The Sky Dragon Strikes Back

Andrew Skolnick has mounted a ferocious attack on the Slayers of the Sky Dragon on Judy Curry's blog as a large set of comments (out of 2000) on the blog post Slaying a Greenhouse Dragon.

The attack is supported by a Youtube clip entitled Needling the Deniers aimed at disproving my new derivation of Planck's law of blackbody radiation showing that the basic postulate of CO2 alarmism of backradiation is fiction.

The clip shows that a needle can be heated in a microwave oven, which is known to everybody with some experience of a such a device. Skolnick thus demonstrates that low frequency waves (microwaves) can heat an absorber to higher temperature than the blackbody temperature corresponding to the frequency.

Does this mean that a blackbody can heat another blackbody of higher temperature, that a cold atmosphere can radiatively heat a warmer Earth surface? Of course not!

But what about the microwave oven then? Isn't this a counter-example? No, it is not because the amplitude of the microwave radiation is much larger than that of blackbody radiation of the corresponding temperature. The heating in a microwave oven is thus not blackbody heating; it is amplifed blackbody heating, and therefore the microwave heating of a needle is not a counter-example to my proof that blackbody backradiation from cold to warm is fiction.

But it is good that Skolnick brings this issue to the table, which allows one more head of the Sky Dragon to be eliminated. Thank you Andrew!

Mathematical Secret of Flight 6: Wikipedia Cover Up

To see that our new theory of flight fills a need, it is instructive to study how Wikipedia covers up the lack of a convincing theory in the literature:

• There are several ways to explain how an airfoil generates lift.
• Some are more complicated or more mathematically rigorous than others; some have been shown to be incorrect.
• For example, there are explanations based directly on Newton’s laws of motion and explanations based on Bernoulli’s principle.
• Both principles can be used to explain lift, but each appeals to a different audience.
• This article will start with the simplest explanation; more complicated and alternative explanations will follow.
• Explaining lift while considering all of the principles involved is a complex task and is not easily simplified.
• In attempting to explain why the air flows the way it does (e.g. why the flow follows the upper surface of the airfoil and why the streamtubes change size), the situation gets considerably more complex.
• It is here that many simplifications are made in presenting lift to various audiences.

We see that one part of Wikipedia struggles to hide that there is no theory of flight, while another part tells the truth by citing John D. Anderson, Curator of Aerodynamics at the National Air and Space Museum:

• It is amazing that today, almost 100 years after the first flight of the Wright Flyer, groups of engineers, scientists, pilots, and others can gather together and have a spirited debate on how an airplane wing generates lift. Various explanations are put forth, and the debate centers on which explanation is the most fundamental.

As a last line of defense Wikipedia presents the classical theory by Kutta-Zhukovsky (which we have shown to be incorrect).

• The effects of viscosity are contained within a thin layer of fluid called the boundary layer, close to the body. As flow over the airfoil commences, the flow along the lower surface turns at the sharp trailing edge and flows along the upper surface towards the upper stagnation point. The flow in the vicinity of the sharp trailing edge is very fast and the resulting viscous forces cause the boundary layer to accumulate into a vortex on the upper side of the airfoil between the trailing edge and the upper stagnation point.[26] This is called the starting vortex. The starting vortex and the bound vortex around the surface of the wing are two halves of a closed loop. As the starting vortex increases in strength the bound vortex also strengthens, causing the flow over the upper surface of the airfoil to accelerate and drive the upper stagnation point towards the sharp trailing edge. As this happens, the starting vortex is shed into the wake, and is a necessary condition to produce lift on an airfoil. If the flow were stopped, there would be a corresponding "stopping vortex". Despite being an idealization of the real world, the “vortex system” set up around a wing is both real and observable; the trailing vortex sheet most noticeably rolls up into wing-tip vortices.

In both politics and science, cover up is a most essential part of the game, because admitting that there are no answers to questions which should have answers, destroys credibility and authority, the core values of both politics and science. But pretending to have answers when no answers are available has a high cost, as demonstrated in Dr Faustus of Modern Physics.

