onsdag 14 oktober 2015

Physics by Law through Censorship of Climate-Alarm Skepticism


A report in the U.K. daily The Telegraph indicates that
  • an international panel of judges is planning to prohibit talk of “climate skepticism.” The article by Christopher Booker said the legal change was endorsed by Prince Charles of the U.K., and would revolutionize the concept of free speech once and for all.
  • Since it is now unlikely that the world will agree in Paris to a legally binding treaty to limit the rise in global temperatures to no more than 2 degrees C from pre-industrial levels, it is now time for the courts to step in, to enforce this as worldwide law.
This is a follow-up of the censorship at KTH that struck my math book Mathematical Simulation Technology (see left widget) in 2010  because of its mathematical climate-alarm skepticism in an orchestrated media race as KTH-gate, KTH-gate2 and KTH-gate3.

See also the Philippe Verdier story.

tisdag 13 oktober 2015

Läroplan Matematik-IT för Grundskolan

Jag har nu skrivit utkast till läroplan Matematik-IT för grundskolan samt givit denna konkret innehåll i en samling poster på Matematik-IT. Nästa steg är att producera en samling korta videos som förklarar konceptet, för både elever, lärare, skoladministratörer och skolpolitiker.

söndag 11 oktober 2015

Multiscale Finite Element Method as Informational Structural Realism


Luciano Floridis concludes in The Philosophy of Information that the world on microscopic scales cannot be neither discrete nor continuous, since each of these standpoints is contradictory, but can maybe instead be described by Informational Structural Realism (ISR) as scale dependent structural description leaving out the true nature of the elements forming the structure. ISR can be viewed as synthesis of the discrete and continuous without internal contradiction and thus potentially as a useful world view.

This is nothing but the finite element method in multi-scale form, originally developed in structural mechanics, as scale dependent discretization of continuous differential equations, where a true physical realisation of the finite elements is not possible nor necessary.

This connects to my attempt to describe a complex world including turbulence and quantum mechanics as analog finite precision computation simulated by digital finite precision computation, where the flow of information under computation represents ISR and the true physical nature of the analog computation is unknowable, but irrelevant.

Why is then both discrete and continuous physics impossible? Because both requires infinite resolution: a discrete point particle or discontinuity has zero size and a continuum has no smallest size. Thus both discrete and continuous physics requires infinitely small resolution and thus an infinite amount of information on any scale. If you don´t think this is asking for too much, then you should reconsider your notion of the infinite.

söndag 4 oktober 2015

Test av Matematik-IT för Grundskolan

Denna vecka börjar jag tillsammans med en grupp elever i åk4 samt lärare vid Lugnets grundskola i Hammarby Sjöstad undersöka om skolmatematiken kan ges en ny mening, innehåll och form genom att utgå från att dagens IT-värld bygger på matematik + datorberäkning.

Min ambition är att visa att elever i åk4 i grundskolan med lämplig IT-matematik kan nå bättre färdighet vad gäller matematisk datorsimulering än teknologer i åk4 på KTH.

Om detta visar sig vara riktigt kan det ge argument som stödjer mitt tidigare framförda förslag att ersätta nuvarande skolmatematik med ett nytt kärnämne i form av Matematik-IT.

Som plattform kommer jag att använda Codea som är ett verktyg för programmering av datorspel eller mer allmänt för datorsimulering av fenomen inom den verkliga värld som omger oss eller de tänkta världar som fantasin kan skapa. Möjligheterna är obegränsade.

Jag kommer här att kontinuerligt rapportera om hur detta test framskrider och jag hoppas kunna stimulera eleverna att dokumentera sina framsteg på lämplig websida.

Mer konkret kommer jag alltså att testa om reformprogrammet BodyandSoul, som användes under min tid på Chalmers 2000-2007, i modifierad form kan användas för att reformera en död skolmatematik i desperat behov av förnyelse och vitalisering.

Mitt mål är, i samband med detta test vid Lugnets grundskola, att med iPad utforma en ny version av BodyandSoul för iPad för skolan. Ledorden är alltså:
  • simuleringsteknik som teknik för simulering och teknik med simulering
  • simuleringsteknik för iPad med iPad.
PS1 Jag har lagt upp en ny blogg Matematik-IT som kommer att samla erfarenheterna från detta projekt, med förhoppningsvis input från elever och rektor, som öppnat skolan och som själv deltar som elev.

PS2 Det återstår att se om KTHs långa arm kan stoppa även detta mitt initiativ till reform av en föråldrad matematikundervisning.

fredag 2 oktober 2015

Why Not TOE?



