence, the total turbulent dissipation (= drag in bluff body flow) shows to be independent of the cut-off length.

In quantum mechanics the question is if the world would look the same with a different value of Planck's constant which sets the cut-off length on atomic scales.

Radiative vs Turbulent vs Frictional Heating

2011-11-25T09:38:00.000-08:00

Mathematical Physics of Blackbody Radiation and Computational Turbulent Incompressible Flow (or Computational Thermodynamics) show a similarity between radiative heating and turbulent heating, which can be viewed as different forms of frictional heating.

In both cases the heating effect shows to be independent of the small coefficient of dissipation/friction connected to the heating (the viscosity in turbulent flow and coefficient of the Abraham-Lorentz recoil force in radiation).This means that macroscopic quantities such as total radiative and turbulent heating show to be insensitive to the absolute scale of the microscopic dissipation creating the heating.

This allows computational simulation of macroscopical features of radiation and turbulent flow without resolution to actual smallest physical scales. This makes in particular turbulent flow computable contrary to common perceptions of state-of-the-art.

One may compare making fire by friction with a bow and drill: What is important is the total power invested, not the specific dimensions of the bow and drill.

Updated Computational Thermodynamics

2011-11-25T02:30:00.000-08:00

I have put up an updated preliminary version of the upcoming book Computational Thermodynamics.

The basic idea is to find the truth by computing turbulent solutions of the Euler/Navier-Stokes equations by EG2 as stabilized General Galerkin finite element method, and understanding that EG2 can serve as a model of thermodynamics.

A basic revelation is that the concept of entropy can be replaced by turbulent dissipation to give the 2nd Law a concrete expression in terms of the physical concepts of heat energy, kinetic energy, work and turbulent dissipation, without any need of introducing the cumbersome notion of entropy with its statistical basis.

EG2 thus offers a computable deterministic model of thermodynamics opening to understanding of basic phenomena and offering the capability of real prediction, without any need of statistics.

The presentation is centered around Joule's experiment from 1845 illustrated above on the thermodynamics of an expanding gas showing fundamental aspects of heat engines, heat pumps and refrigerators.

Massive Swedish Delegation to CMP7 in the Sunny City of Durban

2011-11-22T07:26:00.000-08:00

Sweden sends 45 official delegates to the upcoming COP17/CMP7 climate conference under the motto Saving Tomorrow Today:

The 7th Session of the Conference of the Parties serving as the Meeting of the Parties (CMP7) to the Kyoto Protocol, will be held in the sunny city of Durban, South Africa.

Everybody knows that the Kyoto Protocol will not be renewed, because there is no reason to do so. One may ask why 45 official delegates from Sweden are required to not do anything? To not do anything but profit from the sunny city of Durban and get away a couple of weeks from the darkness now descending over Sweden?

Heat Capacity of Blackbody 2?

2011-11-22T06:32:00.000-08:00

To add to the mystery of the concept of a blackbody as a "cavity absorbing all incident radiation", we now ask about the heat capacity/specific heat of such a thing?

We know that the heat energy/internal energy per unit time (radiance) radiated from a blackbody scales with temperature T like T^4, but what is the connection between T and absorbed/radiated heat energy Q(T), that is what is the heat capacity dQ/dT of a blackbody?

There are different answers:

1. If the cavity is filled with a perfect gas, then Q scales like T.

2. If the cavity is filled with a solid, then Q should scale like T^2 according to Mathematical Physics of Blackbody Radiation.

3. If the cavity filled with a photon gas, then Q scales like T^4.

We thus get a heat capacity dQ/dT scaling with temperature in a wide range from T^0 = constant to T^3.

This is yet another indication that the concept of a blackbody is confusing since it is not at all clear what physics it models, and thus is unfortunate as a scientific concept.

Blackbody as Bottle with Peephole?

2011-11-20T01:08:00.000-08:00

A blackbody is a theoretical idealized object described as something "absorbing all incident radiation" commonly pictured as a cavity or empty bottle/box in which waves/photons are bouncing back and forth between walls at a certain temperature defining the temperature of the cavity. The bottle has a little peephole through which radiation is escaping to be observed, as indicated in the above common illustration of a blackbody.

A blackbody is supposed to capture an essential aspect of the radiation from a real body like the visible glow from a lump of iron at 1000 C, the Sun at 6000 C or the invisible infrared faint glow of a human body at 37 C.

But why is a lump of iron, the Sun or a human body thought of as an empty bottle with a peephole?

Yes, you are right: It is because Planck used this image in his proof of Planck's Law of blackbody radiation based on statistics of energy quanta/photons in a box. Planck's mathematical proof required a certain set up and that set up came to define the idealized concept of a blackbody as an empty bottle with peephole. But to actually construct anything near such a blackbody is impossible.

It is natural to ask if with another proof of Planck's Law, the concept of blackbody would be different, possibly closer to reality?

In Mathematical Physics of Blackbody Radiation I give a different proof of Planck's Law with a different concept of blackbody as a lattice of vibrating atoms absorbing and emitting radiation as electromagnetic waves, which models a real body like a lump of iron, and not a fictional empty bottle with a peephole.

This shows the role of mathematics in the formation of concepts of the World:

With a strange mathematical proof the World may appear strange and incomprehensible.
With a natural mathematical proof the World my become comprehensible.

Interaction Light-Matter or Soul-Body

2011-11-19T02:13:00.000-08:00

One of the big mysteries of physics is the interaction between immaterial light and material matter, or in a wider context the interaction between immaterial soul/mind and material body.

Descartes believed that the interaction soul-body took place in the little pineal gland in the center of the brain. Modern neurobiology does not give much support to Descartes' idea but has not really any better theory and so the mystery of how soul and body interact remains to be resolved.

What does then modern physics say about the interaction of light and matter? There are two competing theories depending on the nature of light as

Deterministic electromagnetic waves described by Maxwell's equations.
Statistics of massless particles.

2. connects to Newton's old corpuscular theory of light, which was revived by Einstein in 1905 after it had been declared dead and had been replaced by Maxwell's wave theory in the late 19th century.

2. became popular because it offered a resolution to the light-matter interaction problem by simply side-stepping the whole question by claiming that everything is (statistics of) particles: If light is not an immaterial electromagnetic wave phenomenon, but simply some sort of material particles (albeit without mass, but never mind) then there is no wave-matter problem to resolve!

Clever, but maybe too clever since after all light is an electromagnetic wave phenomenon. This brings us back to 1. and the real question of how an immaterial wave can interact with a material body?