The above connects to my old controversy with Wikipedia about d'Alembert's paradox discussed in posts on d'Alembertgate and the 2009 knol Wikipedia Inquisition, leading to a banning of my voice on Wikipedia. This makes it impossible to give any form of link to the new theory of flight on Wikipedia, as if understanding what keeps an airplane in the air would be dangerous knowledge which must be kept hidden to the people.

Mathematical Secret of Flight 5: Bird Wing

The thesis by Heather Falconsong Howard studies techniques for generating photo-realistic and fantasy digital bird and avian creatures in film, TV and games, based on an analysis of the design of real birds wings.

Particular attention is given to little covert feathers covering the space between groups of main fetahers, which also seem to act like little wing flaps delaying separation.

This is indicated in the above picture from the thesis which represents the classical Prandtl scenario of separation based on 2d recirculation to stagnation.

Our new analysis of separation and generation of lift opens to a different understanding of the action of birds wings. In particular we expect to find a connection between the separation pattern of our new analysis with point-stagnation and streamwise vorticity, and the arrangement of feathers of a bird wing including covert feathers and a periodic wavy trailing edge. We will report on our findings in upcoming posts...

The design of birds' wings thus suggest that the smooth surface and sharp straight trailing edge of a standard airplane wing may not be optimal. A further indication in this direction is given by the slotted wing tips of gliding hawks and the slotted jet flaps of Skywalk paragliders, to which we will also return...

Backradiation in Stefan-Boltzmann's Law: Folklore or Science?

Stefan-Boltzmann's Law can be formulated in the following two algebraically equivalent, but physically different forms:

1. E = sigma Te^4 - sigma Ta^4, (photon particle model: difference of two-way gross flows)
2. E = sigma (Te^4 - Ta^4) ~ 4 sigma Te^3 (Te - Ta), (wave model: net one-way flow)

where E is the intensity of the heat energy transferred from a blackbody (emitter) of temperature Te to a blackbody (absorber) of temperature Ta smaller than Te, and sigma is a constant.

Version 1 is the basis of CO2 alarmism based on "backradiation" of sigma Ta^4 from absorber to emitter, as transfer of heat energy from cold to warm.

In Slaying the Sky Dragon and Mathematical Physics of Blackbody Radiation I present a derivation of Version 2 based on a principle of finite precision computation in a wave model, without backradiation. And without backradiation CO2 alarmism crumbles.

The original version by Stefan and Boltzmann is formulated with Ta = 0 as Version 0. without backradiation (in which case 1. and 2. look identical), as an integrated version of Planck's law based on a statistical particle model.

Which is the correct formulation? Version o, 1 or 2? Particle statistics or waves? Let's list some answers from the web supposedly reflecting scientific sources:

• Hyperphysics: 2.
• Wikipedia: 0.
• Britannica: 0.
• Wolfram: 0.
• Univ. of Singapore: 2.
• MIT: 2.
• Warwick: 0.
• UNL: 0.
• Physics Handbook: 0.
• Engineering Toolbox: 2.
• ...

The list can be made much longer, but we dont find any support of 1. and backradiation. And without backradiation CO2 alarmism crumbles.

The following questions present themselves:

• Why is 1. found only in the CO2 alarmism of IPCC, and not elsewhere?
• Is 1. a free invention which lacks original scientific source?
• Is 1. a form of hyper-reality for which the original is missing?
• Is 1. a form of folklore known by everybody to be true, yet without any individual scientist claiming to have demonstrated the statement.
• Is 1. an expression of "scientific consensus" for which no original scientific source is required?

What do you think? Is CO2 alarmism based on backradiation, folklore or real science?