Lawrence Krauss summaries the present state of physics in The Trouble with Theories of Everything:
  • There is no known physics theory that is true at every scale—there may never be.
  • When quantum mechanics is combined with relativity, it turns out, rather unexpectedly in fact, that the detailed nature of the physical laws that govern matter and energy actually depend on the physical scale at which you measure them.
  • So, what is going on? Is a universal theory a legitimate goal, or will scientific truth always be scale-dependent?
The trouble Krauss is here talking about is that relativity theory and quantum mechanics are contradictory, a deep trouble which has brought modern physics into a deep crisis. Krauss asks if a universal theory as a theory somehow without contradictions, is thinkable and then crushes all hope that it could take the form of string theory: 
  • There is no example so far where an extrapolation as grand as that associated with string theory, not grounded by direct experimental or observational results, has provided a successful model of nature. In addition, the more we learn about string theory, the more complicated it appears to be, and many early expectations about its universalism may have been optimistic.
Krauss concludes with the pessimistic message that a universal theory as a theory without internal contradictions, is beyond reach for the human mind. The logic is that since both relativity and quantum theory are correct but unfortunately contradictory, no universal theory theory without contradiction is possible.

But why is it not thinkable that relativity or quantum theory is not correct physics? My bet is relativity theory is incorrect physics, supported by in particular the fact that while quantum mechanics has been awarded a countless number of Nobel Prizes, none has been awarded to relativity theory, of course because nobody in the Nobel committee could ever understand anything of Einstein's curved space-time.

Another obstacle to a universal theory is that the nature of quantum mechanics is postulated to be fundamentally different from the continuum mechanics of macroscopic phenomena and as such is beyond description in terms of concepts understandable to the human mind such as the partial differential equations making continuum mechanics understandable. But this is an ad hoc postulate blocking progress. How come that physicists can be so sure that the world of atoms is beyond human comprehension as expressed by Richard Feynman:
  • I think I can safely say that nobody understands quantum mechanics.
So, after all a TOE may be thinkable, if only we do not limit the thinking by relativity and quantum theory beyond reach for the human mind.

It is maybe not necessary as scientist to be paralyzed by ideas and concepts beyond human understanding as characteristics of religion.

lördag 26 september 2015

Volkswagen Emission Scandal vs German Political Correctness Leadership



Germany with Angela Merkel is actively seeking to take the leading role in a giant transformation of the world economy into a new green economy with reductions of CO2 emissions to preindustrial levels as prime goal.  In this giant transformation German car industry has promoted the diesel engine as being more fuel efficient with less CO2 emission than the gasoline engine under strong support from German governmental political correctness.

The Volkswagen emission scandal shows the hollowness and hypocrisy of this grand scale religion: To meet the strict demands of political correctness and moral leadership set by Germany, grand scale cheating is necessary and is accordingly delivered by Germany.

The world is watching with amazement. And in China a new coal power plant is opened every day.

torsdag 24 september 2015

Finite Element Quantum Mechanics 6: Basic Analysis vs Observation

Let us now inspect the basics of the atomic model considered in this sequence of posts.

Consider then a neutral atom of kernel charge $Z$ with $N=Z$ electrons occupying non-overlapping domains in space. Assume that the electrons are partitioned into a sequence of shells $S_m$ of increasing radius $r_m$ with corresponding widths $d_m$ each shell being filled by $2m^2$ electrons, for $m=1,...,M,$ with $M$ the number of shells. We consider a hypothetic atom with all shells fully filled with $2, 8, 18, 32, 50,...,$ electrons in successive shells displaying a basic aspect of the periodicity of the periodic table of elements.

Consider now the case $d_m\sim m$ with $r_m\sim m^2$, and assume $r_1=d_1\sim\frac{1}{Z}$. The electron density $\rho_m$ in $S_m$, assumed to be spherically symmetric,  then satisfies
  • $\rho_mr_m^2d_m\sim m^2$
from which follows that 
  • $\rho_m\sim \frac{m^3}{r_m^3}$.                            (1)
We now compute the following characteristics of this model:
  1. $M^3\sim Z$, that is $M\sim Z^{\frac{1}{3}}$
  2. potential energy in $S_1\sim Z^2$
  3. potential energy in $S_m\sim m^2Z/r_m\sim Z/d_1\sim Z^2$
  4. total potential energy and thus total energy $\sim Z^{\frac{7}{3}}$.                             (2)
We check that indeed there is room for $m^2$ electrons in shell $S_m$, because the volume of $S_m$ is $r_m^2d_m\sim m^5$, while the volume of an electron $\sim d_m^3\sim m^3$.

