tag:blogger.com,1999:blog-1500584444083499721Fri, 18 Apr 2014 06:12:58 +0000theory of flightgreenhouse effectclimate sciencemathematics educationclimate politicsmyth of backradiationRoyal Swedish Academy of Sciencesblack body radiationquantum mechanicsAIAAKTH-gateDLRclimate simulationmatematik-ITclimate sensitivityKTH-gate3physicsscienceengineering education reformtheory of relativityKammarrättenmathematicssimulation technologyBodyandSoulStefan-Boltzmann's LawQuantum Contradictionsthermodynamics of global climateIPCCPlanck's LawHögsta FörvaltningsdomstolenCO2KTH-gate2emissivitycosmologySky Dragongravitationinterviewsradiative heat transferEinsteinPlanck's constant2nd law of thermodynamicsclimategateMattelyftetStandard CaculusFalse-SBOLRfluid mechanicsCFDFundamental Theorem of CalculusKTHOffentlighetsprincipenbig bluffLennart Bengtssonfinite precision computationmany-minds relativityinfrared thermometermodtranIPCC TrickNew View on gravitationmysticism of modern physicsphysics illusionsroy spencerKVAphotonspyrgeometerradiative forcingturbulenceJudy Currysvensk klimatpolitikuncertainty principleNADAfred singerresonanceMuir Russell Inquirybolometerlapse ratelindzensecret of separationteknikdelegationentheory of sailingIR cameraclimate modelsdAlembertgatedark energymany-minds physicsphotoelectric effectCERESDr FaustusFEniCSFakultetsnämnden KTHLaplace demonMSTRoyal SocietySVTSchrödinger's equationSvenska Mekanikdagarfree willBert Bolin Centre for Climate ResearchCMBGlenn Research CenterKirchhoff's lawPrandtlarrow of timeazarcensorshipclay problemcosmological principledark mattereconomical crisisibookkollegialt lärandethermal imaging3rd Nobel SymposiumAcademic Rights WatchAnders ÅngströmFreedom FestHubble's LawPenguin logicboundary layerclimate skepticdefinition vs physical factdirection of timeiducationphlogistonpiano acousticsprinciple of least actionshorttime vs longtime accuracyFinal SolutionHans RoslingHelmholtz ReciprocityHiggs mechanismLorentz transformationMichelson-MorleyOckham's razorQEDRiksbankenSMHISULFZeno's arrow paradoxconstructive physicscrisis in physicsfaint sun paradoxlord moncktonnumerical analysisperiodic tablerelativityrepo ratestellar aberrationstring instrumentswave-particle dualityDNDiscussion ForumEquivalence PrincipleGoogle BooksKTH-studenterKnut ÅngströmMOOCMagnus effectMaxwell's equationsNewton's 2nd lawPopperSRSagnac effectSvenska MatematikersamfundetUnicornWien's displacement lawaeroacousticsaniconismatmosphere spectrumbigbrunobutterfly effectconduction vs radiationcopernicuscritical thinkingdark age of sciencedefinition as factdynamical systememissvitygalileohäggströmmillikannobel prizepeer reviewpokerpryscientific methodseminarsstability-wellposednesstyndallwellposednessÖppna GöteborgClaes Johnson on Mathematics and Sciencetowards understanding by critical constructive inquiryhttp://claesjohnson.blogspot.com/noreply@blogger.com (Claes Johnson)Blogger1304125tag:blogger.com,1999:blog-1500584444083499721.post-6468569715380315940Thu, 17 Apr 2014 12:24:00 +00002014-04-17T21:11:34.555+02:00crisis in physicsmysticism of modern physicsphysicspokerExtremism of Modern Physics as Bluff Poker Physics <div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-AoJVaAUHdWM/U0_FBDMUj6I/AAAAAAAAi-s/uNv0TWoZSQI/s1600/Poker-Bluffs.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-AoJVaAUHdWM/U0_FBDMUj6I/AAAAAAAAi-s/uNv0TWoZSQI/s1600/Poker-Bluffs.jpg" height="240" width="320" /></a></div><br /><br />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...<br /><br />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...<br /><br />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.<br /><br />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.<br /><br />http://claesjohnson.blogspot.com/2014/04/extremism-of-modern-physics-as-bluff.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-6686904449481218505Wed, 16 Apr 2014 13:07:00 +00002014-04-17T14:04:26.744+02:00constructive physicscrisis in physicsfinite precision computationmysticism of modern physicsquantum mechanicsCrisis in Physics vs Computational Physics <div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-swjLqJDJQfk/U05gf4ms1yI/AAAAAAAAi-U/xwjMbC_XNZ8/s1600/383147AB-E14D-4601-94949D896131BC60_article.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-swjLqJDJQfk/U05gf4ms1yI/AAAAAAAAi-U/xwjMbC_XNZ8/s1600/383147AB-E14D-4601-94949D896131BC60_article.jpg" height="320" width="244" /></a></div><br />The May14 issue of Scientific American asks the following questions:<br /><ul><li><a href="http://www.scientificamerican.com/article/does-physics-have-a-problem/">Does Physics Have a Problem?</a></li><li><a href="http://www.scientificamerican.com/article/supersymmetry-and-the-crisis-in-physics/">Crisis in Physics?</a></li></ul><div>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, <a href="http://motls.blogspot.se/2014/04/another-anti-physics-issue-of-sciam.html">advocates of string theory like Lubos,</a> forcefully denies that there is a crisis in physics. <a href="http://www.math.columbia.edu/~woit/wordpress/?p=6836">But there are other blog voices</a><span style="color: #0000ee;"><u>…</u></span>and <a href="http://www.strings.ph.qmul.ac.uk/~dsb/dbwager.pdf">leading physicists show little hope</a>..</div><div><br /></div><div>But modern physicists have a new tool to use and that is <a href="http://claesjohnsonmathscience.wordpress.com/">computational physics,</a> which offers an experimental laboratory without the scale limits of a physical laboratory. </div><div><br /></div><div>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. </div>http://claesjohnson.blogspot.com/2014/04/crisis-in-physics-vs-computational.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-6040455014457832433Mon, 14 Apr 2014 16:24:00 +00002014-04-14T18:31:16.088+02:00constructive physicsquantum mechanicsSchrödinger's equationWanted: Constructive Physics <div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-WcI_82uAh8w/U0wKs9jNfOI/AAAAAAAAi90/Hdx7hACATgs/s1600/Schrodingers-Cat-Wanted-Dead-And-Or-Alive_9759-l.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-WcI_82uAh8w/U0wKs9jNfOI/AAAAAAAAi90/Hdx7hACATgs/s1600/Schrodingers-Cat-Wanted-Dead-And-Or-Alive_9759-l.jpg" height="213" width="320" /></a></div> <i>Wanted: Constructive version of Schrödinger's equation!</i><br /><br />The book <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.312.7132&rep=rep1&type=pdf">Constructive Physics by Y.I. Oshigov</a> has an important message:<br /><ul><li><i>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.</i></li><li><i>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.</i></li><li><i>Today we possess the more exact kit of instruments of the constructive mathematics: <b>algorithms must replace formulas.</b></i></li><li><i>(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.</i></li><li><i>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.</i></li></ul><div>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 <a href="http://www.csc.kth.se/~cgjoh/ambsquantum.pdf">Many-Minds Quantum Mechanics. </a></div><br />http://claesjohnson.blogspot.com/2014/04/wanted-constructive-physics.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-6275382188582404662Wed, 09 Apr 2014 18:55:00 +00002014-04-10T08:04:08.618+02:00Popperquantum mechanicsPopper: Realism vs Quantum Muddle vs Statistics<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-G5wgpnKZJtk/U0WVn2R5XuI/AAAAAAAAizE/wNqk2iMKbIg/s1600/popper.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-G5wgpnKZJtk/U0WVn2R5XuI/AAAAAAAAizE/wNqk2iMKbIg/s1600/popper.jpg" /></a></div><br /><a href="http://en.wikipedia.org/wiki/Karl_Popper">Karl Popper</a> starts out <a href="http://ww.goodreads.com/book/show/593852.Quantum_Theory_and_the_Schism_in_Physics">Quantum Theory and the Schism of Physics</a>, as Vol III of Postscript to <a href="http://en.wikipedia.org/wiki/The_Logic_of_Scientific_Discovery">Logic of Scientific Discovery,</a> with the following declaration:<br /><ul><li><i><b>Realism</b> is the message of this book. </i></li><li><i>It is linked with <b>objectivity</b>…with<b> rationalism</b>, with the reality of the human mind, of human creativity, and human suffering.</i></li></ul><div>In <i>Preface 1982: On a Realistic and Commonsense Interpretation of Quantum Mechanics,</i> <a href="http://www.jstor.org/discover/10.2307/187565?uid=3738984&uid=2129&uid=2&uid=70&uid=4&sid=21103979016753">Popper gives his verdict</a>:</div><div><ul><li><i><b>Today, physics is in a crisis</b>….This crisis is roughly as old as the <b>Copenhagen interpretation</b> of quantum mechanics.</i></li><li><i>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.</i></li><li><i>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.</i></li><li><i>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.</i></li><li><i>The subjectivist dogma was too deeply entrenched within the ruling interpretation of quantum mechanics, the so-called Copenhagen interpretation… this is how the <b>great quantum muddle </b>started….and the whole terminology, introduced in the early period of the theory, conspired to make the <b>muddle worse and worse.</b></i></li><li><i>Another source of the crisis in physics is the persistence of the belief that quantum mechanics is final and complete.</i></li><li><i>Philosophers and physicists have been all too prone under the direct influence of Machian positivism, to take up idealist positions…</i></li><li><i>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. </i><i> </i></li></ul>But Popper, <a href="http://en.wikipedia.org/wiki/Karl_Popper">one of the greatest philosophers of science</a><a href="http://en.wikipedia.org/wiki/Karl_Popper"> of the 20th century</a>, talked to deaf ears and the crisis in physics is deepening every year… <br /><br />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...</div>http://claesjohnson.blogspot.com/2014/04/popper-realism-vs-quantum-muddle.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-5952935268552039337Wed, 09 Apr 2014 12:27:00 +00002014-04-09T14:30:34.153+02:00finite precision computationquantum mechanicsQuantum Theory: Flight from Realism<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-FsTGQ8pk_vM/U0U6LREKGVI/AAAAAAAAiy0/rvWdlwwRxKw/s1600/norris.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-FsTGQ8pk_vM/U0U6LREKGVI/AAAAAAAAiy0/rvWdlwwRxKw/s1600/norris.jpg" height="320" width="209" /></a></div><br />The book <a href="http://www.amazon.com/Quantum-Theory-Flight-Realism-Philosophical/dp/0415223229">Quantum Theory and the Flight from Realism by Christopher Norris</a> is introduced by:<br /><ul><li><i>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.</i></li><li><i>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…</i></li></ul><div>Norris continues: </div><div><ul><li><i>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.</i></li><li><i>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. </i></li></ul><div>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. </div><div><br /></div><div><a href="http://claesjohnson.blogspot.se/2014/03/quantum-physics-as-digital-continuum.html">Today digital computation opens new roads to bring realism back to physics viewed as analog computation.</a> See <a href="http://claesjohnsonmathscience.wordpress.com/">The World as Computation.</a></div></div>http://claesjohnson.blogspot.com/2014/04/quantum-theory-flight-from-realism.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-6451646790653419533Tue, 08 Apr 2014 10:42:00 +00002014-04-08T13:36:22.253+02:00black body radiationquantum mechanicsSchrödinger's equationEssence of Quantum Mechanics: Energy vs Frequency in Wave Models<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-WpwVupfU_Qo/U0PShGCa_iI/AAAAAAAAiyk/DHfooJFeOkA/s1600/averillfwk-fig06_x002.