In Mathematical Physics of Blackbody Radiation I suggest a resolution with immaterial waves interacting with matter by wave resonance and statistics replaced by finite precision computation. This is a resolution in terms of waves with electromagnetic wave motion interacting with wave motion in matter ultimately also consisting of electromagnetic waves.

The wave-matter interaction problem is thus in this case resolved by understanding that everything is (finite precision) wave and wave resonance, both light and matter. In the wider context: everything is soul and soul resonance.

We have thus two possible solutions of the light-matter interaction problem:

Everything is (finite precision) deterministic wave and wave resonance.
Everything is statistics of particles and collision of particles.

Maxwell and Schrödinger said 2. What do you say?

Radiative Cooling

2011-11-17T05:39:00.000-08:00

How quickly will a hot (black) body cool off if all exterior heat sources are shut off and the

heat energy stored in the body radiates from the body? How quickly does the Earth surface cool off during night?

There are different answers:

1. Mathematical Physics of Blackbody Radiation gives the following cooling curve for the temperature T(t) as function of time t starting at t=0:

T(t) = T(0)/(1 + C t)^0.5

as a consequence of the fact that the stored heat energy E scales like T^2 while the heat loss scales like T^4 by Stefan-Boltzmann's Law which also defines the constant C.

2. The standard answer is different:

T(t) = T(0)/(1 + C t)^0.33

with E scaling instead like T.

Which answer is best? Experiments appear to favor 1 with its quicker decay, also shown in the above picture from Comlab.

The difference between 1 and 2 may be the difference between a blackbody in the form of a solid or a gas, where the blackbody nature/spectrum of a gas may be questioned.

Josef Stefan: Backradiation and DLR Pure Fiction!!

2011-11-16T03:03:00.000-08:00

Josef Stefan 1879: Backradiation and DLR is pure fiction!!

Let us quote from Josef Stefan's On the Relation between Radiation and Temperature from 1879 (my translation of page 411):

The absolute value the heat energy emission from a radiating body cannot be determined by experiment. An experiment can only determine the surplus of emission over absorption, with the absorption determined by the emission from the environment of the body.
However, if one has a formula for the emission as a function of temperature (like Stefan-Bolzmann's Law), then the absolute value of the emission can be determined, but such a formula has only a hypothetical meaning.

We see that Stefan understood very well that only the net/surplus has a physical meaning.

Stefan would thus say that the mantra of CO2 alarmism of backradiation or Downwelling Longwave Radiation DLR from the atmosphere to the warmer Earth surface, is pure fiction.

Are CO2 alarmists relying on Stefan-Boltzmann's Law willing to listen to what Stefan has to say? Or can the work of a dead scientist be misused at will without any consequence?

Möte med S: Matematikutbildning för IT-Samhället

2011-11-15T04:43:00.000-08:00

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 gymnasist)
How to Fix Math Education (New York Times 24/9 2011)

mina nya debattinlägg på Newsmill och Teknikdebatt (med äldre här):

rapport från mitt möte med Utbildningsdepartmentet Nov 09, 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 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.

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 paralys 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:
3-åringar skickliga på att använda iPad: spel, film, TV, Youtube
alla elever använder mobil, dator, iPad: facebook, spel, musik, powerpoint
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.

Datorspel som ny pedagogisk metod:

Body and Soul använder datorspel på två sätt:

Använda färdiga datorspel för att lära sig läsa-skriva-räkna
Göra egna datorspel som tillämpning av matematik-programmering.

Datorspel ger feed-back, kan stimulera flera sinnen, fånga intresse och skapa motivation.

Formell kunskap vs reell kunskap:

Den gamla real/gymnasieskolan (Björklunds) gav formell kunskap för få i hierarki:

latin, matematik, grammatik, svåra ord, skriva på tyska

Dagens skola skall ge reell kunskap för många i jämlikhet:

tala och skriva: svenska, engelska,...
använda dator för kalkyl, ekonomi, simulering,...
lära sig hur man kan lära sig olika saker
lära sig att man kan förstå och skapa mening.

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: tex bildbehandling i Photoshop
textbehandling
att kunna göra film, presentation, analys, datorspel i vid mening.

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.

Media:

Epstein P1 24/11: Den bästa undervisningen för eleverna.

Juholt SVD 26/11:

Vi vill bryta den ökade segregationen i skolan och bygga Sverige starkt med en kunskapsbaserad ekonomi.
Att skapa ett utbildningssystem där samtliga elever når målen i grundskolan och alla har en fullständig gymnasieexamen före 25 års ålder.
5 miljarder extra till stadsbudgeten fokuserat på skola och utbildning.

Om CJ:

prof i tillämpad matematik Chalmers 1981-2007, KTH 2007-
100 artiklar, 10 böcker, 15 studenter
på ICI Highly Cited lista av världens mest citerade forskare
Humboldt Research Prize
reform av ingenjörsmatematik: Body&Soul.

Heat Capacity of Blackbody

2011-11-14T06:55:00.000-08:00

In Mathematical Physics of Blackbody Radiation I derive an expression for the heat capacity C(T) of a blackbody in the form of a forced damped wave equation as function of temperature T, of the form

C(T)= c T

with c a constant, thus with a linear dependence on T. This fits pretty well with observations for several solid metals for temperatures T smaller than 200 K, and for diamond up to 500 K, as shown above.

Recall that the theory of specific heats was studied intensely in the beginning of the 20th century: Einstein and Debye offered improvements for low temperatures of the classical Dulong-Petit Law C(T) = constant, using arguments from statistical mechanics.

I do not use statistical mechanics but instead a concept of finite precision computation.

The Secret of Flow Separation Uncovered

2011-11-13T23:19:00.001-08:00

Real flow as potential flow modified by vortical slip separation with point stagnation.

The flow around a body moving through a slightly viscous incompressible fluid like water or air at subsonic speeds, attaches at the front as fluid particles approach the body and separates in the back as fluid particles part from the body.

In slightly viscous flow fluid particles glide along the surface with small skin friction which can be approximated as a slip boundary condition.

Observation shows laminar attachment and turbulent separation, with the flow being close to potential flow (inviscid irrotational flow with slip) prior to separation. In potential flow the separation is simply reverse attachment and thus real flow differs from potential flow at separation.

Ever since the basic mathematics of fluid mechanics was formulated by Euler and d'Alembert in the mid 18th century, a prime goal has been to describe slightly viscous flow around a body as potential flow subject to some modification at separation:

Prandtl as the father of modern fluid mechanics described the modification as a boundary layer effect from a no-slip boundary condition.
Kutta and Zhukovsky as fathers of modern flight mechanics described the modification as large scale circulation around a wing section.

In the new article Analysis of Separation in Turbulent Incompressible Flow together with Johan Hoffman (submitted), we show that the answer is neither boundary layer nor circulation, but instead

vortical slip separation with point stagnation.