We observe that (2) fits with observations. We understand that the electronic density is distributed so that the potential energy and thus total energy in each full shell is basically the same, which may be viewed to be a heavenly socialistic organization of the shell structure of an atom.

Numerical computation seeking the ground state energy by relaxation in the Schrödinger model of post 5 starting from an initial density distribution according to (1), shows good correspondence with observation, supporting the basic analysis of this post. Numbers will be presented in an upcoming post.

The basic aspect of this model as a form of electron density model, is that electrons (or shells in the present spherically symmetric case) keep individuality by occupying different domains of space, which makes it possible to accurately represent electron-electron repulsion.

This feature is not present in standard density models such as Thomas-Fermi and Density Functional Theory. In these models electrons lack individuality as parts of electron clouds, which makes it difficult to represent electron-electron repulsion ab ibnitio.

Recall also that in the standard Schrödinger equations wave functions appear as multi-dimensional linear combinations of products of one-electron wave functions defined in all of space by separate spatial variables, thus with each electron "both nowhere and everywhere" without individuality, which requires a statistical interpretation of the wave function as a multi-dimensional uncomputable monster.

Another basic aspect of the presented model is continuity of electron density across inter-electron or inter-shell boundaries for the electron configuration of ground states. This allows atoms to have stable ground states as non-dissipative periodic states of minimal energy.

Notice further that the size of the atom as $r_M\sim Z^{-\frac{1}{3}}$ with decreasing size as $Z$ increases, corresponds to the observed decrease of size moving to the right in each row of the periodic table:




fredag 18 september 2015

Ripples in the Fabric of Space and Time?


The code word of modern physics is:
  • fabric of space and time
  • observe gravitational waves—ripples in the fabric of space and time. 
If we dare to ask what the meaning of "fabric of space and time" may be, we get the following illuminating lesson by leading physicists:
  • First of all, space-time is not a fabric. Space and time are not tangible 'things' in the same way that water and air are. It is incorrect to think of them as a 'medium' at all. 
  • No physicist or astronomer versed in these issues considers space-time to be a truly physical medium, however, that is the way in which our minds prefer to conceptualize this concept, and has done so since the 19th century. 
  • We really do not know what space-time is, other than two clues afforded by quantum mechanics and general relativity.
  • Space-time does not claim existence in its own right, but only as a structural quality of the [gravitational] field. (Einstein)
  • Space and time coordinates are just four out of many degrees of freedom we need, to specify a self-consistent theory. What we are going to have [in any future Theory of Everything] is not so much a new view of space and time, but a de-emphasis of space and time. (Steven Weinberg)
  • In the theory of gravity, you can't really separate the structure of space and time from the particles which are associated with the force of gravity [ such as gravitons]. The notion of a string is inseparable from the space and time in which it moves. (Michael Greene)
The punch line of this educational experience is presented in this way: 
  • So, the question about what happens to space-time when a particle moves through it at near the speed of light is answered by saying that this is the wrong question to ask. Just because the brain can construct a question doesn't mean that the question has a physical answer!
We understand that LIGO in its search for "ripples in the fabric of space and time" is studying "the wrong question" and thus can be viewed as a study into the ""fabric of fantasy" which has become such a fundamental part of modern physics demanding full devotion by the sharpest brains of modern physicists (see also here ):



torsdag 17 september 2015

LIGO: Absurdity of Big Physics


The Advanced LIGO Project has now been launched as the largest single experiment ever funded by NSF at $0.365 billion:
  • The LIGO scientific and engineering team at Caltech and MIT has been leading the effort over the past seven years to build Advanced LIGO, the world's most sensitive gravitational-wave detector.
  • Gravitational waves were predicted by Albert Einstein in 1916 as a consequence of his general theory of relativity, and are emitted by violent events in the universe such as exploding stars and colliding black holes. 
  • Experimental attempts to find gravitational waves have been on going for over 50 years, and they haven't yet been found. They're both very rare and possess signal amplitudes that are exquisitely tiny.
  • Although earlier LIGO runs revealed no detections, Advanced LIGO, also funded by the NSF, increases the sensitivity of the observatories by a factor of 10, resulting in a thousandfold increase in observable candidate objects. 
  • The original configuration of LIGO was sensitive enough to detect a change in the lengths of the 4-kilometer arms by a distance one-thousandth the diameter of a proton; this is like accurately measuring the distance from Earth to the nearest star—over four light-years—to within the width of a human hair. 
  • Advanced LIGO, which will utilize the infrastructure of LIGO, is much more powerful.
  • The improved instruments will be able to look at the last minutes of the life of pairs of massive black holes as they spiral closer together, coalesce into one larger black hole, and then vibrate much like two soap bubbles becoming one. 
  • In addition, Advanced LIGO will be used to search for the gravitational cosmic background, allowing tests of theories about the development of the universe only $10^{-35}$ seconds after the Big Bang.
Read these numbers: The accuracy of old LIGO was  
  • the diameter of a human hair over a distance of 4 light-years, 
  • $10^{-35}$ seconds after Big Bang,
and yet not the slightest little gravitational wave signal was recorded from even the most violent large scale phenomena thinkable. The conclusion should be clear: There are no gravitational waves. After all, why should there be any? By Einstein's general relativity which nobody claims to grasp?