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-WpwVupfU_Qo/U0PShGCa_iI/AAAAAAAAiyk/DHfooJFeOkA/s1600/averillfwk-fig06_x002.jpg" height="320" width="237" /></a></div><br />In <a href="http://claesjohnson.blogspot.se/2014/04/schrodingers-equation-smoothed-particle.html">Schrödinger's Equation: Smoothed Particle Dynamics</a> we observed that Schrödinger's equation for Hydrogen atom with one electron (normalized to unit mass and charge) reads<br /><ul><li>$i\bar h\dot\psi + H\psi =0$,</li><li>$H\psi =\frac{\bar h^2}{2}\Delta\psi +\frac{1}{\vert x\vert}\psi$,</li></ul><div>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.</div><div><br /></div><div>In terms of the real part $\phi$ and imaginary part $\chi$ of $\psi =\phi +i\chi$, Schrödinger's equation takes the system form<br /><ol><li>$\bar h\dot\phi +H\chi =0$,</li><li>$\bar h\dot\chi - H\phi =0$.</li></ol></div>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<br /><div><ul><li>$\phi (x,t)=\cos(\omega t)\phi_E(x)$, $\chi (x,t)=\sin(\omega t)\phi_E(x)$, </li></ul></div><div>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.<br /><br />We see that the effect of the time derivative term is to connect energy $E$ to (angular) frequency $\omega$ by<br /><ul><li>$\bar h\omega = E$, </li><li>or $h\nu =E$, </li></ul><div>where $h=2\pi\bar h$ and $\nu =\frac{\omega}{2\pi}$ is frequency in Hertz, where $h$ acts as scale factor.</div><div><br /></div><div>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. </div><div><br /></div><div>The basic connection $\nu \sim E$ can also be seen in Planck's radiation law (with simplified high-frequency cut-off)</div><div><ul><li>$R(\nu ,T)=\gamma T\nu^2$ for $\frac{h\nu}{kT} < 1$,</li></ul><div>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 $kT$.<kt as="" atomic="" div="" energy.="" kt="" scaling="" with=""></kt></div><div><br /></div><div>The connection $h\nu =E$ also occurs in the law of photoelectricity</div><div><ul><li>$h\nu = P + K$,</li></ul><div>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. </div></div><div><br /></div><div>The atomic connection $h\nu =E$ between frequency and energy thus has both theoretical and experimental support, but it does not say that energy<b> is </b>"quantized" into discrete packets of energy $h\nu$ carried by particles named photons of frequency $\nu$. </div><div><br /></div><div>The relation $h\nu =E$ is compatible with <a href="http://claesjohnson.blogspot.se/2014/04/comparing-blackbody-radiation-spectrum.html">wave models of both emission from atoms and radiation from clusters of atoms</a> and if so by Ockham's razor particle models have no role to play. <br /><br />Atomic emission and radiation is a resonance phenomenon much like the resonance in a musical instrument, both connecting frequency to matter.</div><div><br /></div><div>Text books state that </div><div><ol><li>Blackbody radiation and the photoelectric effect cannot be explained by wave models.</li><li>Hence discrete quanta and particles must exist. </li><li>Hence there is particle-wave duality. </li></ol></div><div>I give on <a href="http://computationalblackbody.wordpress.com/">Computational Blackbody Radiation</a> 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. </div><div><br /></div><div><br /></div></div></div>http://claesjohnson.blogspot.com/2014/04/essence-of-quantum-mechanics-energy-vs.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-2891146856060118097Mon, 07 Apr 2014 14:35:00 +00002014-04-07T23:02:39.329+02:00mysticism of modern physicsquantum mechanicsThe Strange Story of The Quantum: Physics as Mysticism<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-vGmbEXDirK8/U0K2wHusewI/AAAAAAAAitI/gAZ30bDUz8E/s1600/The-Strange-Story-of-the-Quantum-Hoffman-Banesh-9780486205182.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-vGmbEXDirK8/U0K2wHusewI/AAAAAAAAitI/gAZ30bDUz8E/s1600/The-Strange-Story-of-the-Quantum-Hoffman-Banesh-9780486205182.jpg" height="320" width="213" /></a></div><br /><a href="http://www.amazon.com/Strange-Story-Quantum-Banesh-Hoffmann/dp/0486205185">The Strange Story of The Quantum</a> by Banesh Hoffman bears witness to the general public about modern physics as mysticism: <br /><ul><li><i>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.</i></li><li><i>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.</i></li><li><i>It is a story about turbulent revolution…and of the tempesteous emergence of a much chastened regime - Quantum Mechanics.</i></li><li><i>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.</i></li><li><i>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.</i></li><li><i>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.</i></li><li><i>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.</i></li><li><i>Perhaps it is this which makes it seem so paradoxical.</i></li><li><i>Perhaps there is after all some innate logic in quantum theory.</i></li><li><i>The message of the quantum suddenly becomes clear: space and time are not fundamental.</i></li><li><i>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…</i></li><li><i>Already we have seen waves an particles and causality and space and time all undermined.</i></li><li><i>Let us hasten to bring the curtain down in a rush lest something really serious should happen...</i></li></ul>Hoffman's book was first published in 1947. Since then the mysticism of modern physics has only become deeper...<br /><br />http://claesjohnson.blogspot.com/2014/04/the-strange-story-of-quantum-physics-as.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-8511666320742942498Sun, 06 Apr 2014 12:20:00 +00002014-04-07T11:59:55.859+02:00finite precision computationmany-minds physicsSchrödinger's equationSchrödinger's Equation: Smoothed Particle Dynamics<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-bn36YJnX-18/U0FFiubjAOI/AAAAAAAAiRo/ims8_qOaNhU/s1600/Hydrogen_Density_Plots.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-bn36YJnX-18/U0FFiubjAOI/AAAAAAAAiRo/ims8_qOaNhU/s1600/Hydrogen_Density_Plots.png" height="291" width="320" /></a></div><i>Eigenfunctions of the Hamiltonian for the Hydrogen atom with eigenvalues representing the sum of kinetic and potential energies, with Schrödinger's equation as a smoothed version of the particle dynamics of a harmonic oscillator. </i><br /><br />This is continuation of the previous post <a href="http://claesjohnson.blogspot.se/2014/03/how-to-give-physical-meaning-of.html">How to Make Schrödinger's Equation Physically Meaningful + Computable</a>. Consider the basic case of the Hydrogen atom with one electron (normalized to unit mass and charge):<br /><ul><li>$ih\dot\psi + H\psi =0$,</li><li>$H\psi =\frac{h^2}{2}\Delta\psi +\frac{1}{\vert x\vert}\psi$,</li></ul><div>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 $h$ Planck's constant.</div><div><br /></div><div>In terms of the real part $\phi$ and imaginary part $\chi$ of $\psi =\phi +i\chi$, Schrödinger's equation takes the system form <br /><ol><li>$h\dot\phi +H\chi =0$,</li><li>$h\dot\chi - H\phi =0$.</li></ol></div>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<br /><div><ul><li>$\phi (x,t)=\cos(\omega t)\phi_E(x)$, $\chi (x,t)=\sin(\omega t)\phi_E(x)$, </li></ul></div><div>with $h\omega =E$, which expresses a periodic exchange between the two real-valued wave functions $\phi$ and $\chi$ mediated by the Hamiltonian $H$.<br /><br />We can see 1- 2 as an analog of the equation for a harmonic oscillator $\ddot u+\omega^2u=0$ written in system form (with $h=1$)<br /><ul><li>$\dot\phi + \omega\chi =0$</li><li>$\dot\chi - \omega \phi = 0$,</li></ul><div>where $\phi =\dot u$ and $\chi =\omega u$, with solution</div><ul><li>$\phi (x,t)=\cos(\omega t)$, $\chi (x,t)=\sin(\omega t)$. </li></ul>Here the velocity $\phi =\dot u$ connects to kinetic energy $\phi^2 =\dot u^2$ and $\chi =\omega u$ to potential energy $\chi^2 =\omega^2u^2$ and the dynamics of the harmonic oscillation consists of periodic transfer back and forth between kinetic and potential energy with their sum being constant. <br /><br />Returning now to the Hydrogen atom, we obtain multiplying 1 by $\phi$ and 2 by $\chi$ and integrating in space the following the energy balance<br /><ul><li>$h\frac{d}{2dt}\int\phi^2\, dx + \int \phi H\chi \, dx =0$</li><li>$h\frac{d}{2dt}\int\chi^2\, dx - \int \chi H\phi\, dx =0$, </li></ul><div>where </div><div><ul><li>$ \int \phi H\chi \, dx = \int \chi H\phi\, dx =\frac{h^2}{2}\int\nabla\phi\cdot\nabla\chi\, dx +\int\frac{\phi\chi}{\vert x\vert}\, dx$,</li></ul><div>which shows upon summation (by the symmetry of $H$) that</div></div><ul><li>$\frac{d}{2dt}\int\phi^2\, dx =\frac{d}{2dt}\int\chi^2\, dx =0$, </li></ul><div>which allows normalization to </div><ul><li>$\int\phi^2\, dx = \int\chi^2\, dx = \frac{1}{2}$,</li><li>$\int\vert\psi\vert^2\, dx = 1$, for all time. </li></ul><div>Further, multiplying 1 by $\dot\chi$ and 2 by $\dot\phi$ and subtracting the resulting equations shows that</div><div><ul><li>$\int (\phi H\phi + \chi H\chi)\, dx$ is constant in time. </li></ul><div>We can now summarize as follows:<br /><br /><b>A. </b>We see that the solution pair $(\phi ,\chi )$ of 1 - 2 as the real and imaginary part of Schrödinger's wave function $\phi$, represents a periodic exchange mediated by the Hamiltonian $H$ with balancing associated total energies </div><div><ul><li>$\int \phi H\phi (x,t)\, dx = \frac{h^2}{2}\int\vert\nabla\phi (x,t)\vert^2dx +\int\frac{\phi^2(x,t)}{\vert x\vert}\, dx$,</li><li>$\int \chi H\chi (x,t)\, dx = \frac{h^2}{2}\int\vert\nabla\chi (x,t)\vert^2dx +\int\frac{\chi^2(x,t)}{\vert x\vert}\, dx$ </li></ul></div><div>as the sum of kinetic and potential energies.<br /><br /><b>B.</b> We see that Schrödinger's equation for the Hydrogen atom can be viewed as a smoothed version of a harmonic oscillator with the smoothing effectuated by the Laplacian and with $h$ acting as a smoothing parameter.<br /><br /><b>C.</b> We see that the system form 1- 2 combines the spatial eigenfunction $\phi_E$ with a periodic time dependence without introducing energy beyond the kinetic and potential energies defined by the Hamiltonian, thus associating these energies to frequency as the essence of quantum mechanics. <br /><br /><b>D.</b> We see that quantum mechanics and Schrödinger's equation can be given an interpretation which closely connects to classical mechanics, as smoothed particle mechanics, which avoids the common mystifications of particle-wave duality, complementarity, wave function collapse and statistics forced by insistence to use a multidimensional wave function defying a direct physical meaning.<br /><br /><a href="http://claesjohnsonmathscience.wordpress.com/2013/09/13/deterministic-quantum-mechanics/">Extension to several electrons can be naturally be made following the idea of smoothed particle dynamics</a>. For details see <a href="http://www.csc.kth.se/~cgjoh/ambsquantum.pdf">Many-Minds Quantum Mechanics</a>.</div></div></div>http://claesjohnson.blogspot.com/2014/04/schrodingers-equation-smoothed-particle.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-1143286948545522181Fri, 04 Apr 2014 08:08:00 +00002014-04-04T16:13:35.489+02:00black body radiationPlanck's constantComparing Blackbody Radiation Spectrum to Atomic Emission Spectrum Planck's constant $h$ appears with different roles in a blackbody radiation spectrum and an atomic emission spectrum. Blackbody radiation can be described as a near-resonance phenomenon in a forced harmonic oscillator with small damping in a mathematical model of the form<br /><ul><li>$\ddot u (t) +\omega^2u(t) -\gamma\dddot u = f(t)\approx \sin(\omega t)$, </li></ul>where $u(t)$ is displacement as function of time $t$, $\omega$ is angular velocity, $\gamma$ is a small damping constant, $f(t)$ is forcing in near-resonance with $\omega$ and the dot signifies time differentiation. Here the oscillator described by $\ddot u (t) +\omega^2u(t)$ carries energy as background temperature and the dissipative term $-\gamma\dddot u$ gives off radiation balancing forcing $f(t)$.