Xinhang Shen questions Einstein's special theory of relativity on the same ground as I do in the Physics Essays article Challenge to the special theory of relativity (2016). Xinhang is CEO and President of NAC Geographic Products and expert on remote sensing and GIS Geographic Information System.

A key argument is that clocks tick at the same rate independent of inertial motion and so it is possible to set up a system of universal time, without any effects of time dilation of special relativity. In Xinhang’s words, Einstein’s special theory of relativity SR is fake physics. All users of GPS should be happy that SR there serves no real role; with the jungle of time dilation of SR, GPS could never work. GIS if anything connects to standards of time and space and so even an ardent believer in SR may learn something listening to Xinhang. As scientist it is surely more productive to listen than to close eyes and ears and stubbornly stick to text book physics which may be fake.

## torsdag 31 oktober 2019

## onsdag 30 oktober 2019

### The Fundamental Difference Between First and Second Hand Obervation

The analysis presented in the recent sequence of posts shows that Einstein’s special theory of relativity seeks to answer a question, which should not be posed, because it is in conflict with the Postulate of SR as the theoretical foundation of SR. The question posed by Einstein is illogical and so is Einstein's answer.

More precisely, Einstein’s SR dictates/prescribes through a

*Lorentz transformation*what Observer1 at rest in a coordinate system S1 allowing first hand observation, will observe in a different coordinate system S2 moving with respect to S1 as second hand information transformed from first hand observation of Observer2 at rest in S2.

Observer1 thus has first hand information about time by reading his clock, but only second hand information about the clock of Observer2.

The analysis shows that it is the incompatibility between first and second hand information, which gives rise to the paradoxes/contradictions of SR.

More generally, it is important to distinguish between first hand information based on observation in direct contact with reality and second hand information resulting from a transformation without direct contact with reality.

This is very obvious in criminal cases with a fundamental difference between witness from direct observation of a murder as compared to witness based only on hearsay. Also in science it is important to seek the original source of a both theory and observation, understanding that transformation can distort. Thus text books of physics generally present what is already written in previous text books in a hierarchy of second hand information where the original source is successively distorted or is simply missing.

## tisdag 29 oktober 2019

### Why Did Einstein Ask the Wrong Question?

In the recent sequence of posts on Einstein's special theory of relativity SR, I argue that the question posed by Einstein in SR is a question which is incompatible with the Postulate of SR, and that is the reason why SR is filled with paradoxes/contradictions.

The

The

*Postulate of SR*can be formulated as follows:*The propagation of light in given coordinate system $S$ is described by Maxwell's equations expressed in S with given constant speed of light = c.*

The Postulate acknowledges that there are different coordinate systems (rectilinear Euclidean systems) and one may assume, to stay close the Einstein, that they move with constant velocity (without rotation) with respect to each other, as so-called

*inertial systems.*
An

*Observer*equipped with a coordinate system $S$ and the Postulate of SR as*Measuring Apparatus,*thus has access to a mathematical model in $S$ of a full world of electro-magnetics including all aspects of light propagation. With this model as Measuring Apparatus the Observer can answer any question about propagation of light in $S$ and thus the world.
In particular there is no reason for an Observer with coordinate system $S$ and Maxwell's equations in $S$, to ask for a description in a different inertial system $S^\prime$, which is moving with respect to $S$. Why would the Observer do that if $S$ suffices to describe the world? In fact the Observer cannot ask this question, because the Observer has no Measuring Apparatus in $S^\prime$, only in $S$. Of course the Observer may choose a different coordinate system, but then consider Maxwell's equations in that system to be the model.

Yet, this is the question posed by Einstein in SR, a question which Einstein answers by dictating what the Observer will observe in other inertial systems than his own, in the form of the

*Lorentz transformation.*These are not independent observations of light propagation because the Observer has a Measuring Apparatus only in his chosen system, but fabricated observations dictated by the Lorentz transformation.
To the list of fake-everything today dominating both science, politics and media, we can add Einstein's SR as asking a question, which cannot be asked, and giving an answer which is not based on actual observation but instead is fabricated second hand.

Why did Einstein pose that question? When? Why did Einstein abandon SR after 1907?

Compare with Many-Minds Relativity asking relevant questions based on the Postulate of SR in the above form.