But this is not the way Big Physics works: The fact that nothing was found by the infinitely sensitive LIGO requires an even more infinitely sensitive Advanced LIGO at a cost of a half a billion to be built by eager physicists, and after Advanced LIGO has found nothing, funding for an Advanced Advanced LIGO will be requested and so on...but why are tax payers supplying this Big Money?  



lördag 5 september 2015

Gerhard 't Hooft: Improved Understanding of Quantum Mechanics Needed




Gerhard 't Hooft is one of the Nobel Laureates in Physics who is not happy with the present state of understanding of quantum mechanics and seeks to do something about it: Hooft starts out in Determinism beneath Quantum Mechanics with:
  • The need for an improved understanding of what Quantum Mechanics really is, needs hardly be explained in this meeting. 
  • My primary concern is that Quantum Mechanics, in its present state, appears to be mysterious.
  • It should always be the scientists’ aim to take away the mystery of things. 
  • It is my suspicion that there should exist a quite logical explanation for the fact that we need to describe probabilities in this world quantum mechanically. 
  • This explanation presumably can be found in the fabric of the Laws of Physics at the Planck scale.
  • However, if our only problem with Quantum Mechanics were our desire to demystify it, then one could bring forward that, as it stands, Quantum Mechanics works impeccably. 
  • It predicts the outcome of any conceivable experiment, apart from some random ingredient. This randomness is perfect. There never has been any indication that there would be any way to predict where in its quantum probability curve an event will actually be detected. 
  • Why not be at peace with this situation? 
  • One answer to this is Quantum Gravity. Attempts to reconcile General Relativity with Quantum Mechanics lead to a jungle of complexity that is difficult or impossible to interpret physically. In a combined theory, we no longer see “states” that evolve with “time”, we do not know how to identify the vacuum state, and so on. 
  • What we need instead is a unique theory that not only accounts for Quantum Mechanics together with General Relativity, but also explains for us how matter behaves. 
  • We should find indications pointing towards the correct unifying theory underlying the Standard Model, towards explanations of the presumed occurrence of supersymmetry, as well as the mechanism(s) that break it. We suspect that deeper insights in what and why Quantum Mechanics is, should help us further to understand these issues. 
Hooft thus acknowledges that quantum mechanics is mysterious, which all prominent physicists do, but Hooft is not at peace with this situation, since after all the essence of science is understanding, although most of his colleagues seem to have accepted once and for all that quantum mechanics cannot be understood and cannot be reconciled with general relativity.
Hooft then proceeds to seek a determinism behind quantum mechanics in the form of cellular automatons (also here).

I am pursuing another route to an understandable form of quantum mechanics as analog computation with finite precision, which in a way connects to Hooft's cellular automaton's, but is expressed by Schrödinger type wave equations in a continuum mechanics framework.

In this framework the finite precision computation makes a difference between smooth (strong) solutions and non-smooth (weak) solutions of the wave equations: Smooth solutions satisfy the wave equations exactly (with infinite precision), while non-smooth solutions satisfy the equations only in a weak sense with finite precision and loss of information as a form of dissipative radiation.

This allows the ground state of an atom as a smooth solution without dissipation to be stable over time without dissipation, while an excited state as a non-smooth solution will return to the ground state under dissipative radiation.

The situation is analogous to that described in my work together with Johan Hoffman on fluid mechanics, with turbulent solutions as non-smooth dissipative solutions of formally inviscid Euler equations, which allowed us to resolve d'Alembert's paradox (J Math Fluid Mech 2008) and formulate a new theory of flight (to appear in J Math Fluid Mech 2015), among other things.