<br /><div><br />The dynamics of near-resonance is quite subtle as explained in detail on <a href="http://computationalblackbody.wordpress.com/">Computational Blackbody Radiation</a> showing that Planck's constant enters as a parameter in a high-frequency cut-off reflecting Wien's displacement law. </div><div><br /></div><div>Atomic emission can be described as an eigenvalue problem for Schrödinger's equation of the form</div><div><ul><li>$ih\dot\psi = E\psi$,</li></ul><div>where $E$ is a real eigenvalue of an atomic Hamiltonian, with solution<br /><ul><li>$\psi (t) =\exp(i\omega t) =\cos(\omega t)+i\sin(\omega t)$, </li></ul>which can be seen as a periodic exchange of two forms of energy represented by the real part $\cos(\omega t)$ and the complex part $\sin(\omega t)$ reflecting incoming-outgoing radiation. Atomic emission is thus a direct resonance phenomenon without background temperature. Planck's constant serves to convert angular velocity (angular momentum) $\omega$ to atomic energy $E$ as $\bar h\omega$ with $\bar h=\frac{h}{2\pi}$ with $E$ the sum of kinetic and potential energy. </div><div><br /></div><div>We conclude:</div><div><ol><li>Blackbody radiation is a near-resonance phenomenon of molecules or collections of atoms modeled as a forced harmonic oscillator with small damping. Collections of atoms vibrate without electron configurations changing energy. </li><li>Atomic radiation is a direct resonance phenomenon which can be modeled by a harmonic oscillator. Electrons oscillate between two energy levels representing eigenstates of an atom.</li></ol><div>In both cases $h$ enters combined with frequency $\nu$ in the form $h\nu =\bar h\omega$ as quantity of energy serving in a threshold condition in blackbody radiation, and as an energy eigenvalue in atomic emission.<br /><br />The value of $h$ as setting a conversion scale between light energy and electronic energy can be determined by the photoelectric effect and can then be used by definition in blackbody radiation and Schrödinger's equation. </div></div><div> </div></div>http://claesjohnson.blogspot.com/2014/04/comparing-blackbody-radiation-spectrum.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-489023303388247095Thu, 03 Apr 2014 20:51:00 +00002014-04-04T07:27:27.675+02:00Einsteinphotoelectric effectPlanck's constantWater Dam Analog of Photoelectric Effect <div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-NrBPxnM4hQM/Uz3CG9LzbwI/AAAAAAAAiRU/9DT4d7RE7GA/s1600/threegorges.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-NrBPxnM4hQM/Uz3CG9LzbwI/AAAAAAAAiRU/9DT4d7RE7GA/s1600/threegorges.jpg" height="212" width="320" /></a></div> <a href="http://www.china.org.cn/environment/news/2008-08/14/content_16220081.htm">Open sluice gates in the Three Gorges Dam in the Yangtze River.</a><br /><br />Einstein was awarded the 1921 Nobel Prize in Physics for his <a href="http://claesjohnson.blogspot.se/search/label/Einstein">"discovery of the law of the photoelectric effect</a>", connecting frequency $\nu$ of light shining on a metallic surface with measured potential $U$:<br /><ul><li>$h\nu = h\nu_0 + e\, U$ or $h(\nu -\nu_0) = e\, U$,</li></ul><div>where $h$ is Planck's constant with dimension $eVs = electronvolt\,\times second$, $\nu_0$ is the smallest frequency releasing electrons and $U$ in Volts $V$ is the stopping potential bringing the current to zero for $\nu >\nu_0$ and $e$ is the charge of an electron. Observing $U$ for different $\nu$ in a macroscopic experiment shows a linear relationship between $\nu -\nu_0$ and $U$ with $h$ as scale factor with <a href="http://en.wikipedia.org/wiki/Planck_constant">reference value</a> </div><div><ul><li>$h = 4.135667516(91)\times 10^{-15}\, eVs$,</li></ul><div>with <a href="http://physics.aps.org/story/v3/st23">Millikan's value</a> from 1916 within $0.5\%$.<br /><br />Determining $h$ this way makes Einstein's law of photoelectricity into an<a href="http://claesjohnson.blogspot.se/2014/03/einstein-genius-by-definition-of-law-of.html"> energy conversion standard</a> attributing $h\nu$ electronvolts to the frequency $\nu$, without any implication concerning the microscopic nature of the photoelectric effect.<br /><br />The award motivation "<a href="http://claesjohnson.blogspot.se/search/label/Einstein">discovery of the law of the photoelectric effect</a>" reflected that Einstein's derivation did not convince the committee as expressed by member Gullstrand: </div><div><ul><li><i>When it was formulated it was only a tentatively poorly developed hunch, based on qualitative and partially correct observations. It would look peculiar if a prize was awarded to this particular work. </i></li></ul><div>To give perspective let us as an analog of the law of the photoelectric effect consider a water dam with sluice gates which automatically open when the level of water is $\nu_0$. The sluice gates will then remain locked as long as the water level $\nu <\nu_0$. Lock the sluice gates and let the dam fill to some water level $\nu >\nu_0$ and then unlock the sluices. The sluices will then open and water will flow through under transformation of potential energy into kinetic energy. Assuming the work to open the sluices corresponds to a level loss of $\nu_0$, a net level of $\nu -\nu_0$ potential energy will then be transformed into kinetic energy by the water flow through the sluices. </div><div><br /></div><div>The dam can be seen as an illustration of the photoelectric effect with the water level corresponding to frequency $\nu$ and the gravitational constant corresponding to $h$ and the width of the dam corresponding to the amplitude of incoming light. If $\nu <\nu_0$ then nothing will happen, if $\nu >\nu_0$ then the kinetic energy will scale with $h\nu$ and the total flow will scale with the width of the dam. <br /><br />Notice that noting in this model requires the water to flow in discrete lumps or quanta. The only discrete effect is the threshold $\nu_0$ for opening the sluices.</div></div><div><br /><br /><br /></div></div>http://claesjohnson.blogspot.com/2014/04/water-fall-analog-of-photoelectric.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-7534317702681895097Wed, 02 Apr 2014 09:47:00 +00002014-04-03T10:25:06.827+02:00black body radiationPlanck's constantPlanck's Lawquantum mechanicsSchrödinger's equationUniversal Quantum of Action: Standard Without Universality <div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-GQZXAUaGCtQ/UzvcZzAS5gI/AAAAAAAAiQ8/x8ZNOhiJOrM/s1600/hydrogen-spectra.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-GQZXAUaGCtQ/UzvcZzAS5gI/AAAAAAAAiQ8/x8ZNOhiJOrM/s1600/hydrogen-spectra.jpg" height="224" width="320" /></a></div><br />In recent posts on we have seen that Plank's constant $h$ in physics text books being presented as a <a href="http://en.wikipedia.org/wiki/Planck_units">universal quantum of action as a smallest "packet of action" as a fundamental constant of fundamental significance in the "quantized" world we happen to be part of</a>, in fact is nothing but a conversion standard between two measures of energy, in terms of <i>frequency</i> $\nu$ in periods per second and <i>electronvolt (eV), </i>determined by Einstein's law of photoelectricity<br /><ul><li>$h(\nu - \nu_0) = e\, U$,</li></ul><div>where $\nu_0$ is the smallest frequency releasing electrons from a metallic surface upon exposure of light, $U$ in Volts $V$ is the stopping potential bringing the current to zero for $\nu >\nu_0$ and $e$ is the charge of an electron. Observing $U$ for different $\nu$ shows a linear relationship between $\nu -\nu_0$ and $U$ with $h$ as the scale factor measured in $eVs$ $electronvolts\times second$ as $energy \times time$ as<i> action. </i>The <a href="http://en.wikipedia.org/wiki/Planck_constant">reference value</a> obtained this way is </div><div><ul><li>$h = 4.135667516(91)\times 10^{-15}\, eVs$,</li></ul><div>with <a href="http://physics.aps.org/story/v3/st23">Millikan's value</a> from 1916 within $0.5\%$. Determining $h$ this way makes Einstein's law of photoelectricity simply into a<a href="http://claesjohnson.blogspot.se/2014/03/einstein-genius-by-definition-of-law-of.html"> conversion standard (that is, a definition) </a>of energy attributing $h\nu$ electronvolts to the frequency $\nu$. Another way of finding the conversion from frequency to electronvolt is using a <a href="http://en.wikipedia.org/wiki/Josephson_effect">Josephson junction.</a></div></div><div><br /></div><div>We now turn to Schrödinger's equation</div><div><ul><li>$i\bar h\frac{\partial\psi}{\partial t}+H\psi=0$,</li></ul><div>where $\bar h=\frac{h}{2\pi}$ is Planck's reduced constant as conversion from periods $\nu$ per second to angular velocity $\omega$ with $h\nu =\bar h\omega$, and $H$ is a Hamiltonian of space dependence. An eigenvalue $E$ of the Hamiltonian represents energy with $\psi_E$ a corresponding space dependent eigenfunction satisfying $H\psi_E =E\psi_E$ and $\exp(i\omega t)\psi_E$ a corresponding solution of Schrödinger's equation with </div><div><ul><li>$h\nu = \bar h\omega = E$, </li></ul></div></div><div>expressing energy in terms of frequency. We see that the appearance of $\bar h$ with the time derivative in Schrödinger's equation accounts for the energy conversion and is completely normal and without mystery. </div><div><br /></div><div>Next, we consider the space dependent Hamiltonian in the basic case of the Hydrogen atom:</div><div><ul><li>$H\psi = \frac{\bar h^2}{2m}\Delta\psi + \frac{e^2}{r}\psi$ </li></ul></div><div>where $\psi =\psi (x)$ with $x$ a space coordinate, $r =\vert x\vert$, and $m$ is the mass of the electron. Normalising by changing scale in space $x=a\bar x$ and time $t=b\bar t$, we obtain the Hamiltonian in normalized atomic units in the form</div><div><ul><li>$\bar H = \bar\Delta + \frac{2}{\bar r}$ with smallest eigenvalue $1$, </li><li>$a=\frac{\bar h^2}{me^2}$ as $Bohr\, radius$,</li><li>$b=\frac{\bar h2a}{e^2}$ as $Bohr\, time$<i> </i>with $\omega =\frac{1}{b}$ angular velocity</li><li>$E =\frac{e^2}{2a}$ as $Rydberg\, energy$<i>.</i></li></ul><div>We now observe that</div><div><ul><li>$E\, b = \bar h$,</li></ul></div></div><div><ul><li>$E = \bar h\, \omega$, </li></ul><div>which shows that the also the space dependent part of Schrödinger's equation is calibrated to the energy conversion standard. </div></div><div><br /></div><div>Finally, Planck's constant also appears in <a href="http://computationalblackbody.wordpress.com/plancks-law/">Planck's radiation law</a> and then in the high-frequency cut-off factor</div><div><ul><li>$\frac{\alpha}{\exp(\alpha )-1}$</li><li>$\alpha = \frac{h\nu}{kT}$,</li></ul><div>where $k$ is Boltzmann's constant and $T$ temperature. We see that again $h\nu$ appears as an atomic energy measure with a value that is not very precisely determined in its role in the cut-off factor.</div><div>The value of $h$ from photoelectricity can then serve also in Planck's law.</div><div><br /></div><div>We conclude that Planck's constant $h$ is a conversion standard between two energy measures and as such has no meaning as a universal quantum of action or as integral multiples $nh\nu$ with $n=1,2,3,..