## söndag 27 oktober 2019

### Why Einstein's Special Theory of Relativity is so Confusing

In recent posts I have been searching for the source of the paradoxes/contradictions of Einstein's special theory of relativity SR. My objective is to understand why SR is so confusing. Here is the result of my search in short form:

Ingredients of SR:

- Observers.
- Measuring Apparatus.
- Coordinate systems (inertial systems moving with constant velocity with respect to each other).

Postulate of SR:

- An Observer with Measuring Apparatus at rest in a coordinate system measures the same constant speed of light = c independent of the motion of the light source in the coordinate system.

This Postulate is compatible with a description of propagation of light according to Maxwell's equations (with constant speed of light = c) in a coordinate system with Observer and Measuring Apparatus at rest. In principle this gives the Observer access to the full electromagnetics described by Maxwell’s equations in the given coordinate system with Observer at rest, but Einstein did not use this golden opportunity and started instead from absolutely minimal assumptions with the objective to derive far-reaching revolutionary consequences, as his special contribution to science outmatching Newton.

Einstein now poses the Basic Question to be answered by SR:

- What will Observer1 observe concerning propagation of light in S2? (Q)

Einstein then gives the answer in the form of the Lorentz transformation connecting the coordinates in S1 with those of S2. More precisely, Einstein dictates what Observer1 will have to see in S2 by giving Observer1 special glasses in the form of the Lorentz transformation.

Observer1 with Measuring Apparatus1 can measure the propagation of light in S1 while at rest in S1. Observer1 is not allowed to carry his Measuring Apparatus1 to S2, since it is tied to S1. Einstein is thus asking Observer1 to abandon his Measuring Apparatus1 and then somehow without apparatus make observations in S2. But this is a break of logic with respect to the Postulate of SR only speaking about Observer1 with Measuring Apparatus1 making observations at rest in S1 and not while moving with respect to S2 without apparatus.

We understand that Einstein separates Observer from Measuring Apparatus, which breaks the logic of the Postulate of SR, and leads to asking the question (Q) which should not/cannot be asked. When Einstein insists on answering the question, which cannot be asked, he breaks the logic and paradoxes and contradictions result. This connects to Wittgenstein’s: Whereof you cannot speak, you have to keep quiet.

An example of a question which cannot be posed is the showpiece of medieval scholasticism:

*How many angels can dance on the head of a pin?*

Seeking to give an answer to such a question was/is not helpful to science.

To see a contradiction between theory and observation does not require much imagination, but to understand a logical inconsistency may require more, and so people can get fooled more easily by incorrect logic than incorrect facts.

In Many-Minds Relativity logical reasonable questions are posed based on the Postulate of SR.

To see a contradiction between theory and observation does not require much imagination, but to understand a logical inconsistency may require more, and so people can get fooled more easily by incorrect logic than incorrect facts.

In Many-Minds Relativity logical reasonable questions are posed based on the Postulate of SR.

**Summary:**If a theory, like SR, contains paradoxes/contradictions it may be because the theory breaks logic. This is the case with SR where the paradoxes/contradictions result from seeking to answer a question which breaks the logic of the Postulate of SR.

This was in fact acknowledged by Einstein in his 1905 article stating that the Postulates of SR appear to be contradictory, yet he continued, towards immense fame...:

*We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only***apparently irreconcilable with the former,**namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.

**PS**What about experimental verification of SR? Apparently nil as concerns photons/light.

## lördag 26 oktober 2019

### The Source of the Paradoxes/Contradictions of Special Relativity

In recent posts I have been searching the source of the (infinitely) many paradoxes/contradictions of Einstein's special theory of relativity SR, which must somehow be hidden either in the Postulates of SR, or in theoretical derivations from the Postulates, since real physics cannot be paradoxical or contradictory.

Since SR is a pillar of modern physics, the fact that SR is loaded with paradoxes/contradictions makes modern physics build on shaky ground, which is today coming to expression in a scientific crisis witnessed by many.