The Emitter-Absorber Relation of Radiation

There is a lot of confusion concerning the physics behind Plank's radiation law and its integrated form of Stefan-Boltzmann's law in the following two algebraically equivalent but physically different forms:

1. E = sigma Te^4 - sigma Ta^4, (photon particle model: difference of two-way gross flows)
2. E = sigma (Te^4 - Ta^4) ~ 4 sigma Te^3 (Te - Ta), (wave model: net one-way flow)

where E is the intensity of the heat energy transferred from a blackbody (emitter) of temperature Te to a blackbody (absorber) of temperature Ta smaller than Te, and sigma is a constant.

Version 1 reflects two-way energy transfer by two way photon particles emitted by both emitter and absorber into a void (of zero Kelvin), and can be seen as an a hoc version cooked up from Planck's original law of one blackbody emitting into a void (of zero Kelvin).

In Slaying the Sky Dragon and Mathematical Physics of Blackbody Radiation I present a derivation of Version 2 based on a principle of finite precision computation in a wave model.

Version 1 reflects simple physics of particles with the two bodies like two very young children playing side by side without interaction both spitting out photons in two directions into a void (of zero Kelvin).

Version 2 reflects more complex physics with the two bodies playing together, talking to each other by a two-way wave equation, but with one-way net transfer of heat: The effect of the finite precision computation is a high frequency cut-off depending on temperature limiting the ability of the absorber to re-emit only frequencies below cut-off, with frequencies above cut-off being absorbed and turned into heat.

Version 2 is like two educated people talking and listening to each other, with the emitter being the smarter and the frequencies above the cut-off of the dumber being absorbed by the dumber and then transformed into heat (frustration).

Which version is better? The trivial 1 or the educated 2? Is there an intimate relation between emitter and absorber into a system relation, where emission from one body is directly connected to absorption of another? Is the play between adults more interesting that than between babies?

Are these questions above your cut-off frequency and will only lead to heated frustration?

Answer to Question by Roy Spencer

In an exchange between Roy Spencer and Marty Hertzberg regarding the proper use of the Stefan-Boltzmann equation in climate modeling, Roy asks the question:

• How does the surface 'know' how opaque the atmosphere is before it 'decides' at what rate it should emit IR?

which can be turned around into:

• How does the Earth's surface 'know' what the temperature of the atmosphere is before it 'decides' at what rate it should emit IR?

Roy asks this question to challenge the view put forward by Marty that the temperature Ta

of the environment (the absorber) of a (blackbody) emitter at temperature Te bigger than Ta, determines the amount of energy E emitted according to Stefan-Boltzmann's law written in the form:

• E = sigma (Te^4 - Ta^4) ~ 4 sigma Te^3 (Te - Ta)

expressing E as a multiple of the difference in temperature Te - Ta. In particular, this means that there is no backradiation of energy from a cold atmosphere to a warmer Earth surface, only the other way.

This is different from a common view adopted by Roy of a two-way emission of photons carrying energy between emitter and absorber, in which Stefan-Boltzman's law would be written

• E = sigma Te^4 - sigma Ta^4

expressing the net energy transfer E as the difference between a two way gross flow of energy

with emitter and absorber both emitting into a background of zero K. In this view, a cold atmosphere would be warming a warmer Earth surface by sigma Ta^4, while the Earth surface

would be transferring sigma Te^4 to the atmosphere.

In the new derivation of Planck's law behind Stefan-Boltzmann presented in Slaying the Sky Dragon, with more details in the upcoming book Mathematical Physics of Blackbody Radiation,

I give support to Marty's standpoint, which is in opposition to Roy's.

Roy's question is how the Earth reads the temperature of the atmosphere and an answer is suggested by my analysis: The emitter and absorber stay in contact by two-way electromagnetic waves described by Maxwell's equations. This contact makes it possible for both emitter and absorber to read the temperature of the other by reading the spectrum of the other.

This is like two superpowers reading the destruction capability of the other without pressing the buttons to exchange of mutual destruction, see picture above.

The basic idea is that the contact allowing temperature reading is established by two-way electromagnetic waves, while the transfer of energy is one-way (from warm to cold).