$ of special significance other than by connection to eigenfunctions and eigenvalues. </div><div><br /></div><div>Ultimately, what is measured are atomic emission spectra in terms of frequencies and wave lengths which through Planck's constant can be translated to energies expressed in electronvolts (or Joule). Nothing of the internal atomic structure (in terms of $e$ and $m$) enters into this discussion. <br /><br />Planck introduced $h$ in a statistical argument in 1900 long before atoms were known, Einstein picked up $h\nu$ in his 1905 article on photoelectricity, before atoms were known, and Schrödinger put $h$ into his equation in 1926 to describe atoms. This line of events supports the idea that Planck's constant $h$ is a convention without any universal significance.<br /><br />Understanding the real role of Planck's constant may help to <a href="http://claesjohnson.blogspot.se/2014/03/how-to-give-physical-meaning-of.html">give Schrödinger's equation a physical interpretation which is free from mysteries of "quantization" and statistics.</a> Versions of Schrödinger's equation based on an idea of <a href="http://claesjohnsonmathscience.wordpress.com/2013/09/13/deterministic-quantum-mechanics/">smoothed particle mechanics</a> then naturally present themselves, with $h$ acting as a smoothing parameter.<br /><br /><b>PS </b>Notice that the <a href="http://en.wikipedia.org/wiki/Fine-structure_constant">fine structure constant</a> $\alpha = \frac{e^2}{\bar hc}=\frac{1}{137}$ can be expressed as $\alpha =\frac{2}{c}\frac{a}{b}$ which shows that $\alpha$ relates $Bohr\, speed\, =\frac{a}{b}$ to the speed of light $c$. This relation is viewed to be fundamental, but why is hidden in mystery. </div></div>http://claesjohnson.blogspot.com/2014/04/universal-quantum-of-action-standard.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-848122673108979999Tue, 01 Apr 2014 17:39:00 +00002014-04-01T20:03:27.800+02:00climate scienceIPCCRoyal Swedish Academy of SciencesRoyal Swedish Academy of Sciences: CO2 Warming Can Prevent New Ice Age <div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-tVwyl-ySGAc/Uzr4iFFVoWI/AAAAAAAAiQs/0XpIeii7UoQ/s1600/ice-age-2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-tVwyl-ySGAc/Uzr4iFFVoWI/AAAAAAAAiQs/0XpIeii7UoQ/s1600/ice-age-2.jpg" height="240" width="320" /></a></div><br /><a href="http://www.kva.se/en/">The Royal Swedish Academy has issued a New Statement on the Scientific Basis of Climate Change</a> giving up its <a href="http://www.kva.se/Documents/Vetenskap_samhallet/Miljo_klimat/Yttranden/uttalande_klimat_en_090922.pdf">former support of the CO2 global warming alarmism of IPCC</a> and returning to the standpoint of the legendary foremost leading member of the Academy <a href="https://www.blogger.com/He%20later%20wrote%20V%C3%A4rldarnas%20utveckling%20(1906)%20(German:%20Das%20Werden%20der%20Welten%20[1907],%20English:%20Worlds%20in%20the%20Making%20[1908])%20directed%20at%20a%20general%20audience,%20where%20he%20suggested%20that%20the%20human%20emission%20of%20CO2%20would%20be%20strong%20enough%20to%20prevent%20the%20world%20from%20entering%20a%20new%20ice%20age,%20and%20that%20a%20warmer%20earth%20would%20be%20needed%20to%20feed%20the%20rapidly%20increasing%20population:">Svante Arrhenius</a>, Nobel Prize in Chemistry in 1903, who in <a href="http://books.google.com/books?id=1t45AAAAMAAJ&printsec=frontcover">Worlds in the Making</a> (1908) suggested that the human emission of CO2 would be strong enough to prevent the world from entering a new ice age, and that a warmer earth would be needed to feed the rapidly increasing population, of particular importance for the Swedish people under immediate threat of being covered under 1000 m solid ice:<br /><ul><li><i>Although the sea, by absorbing carbonic acid, acts as a regulator of huge capacity, which takes up about five-sixths of the produced carbonic acid, we yet recognize that the slight percentage of carbonic acid in the atmosphere may by the advances of industry be changed to a noticeable degree in the course of a few centuries. (p54)</i></li><li><i>Since, now, warm ages have alternated with glacial periods, even after man appeared on the earth, we have to ask ourselves: Is it probable that we shall in the coming geological ages be visited by a <b>new ice period that will drive us from our temperate countries into the hotter climates of Africa?</b> </i></li><li><i>There does not appear to be much ground for such an apprehension. The enormous combustion of coal by our industrial establishments suffices to increase the percentage of carbon dioxide in the air to a perceptible degree. (p61)</i></li><li><i><b>By the influence of the increasing percentage of carbonic acid in the atmosphere, we may hope to enjoy ages with more equable and better climates,</b> <b>especially as regards the colder regions of the earth</b>, ages when the earth will bring forth much more abundant crops than at present, for the benefit of rapidly propagating mankind. (p63)</i></li></ul><div>A major revision of Swedish and European climate politics is expected to follow from the U-turn in the scientific view of the Academy. The Swedish King says he is ready to act, and turn on the heat in his many huge poorly insulated royal castles.</div>http://claesjohnson.blogspot.com/2014/04/royal-swedish-academy-of-sciences-co2.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-2701302132691521784Tue, 01 Apr 2014 12:02:00 +00002014-04-01T14:31:06.708+02:00finite precision computationtheory of flightturbulenceNew Theory of Flight Presented to the World<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-_21O_tQ9gwI/UzqpvykTP3I/AAAAAAAAiQc/NhIZZ1Kpz00/s1600/bodywing.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-_21O_tQ9gwI/UzqpvykTP3I/AAAAAAAAiQc/NhIZZ1Kpz00/s1600/bodywing.jpg" height="240" width="320" /></a></div><a href="https://www.youtube.com/watch?v=TSxCFoBgxUw&list=PLE2FCB8CABFBC0965"><i>Simulation movie of airflow around a jumbojet in landing configuration at large angle of attack.</i></a><br /><br />The revised version of <a href="http://www.csc.kth.se/~jhoffman/Johan_Hoffman_KTH/Pub_files/kth-ctl-4044.pdf">New Theory of Flight</a> has now been submitted to Journal of Mathematical Fluid Mechanics for expected swift publication.<br /><br />This article together with my former students Johan Hoffman and Johan Jansson represents the summit of my scientific career as a combination of mathematical analysis and computation. The article asks for a major revision of text book aerodynamics and opens new roads to aerodynamic design. And it is not a joke…Finally, <a href="http://secretofflight.wordpress.com/">The Secret of Flight</a> can be revealed to humanity.<br /><br />Once the article has appeared in JMFM the new theory will be launched in a press release to media. Stay tuned….<br /><br />Here is the Summary of article:<br /><ul><li><i>The new theory shows that the miracle of flight is made possible by the combined effects of (i) incompressibility, (ii) slip boundary condition and (iii) 3d rotational slip separation, creating a flow around a wing which can be described as (iv) potential flow modified by 3d rotational separation. </i></li><li><i>The basic novelty of the theory is expressed in (iii) as a fundamental 3d flow phenomenon only recently discovered by advanced computation and analyzed mathematically, and thus is not present in the classical theory. </i></li><li><i>Finally, (iv) can be viewed as a realization in our computer age of Euler’s original dream to in his equations capture an unified theory of fluid flow. </i></li><li><i>The crucial conditions of (ii) a slip boundary condition and (iii) 3d rotational slip separation show to be safely satisfied by incompressible flow if the Reynolds number is larger than 106. For lower Reynolds numbers the new theory suggests analysis and design with focus on maintaining (ii) and (iii).</i></li></ul>http://claesjohnson.blogspot.com/2014/04/new-theory-of-flight-presented-to-world.htmlnoreply@blogger.com (Claes Johnson)1tag:blogger.com,1999:blog-1500584444083499721.post-7420445487774083057Mon, 31 Mar 2014 08:53:00 +00002014-04-01T07:51:44.264+02:00photoelectric effectPlanck's constantPlanck's Constant = Human Convention Standard Frequency vs Electronvolt<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-sNp9JRBvzVs/UzksWWyHe8I/AAAAAAAAiQM/Nr2c8wJXaLw/s1600/double-standards.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-sNp9JRBvzVs/UzksWWyHe8I/AAAAAAAAiQM/Nr2c8wJXaLw/s1600/double-standards.png" height="306" width="320" /></a></div><br />The recent posts on the <a href="http://claesjohnson.blogspot.se/search/label/photoelectric%20effect">photoelectric effect</a> exhibits <a href="http://claesjohnson.blogspot.se/2014/03/why-same-universal-quantum-of-action-h.html">Planck's constant $h$ as a conversion standard </a>between the units of light <i>frequency</i> $\nu$ in $Hz\, = 1/s$ as periods per second and<i> electronvolt </i>($eV$<i>), </i>expressed in Einstein's law of photoelectricity:<br /><ul><li>$h\times (\nu -\nu_0) = eU$, </li></ul><div>where $\nu_0$ is smallest frequency producing a photoelectric current, $e$ is the charge of an electron and $U$ the stopping potential in Volts $V$ for which the current is brought to zero for $\nu > \nu_0$. Einstein obtained, referring to Lenard's 1902 experiment with $\nu -\nu_0 = 1.03\times 10^{15}\, Hz$ corresponding to the ultraviolet limit of the solar spectrum and $U = 4.3\, V$ </div><div><ul><li>$h = 4.17\times 10^{-15} eVs$</li></ul><div>to be compared with the <a href="http://en.wikipedia.org/wiki/Planck_constant">reference value</a> $4.135667516(91)\times 10^{-15}\, eV$ used in Planck's radiation law. We see that here $h$ occurs as a conversion standard between Hertz $Hz$ and electronvolt $eV$ with </div><div><ul><li>$1\, Hz = 4.17\times 10^{-15}\, eV$ </li></ul></div></div><div>To connect to quantum mechanics, we recall that Schrödinger's equation is normalized with $h$ so that the first ionization energy of Hydrogen at frequency $\nu = 3.3\times 10^{15}\, Hz$ equals $13.6\, eV$, to be compared with $3.3\times 4.17 = 13.76\, eV$ corresponding to Lenard's photoelectric experiment. </div><div><br /></div><div>We understand that Planck's constant $h$ can be seen as a conversion standard between light energy measured by frequency and electron energy measured in electronvolts. The value of $h$ can then be determined by photoelectricity and thereafter calibrated into Schrödinger's equation to fit with ionization energies as well as into Planck's law as a parameter in the high-frequency cut-off (without a very precise value). The universal character of $h$ as a smallest unit of action is then revealed to simply be a human convention standard without physical meaning. What a disappointment!</div><div><br /></div><div>This fits with the article <a href="http://arxiv.org/abs/1203.5557">Quantum Theory without Planck's Constant ny John P. Ralston:</a></div><ul><li><i>Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention.</i></li></ul><div>Finally: It is natural to view frequency $\nu$ as a measure of energy per wavelength, since radiance as energy per unit of time scales with $\nu\times\nu$ in accordance with Planck's law, which can be viewed as $\nu$ wavelengths each of energy $\nu$ passing a specific location per unit of time. We thus expect to find a linear relation between frequency and electronvolt as two energy scales: If 1 € (Euro) is equal to 9 Skr (Swedish Crowns), then 10 € is equal to 90 Skr.</div><div><br /></div>http://claesjohnson.blogspot.com/2014/03/plancks-constant-human-convention.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-4558643811096326467Sun, 30 Mar 2014 20:10:00 +00002014-03-30T22:13:57.196+02:00Einsteinmillikanphotoelectric effectPhotoelectricity: Millikan vs Einstein<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-gRAZb8cQxJc/UzhQjKhnFoI/AAAAAAAAiPs/4VBwKVNQMzI/s1600/photo-electric-effect.