I have found the source to be the Second Postulate of SR speaking about the speed of light as expressed by Einstein in Collected Papers, Vol. 2, 1989, p.143:

*Each ray of light moves in the coordinate system “at rest” with the definite velocity V (or c) independent of whether this ray of light is emitted by a body at rest or in motion.*

Let us now subject this statement to a critical analysis starting by listing its ingredients:

*There are rays of light.**Each ray of light moves in a certain coordinate system, which is assumed to be "at rest".**The speed of propagation of the ray of light is always the same = c.**The speed of propagation of the ray is independent of the motion of the body emitting the ray.*

*inertial systems.*

*The Postulates of SR thus can be expressed as 1- 4, which are compatible with describing propagation of light by (the same) Maxwell's equations in each coordinate system chosen to be "at rest".*

What its then SR based on these Postulates?

The essence of SR is to coordinate Observations made by Observers in different inertial systems according to the

*Lorentz transformation.*

But the Postulates contain no Observer nor any Observation using some Measuring Apparatus, and so they require some further assumptions or postulates to have a meaning, and this is where we now proceed to seek the Source of the Paradoxes of SR focussing on the following key question:

*Is the Observation of the speed of propagation of light in a chosen inertial system (viewed to be "at rest") made by an Observer with Measuring Apparatus assumed to be at rest in the system or allowed to be moving in the system?*

Since Einstein's Second Postulate explicitly speaks about the possibility of a moving light source, but does not say anything about a possibly moving Observer, a logical conclusion is that the Observer with Measuring Apparatus is not allowed to move. We are then led to the conclusion that the Postulates of SR implicitly state that

*An Observer can only make an Observation (of the speed of light) in an inertial system in which the Observer with Measuring Apparatus is at rest. The Observer with Measuring Apparatus and the inertial system are thus tied together, while the source can move.*

More precisely, in Einstein's SR a distinction is being made between Observer and Measuring Apparatus giving the Observer the possibility to observe the propagation of light in systems with respect to which the Observer is moving (according to the Lorentz transformation), while a Measuring Apparatus is assumed to at rest in its system. By separating Observer from Measuring Apparatus Einstein thus steps outside the realm of the Second Postulate with Measuring Apparatus at rest, which leads to confusion, paradox and contradiction.

We now consider the alternative that the Postulates of SR implicitly state, as expressed in many texts (then apparently not reading Einstein carefully):

*Observation (of the constant speed of light) is independent of the motion of both source and Observer.*

as a common inertial system which can be used by all Observers, and SR would have no role to play.

This would be like the speed of propagation of sound in still air, which is independent of motion of both source and observer, and without any relativity.

The idea that the speed of light is independent of the motion of the Observer is often presented as the essence of SR as in

*Experimental Basis for Special Relativity in the Photon Sector Daniel Y. Gezari:*

*Surprisingly, none of the five new optical effects assumed or predicted by special relativity have ever been observed to occur in nature or demonstrated in the laboratory. Principal among the unobserved effects is the invariance of c to motion of the observer, the tacit assumption underlying all of the predictions of special relativity in the matter and photon sectors.*

We read that this paper exhibits the weak experimental support of SR, which goes against the common propaganda that the support is massive.

We conclude that the Postulates of SR do not admit Einstein's SR to serve any role. This was understood by the Nobel Physics Prize committee, which never awarded SR.

The paradoxes/contradictions thus result from breaking of logic, by giving SR the mission to answer the following question, which cannot be posed:

*What is the Observation in an inertial system by a moving Observer?*

The source of the paradoxes/contradictions of SR is thus that SR seeks to give an answer to a question, resulting from disconnecting Observer from Measuring Apparatus, a question which according to the Postulates of SR cannot be posed, because it violates the logic of Observer and Measuring Appears being connected. No wonder that paradoxes/contradictions follow.

Think of that! Science is about posing the right question, and in particular not focussing on answering the wrong question.

Of course, physicists will argue that, despite the fact that SR with its infinitely many paradoxes/contradictions has no role to fill, SR serves as a foundation of modern physics and has shown to be immensely useful to humanity. Thus even if SR does not make any sense, it is kept beyond criticism and discussion by modern physicists pretending that SR is true physics so deep that it cannot be understood at all. But SR is understandable and as such seen to be meaningless.

More precisely, a physicist defending SR as a foundation modern physics, may argue that in case that the Second Postulate says nothing about the Observer, the objective of SR is to uncover the effects of a moving Observer as an exploration into something beyond the scope of the Postulates of SR, and as such an open game, which however has shown to lead to paradoxes and contradictions putting the game into question. Better then to play a safe game from clear premises.