We give evidence in the form of

mathematical analysis of basic instability of potential flow at separation
computational solution of Navier-Stokes equations
experimental observation.

We thus present strong evidence that the dream of Euler and d'Alembert can be fulfilled by describing slightly viscous flow around a body as

potential flow modified by vortical slip separation with point stagnation.

The article gives the details.

As an application we uncover The Secret of Flight (upcoming book) and The Mathematical Secret of Flight (article and talk).

The Poynting Vector

2011-11-13T01:50:00.000-08:00

The Poynting vector $E\times H$ representing the energy flux of an electromagnetic field.

Mathematical Physics of Blackbody Radiation gives a new wave based proof of Planck's radiation law in the form

$Radiation + Heating = Forcing$,

where

$Forcing = \int\int f^2(x,t)\, dxdt$

with $f(x,t)$ the amplitude of the incoming wave.

The measure of $Forcing$ as the (integral of the) square $f^2$ of the amplitude $f$ connects to the Poynting vector $E\times H$ representing the energy flux of an electromagnetic field with $E$ the electric field and $H$ the magnetic field having the same amplitude.

Is the Economical Crisis a Climate Crisis?

2011-11-08T02:29:00.000-08:00

Two facts fly in our faces today:

EU is in a deep economical crisis.
EU has the most ambitious plan for reduction of CO2 emissions.

Is there a connection? Many questions present themselves:

Has the financial market already adjusted to the new reality of a carbon-free society projected by the Royal Swedish Academy of Sciences to 2050?
Would the economical crisis evaporate if EU leaders gave up their plans for a Great Transformation?
Was the climate crisis invented to give clever EU political leaders a mission to lead the World into a new future?
Is the economicial crisis triggered by the climate crisis now driving the same clever EU politicians out of business ?

The Essence of Planck's Radiation Law and Its Proof

2011-11-07T12:06:00.000-08:00

Planck trying to convince a disbelieving Bohr that his proof of Planck's Law is correct. On the blackboard: Maxwell's equations.

The derivation of Planck's Law (of blackbody radiation) given by Planck is based on particle statistics borrowed from thermodynamics with little connection to the real physics of radiation as interaction of matter and electromagnetic wave motion.

Planck was forced into particle statistics because a radiation law based on wave motion seemed to lead a Rayleigh-Jeans law with an "ultraviolet catastrophe" with energy exploding to infinity like $\nu^2$ with frequency $\nu$ without upper bound. By a statistical assumption that highly energetic waves are rare Planck gave physics a way to avoid the catastrophe which earned almost infinite fame and a Nobel Prize.

But Planck left a question without answer: Is it possible to derive a correct radiation law without resort to statistics, using instead classical electrodynamics described by Maxwell's wave equations?

In Mathematical Physics of Blackbody Radiation and Computational Blackbody Radiation I show that this is indeed possible, by replacing statistics by a much more basic physical assumption of finite precision computation. Let me here presents the essence of my argument:

I consider mathematical 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

$U_{tt} - U_{xx}$: material force from vibrating string with U displacement
$- \gamma U_{ttt}$ is Abraham-Lorentz (radiation reaction) force
$- \delta^2U_{xxt}$ is a viscous force
$f$ is exterior forcing,

and $\gamma$ and $\delta^2$ are (small) positive coefficients subject to a frequency dependent switch from outgoing radiation with to absorption/internal heating defined below.

The finite precision computation is represented by the $\delta^2$ viscosity which sets a smallest scale in space of size $\delta$ by damping frequencies higher than $\frac{1}{\delta}$.

The coefficients $\gamma$ and $\delta$ are chosen so that only one is positive for a certain frequency $\nu$ in a spectral decomposition, with a switch from $\gamma >0$ to $\delta >0$ at $\nu = \frac{T}{h}$, where $T$ is temperature and $h$ is a fixed precision parameter representing atomic dimension in the string of atoms modeled by the wave equation.

The switch thus defines a temperature dependent cut-off frequency $\frac{T}{h}$ with the effect that only frequencies below the cut-off are emitted as radiation while frequencies above cut-off are stored as internal heat energy of the string.

The essence of the proof is the following energy balance established by a spectral analysis assuming periodicity in space and time:

$\int \gamma U_{tt}^2dxdt + \int \delta^2U_{xt}^2dxdt = \epsilon \int f^2 dxdt$

with $\epsilon\approx 1$ is a coefficient of emissivity (= absorptivity), which we write in condensed form as

$R + A = F$, or in a spectral decomposition $R_\nu + A_\nu = F_\nu$, or in words
Radiation + Absorption = Forcing,

where $R = \int \gamma U_{tt}^2dxdt$, $A=\int \delta^2U_{xt}^2dxdt$ and $F=\epsilon \int f^2 dxdt$.

As just said, the switch effectively means that

$R_\nu = F_\nu$ for $\nu <\frac{T}{h}$
$A_\nu = F_\nu$ for $\nu >\frac{T}{h}$,

which expresses that the forcing $F_\nu$ is remitted as outgoing radiation for $\nu<\frac{T}{h}$, and is absorbed and stored as internal heat energy for $\nu > \frac{T}{h}$.

The coefficient $\epsilon$ represents emissivity = absorptivity, in accordance with Kirchhoff's Law. An essential aspect is that $\epsilon$ is independent of $\gamma$ and $\delta$, which expresses that radiation (to up to the constant $\epsilon$) is independent of the nature of the radiating/absorbing body.

Planck's law in the form $R+A = F$ with only one of $R$ and $A$ non-zero for each frequency

is a variant of Planck's classical law with a sharp switch instead of a continuous transition from radiation to absorption/heating.

Planck's law in the form $R + A = F$ thus contains the classical law for radiation as $R=F$ but also the further information that absorption into internal heat energy $A=R$ only occurs for frequencies above cut-off.

The proof that $R + A = F$ is non-trival and expresses a fundamental aspect of near-resonance

in systems of oscillators with small damping. The proof shows Planck's Law $R_\nu\sim \gamma T\nu^2$ for $\nu <\frac{T}{h}$ and Kirchhoff's Law, without resort to statistics.

The effects of Planck's statistics in modern physics are subject to an investigation in Dr Faustus of Modern Physics: Is it true that Planck's technique for avoiding the ultraviolet catastrophe led to a much bigger catastrophe of abandoning rationality in physics?

