torsdagen den 24:e april 2014

Quantum Mechanics as Gift from God More Intelligent than Man

  • Quantum mechanics is, with relativity, the essence of the big conceptual revolution of the physics of the 20th century. 
  • Now, do we really understand quantum mechanics? 
  • It is probably safe to say that we understand its machinery pretty well; in other words, we know how to use its formalism to make predictions in an extremely large number of situations, even in cases that may be very intricate. 
  • Heinrich Hertz, who played such a crucial role in the understanding of electromagnetic waves in the 19th century (Hertzian waves), remarked that, sometimes, the equations in physics are “more intelligent than the person who invented them” [182]. 
  • The remark certainly applies to the equations of quantum mechanics, in particular to the Schrödinger equation, or to the superposition principle: they contain probably much more substance that any of their inventors thought, for instance in terms of unexpected types of correlations, entanglement, etc. 
  • It is astonishing to see that, in all known cases, the equations have always predicted exactly the correct results, even when they looked completely counter-intuitive. 
  • Conceptually, the situation is less clear. 
  • Nevertheless, among all intellectual constructions of the human mind, quantum mechanics may be the most successful of all theories since, despite all efforts of physicists to find its limits of validity (as they do for all physical theories), and many sorts of speculation, no one for the moment has yet been able to obtain clear evidence that they even exist. Future will tell us if this is the case; surprises are always possible!
We read that Laloe describes the fact that modern physicists (and nobody else) do not understand the modern physics of quantum mechanics, and do not even pretend to do so,  as a conceptual revolution away from to classical physics based on understanding. The argument is that the linear Schrödinger equation must be more intelligent than Schrödinger, since Schrödinger admitted that he could not understand it and nobody else has ever claimed to understand it either. 

If the difference between science and religion is that science is all about understanding, while religion leaves understanding to divinity, modern physics is more religion than science. 

No, We Don't Understand Quantum Mechanics, But There Is Hope.

                                                            Yes, QM is a strange world.

The Preface of book Do We Really Understand Quantum Mechanics by Franck Laloe supplemented by an article with the same title, tells the truth about quantum mechanics:
  • In many ways, quantum mechanics QM is a surprising theory... because it creates a big contrast between its triumphs and difficulties. 
  • On the one hand, among all theories, quantum mechanics is probably one of the most successful achievements of science.  The applications of quantum mechanics are everywhere in our twentyfirst century environment, with all sorts of devices that would have been unthinkable 50 years ago. 
  • On the other hand, conceptually this theory remains relatively fragile because of its delicate interpretation – fortunately, this fragility has little consequence for  its efficiency. 
  • The reason why difficulties persist is certainly not that physicists have tried to ignore them or put them under the rug!
  • Actually, a large number of interpretations have been proposed over the decades, involving various methods and mathematical techniques. 
  • We have a rare situation in the history of sciences: consensus exists concerning a systematic approach to physical phenomena, involving calculation methods having an extraordinary predictive power; nevertheless, almost a century after the introduction of these methods, the same consensus is far from being reached concerning the interpretation of the theory and its
  • This is reminiscent of the colossus with feet of clay.
  • The difficulties of quantum mechanics originate from the object it uses to describe physical systems, the state vector (wave function) $\Psi$.
  • Without any doubt, the state vector is a curious object to describe reality!
The message is that QM a formidable achievement of the human intellect which is incredibly useful in practice, but like a colossus with feet of clay has a main character flaw, namely that it is a curious way to describe reality and as such not understood by physicists. 

There are two ways the handle if a physical theory is not understood because it is so curious, either the theory is dismisssed as being seriously flawed or the curiosity is chosen as a sign that the theory is correct and beyond questioning by human minds.

The reason QM is so mysterious is that the wave function $\Psi =\Psi (x_1,x_2,…,x_N)$ for an atom or molecule with $N$ electrons depends on $N$ independent three-dimensional space variables $x_1$, $x_2$,…, $x_N$, together with time, thus is a function in $3N$ space dimensions plus time and as such has no direct real physical meaning since real physics takes place in $3$ space dimensions. 