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-gRAZb8cQxJc/UzhQjKhnFoI/AAAAAAAAiPs/4VBwKVNQMzI/s1600/photo-electric-effect.png" height="212" width="320" /></a></div><a href="http://1.bp.blogspot.com/-ZwJ2KuuMd9A/UzhtwHrotZI/AAAAAAAAiP8/FVvfyM0PQA4/s1600/Portrait_of_Robert_Andrews_Millikan_(1868-1953),_Physicist.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-ZwJ2KuuMd9A/UzhtwHrotZI/AAAAAAAAiP8/FVvfyM0PQA4/s1600/Portrait_of_Robert_Andrews_Millikan_(1868-1953),_Physicist.jpg" height="200" width="126" /></a><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />The American physicist <a href="http://en.wikipedia.org/wiki/Robert_Andrews_Millikan">Robert Millikan</a> received the Nobel Prize in 1923 for (i) experimental determination of the charge $e$ of an electron and (ii) experimental verification of Einstein's law of photoelectricity awarded the 1921 Prize.<br /><br />Millikan started out his experiments on photoelectricity with the objective of disproving Einstein's law and in particular the underlying idea of light quanta. To his disappointment Millikan found that according to his experiments Einstein's law in fact was valid, but he resisted by questioning the conception of light-quanta even in his Nobel lecture: <br /><ul><li><i>In view of all these methods and experiments the general validity of Einstein’s equation is, I think, now universally conceded, and to that extent <b>the reality of Einstein’s light-quanta may be considered as experimentally established. </b></i></li><li><i>But the conception of <b>localized light-quanta </b>out of which Einstein got his equation must still be regarded <b>as far from being established. </b></i></li><li><i>Whether the mechanism of interaction between ether waves and electrons has its seat in the unknown conditions and laws existing within the atom, or is to be looked for primarily in the essentially corpuscular Thomson-Planck-Einstein conception as to the nature of radiant energy is the <b>all-absorbing uncertainty upon the frontiers of modern Physics.</b></i></li></ul>Millikan's experiments consisted in subjecting a metallic surface to light of different frequencies $\nu$ and measuring the resulting photovoltic current determining a smallest frequency $\nu_0$ producing a current and (negative) stopping potential required to bring the current to zero for frequencies $\nu >\nu_0$. Millikan thus measured $\nu_0$ and $V$ for different frequencies $\nu > \nu_0$ and found a linear relationship between $\nu -\nu_0$ and $V$, which he expressed as <br /><ul><li>$\frac{h}{e}(\nu -\nu_0)= V$, </li></ul>in terms of the charge $e$ of an electron which he had already determined experimentally, and the constant $h$ which he determined to have the value $6.57\times 10^{-34}$. The observed linear relation between $\nu -\nu_0$ and $V$ could then be expressed as<br /><ul><li>$h\nu = h\nu_0 +eV$ </li></ul><div>which Millikan had to admit was nothing but Einstein's law with $h$ representing Planck's constant. </div><div><br /></div><div>But Millikan could argue that, after all, the only thing he had done was to establish a macroscopic linear relationship between $\nu -\nu_0$ and $V$, which in itself did not give undeniable evidence of the existence of microscopic light-quanta. What Millikan did was to measure the current for different potentials of the plus pole receiving the emitted electrons under different exposure to light and thereby discovered a linear relationship between frequency $\nu -\nu_0$ and stopping potential $V$ independent of the intensity of the light and properties of the metallic surface. </div><div><br /></div><div>By focussing on frequency and stopping potential Millikan could make his experiment independent of the intensity of incoming light and of the metallic surface, and thus capture a conversion between light energy and electron energy of general significance. </div><div><br /></div><div>But why then should stopping potential $V$ scale with frequency $\nu - \nu_0$, or $eV$ scale with frequency $h(\nu - \nu_0)$? Based on the analysis on <a href="http://computationalblackbody.wordpress.com/">Computational Blackbody Radiation</a> the answer would be that $h\nu$ represents a threshold energy for emission of radiation in Planck's radiation law and $eV$ represents a threshold energy for emission of electrons, none of which would demand light quanta.</div><div><br /></div><div> </div><div></div>http://claesjohnson.blogspot.com/2014/03/photoelectricity-millikan-vs-einstein.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-3492420151708366605Sat, 29 Mar 2014 09:41:00 +00002014-03-31T15:01:58.418+02:00black body radiationEinsteintheory of relativityEinstein: Genius by Definition of Law of Photoelectricity<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-Mbl4T12OIMY/UzV59BCW75I/AAAAAAAAiPU/JM4hP4YMmjw/s1600/pelec.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-Mbl4T12OIMY/UzV59BCW75I/AAAAAAAAiPU/JM4hP4YMmjw/s1600/pelec.gif" height="200" width="320" /></a></div><br />Einstein opened to the new brave world of modern physics in two articles in his 1905 annus mirabilis, one giving humanity a breath-taking entirely new view on space and time through the special theory of relativity, and the other on photoelectricity introducing light quanta carried by light particles later named photons preparing the development of quantum mechanics.<br /><br />Einstein's science is difficult to understand because it is never clear if the basic postulates of his theories are definitions without physics content, that is tautologies which are true by semantic construction, or if they are statements about physics which may be true or not true depending on realities.<br /><br />The special theory of relativity is based on a postulate that the speed of light (in vacuum) is the same for all observers independent of motion with constant velocity. With the new definition of length scale of a lightsecond to be used by all observers, the speed of light for all observers is equal to one lightsecond per second and thus simply a definition or agreement between different observers.<br /><br />Yet physicists by training firmly believe that the speed light <b>is </b>constant as physical fact behind the definition. For Einstein and all modern physicists following in his footsteps, definition and statement about physics come together into one postulate of relativity which can flip back and forth between definition and statement about physics and thereby ruin any attempt to bring clarity in a scientific discussion. Einstein played this game masterfully by formulating special relativity as a prescription or definition or dictate that different observers are to coordinate observations by Lorentz transformation. A dictate cannot be false. It can only be disastrous.<br /><br />Let us now check if Einstein's law of photoelectricity, which gave him the 1921 Nobel Prize in Physics is also a definition and thus empty of physics content. The law takes the form<br /><ul><li>$h(\nu -\nu_0) =eV$, </li></ul><div>which expresses an energy balance for one electron of charge $e$ being ejected from a certain metallic surface by incoming light of frequency $\nu$ with $\nu_0$ the smallest frequency for which any electrons are ejected and $V$ is the potential required to stop a current of electrons for $\nu > \nu_0$. The relation can be written </div><div><ul><li>$h\nu = h\nu_0 + eV$</li></ul><div>expressing a balance of incoming energy $h\nu$ as release energy $h\nu_0$ and electron (kinetic) energy after ejection $eV$ measured by the stopping potential $V$. </div><div><br /></div><div>There is one more parameter in the energy balance and that is $h$, which is Planck's constant.</div><div>Measuring the stopping potential $V$ for light of different frequencies $\nu$ including determining $\nu_0$ and finding a linear relationship between $\nu -\nu_0$ and $V$, would then allow the determination of a value of $h$ making the law true. This shows to work and is in fact a standard way of experimentally determining the value of Planck's constant $h$. </div><div><br /></div><div>In this perspective Einstein's law of photoelectricty comes out as a definition through which the value of $h$ is determined, which effectively corresponds to a conversion standard from the dimension of Joule of $h\nu$ as light energy to the dimension of electronvolt of $eV$ as electron energy, which says nothing about the existence of discrete packets of energy or light quanta. </div><div><br /></div><div>The physics enters only in the assumed <a href="http://claesjohnson.blogspot.se/2014/03/plancks-constant-human-convention.html">linear relation between $\nu$ and $V$</a>. From the derivation of Planck's law on <a href="http://computationalblackbody.wordpress.com/">Computational Blackbody Radiation</a> it is clear that $h\nu$ in the high-frequency cut-off factor $\frac{\alpha}{\exp(\alpha )-1}$ with $\alpha=\frac{h\nu}{kT}$ in Planck's law, acts as a threshold value, that is as a certain quantity $h\nu$ of energy per atomic energy $kT$ required for emission of radiation. This strongly suggests a linear relationship between $\nu$ and $V$ since $V$ also serves as a threshold.</div><div><br /></div><div>We thus conclude that the general form of Einstein's law of photoelectricity as a linear relationship in an energy balance for each electron between the frequency of incoming light $\nu$ and the stopping potential $V$, naturally comes out from the role of $h\nu$ as threshold value modulo $kT$. </div><div><br /></div><div>Once the linear relationship is postulated as physics, the value of $h$ to make the law fit with observation is a matter of definition as effectively determining energy conversion between light energy as $h\nu$ in Joule and electron energy as $eV$ in electronvolt. The quantity $h\nu$ is then a threshold value and not a discrete packet of energy and $\frac{h}{e}$ sets an exchange rate between two different currencies of frequency and stopping potential.</div><div><br /></div><div>In other words, Einstein received the Nobel Prize for formulating a definition almost empty of physics content. It shows that the concept of a photon as a light particle carrying the discrete packet of energy $h\nu$ is also a definition empty of physics content. </div><div><br /></div><div>Another aspect emerging from the above analysis is an expected (<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2894105/">and observed</a>) temperature dependence of photoelectricity, which is not expressed in Einstein's law. The release energy is expected to depend on temperature and there is no reason to expect that the stopping potential should compensate so as to make determination of $h$ by photoelectricity independent of temperature. What is needed is then an extension of Einstein's law to include dependence on temperature.<br /><br />It remains to sort out the appearance of the parameter $h$ (determined by photoelectricity) in Planck's radiation law and in Schrödinger's equation, which has already been touched in a <a href="http://claesjohnson.blogspot.se/2014/03/why-same-universal-quantum-of-action-h.html">previous post</a>, but will be addressed in more detail in an upcoming post.<br /><br />The advantage of using definitions as postulates about physics is that you can be absolutely sure that your physics is correct (but empty). This aspect came out when Einstein confronted with an observation claimed to contradict special relativity, with absolute confidence could say that the observation was wrong:<br /><ul><li>I<i>f the facts don't fit the theory, change the facts.</i></li><li><i>Whether you can observe a thing or not depends on the theory which you use.