Generic Model of Resonant Interaction Matter-Wave

2011-11-02T00:38:00.000-07:00

I analyze in Mathematical Physics of Blackbody Radiation and Computational Blackbody Radiation a mathematical model of radiative heat transfer 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

$U_{tt} - U_{xx}$: material force from vibrating string with U displacement
$- \gamma U_{ttt}$: radiation pressure from outgoing radiation = emission
$- \delta^2U_{xxt}$: viscous force from internal heating = absorption
$f$ is exterior forcing,

and $\gamma$ and $\delta^2$ are (small) positive constants connected to dissipative losses as outgoing radiation = emission and internal heating = absorption. Let me here clarify the physics behind the dissipative terms:

$- \gamma U_{ttt}$ represents the Abraham-Lorentz (radiation reaction) force
$- \delta^2U_{xxt}$ represents a viscous force from internal friction in the string.

The corresponding dissipation energies are obtained by multiplication of the forces with $U_t$ followed by integration (by parts) in space-time over a period, assuming periodicity, to give

$R=\int \gamma U_{tt}^2dxdt$ Larmor's formula for radiance $R$
$IE =\int \delta^2 U_{xt}^2dxdt$ internal energy IE stored as heat energy.

Recall that damping in the wave equation $U_{tt} - U_{xx} = f$ can take the from

$\nu U_{t}$ with $\nu$ a viscosity coefficient, or as above $-\gamma U_{ttt}$ and $- \delta^2U_{xxt}$, thus with the following derivatives:

$U_{t}$
$U_{ttt}$
$U_{xxt}$

where $U_t$ appears in acoustic viscous damping, and can be seen as a simplified version of both $U_{ttt}$ and $U_{xxt}$.

The above model thus can be viewed as the generic model of wave motion with damping describing of interaction matter (string) and electromagnetic waves (radiation term and forcing) with a very rich area of application including:

The mathematical analysis exhibits a fundamental phenomenon of near resonance in wave motion with small damping, as explained in How to Push a Swing: In near resonance the forcing is in phase with the displacement, while in perfect resonance (with large damping) the forcing is in phase with the velocity. The effect is that in near resonance the exterior forcing is balanced by both the string force and the Abraham-Lorentz radiation force, while in perfect resonance only by the radiation force.

Near resonance appears when the radiative damping is small ($\gamma$ is small), which is the real case of radiation with full interaction between matter (string) and radiation.

Möte med S: Matematikutbildning för IT-Samhället

2011-10-31T06:43:00.000-07:00

PM inför Möte med Socialdemokraterna i Riksdagens Utbildningsutskott 30/11

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:

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:

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.

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:

Difference Between Emission and Absorption of Radiation

2011-10-31T00:32:00.000-07:00

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

$U_{tt} - U_{xx}$ represents a vibrating string with U displacement
$- \gamma U_{ttt}$ is a dissipative term modeling outgoing radiation = emission
$- \delta^2U_{xxt}$ is a dissipative modeling internal heating = absorption
$f$ 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:

How is the distinction between emission and absorption expressed in this model?
Is Helmholtz Reciprocity valid (emission and absorption are reverse processes)?
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

2011-10-30T03:00:00.000-07:00

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

2011-10-30T01:34:00.000-07:00

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

2011-10-29T03:58:00.000-07:00

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:

one-way transfer from hot to cold,
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) with one-way heat transfer from integration of net forcing,
(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?

2011-10-27T23:36:00.000-07:00

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:

Kirchhoff (1859): Thought experiments with mirrors, basic thermodynamics.
Planck (1906); Heat rays, basic thermodynamics.
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

2011-10-27T12:31:00.000-07:00

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

One-way transfer from hot body to cold body (Pictet)
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

2011-10-27T06:30:00.000-07:00

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

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

2011-10-26T23:36:00.000-07:00

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

2011-10-26T00:38:00.000-07:00

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

2011-10-25T05:31:00.000-07:00

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

2011-10-25T01:48:00.000-07:00

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

One-way net transfer from hot to cold.
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

2011-10-24T23:07:00.000-07:00

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:

One-way net transfer from hot to cold.
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

$U_{tt} - U_{xx}$ represents the oscillators in a wave model with U displacement
$- \gamma U_{ttt}$ is a dissipative term modeling outgoing radiation
$- h^2U_{xxt}$ is a dissipative modeling internal heating
$f$ 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

2011-10-24T04:50:00.000-07:00

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:

as immaterial electromagnetic wave
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

2011-10-24T00:37:00.000-07:00

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?

2011-10-23T01:37:00.000-07:00

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:

Is radiative heat transfer one-way from hot to cold, as my analysis suggests?
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

2011-10-21T01:07:00.000-07:00

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:

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.
Cosmic Microwave Background Radiation (CMB) is a "faint glow" of empty space with heating effect according to SB with $T\approx 3\, K$.
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.
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

2011-10-20T21:21:00.000-07:00

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:

CMB is measured by radio resonance into a spectrum without physical scale because of signal amplification.
The recorded spectrum is matched with Planck's law to give a temperature $T_b$.
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

2011-10-19T13:52:00.000-07:00

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

2011-10-19T04:07:00.000-07:00

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

$U_{tt} - U_{xx}$ represents the oscillators in a wave model
$- \gamma U_{ttt}$ is a dissipative term modeling outgoing radiation
$- h^2U_{xxt}$ is a dissipative modeling internal heating
$f$ 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.

Learning by Seeing

2011-10-19T00:34:00.001-07:00

Everyday you may learn something new. I just discovered that I made a mistake in the recent post on IR-detectors believing that an optical lens may increase the radiance from a target onto a detector, because a (positive) lens increases the amplitude of the incoming light waves by making the rays converge.

But then I missed that the viewing angle also increases which makes the radiance the same after the lens as before. This means that the detector even with an optical lens cannot reach a higher temperature than the target, in full accordance with the 2nd law.

Climate Crisis vs Financial Crisis?

2011-10-18T14:04:00.000-07:00

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

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

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

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

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

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

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

Evidence that DLR is Fiction?

2011-10-18T10:11:00.000-07:00

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

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

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

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

The following questions present themselves:

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

IR Detectors and True-SB

2011-10-17T23:41:00.000-07:00

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

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

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

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

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

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

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

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

but this is not IR.)

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

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

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

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

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

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

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

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

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

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

S Vill Satsa på IT i Skolan

2011-10-17T01:40:00.000-07:00

Jag har nu fått följande respons från S beträffande matematik och IT i morgondagens skola:

Hej Claes!
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 iskolan bör utvecklas och undrar om du har möjlighet att träffa Socialdemokraterna i riksdagens utbildningsutskott onsdagen den 30 november kl 14.00-15.30. Inbjuden till detta tillfälle är också Trevor Dolan för att ge sin syn på matematik och kreativitet.
Med vänlig hälsning, Kristina Persdotter.