The wave function $\Psi$ is introduced as a the solution to a linear multi-dimensional linear wave equation named Schrödinger's equation of the form
  • $i\frac{\partial\Psi}{\partial t}+H\Psi = 0$,
where $H$ is a Hamiltonian operator acting on wave functions. The mysticism of QM thus originates from Schrödinger's equation and is manifested by the fact that there is no real derivation of Schrödinger's equation from basic physical laws. Instead, Schrödinger's equation is motivated as a purely formal manipulation of classical Hamiltonian mechanics without physical meaning. 

The main trouble with QM based on a linear multi-d Schrödinger equation is thus the physical interpretation of the multi-d wave function and the accepted answer to this enigma is to view 
  • $\vert\Psi (x_1,…,x_N)\vert^2$ 
as a probability distribution of a particle configuration described by the coordinates $(x_1,…,x_N)$ representing human knowledge about a physics and not physics itself. Epistemology of what we can know is thus allowed to replace ontology of what is.

The linear multi-d Schrödinger equation thus lacks connection to physical reality. Moreover, because of its many dimensions the equation cannot be solved (analytically or computationally), and the beautiful net result is that QM is based on an equation without physical meaning which cannot be solved. No wonder that physicists still after 100 years of hard struggle do not really understand QM. 

But since Schrödinger's linear multi-d equation lacks physical meaning (and neither can be solved) there is no compelling reason to view it as the foundation of atomistic physics. 

It appears to be more constructive to consider instead systems of non-linear Schrödinger equations in $N$ three-dimensional wave functions $\psi_1(x),…,\psi_N(x)$ with $x$ a 3d space coordinate,  in the spirit of of Hartree models, as physically meaningful computable models of potentially great practical usefulness. 

Sums of such wave functions then play a basic role and have physical meaning, to be compared the standard setting with $\Psi (x_1,…,x_N)$ in the form of Slater determinants as sums of muli-d products $\psi (x_1)\psi (x_2)…\psi (x_N)$ of complicated unphysical nature. 


tisdagen den 22:e april 2014

Omodern Matematikundervisning Utan Ansvariga Matematiker

Matematikinstitutionerna vid KTH och Chalmers skickar varje år en ny larmrapport om ytterligare försämrade matematikkunskaper hos nyantagna teknologer och nu var det dags igen:
Med larmrapporten friskriver sig högskolematematikerna från sitt ansvar att se till att landets matematikutbildning är modern och funktionell, genom att skylla på skolmatematiken:  
  • De högskolelärare som SvD pratar med är överens om att studenternas svaga grundkunskaper gjort att utbildningsnivån vid högskolorna sänkts undan för undan.
  • Visst har vi anpassat nivån, men det är inget folk vill tala högt om. 
  • För svag matteundervisning i grundskola och gymnasium, i kombination med en för generös betygsättning, ligger bakom problemen.
Men skolmatematiken är en (förenklad) variant av högskolematematiken och anledningen att skolmatematiken inte längre fungerar är att högskolematematiken är omodern och inte motsvarar datorsamhällets nya möjligheter och behov.  

När jag försöker få högskolematematikerna att bära sitt ansvar och modernisera utbildningen möts jag av oförstående och uppgivenhet och mitt öppna brev till Svenska Matematikersamfundet och Nationalkommitten för Matematik leder ingenstans. Se också mitt inlägg i kommande maj-nummer av SMS-Bulletinen.

torsdagen den 17:e april 2014

Extremism of Modern Physics as Bluff Poker Physics

Modern physics has been driven into an increasingly extremist position with focus on extremely small or large spatial or temporal scales or extremely large energies. When problems were met on a certain (extreme) scale, the study was directed to yet more extreme scales and energies, as in a steadily increasing bet in a game of poker with little on hand to never get called. When LHC does not deliver, then the bet is raised to a new bigger more powerful LHC...

When Einstein was pressed about the meaning of his special theory of relativity, he increased the bet to general relativity and when pressed about the meaning of general relativity he jumped the bet to cosmology...