But there is an alternative to SR based on the Second Postulate of SR with Observers at rest, in the form of Many-Minds Relativity, where the questions are different, meaningful and possible to answer. Take a look!

If (i) then SR has no mission. If (ii) then SR asks an illegal question. Conclusion?

More precisely, a physicist defending SR as a foundation modern physics, may argue that in case that the Second Postulate says nothing about the Observer, the objective of SR is to uncover the effects of a moving Observer as an exploration into something beyond the scope of the Postulates of SR, and as such an open game, which however has shown to lead to paradoxes and contradictions putting the game into question. Better then to play a safe game from clear premises.

But there is an alternative to SR based on the Second Postulate of SR with Observers at rest, in the form of Many-Minds Relativity, where the questions are different, meaningful and possible to answer. Take a look!

**Summary1:**The Second Postulate of SR states that observations of the speed of light is independent of either (i) source and observer, or (ii) source. Which is the correct formulation?If (i) then SR has no mission. If (ii) then SR asks an illegal question. Conclusion?

**Summary2:**The separation of Observer and Measuring Apparatus made by Einstein is apparent in the familiar Train-Embankment situation, where an Observer with Measuring Apparatus at rest on the Embankment is supposed to observe a light signal in the system of the moving Train. And conversely, an Observer with Measuring Apparatus inside the moving Train is supposed to observe a light signal in the stationary system of the Embankment. But separating Observer from Measuring Apparatus lacks logic and so does SR.**PS**Recall that Einstein describes in*Relativity, the special and general theory,*SR as follows connecting a childs view with deepest intellectual endeavour:*In short, let us assume that the simple law of the constancy of the velocity of light c (in vacuum) is justifiably believed by the child at school. Who would imagine that this simple law has plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties?*

This connects to the proverb:

*A child can ask more than hundred wise men can answer.*

## torsdag 24 oktober 2019

### Eco-Madness vs Flight Security?

Two themes on this blog come together in the following post by

*Miranda Devine New York Post: Eco Madness May Be The Reason For Disastrous Boeing 737 MAX Crash:**We need to know if safety considerations at Boeing took a back seat to producing a climate-friendly plane.*

Read and think.

### What is the Postulate of Einstein's Special Theory of Relativity?

As a follow up to the 2019 Nobel Prize in Physics, I have asked a panel of physicists which formulation of the Basic Postulate of Special Relativity SR is the correct one?

James Peebles received the Prize "for theoretical discoveries in physical cosmology", based on Einstein's relativity theory, which never was awarded any Nobel Prize, and so it is of interest to figure out why? Is relativity theory bogus? While Peebles' work is not?

James Peebles received the Prize "for theoretical discoveries in physical cosmology", based on Einstein's relativity theory, which never was awarded any Nobel Prize, and so it is of interest to figure out why? Is relativity theory bogus? While Peebles' work is not?

Let us start by noting that all the confusion and the many paradoxes of SR can be traced back to the Basic Postulate of SR, which occurs in two different forms in the literature:

The essential difference between Version 1 and 1A is that the act of observation is present explicitly in Version 1, while it must be implicitly present in Version 1A, since some form of Observation by some Observer is necessary to give meaning to the concept of speed of propagation of light.

**Version 1: (**Einstein's formulation)*Observations of the speed of light in all inertial systems give the same result = c independent of the motion of the source vs the inertial system.*

**Version 2:**(In some books):

*Observations of the speed of light in all inertial systems give the same result = c independent of the motion of both the source and the observer vs the inertial system.*

To be more exact, Version 1 is a condensation of the two postulates made in Einstein's 1905 article presenting SR, which take the following verbatim form:

**Version 1A:**

*The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.**Light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.*

Or alternatively from The Collected Papers, Vol. 2, 1989, p.143:

*Each ray of light moves in the coordinate system “at rest” with the definite velocity V independent of whether this ray of light is emitted by a body at rest or in motion.*

Version 2 allows both source and Observer to move with respect to the inertial system used.

Version 1 states that the source can move, but says nothing about the observer, which leaves room for confusion with the following alternatives concerning Observations in a given inertial system S:

- Observers are assumed to be fixed in S.
- Observers are allowed to move in S.