Äntligen, kan man väl säga. S förstår någonting mycket viktigt som Björklund inte alls förstår. IT kommer att revolutionera lärande på alla nivåer. Inom ett par år, då alla elever har en iPad.

Denna fråga kan lyfta S ur sitt svarta hål. Det skall bli mycket intressant att se om S är förmöget att utnyttja den möjlighet att ta initiativet från oppositionen som Björklund nu serverar med sin "katederundervisning" utan IT och framtid.

Rapport inför och efter mötet den 30 november kommer så småningom.

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

2011-10-16T22:51:00.000-07:00

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

True-SB.

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

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

with the high-frequency cut-off factor

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$R_{False} = (R(T,T_b) + C) - C$,

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

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

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

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

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

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

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

Curry on Straw Dog of False-SB

2011-10-16T10:13:00.000-07:00

Judy Curry answers on her blog my question about Stefan-Boltzmann's radiation law and DLR:

Claes, true to form, you set up a straw dog to knock down. The Stefan Boltzmann equation is the integral of the Planck function.
No one calculates atmospheric radiative heat transfer using the Stefan Boltzmann equation (not since the 1960′s, anyways).

I follow up with the following questions related to Judy's statement that DLR/False-SB is a straw dog:

Do you agree with me that DLR should once and for all be removed from climate science?
Do you agree with me that the Kiehl-Trenberth energy budget with DLR is grossly incorrect?
Do you agree with me that climate scientists have invented a form of SB which does not have support in physics literature, and which in fact is false because it involves a violation of the 2nd law?
Have you read an digested my derivations of Planck/SB without statistics of quanta?I appreciate prompt answers, which should be possible since you are now on line.

I will report on Judy's answers...It appears that Judy is thinking deeply about what to say and

this may take time, but the questions remain and will not disappear just because Judy closes her eyes...

False-SB Violates the 2nd Law

2011-10-16T03:53:00.000-07:00

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stability of True-SB vs False-SB

2011-10-16T01:53:00.000-07:00

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

$R = T_1 - T_2$
$R = T_3$ where $T_3 = T_1 - T_2$,

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

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

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

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

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

which is to be compared with

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

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

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

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

Question to Curry about Stefan-Boltzmann and DLR

2011-10-16T00:52:00.000-07:00

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

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

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

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

Petty on DLR 4

2011-10-15T07:38:00.000-07:00

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

If you're going to publicly blog about what I have said in a non-public email exchange, at least do both me and your readers the courtesy of honestly representing what I said.
You wrote "The argument of Prof Petty is now the following: If there is no experiment in sight capable of making a distinction between True-SB and False-SB, it must mean that if True-SB is true then False-SB is equally true. Is this a correct scientific argument?"What I in fact said was quite different, as anyone who actually read my message will agree. I said that if the difference can't be detected experimentally, then "it matters not a whit for climate."
You argue in your blog that the difference does matter for "stability aspects." And I return to my original claim, which is that if it matters in any way for the response of the climate system, it must also be experimentally detectable.
Again, please describe a realizable experiment in which a measurement of X yields an outcome of Y according to one theory and an outcome of Z according to the other. If you cannot, then I claim you are engaging in mere sophistry.
My answer:
It is not up to me to prove that your False-SB is not true.
It is up to you to prove that the False-SB you are using is true.
You have given a proof of False-SB consisting of applying True-SB twice, and I have shown that you cannot do that because you are using True-SB in way which is not consistent with the proof of True-SB. Your proof of False-SB is incorrect.
It is up to you to give an experiment recording a difference between False-SB and True-SB. If you cannot do that it means that your False-SB is identical with the True-SB and then False-SB can be removed from the discussion completely, unless you insist on mere sophistry.
Do you see what I am saying?
Here is the response from Prof Petty:

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

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

How to Measure Downwelling Longwave Radiation

2011-10-15T07:10:00.000-07:00

Experimental setup for direct measurement of Downwelling Longwave Radiation DLR.

True-SB or False-SB by Experiment?

2011-10-15T01:24:00.000-07:00

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

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

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

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

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

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

0 = 100 - 100.

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

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

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

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

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

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

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

From Modern to Post-Modern Physics

2011-10-14T01:08:00.000-07:00

Physics has the top position in the hierarchy of sciences because physics is the science where a Principle of Objectivity (PO) comes to its fullest expression.

Modern physics was born in the beginning of the 19th century when the PO of classical physics of Newton's absolute space and time was confronted with the null-result of the Michelson-Morley experiment indicating that the speed of Earth through an aether of absolute space was zero, as if the Earth was dragging the aether of absolute space along on its path around the Sun. This was in direct conflict with the PO of the Copernican principle stating that the Earth is not the center of the Universe as the anchor of absolute space.

Einstein solved the dilemma by simply declaring that there is no aether whatsoever and then developed his special theory of relativity as an ultimate expression of a PO declaring that physical laws must look the same in all reference/coordinate systems. A physical law which takes different forms in different coordinate systems, would then not be a true fundamental physical law because it would violate PO.

Einstein thus managed to keep physics at its top position by initiating a modern form of physics in accordance with PO, based on the following fundamental expressions of objectivity:

no-aether special theory of relativity
universal wave function of quantum mechanics
Cosmological Principle (CP): the universe is homogeneous and isotropic.

Modern physics thus kept the top position in the hierarchy of sciences by claiming superior full objectivity, but the price of maintaining PO has shown to be very high and has led modern physics into a free fall diverging from reality into string theory on small scales beyond rationale and cosmology on large scales beyond comprehension, topped with a new completely unknown form of dark energy as a result of CP.

From this crisis new forms of physics as post-modern physics, are now emerging where special reference systems are again allowed as in classical physics and the PO is no longer worshipped in extreme. This makes physics more like other sciences, more human and more useful. In fact, Einstein re-introduced in his general theory of relativity the aether he had eliminated in his special theory of relativity. Einstein was very clever.

I describe possible forms of post-modern physics as many-minds physics in the upcoming books:

and the collapse of modern physics is recorded in:

Dr Faustus of Modern Physics.

Is CMB Heating the Earth?

2011-10-12T23:48:00.000-07:00

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

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

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

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

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

False SB Not Part of Physics Literature

2011-10-12T04:14:00.000-07:00

The scientific explanation of the greenhouse effect of climate science.