When physicists after the introduction of quantum mechanics faced questions about the electronic structure of atoms and molecules, they turned to the three orders of magnitude smaller proton and neutron forming atomic kernels, and then to the quarks forming the proton and neutron and then ultimately to string theory on scales 15 orders of magnitude smaller than the proton in an ulitmate attempt to find the origin of gravitation acting on cosmological scales. In each case the problems met on one scale were met by resort to smaller or larger scales, steadily increasing the bet and preventing a call.

Today cosmology is directed to multiversa and inflation after Big Bang as the next step after Einstein's cosmology of general relativity supposedly all originating from string theory.  But this may be the last possible bet and a call is approaching anticipated as a crisis in physics.

onsdagen den 16:e april 2014

Crisis in Physics vs Computational Physics

The May14 issue of Scientific American asks the following questions:
These questions naturally present themselves because modern theoretical physicists have driven themselves to search for the truth on scales which are either too small (string theory) or too big (cosmology) to be assessed experimentally. But theory without experiment may well be empty theory and that may be the meaning of the crisis. Of course, advocates of string theory like Lubos, forcefully denies that there is a crisis in physics. But there are other blog voicesand leading physicists show little hope..

But modern physicists have a new tool to use and that is computational physics, which offers an experimental laboratory without the scale limits of a physical laboratory. 

Computational physics needs computable models, but both quantum mechanics and general relativity are based on models which are not computable, and so there is a lot of work to be done. The question is if modern theoretical physicists have the right training to do this work.     

måndagen den 14:e april 2014

Wanted: Constructive Physics

                                     Wanted: Constructive version of Schrödinger's equation!

The book Constructive Physics by Y.I. Oshigov has an important message:
  • Only in the rebuilding of the gigantic construction of the modern physics in the constructive manner can open doors to the understanding of the complex processes in the sense of exact sciences.
  • The modern situation in physics looks like a crisis, and the genealogy of this crisis is the same as for the crisis in mathematics in the first third of the 20th century: this is the crisis in the axiomatic method.
  • Today we possess the more exact kit of instruments of the constructive mathematics: algorithms must replace formulas.
  • (The multidimensional wave function) harbors serious defects….it does not allow the computation of such functions already for a small number of particles, for example 10, let alone for the more complex systems.
  • This complexity barrier is principal. We should not think then that the quantum theory for many bodies gives such reliable answers to questions as it was the case in one particle case.
In short, quantum mechanics based on Schrödinger's equation for a wave function in $3N$ space dimensions for $N$ particles (electrons or kernels) must be given a new constructive form. A real challenge! My answer is given as Many-Minds Quantum Mechanics. 

onsdagen den 9:e april 2014

Popper: Realism vs Quantum Muddle vs Statistics

Karl Popper starts out Quantum Theory and the Schism of Physics, as Vol III of Postscript to Logic of Scientific Discovery, with the following declaration:
  • Realism is the message of this book. 
  • It is linked with objectivity…with rationalism, with the reality of the human mind, of human creativity, and human suffering.
In Preface 1982: On a Realistic and Commonsense Interpretation of Quantum Mechanics, Popper gives his verdict:
  • Today, physics is in a crisis….This crisis is roughly as old as the Copenhagen interpretation of quantum mechanics.
  • In my view, the crisis is, essentially, due to two things: (a) the intrusion of subjectivism into physics; and (b) the victory of the idea that quantum theory has reached a complete and final truth.
  • Subjectivism in physics can be traced to several great mistakes. One is the positivism or idealism of Mach. Another is the subjectivist interpretation of the calculus of probability.
  • The central issue here is realism. That is to say, the reality of the physical world we live in: the fact that this world exists independently of ourselves; that it existed before life existed,…and that it will continue to exist long after we have all been swept away.
  • The subjectivist dogma was too deeply entrenched within the ruling interpretation of quantum mechanics, the so-called Copenhagen interpretation… this is how the great quantum muddle started….and the whole terminology, introduced in the early period of the theory, conspired to make the muddle worse and worse.
  • Another source of the crisis in physics is the persistence of the belief that quantum mechanics is final and complete.
  • Philosophers and physicists have been all too prone under the direct influence of Machian positivism, to take up idealist positions…
  • One of the things that this volume of the Postscript tries to to is to review many of the past arguments for idealism - which many current physicists still simply take for granted - and to show their error.  
But Popper, one of the greatest philosophers of science of the 20th century, talked to deaf ears and the crisis in physics is deepening every year…