With alternative 2, we end up Version 2, while with 1 we get the following more precise version of Einstein's 1905 formulation:

**Version 1B: (**Possible Einstein formulation)*Observations of the speed of light in all inertial systems give the same result = c independent of the motion of the source vs the inertial system. Observers are assumed to be stationary in the inertial system where observations are made.*

The question is now which formulation of the Basic Postulate of SR is the correct one, if any?

Einstein's formulation as Version 1, 1A or 1B, or the common text book formulation as Version 2.

In short:

- Is the Observer allowed to move in the inertial system in which light is assumed to propagate ("move") when making Observation of the speed of light?

Yes or No? The panel of physicists does not seem eager to give an answer. Maybe the question is too difficult. But maybe someone outside the panel has some idea to report?

The answer will show to have far-reaching consequences...watch out...

The answer will show to have far-reaching consequences...watch out...

**PS1**Unfortunately we cannot ask Einstein, but even if it was possible we would probably not get a clear answer, since Einstein was a master of cryptic answers...but the question is not cryptic...**PS2**Note the ambiguity in Version 1A with the role of Observer/Observation not spelled out, while the Observer has a completely central role in SR.## torsdag 17 oktober 2019

### The Trauma of Paradoxes of Modern Physics

*How wonderful that we have met with a paradox. Now we have some hope of making progress.*(Niels Bohr)

Science appears to be filled with paradoxes, which it itself is a paradox, because true science should be free of paradox. For a true scientist a scientific paradox is thus something unbearable, which requires immediate action, because one paradox is enough to kill a whole theory.

There are logical paradoxes as contradiction between words and there are physical paradoxes as contradictions between theory and observation.

One logical paradox is enough to kill a mathematical theory. Thus Russell's paradox killed set theory as the foundation of mathematics in the early 20th century.

Zeno's paradox (still unresolved) of the arrow which is moving although it is not moving at every instant, triggered the development of Calculus, but with a delay of 2000 years!

One physical paradox is enough to kill a physical theory as a mathematical theory about phenomena of physics, all according to the famous physicist Feynman:

A paradox may be thus devastating to existing theory, while leading to new better theory by focussing on weak points.

Yet, the list of physical paradoxes has remained through the development of modern physics and in fact have multiplied since modern physics is loaded with many more paradoxes than classical rational physics, as if modern physics is irrational. Thus the pillars of modern physics in the form of relativity theory and quantum mechanics are both filled with paradoxes, which have remained unresolved for 100 years. This has formed the deep trauma of modern physics with no escape from ever more paradoxes.

Niels Bohr was a master of handling the many paradoxes of quantum mechanics lifting sophistry to a new level with his "complementarity principle" addressing the wave-particle contradiction with murky statements like:

The first defence line for a classical physicist is to simply deny the existence of a paradox formulated by some renegades. The next is to accept that there is indeed a paradox and then come up with an ad hoc explanation for the contradiction between theory and reality, showing that the contradiction is in fact only apparent, but not really real. If the ad hoc explanation is refuted, a new ad hoc explanation is presented and so on.

For a modern physicist, a paradox thus poses no real problem, but of course it is some kind of nuisance and so occasionally may get some attention. Like the Twin Paradox of special relativity discussed in earlier posts, unresolved since 100 years.

The prime paradox of fluid mechanics is d'Alembert's paradox comparing the prediction of zero resistance to motion through a fluid from potential flow solutions to Euler's equations of slightly viscous flow like air and water, with the observation of heavy resistance increasing quadratically with velocity.

The paradox was formulated by d'Alembert in 1755 but nobody was able to come up with a resolution until the young German fluid mechanician Ludwig Prandtl in 1904 came up with the ad hoc solution to discriminate the zero drag potential solution of Euler's equations because potential flow does not satisfy a no-slip boundary condition coming with a thin boundary layer. With the potential solution thus eliminated form the discussion, the paradox simply disappeared. But the act of discrimination of solutions of the Euler equations of course was not so glorious. Discrimination of prefect exact solutions on formal grounds carries the same weakness as discrimination of good citizens on purely formal grounds.