</i></li><li><i>It is the theory which decides what we can observe.</i></li><li><i>What I'm really interested in is whether God could have made the world in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all.</i></li></ul><div>In this form of physics what you see depends on the glasses you put on and not on what you are looking at. In this form of physics the observer decides if Schödinger's cat is dead or alive by the mere act of looking at the cat, and not the cat itself even if it has nine lives.<br /><br /></div><div></div><div><b>PS1 </b>To view $h\nu$ as a packet of energy carried by a photon is non-physical and confusing for several reasons, one being that radiation intensity as energy per unit of time scales as $\nu^2$ and thus the scaling as $\nu$ of photon energy is compensated by a flow of photons per unit time scaling as $\nu$, with each photon occupying a half wave length.<b> </b><br /><b><br /></b><b>PS2 </b>If now Einstein is a genius by definition, there is as little reason to question that as questioning that there are 100 centimeters on a meter.<br /><br /><br /></div></div><div></div></div>http://claesjohnson.blogspot.com/2014/03/einstein-genius-by-definition-of-law-of.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-4952059396118636517Thu, 27 Mar 2014 13:41:00 +00002014-03-29T13:53:20.463+01:00quantum mechanicsSchrödinger's equationHow to Make Schrödinger's Equation Physically Meaningful + Computable <div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-dtFBClMx1T8/UzQpzPnw1jI/AAAAAAAAiO4/SiLP3LPkk6U/s1600/sch1.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-dtFBClMx1T8/UzQpzPnw1jI/AAAAAAAAiO4/SiLP3LPkk6U/s1600/sch1.gif" height="222" width="400" /></a></div><br />The derivation of Schrödinger's equation as the basic mathematical model of quantum mechanics is hidden in mystery: The idea is somehow to start considering a classical Hamiltonian $H(q,p)$ as the total energy equal to the sum of kinetic and potential energy:<br /><ul><li>$H(q,p)=\frac{p^2}{2m} + V(q)$,</li></ul><div>where $q(t)$ is position and $p=m\dot q= m\frac{dq}{dt}$ momentum of a moving particle of mass $m$, and make the formal ad hoc substitution with $\bar h =\frac{h}{2\pi}$ and $h$ Planck's constant:</div><div><ul><li>$p = -i\bar h\nabla$ with formally $\frac{p^2}{2m} = - \frac{\bar h^2}{2m}\nabla^2 = - \frac{\bar h^2} {2m}\Delta$, </li></ul><div>to get Schrödinger's equation in time dependent form </div></div><div><ul><li>$ i\bar h\frac{\partial\psi}{\partial t}=H\psi $,</li></ul><div>with now $H$ a differential operator acting on a wave function $\psi (x,t)$ with $x$ a space coordinate and $t$ time, given by </div><ul><li>$H\psi \equiv -\frac{\bar h^2}{2m}\Delta \psi + V\psi$,</li></ul><div>where now $V(x)$ acts as a given potential function. As a time independent eigenvalue problem Schrödinger's equation then takes the form:</div></div><div><ul><li> $-\frac{\bar h^2}{2m}\Delta \psi + V\psi = E\psi$,</li></ul><div>with $E$ an eigenvalue, as a stationary value for the total energy</div></div><div><ul><li>$K(\psi ) + W(\psi )\equiv\frac{\bar h^2}{2m}\int\vert\nabla\psi\vert^2\, dx +\int V\psi^2\, dx$, </li></ul><div>as the sum of <i>kinetic energy</i> $K(\psi )$ and potential energy $W(\psi )$, under the normalization $\int\psi^2\, dx = 1$. The <i>ground state </i>then corresponds to minimal total energy,<br /><br />We see that the total energy $K(\psi ) + W(\psi)$ can be seen as smoothed version of $H(q,p)$ with<br /><ul><li>$V(q)$ replaced by $\int V\psi^2\, dx$,</li><li>$\frac{p^2}{2m}=\frac{m\dot q^2}{2}$ replaced by $\frac{\bar h^2}{2m}\int\vert\nabla\psi\vert^2\, dx$,</li></ul><div>and Schrödinger's equation as expressing stationarity of the total energy as an analog the classical equations of motion expressing stationarity of the Hamiltonian $H(p,q)$ under variations of the path $q(t)$. </div><div><br /></div><div>We conclude that Schrödinger's equation for a one electron system can be seen as a smoothed version of the equation of motion for a classical particle acted upon by a potential force, with Planck's constant serving as a smoothing parameter. </div><div><br /></div><div>Similarly it is natural to consider smoothed versions of classical many-particle systems as quantum mechanical models resembling Hartree variants of Schrödinger's equation for many-electrons systems, that is <a href="http://claesjohnsonmathscience.wordpress.com/2013/09/13/deterministic-quantum-mechanics/">quantum mechanics as smoothed particle mechanics</a>, thereby (maybe) reducing some of the mystery of Schrödinger's equation and opening to computable quantum mechanical models.<br /><br />We see Schrödinger's equation arising from a Hamiltonian as total energy kinetic energy + potential energy, rather that from a Lagrangian as kinetic energy - potential energy. The reason is a confusing terminology with $K(\psi )$ named kinetic energy even though it does not involve time differentiation, while it more naturally should occur in a Lagrangian as a form of the potential energy like elastic energy in classical mechanics. </div></div></div>http://claesjohnson.blogspot.com/2014/03/how-to-give-physical-meaning-of.htmlnoreply@blogger.com (Claes Johnson)12tag:blogger.com,1999:blog-1500584444083499721.post-1642073797860815777Wed, 26 Mar 2014 12:54:00 +00002014-03-26T14:03:42.223+01:00quantum mechanicsNew Paradigm of Computational Quantum Mechanics vs ESS <div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-si9XJ_d3ux0/UzLKpkHk1HI/AAAAAAAAiN8/PyNTmJKayjs/s1600/ESS-507.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-si9XJ_d3ux0/UzLKpkHk1HI/AAAAAAAAiN8/PyNTmJKayjs/s1600/ESS-507.jpg" height="226" width="320" /></a></div><a href="http://europeanspallationsource.se/why-ess">ESS as European Spallation Source</a> is a €3 billion projected research facility captured by clever Swedish politicians to be allocated to the plains outside the old university town Lund in Southern Sweden with start in 2025: <i>Neutrons are excellent for probing materials on the molecular level – everything from motors and medicine, to plastics and proteins. ESS will provide around 30 times brighter neuutron beams than existing facilities today. The difference between the current neutron sources and ESS is something like the difference between taking a picture in the glow of a candle, or doing it under flash lighting.</i><br /><i><br /></i>Quantum mechanics was invented in the 1920s under limits of pen and paper computation but allowing limitless theory thriving in Hilbert spaces populated by multidimensional wave functions described by fancy symbols on paper. Lofty theory and sparse computation was compensated by inflating the observer role of the physicist to a view that only physics observed by a physicist was real physics, with extra support from a conviction that the life or death of Schrödinger's cat depended more on the observer than on the cat and that supercolliders are very expensive. The net result was (i) uncomputable limitless theory combined with (ii) unobservable practice as the essence of the Copenhagen Interpretation filling text books.<br /><br />Today the computer opens to a change from impossibility to possibility, but this requires a fundamental change of the mathematical models from uncomputable to <a href="http://claesjohnsonmathscience.wordpress.com/2013/09/13/deterministic-quantum-mechanics/">computable non-linear systems of 3d of Hartree-Schrödinger equations (HSE)</a> or Density Functional Theory (DFT). This brings theory and computation together into a new paradigm of Computational Quantum Mechanics CQM shortly summarized as follows: <br /><ol><li>Experimental inspection of microscopic physics difficult/impossible.</li><li>HSE-DFT for many-particle systems are solvable computationally. </li><li>HSE-DFT simulation allows detailed inspection of microscopics.</li><li>Assessment of HSE simulations can be made by comparing macroscopic outputs with observation. </li></ol><div>The linear multidimensional Schrödinger equation has no meaning in CQM and a new foundation is asking to be developed. The role of observation in the Copenhagen Interpretation is taken over by computation in CQM: Only computable physics is real physics, at least if <a href="http://claesjohnsonmathscience.wordpress.com/">physics is a form of analog computation,</a> which may well be the case. The big difference is that anything computed can be inspected and observed, which opens to non-destructive testing with only limits set by computational power.</div><div><br /></div><div>The Large Hadron Collider (LHC) and the projected neutron collider <a href="http://europeanspallationsource.se/">European Spallation Source (ESS)</a> in Lund in Sweden represent the old paradigm of smashing to pieces the fragile structure under investigation and as such may well be doomed.</div>http://claesjohnson.blogspot.com/2014/03/new-paradigm-of-computational-quantum.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-8143912095892713103Tue, 25 Mar 2014 13:20:00 +00002014-03-26T09:24:20.226+01:00finite precision computationquantum mechanicsturbulenceFluid Turbulence vs Quantum Electrodynamics<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-cUmoR97xAls/UzF_FU6exxI/AAAAAAAAiNk/csYZPoxIrDQ/s1600/lamb.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-cUmoR97xAls/UzF_FU6exxI/AAAAAAAAiNk/csYZPoxIrDQ/s1600/lamb.jpg" height="320" width="217" /></a></div><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19px;">Horace Lamb (1849 - 1934) author of the classic text <a href="https://archive.org/details/hydrodynamics02lambgoog">Hydrodynamics</a>: </span><i>It is asserted that the velocity of a body not acted on by any force will be constant in magnitude and direction, whereas the only means of ascertaining whether a body is, or is not, free from the action of force is by observing whether its velocity is constant.</i><br /><br />There is famous quote by the British applied mathematician <a href="http://en.wikipedia.org/wiki/Horace_Lamb">Horace Lamb</a> summarizing the state of classical fluid mechanics and the new quantum mechanics in 1932 as follows:<br /><div><ul><li><i>I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is <a href="http://en.wikipedia.org/wiki/Quantum_electrodynamics">quantum electrodynamics</a>, and the other is the turbulent motion of <a href="http://en.wikipedia.org/wiki/Fluid">fluids</a>. And about the former I am rather optimistic.</i></li></ul></div><div>Concerning the turbulent motion of fluids I am happy to report that this matter is now largely resolved by computation, as made clear in the article New Theory of Flight soon to be delivered for publication in Journal of Mathematical Fluid Mechanics, with lots of supplementary material on <a href="http://secretofflight.wordpress.com/">The Secret of Flight.</a> This gives good hope that the other problem of quantum electrodynamics can likewise be unlocked by viewing <a href="http://claesjohnsonmathscience.wordpress.com/">The World as Computation</a>:<br /><ul><li><i>In a time of turbulence and change, it is more true than ever that knowledge is power. </i>(JFK)</li></ul><div><br /></div></div>http://claesjohnson.blogspot.com/2014/03/fluid-turbulence-vs-quantum.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-7585976081765084915Tue, 25 Mar 2014 08:02:00 +00002014-03-25T12:17:00.595+01:00black body radiationPlanck's constantquantum mechanicsQuantum Physics as Digital Continuum Physics<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-m4C_91SR0cQ/UzE3_Hp2V6I/AAAAAAAAiNE/5NGtNvN7NEQ/s1600/Seageropen.