Another thing is that Popper deepened the crisis be dwelling deeper into the statistical interpretation of the wave function of Born as the basis of the Copenhagen interpretation. Popper thus identified the crisis but then himself got drowned by the muddle...

Quantum Theory: Flight from Realism

The book Quantum Theory and the Flight from Realism by Christopher Norris is introduced by:
  • Norris examines the premises of orthodox quantum theory as formulated most influentially by Bohr and Heisenberg….as requiring a drastic revision of principles which had hitherto defined the very nature of scientific method, casual explanation and rational enquiry.
  • Putting the case for a realist approach which adheres to well-tried scientific principles of casual reasoning and interference to the best explanation, Norris clarifies the debate…
Norris continues:  
  • In this book I examine various aspects of the near century-lonh debate concerning the conceptual foundation of quantum mechanics (QM) and the problems it has posed for physicists and philosophers from Einstein to the present. They include the issue of wave-particle dualism; the uncertainty attaching to measurements of particle location or momentum, the (supposedly) observer-induced "collapse of the wave-function"; and the evidence of remote superluminal interaction between widely separated particles.
  • It is important to grasp exactly how the problems arose and exactly why - on what scientific or philosophical grounds - any alternative (realist) contrual should have been so often and routinely ruled out as a matter of orthodox QM wisdom. 
This is an important book with the important mission of bringing realism back to physics after a century  of anti-realist confusion ultimately corrupting all of science and with the adoption of climate alarmism by the American Physical Society as the tragic anti-realist irrational expression. 

tisdagen den 8:e april 2014

Essence of Quantum Mechanics: Energy vs Frequency in Wave Models

In Schrödinger's Equation: Smoothed Particle Dynamics we observed that Schrödinger's equation for Hydrogen atom with one electron (normalized to unit mass and charge) reads
  • $i\bar h\dot\psi + H\psi =0$,
  • $H\psi =\frac{\bar h^2}{2}\Delta\psi +\frac{1}{\vert x\vert}\psi$,
where $\psi (x,t)$ the complex-valued wave function depending on coordinates of space $x$ and time $t$ with the dot denoting differentiation with respect to time, $H$ is the Hamiltonian operator and $\bar h$ Planck's (reduced) constant.

In terms of the real part $\phi$ and imaginary part $\chi$ of $\psi =\phi +i\chi$, Schrödinger's equation takes the system form
  1. $\bar h\dot\phi +H\chi =0$,
  2. $\bar h\dot\chi - H\phi =0$.
If $\phi_E(x)$ is an eigenfunction of the Hamiltonian satisfying $H\phi_E =E\phi_E$ with $E$ the corresponding eigenvalue, then the solution can be represented as
  • $\phi (x,t)=\cos(\omega t)\phi_E(x)$,     $\chi (x,t)=\sin(\omega t)\phi_E(x)$, 
with $\bar h\omega =E$, which expresses a periodic exchange between the two real-valued wave functions $\phi$ and $\chi$ mediated by the Hamiltonian $H$. The parallel to a harmonic oscillator (with $H$ the identity) is obvious.

We see that the effect of the time derivative term is to connect energy $E$ to (angular) frequency $\omega$ by
  • $\bar h\omega = E$, 
  • or $h\nu =E$, 
where $h=2\pi\bar h$ and $\nu =\frac{\omega}{2\pi}$ is frequency in Hertz, where $h$ acts as scale factor.