Mathematically the two versions of Stefan-Boltzmann may look equivalent, but the physics behind the two is different: Roy's is two-way stream of particles carrying energy back and forth.

Marty's and mine is two-way electromagnetic waves carrying information with one-way transfer of energy.

The difference comes out when looking at perturbations of forcing, as perturbations of net one-way flow of energy (small) vs perturbations of gross two-way flow of energy (big). This is the origin of CO2 alarmism: How to make something small into something big.

Does this answer your question Roy?

In support of Marty's and my view, one may add that a precise macroscopic mathematical model for electromagnetic waves is known (Maxwell's equations), while that of photon flight appears to be unknown (unless it is assumed to be a trivial ray model).

Monstrosity of Quantum Mechanics 7: Basic Postulates

In what sense are the basic postulates of quantum mechanics not Harry Potter fantasy?

Lubos Motl makes in The Unbreakable Postulates of Quantum Mechanics a heroic effort to justify quantum mechanics almost 100 years after its formulation, starting with:

• Many people try to use every opportunity to diminish the importance of the principles of quantum mechanics and to cover them by fog and shadows - even though they're the most important and most robustly established insights of the 20th century science.

The mission is to convince skeptics about the truths of the following basic postulates:

1. The set of possibilities in which a physical system may be found is described by a linear Hilbert space (more precisely by the rays in this space) equipped with an inner product.
2. Complex (nonzero) linear combinations of allowed states are allowed states, too.
3. A physical system composed out of N separated (or fully independent) subsystems has the Hilbert space equal to the tensor product of the Hilbert space describing the individual subsystems.
4. Physical quantities, also referred to as "observables" in the fancy quantum mechanical context, are encoded in Hermitean (linear) operators acting on the Hilbert space.
5. In particular, the evolution in time is generated by the operator known as the Hamiltonian.
6. The exponentials of its imaginary multiples are the operators that evolve the system over a finite interval and these operators are unitary; similarly, other symmetry transformations are given by other unitary (or anti-unitary, if the time reversal is included) operators.
7. The expectation values of the quantity "A" are given by the inner product ; if "A" is replaced by the projection operator "P", this expectation value expresses the probability that the condition connected with "P" will be satisfied once the system is measured.

The motivations for 1 - 7 presented by Lubos tell us something essential about the solidity of quantum mechanics. Let see how Lubos motivates 1 - 3:

1. Why do we know that there is a Hilbert space? If a physical theory has a content, it must be able to manipulate with the information. We insert some information that we know - and it spits out another piece of information that we didn't know but that is predicted, or postdicted, by the theory. So there must exist some states; which state was realized in Nature, is realized in Nature, or will be realized in Nature, is the way to phrase all the information we have or we want to have about the world or its pieces. That was true even in classical physics: different states of a physical system were given by points in the phase space (spanned by the positions and their canonical momenta).
2. The new thing about quantum mechanics is that the complex linear superpositions of two allowed states are also allowed states. How do we know that? Well, we may actually design procedures that create such combined states in practice.
3. Now, there are other postulates and universal rules of quantum mechanics. For example, the composite systems are described by tensor products of Hilbert spaces. It's not hard to see why: if the dimensions of Hilbert spaces H1, H2 are equal to d1, d2, there are clearly d1 basis vectors of H1 and d2 basis vectors of H2. These basic vectors parameterize some linearly independent (i.e. fully mutually exclusive) possibilities. The set of linearly independent possibilities for the composite system obviously has to be the Cartesian product of the two sets for the separate subsystems. And the "linear envelope" of this Cartesian product - the new basis - is the tensor product of the original spaces. Its dimension - its number of basis vectors - is equal to d1.d2 as expected. This conclusion is pretty much inevitable, by basic logic.