In 2008 we gave a different resolution of d'Alembert's paradox than Prandtl's, based on the fact that potential solutions of the Euler equations are unstable and thus turn into turbulent solutions with substantial pressure drag. This was not discrimination on formal grounds, but on real grounds; an unstable solution does not persist over time. This opened to a revolution in computational fluid dynamics freed from a perceived necessity to computationally resolve unresolvable thin boundary layers.

You find on this web site, if you are interested and make a search, resolutions of the following paradoxes:

There are logical paradoxes as contradiction between words and there are physical paradoxes as contradictions between theory and observation.

One logical paradox is enough to kill a mathematical theory. Thus Russell's paradox killed set theory as the foundation of mathematics in the early 20th century.

Zeno's paradox (still unresolved) of the arrow which is moving although it is not moving at every instant, triggered the development of Calculus, but with a delay of 2000 years!

One physical paradox is enough to kill a physical theory as a mathematical theory about phenomena of physics, all according to the famous physicist Feynman:

*It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.*

A paradox may be thus devastating to existing theory, while leading to new better theory by focussing on weak points.

Yet, the list of physical paradoxes has remained through the development of modern physics and in fact have multiplied since modern physics is loaded with many more paradoxes than classical rational physics, as if modern physics is irrational. Thus the pillars of modern physics in the form of relativity theory and quantum mechanics are both filled with paradoxes, which have remained unresolved for 100 years. This has formed the deep trauma of modern physics with no escape from ever more paradoxes.

Niels Bohr was a master of handling the many paradoxes of quantum mechanics lifting sophistry to a new level with his "complementarity principle" addressing the wave-particle contradiction with murky statements like:

*The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.*

The first defence line for a classical physicist is to simply deny the existence of a paradox formulated by some renegades. The next is to accept that there is indeed a paradox and then come up with an ad hoc explanation for the contradiction between theory and reality, showing that the contradiction is in fact only apparent, but not really real. If the ad hoc explanation is refuted, a new ad hoc explanation is presented and so on.

For a modern physicist, a paradox thus poses no real problem, but of course it is some kind of nuisance and so occasionally may get some attention. Like the Twin Paradox of special relativity discussed in earlier posts, unresolved since 100 years.

The prime paradox of fluid mechanics is d'Alembert's paradox comparing the prediction of zero resistance to motion through a fluid from potential flow solutions to Euler's equations of slightly viscous flow like air and water, with the observation of heavy resistance increasing quadratically with velocity.

The paradox was formulated by d'Alembert in 1755 but nobody was able to come up with a resolution until the young German fluid mechanician Ludwig Prandtl in 1904 came up with the ad hoc solution to discriminate the zero drag potential solution of Euler's equations because potential flow does not satisfy a no-slip boundary condition coming with a thin boundary layer. With the potential solution thus eliminated form the discussion, the paradox simply disappeared. But the act of discrimination of solutions of the Euler equations of course was not so glorious. Discrimination of prefect exact solutions on formal grounds carries the same weakness as discrimination of good citizens on purely formal grounds.

In 2008 we gave a different resolution of d'Alembert's paradox than Prandtl's, based on the fact that potential solutions of the Euler equations are unstable and thus turn into turbulent solutions with substantial pressure drag. This was not discrimination on formal grounds, but on real grounds; an unstable solution does not persist over time. This opened to a revolution in computational fluid dynamics freed from a perceived necessity to computationally resolve unresolvable thin boundary layers.

You find on this web site, if you are interested and make a search, resolutions of the following paradoxes:

- D'Alembert's paradox and other paradoxes of fluid mechanics.
- The Reversibility paradox of classical and quantum mechanics (Loschmidt's paradox)
- Paradoxes of special relativity including the Twin paradox.
- Paradoxes of wave-particle and collapse of the wave function of quantum mechanics.

Yes, it is wonderful to discover a paradox and even more wonderful to resolve it!

## onsdag 16 oktober 2019

### Paradoxes of Fluid Mechanics

The book

*Hydrodynamics A study in logic, fact and similitude*(1950) by Garrett Birkhoff gives a long list of paradoxes of fluid mechanics including the following concerning incompressible flow:

**D'Alembert's paradox**(zero drag of (potential) inviscid flow).**Reversibility paradox**(reversion of flow direction does not reverse flow).**Fatness paradox**of Kutta-Joukowsky theory (lift decreases with thickness of wing).**Magnus effect**(lift of backspin tennis ball opposite to that of table tennis ball).**Eiffel paradox**("drag crisis" as sudden drop of drag).**Dubaut paradox**(smaller drag of stationary pole in streaming fluid than pole moving through stationary fluid).