Schrödinger's equation thus sets up a connection between frequency $\nu$, which can be observed as atomic emission lines, and a model of internal atomic energy $E$ as the sum of kinetic and potential energies of eigenfunctions of the Hamiltonian with the connection $\bar h\omega =h\nu = E$. Observations of atomic emission then show to fit with energy levels of the model, which gives support to the functionality of the model. 

The basic connection $\nu \sim E$ can also be seen in Planck's radiation law (with simplified high-frequency cut-off)
  • $R(\nu ,T)=\gamma T\nu^2$ for $\frac{h\nu}{kT} < 1$,
where $R(\nu ,T)$ is normalized radiance as energy per unit time, with $\gamma =\frac{2k}{c^2}$, $T$ is temperature and $k$ is Boltzmann's constant, which gives an energy per cycle scaling with $\nu$ and a high frequency cut-off $h\nu$ scaling with atomic energy $kT$.

The connection $h\nu =E$ also occurs in the law of photoelectricity
  • $h\nu = P + K$,
where $P$ is the release energy and $K=eU$ is the kinetic energy of a released electron with $e$ the electron charge and $U$ the stopping potential. 

The atomic connection $h\nu =E$ between frequency and energy thus has both theoretical and experimental support,  but it does not say that energy is "quantized" into discrete packets of energy $h\nu$ carried by particles named photons of frequency $\nu$. 

The relation $h\nu =E$ is compatible with wave models of both emission from atoms and radiation from clusters of atoms and if so by Ockham's razor particle models have no role to play.

Atomic emission and radiation is a resonance phenomenon much like the resonance in a musical instrument, both connecting frequency to matter.

Text books state that 
  1. Blackbody radiation and the photoelectric effect cannot be explained by wave models.
  2. Hence discrete quanta and particles must exist. 
  3. Hence there is particle-wave duality.    
I give on Computational Blackbody Radiation evidence that 1 is incorrect, and therefore also 2 and 3. Without particles a lot of the mysticism of quantum mechanics can be eliminated and progress made. 

måndagen den 7:e april 2014

The Strange Story of The Quantum: Physics as Mysticism

The Strange Story of The Quantum by Banesh Hoffman bears witness to the general public about modern physics as mysticism:  
  • This book is designed to serve as a guide to those who would explore the theories by which the scientist seeks to comprehend the mysterious world of the atom.
  • The story of the quantum is the story of a confused and groping search for knowledge…enlivened by coincidences such as one would expect to find only in fiction.
  • It is a story about turbulent revolution…and of the tempesteous emergence of a much chastened regime - Quantum Mechanics.
  • The magnificent rise of the quantum to a dominant position in modern science and philosophy is a story of drama and high adventure often well-nigh incredible. It is a chaotic tale…apparent chaos…nonsensical…intricate jagsaw…major discovery of the human mind.
  • Planck called his bundle or quota a QUANTUM of energy…This business of bundles of energy was unpardonable heresy, frightening to even the bravest physicist. Prandtl was by no means happy... But all was to no avail….to Max Planck had fallen the immortal honor of discovering them.
  • Einstein insisted...that each quantum of energy  somehow must behave like a particle: a particle of light; what we call a photon…But how could a particle theory possibly hope to duplicate the indisputable triumphs of the wave theory? To go back to anything like the particle theory would be tantamount to admitting that the elaborately confirmed theory of electromagnetic phenomena was fundamentally false. Yet Einstein...was actually proposing such a step.
  • It is difficult to decide where science ends and mysticism begins….In talking of the meaning of quantum mechanics, physicists indulge in more or less mysticism according to their individual tastes.
  • Perhaps it is this which makes it seem so paradoxical.
  • Perhaps there is after all some innate logic in quantum theory.
  • The message of the quantum suddenly becomes clear: space and time are not fundamental.
  • Out of it someday will spring a new and far more potent theory…what will then survive of our present ideas no one can say…
  • Already we have seen waves an particles and causality and space and time all undermined.
  • Let us hasten to bring the curtain down in a rush lest something really serious should happen...
Hoffman's book was first published in 1947. Since then the mysticism of modern physics has only become deeper...