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

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

The result can be generalized as follows:

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

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

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

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

CO2 Alarmism Collapses under False SB Law

2011-10-11T23:54:00.000-07:00

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

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

$R = \sigma T^4 - \sigma T_b^4$

and one named True-SB:

$R = \sigma (T^4 - T_b^4)$

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

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

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

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

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

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

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

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

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

1. Application of True-SB twice:

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

2. Distributive law of algebra:

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

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

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

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

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

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

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

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

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

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

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

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

Climate Alarmism Based on False Stefan-Boltzmann Law

2011-10-11T05:56:00.000-07:00

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

The original true-SB reads:

R = sigma (T^4 - T_b^4)

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

The false-SB reads:

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

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

R = sigma T^4 - sigma T_b^4,

using formally the distributive law of algebra:

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

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

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

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

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

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

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

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

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

R = 10 = 100 - 90 = R_out - R_in

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

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

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

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

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

CO2 Alarmism Debunked by Mathematics

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

Computational Blackbody Radiation in the book Slaying the Sky Dragon.

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

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

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

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

I will report if some answers come in...

Petty on DLR 3: Incorrect Science Exposed

2011-10-11T00:46:00.000-07:00

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

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

Prof Petty writes:

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

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

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

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

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

R = sigma (T^4 - T_b^4)

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

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

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

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

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

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

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

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

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

Petty on DLR 2

2011-10-10T23:58:00.001-07:00

I have now received an answer from Prof Petty on my question concerning the scientific basis of the following SB law:

(SB-invented) R = sigma T^4 - sigma T_b^4 = R_out - R_in

expressing the radiative heat transfer R between a blackbody at temperature T in exchange with a blackbody background of temp T_b, as the difference of two gross flows, sigma T^4 and

sigma T_b^4.

Prof Petty states:

It would be more accurate to say that I recognize the SB law (F=sigma*T^4) being applied twice, once for each body.
The full expression is not a form of the SB Law but rather a consequence of the SB law.

This is precisely what I have been waiting Petty to state himself: Petty offers a proof of (SB-invented) consisting of applying twice a (SB-original) of the form F = sigma T^4.

Petty thus claims (SB-invented) to be a consequence of (SB-original) and the proof consists in "applying (SB-original) twice".

But (SB-original) was not proved to applicable twice, only once. To apply it twice takes it outside that realm of its original proof. To apply it twice is an ad hoc procedure and free invention, which is viewed to be true only because it looks so trivial and innocent.

But it is not at all trivial, and not innocent. What would be needed is a direct proof of (SB-invented), a proof which is not simply a free invention. But a direct proof cannot to be found in the literature.

Will Prof Petty be willing to understand what I am saying? That DLR is based on an invented

SB law without scientific basis. And what is CO2 alarmism without DLR?

What Does a (Climate) Scientist Need to Know?

2011-10-10T11:04:00.000-07:00

The recent posts on DLR brings up the following question concerning the responsibility of a scientist:

We know that an engineer is responsible for calculating the load capacity of a bridge, and that a medical doctor is responsible for the treatment of a patient. If the engineer is miscalculating and the bridge collapses or the doctor is prescribing the wrong medication and the patient dies, then legal process may follow. Engineers and doctors are simply required to know enough.

But what is a scientist required to know? Is a scientist required to understand the physical laws the scientist is using? Can a scientist be sued for using an incorrect law without justification?

Is a scientist required to know enough?

A concrete case is offered by the phenomenon of DLR underlying CO2 climate alarmism, which is based on a Stefan Boltzmann law of the form

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

where R is the net radiance from a (black) body of temperature T into a background of temperature T_b, and R_out is the radiance from the body and R_in is the radiance received by the body from the background. The net radiance/flow R is thus expressed as the difference between two gross flows R_out and R_in.

Suppose now that there is no original source of this SB law, that the law is a misinterpretation of correct law with scientific source of the form

R = sigma (T^4 - T_b^4),

with only net flow and no gross flows, and as misinterpretation is a law without physical meaning. Suppose that a scientist is using the false law without asking for its justification, simply taking it for granted because this is what some other scientists seem to be doing.

What is then the responsibility of the scientist? Does a scientist need to understand the physical laws used in the scientific work, or is it enough to simply copy and paste taking for granted that what is printed is correct? Can a scientist be sued for malpractice?

Does a climate scientist need to understand the proof of the SB law the scientist is using, or is it enough to copy and paste the law?

Suppose somebody asks for the origin of a certain SB law used by a certain scientist. Is the scientist then required to supply the origin?

These questions connect to the question I have posed to Prof Petty concerning DLR.

Petty on DLR 1

2011-10-10T09:51:00.000-07:00

Here is the response by Prof Petty on my question concerning the original scientific source of the Stefan-Boltzmann law supposedly underlying the phenomenon of Downwelling Longwave Radiation DLR, which is a cornerstone of CO2 alarmism:

To my recollection, the derivation of Planck's Law was always referenced to the interior of an enclosed cavity. That's why one German term for blackbody radiation is Hohlraumstrahlung (hollow space radiation). There is no "background" radiation in an enclosed cavity.
Notwithstanding your repeated claim that the law is valid only for a 0 K background, this is neither consistent with observation, nor is it consistent with the observed fact that radiation emitted BY any body isn't influenced by the radiation incident ON that body.
Physicists have been using Planck's function in the standard way long before climate scientists got involved. There is no inconsistency between climate scientists' use of it and astrophysicists' use of it.
CJ's understanding...is simply wrong. It is experimentally wrong. It is theoretically wrong. It is amazingly wrong.
CJ is right in one narrow sense: the SB law isn't two-way because it is UNDERSTOOD by anyone who actually works with radiation to apply only to the radiation EMITTED by a surface. If you want the two-way exchange between two plates with different temperature, you apply the SB law to each plate separately to get the component of the flux emitted toward the other flux.
This is not climate science. This is routine undergraduate-level physics.
Don't take climate scientists' word for it. Ask any competent astrophysicist.

Prof Petty is not answering my question, but refers to some unknown astro-physicist. Not very helpful. I think Prof Petty should be able to answer himself. Like Judy Curry he seems to refer to undergraduate students.

Surprisingly, Prof Petty acknowledges that I am right in stating that SB expresses one-way net flow, and not the difference of two-way gross flow. Surprisingly, Prof Petty thus seems to agree with me on the essential point. Yet he expresses very clearly that I am all wrong. It does not make much sense, to me.

Prof Petty has a only a vague confused recollection of Planck's derivation of his radiation law, and has not understood that the radiation from the cavity representing the blackbody, is radiation into a background at 0 K.

Prof Petty believes that the SB law of astrophysics is the SB law of climate science, and does not appear to understand that there is an important difference between the radiative net exchange of Sun-Earth and that of Earth-atmosphere, because the Sun is very hot and very far away.

So I repeat my question Prof Petty:

Which is the original scientific source of the SB law you are using in your climate science?