When you read this as a mathematician you understand that the motivation is weak, formal and touches triviality elevated to deep insight into the true inner mechanisms of the microscopic world. The Hilbert space assumption essentially reflects that the Schrödinger equation is linear. But why physics on atomic scales is linear allowing superposition, is not motivated. This appears as an ad hoc assumption which could be made by one who has recently fallen in love with linear Hilbert space theory and has been so overwhelmed by emotion that rational thinking has disappeared.

The argument that "we may actually design procedures that create such combined states (superposed) in practice" sounds hollow, knowing that this principle of quantum computing has shown to be very difficult to demonstrate.

Atomic physics concerns the interaction of elementary particles by certain forces and thus can be thought as N-body problems. But an N-body problem is not linear, and so it requires a lot of fantasy to believe that the N-body problem of quantum mechanics through some miracle decides to show up as linear.

Lubos adds to skepticism by listing the many different interpretations of quantum mechanics

without being able to find any reasonable one.

Why Prandtl Was Wrong 4

Lift and drag of a NACA0012 wing in computation by Unicorn and experiment.

We have asked if it is possible to check if drag and lift of a body moving through a fluid originate from a thin boundary layer which separates from the body surface into the fluid, as is the mantra of Ludwig Prandtl, the father of modern fluid mechanics, formulated in an 8 page note in 1904.

To check in experiment is cumbersome because the viscosity of a real fluid is never exactly zero and thus it can be argued that no real fluid can satisfy a slip boundary condition with zero skin friction without any boundary layer.

But to check in computation is perfectly possible: just set the skin friction to zero in a Navier-Stokes code, that is use a slip boundary condition and see what happpens. Will drag and lift develop in accordance with observation in solutions of the Navier-Stokes equations with slip

without boundary layers?

Yes! Computations without boundary layer give correct drag and lift!

The conclusion is inevitable:

• Prandtl was wrong: Drag and lift do not originate from boundary layers.
• Prandtl's scenario of fluid separation is incorrect.
• The mantra of modern fluid mechanics is incorrect.

For further details see the new article Analysis of Separation in Turbulent Incompressible Flow which exhibits a scenario of fluid separation which is fundamentally different from that of Prandtl and which is supported by mathematical analysis, computation and observation.

Blackbody Radiation as a Generic Emergent Phenomenon

A body of temperature T emits radiation with an intensity E similar to that of an ideal blackbody given by Planck's law (Rayleigh-Jeans law with cut-off):

• E = gamma T f^2,
• with a high frequency cut-off proportional to T,

where f is the frequency and gamma is a constant.

The radiation spectrum thus only depends on the temperature and not of the material of the body. This indicates that blackbody radiation is a generic emergent phenomenon resulting from collective atomic vibrations and not from individual atoms or molecules which have different line spectra.

This idea is explored in the upcoming book Mathematical Physics of Blackbody Radiation (and in one of my chapters in Slaying the Sky Dragon) by an analysis of resonance in a wave equation with radiation.

In this model blackbody radiation can be thought of as the sound of a piano with all keys being struck at the same time with the same force: a complex chord which sounds the same for all pianos. An generic emergent phenomenon which cannot be understood by looking at just one key.

It can also be thought of as the complex sound of a big gong with a big range of frequencies. There is an interesting experiment showing that a gong can be made to sound by a short laser pulse kicking the gong atoms into an emergent collective vibrational motion producing sound waves hitting your ear.

Large Boundary Layer Collider: Why Prandtl Was Wrong 3

Part of the Large Boundary Layer Collider at the European Spallation Source in Lund, Sweden.

According to Ludwig Prandtl, named the father of modern fluid mechanics, both drag and lift of a body moving through air or water originate for a thin boundary layer.

This is the fundamental postulate of modern fluid mechanics formulated in 1904, but it is now being questioned. Is modern fluid mechanics based on a postulate which is does not correspond to physical reality?

The answer may be given by the European Spallation Source (ESS) in Lund, Sweden: The world's biggest proton accelerator (see picture).