Birkhoff describes the role of paradoxes:

*These paradoxes have been the subject of many witticisms. Thus, it has recently been said**that in the nineteenth century, " fluid dynamicists were divided into hydraulic engineers who observed what could not be explained, and mathematicians who explained things that could not be observed." (It is my impression that many survivors of both species are still with us.)—Again, Sydney Goldstein has observed that one can read all of Lamb without realizing that water is wet!**I think we should welcome the discovery of hydrodynamical paradoxes—recognizing frankly the inadequacy of existing mathematics (and logic) to analyze the complex wonders of Nature. Experience shows that man's imagination is far more limited than Nature's resources: as Pascal wrote, "l'imagination se lassera plutot de concevoir que la nature de fournir.*

Solving paradoxes thus may open roads to progress. The mother of all paradoxes of incompressible flow is d'Alembert's paradox. Prandtl was crowned Father of Modern Fluid Mechanics because he saved the face of fluid mechanics confronted by the paradox, by coming to rescue in a short 1904 article selling the idea that drag somehow is an effect of a boundary layer caused by an imagined necessity of a no-slip boundary condition forcing a fluid to "stick" to a solid wall. However, Prandtl's boundary layer theory came with a serious side effect as the impossibility to computational resolve thin boundary which has paralysed Computational Fluid Dynamics CFD throughout the 20th century.

The paralysis was lifted only in 2008 with a new resolution of d'Alembert's paradox (check video) showing that inviscid flow modeled by the Euler equations can be described as potential flow modified by 3d rotational slip separation into turbulent flow, which can be resolved computationally by Direct Finite Element Simulation DFS. This is described in Computational Turbulent Incompressible Flow with subsequent elaborations, resolving all the paradoxes listed by Birkhoff, and more as shown in the previous post with references including revealing The Secret of Flight (check video).

## tisdag 15 oktober 2019

### Towards Resolution of Gray's Paradox

Gray's paradox concerns the contradiction between standard fluid mechanics predictions of the resistance to motion (drag) of a dolphin and the observed speed of a dolphin. Gray estimated that the required muscle power would be seven times bigger than that available. A real paradox!

The search to resolve the paradox has tried different routes: One is to claim that the muscle power of dolphin in fact is much bigger (seven times) than what can be envisioned. Another is to claim that the skin of a dolphin has a magical composition somehow decreasing drag by a factor of seven.

None of the attempts has been successful.

Let us see if the new approach to computational fluid dynamics presented in Computational Turbulent Incompressible Flow and The Secret of Flight, offers a resolution.

We term the new approach DFS Direct Finite Element Simulation (of turbulent flow) based on computing turbulent solutions to the Euler equations for incompressible flow with slip/small skin friction boundary conditions. We have found that DFS predicts the drag of a wing, full airplane and car in close correspondence with observation, with slip as zero skin friction.

Our conclusion is that skin friction gives a minor contribution to total drag as pressure drag plus skin friction in many applications of aero- and hydromechanics, including the locomotion of a dolphin.

This is against the common view of the fluid dynamics community that skin friction is 50-90% of total drag. DFS thus gives design fundamentally new conditions to work from.

DFS in particular seems to offer a resolution of Gray's paradox, by showing that the drag of a dolphin is severely overestimated by conventional techniques as being based on a formula for flat plate drag.

The resolution is a spin-off of the resolution of D'Alembert's paradox (check video) as the mother of the paradoxes of fluid mechanics, a resolution which is intimately connected to DFS.