I will report the answer...Here it is:

From now on, I will only debate the correctness of "standard" radiation physics with those who prove that they are at least familiar with those basics -- and with the applicable terminology -- at the level of the first 8 chapters of my introductory book.
You are welcome to insist that something in those 8 chapters is wrong, but you'd better be prepared to point out specifically what you think is wrong, at the earliest point where it appears in the development, and why you are so damned sure it's wrong. And then we can go from there.
Otherwise, it's like debating the physics of flight with someone who's never seen an airplane.

OK, I repeat my question about the source of the SB law. I think it is a fair question on a central problem.

It is funny that Prof Petty wants to discuss the physics of flight with me. Maybe he has (not) read my work on this topic:

The Secret of Flight (book)
The Mathematical Secret of Flight (article)
The Mathematical Secret of Flight (talk).

DLR as Voodo Science

2011-10-09T11:12:00.000-07:00

The previous posts on Downwelling Longwave Radiation DLR suggest to describe DLR as a voodo fetish, that is, a man-made object with supernatural power.

Sticking pins in a voodo doll is believed to cause real wounds. Imagining DLR hitting from above is believed to cause global warming.

How can you convince yourself if a scientific phenomenon is a fetish or reality? Well, it depends on how the phenomenon is made by man. If it is the result of a rational scientific argument, then it may be reality. If it is an ad hoc assumption, then it may be only a fetish.

What about DLR then? Reality or fiction/fetish? How is DLR made? It is made up from an extension of Stefan-Boltzmann's law. How is this extension made up? It is an ad hoc assumption which is not described in physics literature. The conclusion is that DLR is voodo science.

Aniconism in Islam vs Science

2011-10-09T05:29:00.000-07:00

The previous posts on the fiction of DLR and climate alarmism, connect to the aniconism in Islam as the proscription against the creation of images of God, followed by Depictions of Muhammad, the Prophets including relatives, and more generally all humans and animals, which has led to Islamic art being dominated by Islamic geometric patterns.

On the other hand, in Christianity images play a very important role. Images are also very important in science and technology, and icons have a key role in modern life.

Images are suggestive and the aniconism of Islam may stem from experience that pictures may be too suggestive. Refraining from making images decreases the risk of believing that something is real, which in fact is only illusion. A colorful image of Hell, can make people believe that Hell (or Heaven) is real.

As an example, the reality of DLR is evidenced by colored images of DLR, as shown in the previous post.

Mathematical formulas can be viewed as a images, and as such are supposed to be maximally suggestive at the risk of being misinterpreted. An example is the Stefan-Boltzmann law underlying DLR, which is suggested by the following image:

R = sigma (T^4 - T_b^4) = sigma T^4 - sigma T_b^4 = R_out - R_in,

where the net radiance R is torn apart into the difference between the two quantities R_in and R_out appearing after a manipulation of the image according to a certain algebraic rule, Here where R_in may represent DLR.

This is like a Photoshop manipulation of an image of something real, with the manipulated image without real origin, as in hyperreality.

Fiction of Downwelling Longwave Radiation DLR

2011-10-09T02:33:00.000-07:00

Pictures of DLR. Because the pictures are real, also DLR must have physical reality, right?

In previous posts, in particular in How to Fool Yourself with a Pyrgeometer I have given evidence that Downwelling Longwave Radiation (DLR), which serves an important role in CO2 climate alarmism, is a fictitious phenomenon without physical reality.

So what is the truth? Is DLR reality or fiction? Is CO2 alarm reality or fiction?

Let us scrutinize the evidence put forward for the reality of DLR with an illustration from recent communication with Prof Grant W. Petty, who states:

We routinely MEASURE it using any of a variety of commercially available instruments (do a search on 'Eppley pyrgeometer', for example;
We routinely and accurately PREDICT its magnitude based solely on knowledge of the temperature, humidity, and cloud structure of the atmospheric column (as exemplified, for example, by a class project I and 15 other students had to complete as first-year graduate students, in which our fairly simple (<200 lines of code) model calculations yield results within a 1-2 W/m^2 of the MEASURED IR flux value for a MEASURED atmospheric profile);
Both Planck's Law and the Stefan-Boltzman Law (the latter is just an integration of the former over wavelength) have been known for generations to accurately predict EMISSION (one-way) from a blackbody. Nothing in either formulation requires one to know the temperature of the body (if any) RECEIVING the radiation. And Planck's Law was itself derived via thermodynamic arguments by a guy who understood the 2nd Law extremely well.

Prof Petty here refers to a Stefan-Boltzmann Law of the form (with sigma SB's constant)

R = sigma T^4 - sigma T_b^4 = R_out - R_in,

where R is the radiance from a black body of temperature T into a background of temperature T_b. Petty believes that there is a two-way flow of energy represented by R_out = sigma T^4 and R_in = sigma T_b^4, and that Stefan-Boltzmann's law expresses the net flow R = R_out -R_in as the difference between R_out and R_in.

Prof Petty gives even more weight to his SB law by stating:

It is settled science and has been for more than a century.

But Prof Petty is fooling himself and the society. His SB law does not appear in the physics literature. The original SB law has the form

E = sigma T^4

under the assumption that the background is at 0 K. This form of SB follows by integration of Planck's law, which is proved in the case of radiation into a background at 0 K.

But there is no proof of Prof Petty's SB law in the literature. Prof Petty's SB law is a free invention outside physics and as such of no scientific significance, a free invention which is used to fool people about the existence of DLR by claiming that it is measured with a pyrgeometer and hence must exist. But what a pyrgeometer effectively measures is temperature and the translation to radiance is done by a SB law without scientific justification.

I have asked Prof Petty abut the original scientific source of his SB Law. I have not received any answer.

Note that what can be proved in the case of a background T_b > 0 is the following SB law

R = sigma (T^4 - T_b^4)

with only the net radiance R and not R_in and R_out. Prof Petty would now argue that this law trivially can be written on his form, simply by trivially splitting the right hand side as follows:

sigma (T^4 - T_b^4) = sigma T^4 - sigma T_b^4 = R_out - R_in.

But this is fooling yourself by believing that a certain algebraic operation directly translates to physical reality.

As a defense Prof Petty would probably argue that the only thing that matters in the end is the net flow, and that the net flow anyway is the same in both forms of the SB law, and thus that it does not really matter if DLR is reality or fiction. From scientific point of view this argument has an obvious weakness. From political point of view it may not matter if CO2 alarm is reality or fiction, but from scientific point of view it cannot be without importance.

I have asked Prof Petty about a reaction, and will report if I get any.