The idea is to eliminate the boundary layer by bombarding it with high energy protons, and once the boundary layer has been removed completely this way, drag and lift will be measured. If drag and lift remain the same under removal of the boundary layer, then drag and lift do not originate from any boundary layer, and modern fluid mechanics is based on incorrect physics.

But ESS will not be ready to use before 2020, and thus it is natural to ask if there is some other quicker and cheaper way of eliminating a boundary layer? Yes, there is. But what is it?

Follow the thrilling uncovering of one of modern physics most well kept secrets...

PS An alternative to ESS would be to use liquid helium with next to zero viscosity, but to reach a sufficiently large Reynolds number, the dimension of the experiment needs to be 10 times bigger than that of the Large Hadron Collider and thus is out of reach, for the moment at least.

But as UN global warming alarmism is now fading away maybe this experiment could become the next big initiative by the UN backed by EU. DS

Why Prandtl Was Wrong 2

One way of eliminating a butterfly.

Question and Answer 1:

• How can one prove that a butterfly in Brazil cannot cause a tornado in Texas?
• Eliminate the butterfly and notice tornado without butterfly!

Question and Answer 2:

• How can one prove that a boundary layer is not the origin of drag and lift of a body?
• Eliminate the boundary layer and notice drag and lift without boundary layer.

But how to eliminate a butterfly and how to eliminate a boundary layer? Follow the thrilling

continuation of this story...

Why Prandtl Was Wrong 1

Prandtl initating modern fluid mecahnics in 1904: A very satisfactory explanation of the physical process in the boundary layer between a fluid and a solid body could be obtained by the hypothesis of an adhesion of the fluid to the walls, that is, by the hypothesis of a zero relative velocity between fluid and wall (no-slip).

Ludwig Prandtl is named the father of modern fluid mechanics because he discovered the boundary layer of a slightly viscous fluid flowing around a solid body, like air flowing around a moving car or airplane, as a thin layer where the fluid velocity rapidly changes from the free flow velocity away from the body to that of the body surface as an expression of a no-slip boundary condition.

Prandtl claimed that the that turbulent flow in the aft of a body results from separation of turbulent boundary layer away from the body surface into the free flow.

This has become the mantra of modern fluid mechanics: The truth of slightly viscous fluid flow is to be found in thin boundary layers. Both drag and lift of a body moving through a fluid are effects of a no-slip boundary condition creating a thin boundary layer.

In a sequence of posts we shall show that Prandtl was wrong: Drag and lift do not originate from a thin no-slip boundary layer.

But how can one show that Prandtl was wrong? Something to reflect upon a rainy summer day.

Hint 1: Suppose you observe the same drag and lift with the boundary layers eliminated. Can you then be sure that drag and lift do not originate from boundary layers? Yes, you probably say. But how to "eliminate" the boundary layers?

Hint 2: Browse: Dr Faustus of Modern Physics

The Secret of Separation

The Secret of Flight revealed in previous posts is hidden in the secret of separation of the flow at the trailing edge of a wing. The above picture reveals the Secret of Separation:

You see a piece of the trailing edge of a horisontal wing as viewed from behind with opposing (more or less) vertical flows from the upper and lower side of the wing which are meeting in retardation and somehow have to be directed into a (more or less) horisontal backward direction to leave the wing (out of the screen). You can think of two opposing armies approaching each other and the question is how the conflict is to be resolved.

Now, retardation in opposing flows is exponentially unstable (direct confrontation is unstable) and thus the flow seeks a flow pattern without opposing flow, and finds one as depicted above: The opposing flows are shifted horsiontally and turned into a set of counter-rotating swirling vortical motions like the one you can see in a bathtub drain, as seen here in a different perspective.

The result is a separation without unstable opposing flows supported by a zig-zag pattern of low/high pressure with low pressure inside the vortices, as shown here. The resulting pressure distribution is what gives both drag and lift to a wing.

Something to think about in the hammock, or in your sailing boat because the secret of sailing is the same.