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-m4C_91SR0cQ/UzE3_Hp2V6I/AAAAAAAAiNE/5NGtNvN7NEQ/s1600/Seageropen.jpg" height="232" width="320" /></a></div><br />Quantum mechanics was born in 1900 in Planck's theoretical derivation of a modification of Rayleigh-Jeans law of blackbody radiation based on statistics of discrete "quanta of energy" of size $h\nu$, where $\nu$ is frequency and $h =6.626\times 10^{-34}\, Js$ is Planck's constant.<br /><br />This was the result of a long fruitless struggle to explain the observed spectrum of radiating bodies using deterministic eletromagnetic wave theory, which ended in Planck's complete surrender to statistics as the only way he could see to avoid the "ultraviolet catastrophe" of infinite radiation energies, in a return to the safe haven of his dissertation work in 1889-90 based on Boltzmann's statistical theory of heat.<br /><br />Planck described the critical step in his analysis of a radiating blackbody as a discrete collection of resonators as follows:<br /><ul><li><i>We must now give the distribution of the energy over the separate resonators of each frequency, first of all the distribution of the energy $E$ over the $N$ resonators of frequency . If E is considered to be a continuously divisible quantity, this distribution is possible in infinitely many ways. </i></li><li><i>We consider, however this is the most essential point of the whole calculation $E$ to be composed of a well-defined number of equal parts and use thereto the constant of nature $h = 6.55\times 10^{-27}\, erg sec$. This constant multiplied by the common frequency of the resonators gives us the energy element in $erg$, and dividing $E$ by we get the number $P$ of energy elements which must be divided over the $N$ resonators. </i></li><li><i>If the ratio thus calculated is not an integer, we take for $P$ an integer in the neighbourhood. It is clear that the distribution of P energy elements over $N$ resonators can only take place in a finite, well-defined number of ways.</i></li></ul><div>We here see Planck introducing a <i>constant of nature</i> $h$, later referred to as <i>Planck's constant,</i> with a corresponding smallest<i> quanta of energy</i> $h\nu$ for radiation (light) of frequency $\nu$. </div><div><br /></div><div>Then Einstein entered in 1905 with a law of photoelectricity with $h\nu$ viewed as the energy of a <i>light quanta</i> of frequency $\nu$ later named<i> photon</i> and crowned as an <i>elementary particle.</i></div><div><i><br /></i></div><div>Finally, in 1926 Schrödinger formulated a wave equation for involving a formal momentum operator $-ih\nabla$ including Planck's constant $h$, as the birth of quantum mechanics, as the incarnation of modern physics based on postulating that microscopic physics is</div><div><ol><li>"quantized" with smallest quanta of energy $h\nu$,</li><li>indeterministic with discrete quantum jumps obeying laws of statistics.</li></ol><div>However, microscopics based on statistics is contradictory, since it requires microscopics of microscopics in an endeless regression, which has led modern physics into an impasse of ever increasing irrationality into manyworlds and string theory as expressions of scientific regression to microscopics of microscopics. The idea of "quantization" of the microscopic world goes back to the atomism of Democritus, a primitive scientific idea rejected already by Aristotle arguing for the continuum, which however combined with modern statistics has ruined physics. <br /><br /></div><div>But there is another way of avoiding the ultraviolet catastrophe without statistics, which is presented on <a href="http://computationalblackbody.wordpress.com/">Computational Blackbody Radiation</a> with physics viewed as <a href="http://claesjohnsonmathscience.wordpress.com/">analog finite precision computation which can be modeled as digital computational simulation</a>. </div><div><br /></div><div>This is physics governed by deterministic wave equations with solutions evolving in analog computational processes, which can be simulated digitally. This is physics without microscopic games of roulette as rational deterministic classical physics subject only to natural limitations of finite precision computation.</div><div><br /></div><div>This opens to a view of quantum physics as digital continuum physics which can bring rationality back to physics. It opens to explore an analog physical atomistic world as a digital simulated world where the digital simulation reconnects to analog microelectronics. It opens to explore physics by exploring the digital model, readily available for inspection and analysis in contrast to analog physics hidden to inspection.<br /><br />The microprocessor world is "quantized" into discrete processing units but it is a deterministic world with digital output:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-3E1a86DdjLY/UzFLyTUzapI/AAAAAAAAiNU/_b2ocoJtekU/s1600/4004ff.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-3E1a86DdjLY/UzFLyTUzapI/AAAAAAAAiNU/_b2ocoJtekU/s1600/4004ff.jpg" height="239" width="320" /></a></div><br /></div><div><br /></div></div><div><br /></div>http://claesjohnson.blogspot.com/2014/03/quantum-physics-as-digital-continuum.htmlnoreply@blogger.com (Claes Johnson)1tag:blogger.com,1999:blog-1500584444083499721.post-7522796862570775483Mon, 24 Mar 2014 14:39:00 +00002014-03-24T15:39:09.296+01:00principle of least actionHollywood vs Principle of Least Action The fictional character of the <a href="http://claesjohnson.blogspot.se/search/label/principle%20of%20least%20action">Principle of Least Action</a> viewed to serve a fundamental role in physics, can be understood by comparing with making movies:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-j2h8Ktc7wuA/UzA_CLDaS1I/AAAAAAAAiMw/8S4E3KfaJmg/s1600/movie-clapper-board-with-action-call-in-3d-and-on-white.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-j2h8Ktc7wuA/UzA_CLDaS1I/AAAAAAAAiMw/8S4E3KfaJmg/s1600/movie-clapper-board-with-action-call-in-3d-and-on-white.jpg" height="243" width="320" /></a></div><br />The dimension of action as<i> energy x time </i>comes out very naturally in movie making as <i>actor energy x length of the scene. </i>However, outside Hollywood a quantity of dimension <i>energy x time </i>is questionable from physical point of view, since there seems to be no natural movie camera which can record and store such a quantity. http://claesjohnson.blogspot.com/2014/03/hollywood-vs-principle-of-least-action.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-6129282285866813515Sun, 23 Mar 2014 18:35:00 +00002014-03-27T18:59:33.115+01:00black body radiationphotoelectric effectphotonsPlanck's constantPlanck's Lawquantum mechanicsWhy the Same Universal Quantum of Action $h$ in Radiation, Photoelectricity and Quantum Mechanics? <div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-vPYPqthySjk/Uy8oq7qC4bI/AAAAAAAAiMc/M8WKNonshEA/s1600/quote-vedanta-teaches-that-consciousness-is-singular-all-happenings-are-played-out-in-one-universal-erwin-schrodinger-265342.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-vPYPqthySjk/Uy8oq7qC4bI/AAAAAAAAiMc/M8WKNonshEA/s1600/quote-vedanta-teaches-that-consciousness-is-singular-all-happenings-are-played-out-in-one-universal-erwin-schrodinger-265342.jpg" height="187" width="400" /></a></div><br />Planck's constant $h$ as <a href="http://en.wikipedia.org/wiki/Planck_constant">The Universal Quantum of Action</a> was <a href="http://www.chemteam.info/Chem-History/Planck-1901/Planck-1901.html">introduced by Planck in 1900 </a>as a mathematical statistical trick to supply the classical Rayleigh-Jeans radiation law $I(\nu ,T)=\gamma T\nu^2$ with a high-frequency cut-off factor $\theta (\nu ,T)$ to make it fit with observations including Wien's displacement law, where<br /><ul><li>$\theta (\nu ,T) =\frac{\alpha}{\exp(\alpha )-1}$,</li><li>$\alpha =\frac{h\nu}{kT}$, </li></ul><div>$\nu$ is frequency, $T$ temperature in Kelvin $K$ and $k =1.38066\times 10^{-23}\, J/K$ is Boltzmann's constant and $\gamma =\frac{2k}{c}$ with $c\, m/s$ the speed of light in vaccum. Planck then determined $h$ from experimental radiation spectra to have a value of $6.55\times 10^{-34} Js$, as well as Boltzmann's constant to be $1.346\times 10^{-23}\, J/K$ with $\frac{h}{k}= 4.87\times 10^{-11}\, Ks$ as the effective parameter in the cut-off. </div><div><br /></div><div>Planck viewed $h$ as a fictional mathematical quantity without real physical meaning, with $h\nu$ a fictional mathematical quantity as a smallest packet of energy of a wave of frequency $\nu$, but in 1905 the young ambitious Einstein suggested an energy balance for photoelectricity of the form </div><div><ul><li>$h\nu = W + E$,</li></ul><div>with $W$ the energy required to release one electron from a metallic surface and E the energy of a released electron with $h\nu$ interpreted as the energy of a <i>light photon</i> of frequency $\nu$ as a discrete lump of energy. Since the left hand side $h\nu$ in this law of photoelectricity was determined by the value of $h$ in Planck's radiation law, a new energy measure for electrons of <i>electronvolt </i>was defined by the relation $W + E =h\nu$. As if by magic the same Universal Quantum of Action $h$ then appeared to serve a fundamental role in both radiation and photoelectricity.<br /><br />What a wonderful magical coincidence that the energy of a light photon of frequency $\nu$ showed to be exactly $h\nu \, Joule$! In one shot Planck's fictional smallest quanta of energy $h\nu$ in the hands of the young ambitious Einstein had been turned into a reality as the energy of a light photon of frequency $h\nu$, and of course because a photon carries a definite packet of energy a photon must be real. Voila!</div></div><br /><div><div>In 1926 Planck's constant $h$ showed up again in a new context, now in Schrödinger's equation</div></div><div><ul><li>$-\frac{\bar h^2}{2m}\Delta\psi = E\psi$</li></ul></div><div> with the formal connection </div><div><ul><li>$p = -i\bar h \nabla$ with $\bar h =\frac{h}{2\pi}$,</li><li>$\frac{\vert p\vert^2}{2m} = E$, </li></ul><div>as a formal analog of the classical expression of kinetic energy $\frac{\vert p\vert ^2}{2m}$ with $p=mv$ momentum, $m$ mass and $v$ velocity.</div></div><div><br />Planck's constant $h$ originally determined to make theory fit with observations of radiation spectra and then by Planck in 1900 canonized as <i>The Universal Quantum of Action</i>, thus in 1905 served to attribute the energy $h\nu$ to the new fictional formal quantity of a<i> photon</i> of frequency $\nu$ . In 1926 a similar formal connection was made in the formulation of Schrödinger's wave equation. </div><div><br /></div><div>The result is that the same Universal Quantum of Action $h$ by all modern physicists is claimed to play a fundamental role in both (i) radiation, (ii) photolelectricity and (iii) quantum mechanics of the atom. This is taken as an expression of a deep mystical one-ness of physics which only physicists can grasp, while it in fact it is a play with definitions without mystery, where $h$ appears as a parameter in a high-frequency cut-off factor in Planck's Law, or rather in the combination $\hat h =\frac{h}{k}$, and then is transferred into (ii) and (iii) by definition. Universality can this way be created by human hands by definition. The power of thinking has no limitations, or cut-off.</div><div><br /></div><div>No wonder that Schrödinger had lifelong interest in the Vedanta philosophy of Hinduism "played out on one universal consciousness".<br /><br />But Einstein's invention of the photon as light quanta in 1905 haunted him through life and approaching the end in 1954, he confessed:<br /><ul><li><i>All these fifty years of conscious brooding have brought me no nearer to the answer to the question, "What are light quanta?" Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. </i></li></ul>Real physics always shows up to be more interesting than fictional physics, cf. <a href="http://books.google.se/books?id=5kcdpa3Qhj8C&lpg=PP1&pg=PP1&redir_esc=y#v=onepage&q&f=false">Dr Faustus ofd Modern Physics.</a><br /><br /><b>PS </b>Planck's constant $h$ is usually measured by (ii) and is then transferred to (i) and (iii) by ad hoc definition.</div>http://claesjohnson.blogspot.com/2014/03/why-same-universal-quantum-of-action-h.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-2873346770811911577Sun, 23 Mar 2014 11:01:00 +00002014-03-23T12:03:42.100+01:00quantum mechanicsuncertainty principleThe Torturer's Dilemma vs Uncertainty Principle vs Computational Simulation <div><div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-3sn0Exg7mpY/Uy6-PASLaaI/AAAAAAAAiME/3natoT5on70/s1600/Torture_Chamber_of_the_Inquisition_from_Moore's_Martyrology.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-3sn0Exg7mpY/Uy6-PASLaaI/AAAAAAAAiME/3natoT5on70/s1600/Torture_Chamber_of_the_Inquisition_from_Moore's_Martyrology.png" height="275" width="400" /></a></div><br />Bohr expressed in Light and Life (1933) the Thantalogical Principle stating that to check out the nature of something, one has to destroy that very nature, which we refer to as <a href="http://www.walternelson.com/dr/torture">The Torturer's Dilemma:</a></div><div><ul><li><i>We should doubtless kill an animal if we tried to carry the investigations of its organs so far that we could describe the role played by single atoms in vital functions. In every experiment on living organisms, there must remain an uncertainty as regards the physical conditions to which they are subjected…the existence of life must be considered as an elementary fact that cannot be explained, but must be taken as a starting point in biology, in a similar way as the quantum of action, which appears as an irrational element from the point of view of classical mechanics, taken together with the existence of the elementary particles, forms the foundation of atomic physics.</i></li><li><i>It has turned out, in fact, that all effects of light may be traced down to individual processes, in which a so-calles light quantum is exchanged, the energy of which is equal to the product of the frequency of the electromagnetic oscillations and the universal quantum of action, or Planck's constant. The striking contrast between this atomicity of the light phenomenon and the continuity of of the energy transfer according to the electromagnetic theory, places us before a dilemma of a character hitherto unknwown in physics.</i></li></ul><div>Bohr's starting point for his "Copenhagen" version of quantum mechanics still dominating text books, was:</div><div><ul><li><i>Planck's discovery of the universal quantum of action which revealed a feature of wholeness in individual atomic processes defying casual description in space and time.</i></li><li><i>Planck's discovery of the universal quantum of action taught us that the wide applicability of the accustomed description of the behaviour of matter in bulk rests entirely on the circumstance that the action involved in phenomena on the ordinary scale is so large that the quantum can be completely neglected. (The Connection Between the Sciences, 1960)</i></li></ul><div>Bohr thus argued that the success of the notion of universal quantum of action depends on the fact that in can be completely neglected. </div><div><br /></div><div>The explosion of digital computation since Bohr's time offers a new way of resolving the impossibility of detailed inspection of microscopics, by a allowing detailed non-invasive inspection of computational simulation of microscopics. With this perspective efforts should be directed to development of computable models of microscopics, rather than smashing high speed protons or neutrons into innocent atoms in order to find out their inner secrets, without getting reliable answers. </div><div><br /></div><div></div></div><div><i><br /></i></div></div><div><br /></div><div></div></div><div><br /></div>http://claesjohnson.blogspot.com/2014/03/the-torturers-dilemma-vs-uncertainty.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-2193355478465874597Sat, 22 Mar 2014 15:38:00 +00002014-03-23T11:19:41.399+01:00black body radiationPlanck's constantPlanck's Lawquantum mechanicsThe True Meaning of Planck's Constant as Measure of Wavelength of Maximal Radiance and Small-Wavelength Cut-off.<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-W4F0uL9bmdI/Uy2uRwGBJMI/AAAAAAAAiLw/ED4H_niQqmQ/s1600/Planck_law_log_log_scale.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-W4F0uL9bmdI/Uy2uRwGBJMI/AAAAAAAAiLw/ED4H_niQqmQ/s1600/Planck_law_log_log_scale.png" height="239" width="320" /></a></div><br />The modern physics of quantum mechanics was born in 1900 when Max Planck after many unsuccessful attempts in an "act of despair" introduced a<i> universal smallest quantum of action</i> $h= 6.626\times 10^{-34}\, Js = 4.12\times 10^{-15}\, eVs$ named Planck's constant in a theoretical justification of the spectrum of radiating bodies observed in experiments, based on statistics of packets of energy of size $h\nu$ with $\nu$ frequency.<br /><br />Planck describes this monumental moment in the history of science in his 1918 <a href="http://www.nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html">Nobel Lecture</a> as follows:<br /><div><ul><li><i>For many years, such an aim for me was to find the solution to the problem of the distribution of energy in the normal spectrum of radiating heat.</i></li><li><i>Nevertheless, the result meant no more than a preparatory step towards the initial onslaught on the particular problem which now towered with all its fearsome height even steeper before me. The first attempt upon it went wrong…</i></li><li><i>So there was nothing left for me but to tackle the problem from the opposite side, that of thermodynamics, in which field I felt, moreover, more confident. </i></li><li><i>Since the whole problem concerned a universal law of Nature, and since at that time, as still today, I held the unshakeable opinion that the simpler the presentation of a particular law of Nature, the more general it is… </i></li><li><i>For this reason, I busied myself, from then on, that is, from the day of its establishment, with the task of elucidating a true physical character for the formula, and this problem led me automatically to a consideration of the connection between entropy and probability, that is, Boltzmann's trend of ideas; until after some weeks of the most strenuous work of my life, light came into the darkness, and a new undreamed-of perspective opened up before me.</i></li></ul><div><div>Planck thus finally succeeded to prove Planck's radiation law as a modification of Rayleigh-Jeans law with a <i>high-frequency cut-off factor </i>eliminating "the ultraviolet catastrophe" which had paralyzed physics shortly after the introduction of Maxwell's wave equations for electromagnetics as the culmination of classical physics.</div><br />Planck's constant $h$ enters Planck's law<br /><ul><li>$I(\nu ,T)=\gamma \theta (\nu , T)\nu^2 T$, where $\gamma =\frac{2k}{c^2}$,</li></ul>where $I(\nu ,T)$ is normalized radiance, as a parameter in the<i> </i>multiplicative factor<br /><ul><li>$\theta (\nu ,T)=\frac{\alpha}{e^{\alpha} -1}$, </li><li>$\alpha=\frac{h\nu}{kT}$,</li></ul><div>where $\nu$ is frequency, $T$ temperature in Kelvin $K$ and $k = 1.38\times 10^{-23}\, J/K = 8.62\times 10^{-5}\, eV/K$ is Boltzmann's constant and $c\, m/s$ the speed of light.</div><div><br /></div><div>We see that $\theta (\nu ,T)\approx 1$ for small $\alpha$ and enforces a <i>high-frequency small-wavelength cut-off</i> for $\alpha > 10$, that is, for </div><ul><li>$\nu > \nu_{max}\approx \frac{10T}{\hat h}$ where $\hat h =\frac{h}{k}=4.8\times 10^{-11}\, Ks$,</li><li>$\lambda < \lambda_{min}\approx \frac{c}{10T}\hat h$ where $\nu\lambda =c$,</li></ul><div>with maximal radiance occuring for $\alpha = 2.821$ in accordance with Wien's displacement law. With $T = 1000\, K$ the cut-off is in the visible range for $\nu\approx 2\times 10^{14}$ and $\lambda\approx 10^{-6}\, m$. We see that the relation </div><div><ul><li>$\frac{c}{10T}\hat h =\lambda_{min}$,</li></ul><div>gives $\hat h$ a physical meaning as measure of wave-length of maximal radiance and small-wavelength cut-off of atomic size scaling with $\frac{c}{T}$. </div><div><br /></div><div>Modern physicsts are trained to believe that Planck's constant $h$ as the<i> universal quantum of action </i>represents a smallest unit of a "quantized" world with a corresponding Planck length $l_p= 1.62\times 10^{-35}$ as a smallest unit of length, about 20 orders of magnitude smaller than the proton diameter.<br /><br />We have seen that Planck's constant enters in Planck's radiation law in the form $\hat h =\frac{h}{k}$, and not as $h$, and that $\hat h$ has the role of setting a small-wavelength cut-off scaling with $\frac{c}{T}$.<br /><br />Small-wavelength cut-off in the radiation from a body is possible to envision in wave mechanics as an expression of <a href="http://computationalblackbody.wordpress.com/">finite precision analog computation</a>. In this perspective Planck's universal quantum of action emerges as unnecessary fiction about exceedingly small quantities beyond reason and reality.<br /><br /><br /><br /></div></div></div></div>http://claesjohnson.blogspot.com/2014/03/the-true-meaning-of-plancks-constant-as.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-4958659872153759861Thu, 20 Mar 2014 12:02:00 +00002014-03-20T13:13:35.503+01:00principle of least actionquantum mechanicsPrinciple of Least Action vs Adam Smith's Invisible Hand<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-YYVADlfrDC8/UyrYDiplFeI/AAAAAAAAiLQ/JKOpaPTOojM/s1600/the-great-depression%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-YYVADlfrDC8/UyrYDiplFeI/AAAAAAAAiLQ/JKOpaPTOojM/s1600/the-great-depression%5B1%5D.jpg" height="245" width="320" /></a></div> <i>Violation of the PLA of the capitalistic system in 1929.</i><br /><br />The Principle of Least Action (PLA) expressing<br /><ul><li><i>Stationarity of the Action (the</i> <i>integral in time of the Lagrangian),</i> </li></ul>with the Lagrangian the difference between kinetic and potential energies, is cherished by physicists as a deep truth about physics: Tell me the Lagrangian and I will tell you the physics, because a dynamical system will (by reaction to local forces) evolve so as to keep the Action stationary as if led by an invisible hand steering the system towards a final cause of least action.<br /><br />PLA is similar to the <a href="http://en.wikipedia.org/wiki/Invisible_hand">invisible hand of Adam Smith</a> supposedly steering an economy towards a final cause of maximal effectivity or least action (maximal common happiness) by asking each member of the economy to seek to maximize individual profit (individual happiness). This is the essence of the capitalistic system. The idea is that a final cause of maximal effectivity can be reached without telling the members the meaning of the whole thing, just telling each one to seek to maximize his/her own individual profit (happiness).<br /><br />Today the capitalistic system is shaking and nobody knows how to steer towards a final cause of maximal efficiency. So the PLA of economy seems to be rather empty of content. It may be that similarly the PLA of physics is void of real physics. In particular, the idea of a smallest quantum of action as a basis of quantum mechanics, may well be unphysical.<br /><br /> http://claesjohnson.blogspot.com/2014/03/principle-of-least-action-vs-adam.htmlnoreply@blogger.com (Claes Johnson)26