That skin friction drag predicted from flat plate experiments gives an overestimate of the drag of a streamlined body, like a dolphin, is supported by the article TURBULENT SKIN-FRICTION DRAG ON A SLENDER BODY OF REVOLUTION AND GRAY’S PARADOX, by Nesteruk and Cartwright (13th European Turbulence Conference (ETC13), Journal of Physics: Conference Series 318 (2011) 022042):

*The presented analysis shows that***turbulent frictional drag**on a slender rotationally symmetric body**is much smaller than the flat-plate concept**gives and the flow can remain laminar at larger Reynolds numbers. Both facts are valid for an unseparated flow pattern and enable us to**revise the turbulent drag estimation of a dolphin**, presented by Gray 74 years ago, and to resolve his paradox, since experimental data testify that dolphins can achieve flow without separation. The small values of turbulent skin-friction drag on slender bodies of revolution have additional interest for further experimental investigations and for applications of shapes without boundary-layer separation to diminish the total drag and noise of air- and hydrodynamic hulls.

We will now compute the drag of a dolphin by DFS and report the results shortly. Reducing prediction of skin friction from 70% to 10% may correspond to Gray's factor seven...

**PS**From Passive and Active Flow Control by Swimming Fishes and Mammals by F.E. Fish and G.V. Lauder:*Dolphins have the muscular capacity to swim at high speeds for short durations while maintaining a fully attached turbulent boundary layer. The turbulent flow conditions would delay separation of the boundary layer (Figure 1; Rohr et al. 1998). When the boundary layer separates from the skin surface and interacts with outer flow, this results in a broader wake and increased drag, so delaying separation is beneficial to the dolphin. Separation is more likely to occur with a laminar boundary flow, producing a greater drag penalty compared to turbulent boundary conditions. Thus, the turbulent boundary layer remains attached longer because it has more energy than the laminar boundary layer. The increased drag of a turbulent boundary layer is small compared to the increase in drag due to separation, which is more prone to occur with a laminar boundary layer.*

This conforms with the theory and practice presented in Computational Turbulent Incompressible Flow showing in particular that flow with a slip boundary condition stays attached with small drag, while flow with a no-slip laminar boundary layer separates early with large drag. The observed small drag of a dolphin thus can be explained by the theory behind DFS, but not by any commonly accepted theory seeking the origin of drag in thin boundary layers following the legacy of Prandtl.

## lördag 12 oktober 2019

### What is the "Relic Radiation" of CMBR?

The 2019 Nobel Prize in Physics is awarded to the Big Bang theory supposedly supported by a the observation of "relic radiation" as a "remnant" from the bang:

*The cosmic microwave background (CMB, CMBR), in Big Bang cosmology, is electromagnetic radiation as a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space.*

But there are views contesting the "consensus" adopted by the Prize Committee, claiming that CMBR is nothing but (black body) radiation from "cosmic dust" at 2.7 K surrounding the Milky Way.

What to believe? Let me seek an answer in the analysis of blackbody radiation presented at Computational Black Body Radiation based on a model of radiative heat transfer as a resonance phenomenon between a material source and material receiver transmitted by (standing) electromagnetic waves connecting source and receiver.

In this model there are waves connecting source and receiver, but no "ocean of photons" filling space as a "remnant" of a disappeared Big Bang source. Instead, the model is compatible with the presence of cosmic dust.

What do you think? Is it possible that there is some form of "remnant radiation" filling all of space even though the source of the radiation disappeared 15 billion years ago?

In any case, maybe this gives some incentive to review conceptions of black body radiation.

And what is even more unbelievable than relic radiation? Right, Big Bang. Utterly improbable and impossible. How is it possible that this has become the highest wisdom of the Nobel Committee in Physics? A Committee that never gave the Prize to relativity theory.

And what is even more unbelievable than relic radiation? Right, Big Bang. Utterly improbable and impossible. How is it possible that this has become the highest wisdom of the Nobel Committee in Physics? A Committee that never gave the Prize to relativity theory.

## tisdag 8 oktober 2019

### Nobel Prize to Cosmology with Dark Energy

Dark energy filling the announcement of the 2019 Nobel Prize in Physics. |

*for contributions to our understanding of the evolution of the universe and Earth’s place in the cosmos*

**dark energy**apparently filling 68% of the Universe,

is not understood at all.

As a compensation, the previous post contributes the understanding that the exponential expansion being observed and then believed to require massive dark energy, in fact can largely be viewed to be an optical illusion from misinterpretation of red-shifts and if true reduces the need of massive dark energy.

Take a look and see if light enters your mind. There is a new Prize to collect 2020.

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