Many-Minds Cosmology and Jante Law

2011-10-08T00:26:00.000-07:00

In Many-Minds Relativity and Many-Minds Quantum Mechanics I explore an idea which can also be applied to cosmology, as discussed in previous posts. This idea has developed as an alternative to the following two views on the choice of reference or coordinate system for description of phenomena in space and time dominating physics:

There is a unique preferred reference system (Newton's absolute space and time).
There is no preferred reference system (Einstein's relativity theory).

We know that 2 came out as a reaction to the fruitless attempts to identify Newton's absolute space in the form a luminoferous aether medium carrying electromagnetic waves in the Michelson-Morley experiments.

2 is a generalization of Galileo's departure from geocentrism into heliocentrism relating to the Cosmological Principle (CP) or (generalized) Copernican Principle:
If the Earth is not the center of the Universe, then there is no center of the Universe at all.
Einstein formulated 2 as
If my aether cannot be everybody's aether, then there is no aether at all.
2 connects to the first rule of the Jante Law identified by the Danish-Norwegian author Aksel Sandemose in his novel A fugitive crosses his tracks, as a characteristic of Scandinavian mentality:

Don't think you're anything special,

which expresses a form of CP:

If I am not special, then nobody else is special.

But we are not forced to conclude 2, if we agree that 1 is not true, since it is also possible that

There are many preferred reference systems.
There are many aethers.
There are many centers of the Universe.
There are many special people.

This is is the idea of Many-Minds physics, which offers to take physics out of a paralyzing grip of 2 including

paradoxes of Einstein's special relativity
difficulties of interpretation of the wave function of quantum mechanics
CP of an isotropic and homogeneous universe requiring dark energy
Swedish trauma of lacking self-esteem.

The question is if Many-Minds physics can attract the minds of many, or if is to remain the special idea of a special person?

Note that the basic idea of Einstein's (unique) special theory of relativity is that there is no special reference system. A contradiction?

Recall that the temptation to put forward 2 is very strong, since it gives physics the special top position in the hierarchy, as the objective science with arts, literature, political and social sciences ranking much lower as deploringly subjective. But 2 has brought physics into a

dead end of objective dark energy, string theory and statistics.

So what will then be best, to stick to 2 and be the best but have nothing to offer, or to subdue to reality, give up the special position and step forward?

Of course, Many-Minds connects to a pluralistic society, while One-Mind or No-Mind connects to an autocratic society.

Cosmology as Thermodynamics with Gravitation

2011-10-06T23:23:00.000-07:00

It may be that the large scale dynamics of the universe (cosmology) can be described as the thermodynamics of a compressible gas subject to gravitation in the form of the Euler equations, see Computational Thermodynamics (Chapter 32).

The basic laws of thermodynamics resulting (by integration in space) from the Euler equations, take the form:

dK/dt = W - D + GP (conservation of (total) kinetic energy K)
dE/dt = - W + Q + D (conservation of (total) internal/heat energy E)

where

W = Integral P div V dx is work by pressure P on velocity V
GP = Integral Phi div V dx is work by (negative) gravitational potential Phi on V,

Q is a heat source and D is turbulent dissipation. Notice that

W + GP = Integral (P + Phi) div V dx,

showing the similar action of the pressure P and gravitational potential Phi with P + Phi > 0

under accelleration with dK/dt > 0.

The standard cosmological model is that of Friedmann-Lemaitre-Robertson-Walker (FLRW) which expresses 1. + 2. assuming the validity of the Cosmological Principle (CP) of an isotropic and homogeneous universe.

CP is extremely restrictive by reducing space dependence to a simple scale factor depending only on time with the FLRW model being simply a system of two time-dependent scalar equations. CP predicts a decelerating expanding universe, while observations show instead acceleration, and thus CP must be abandoned, and cosmology thus today struggles to get out of the paralyzing grip of CP.

Let us then see what 1. + 2. may tell in a case without CP. Let us then assume that the gas/universe starts out at rest as a hot compressed sphere (centered at the origin of a Euclidean coordinate system) subject to a heat source Q > 0 and develops in a Big Bang scenario according to 1. + 2. as follows (assuming here for simplicity that D = 0):

expansion (dK/dt > 0) with W + GP > 0 sustained by Q > W.

In words: the heat source Q creates a pressure P sufficiently large to expand the gas under

gravitation with W + GP > 0. For a perfect gas P = Rho T where Rho is density and T temperature. It is natural to connect T to the intensity q of the heat source by the Poisson equation

- Laplace T = q

which in the case of constant q gives T(r) quadratic and dT/dr linear in the distance r to the origin. With Rho roughly constant that leaves a pressure gradient dP/dr which is also linear resulting in a velocity V_1(r) increasing linearly in r from V(0) = 0 during Big Bang. Wiith q variable, velocities V_1(r) with sublinear (or superlinear) variation may also arise.

After the initial Big Bang expansion phase just described, assume that the heat source Q is turned off, and the gas expands mainly by inertia with dK/dt = 0 from the initial velocity V_1(r), with W = 0 and Q = 0 assuming that inertia dominates gravitation. The initial velocity V_1(r) will then be carried to later time.

A sublinear V_1(r) could then, when observed at some later time and taking the finite speed of light into account, be interpreted as an indication of an accelerating expansion corresponding to a Hubble constant seemingly increasing with time, with more distant galaxies appearing to have a smaller Hubble constant.

This was the observation giving the 2011 Nobel Prize in physics. But the observed acceleration could be an illusion reflecting a sublinear velocity V_1(r) resulting from specifics of the pressure gradient forcing during the initial Big Bang expansion. This would reflect that inertia dominates gravitation on intergalactical scales, while gravitation would balance inertia on galactical scales (compare with The Hen and the Egg of Dark Matter).

In this case there would then be no need to introduce any dark energy behind the observed acceleration, because an illusion is an illusion, and physics could focus on something more constructive than searching for something that may not exist, as in the Scarlet Pimpernel:

We seek him here, we seek him there,

Those Frenchies seek him everywhere.
Is he in heaven? — Is he in hell?
That damned, elusive Pimpernel.

CP reflects the following extension of Galileo's departure from geocentrism into heliocentrism:
If the Earth is not the center of the Universe, then there is no center of the Universe at all.
Incidently, this connects to Einstein's elimination of any form of aether (see Many-Minds Relativity)
If my aether is not everybody's aether, then there is no aether at all.
CP connects to the first rule of the Jante Law identified by the Danish-Norwegian author Aksel Sandemose in his novel A fugitive crosses his tracks, as a characteristic of Scandinavian mentality:

Don't think you're anything special,

which expresses the Galilean principle:

If I am not special, then nobody else is special.

But the Jante Law is today questioned (also in Sweden) and so maybe CP also should be questioned?