tag:blogger.com,1999:blog-1500584444083499721Fri, 04 Sep 2015 13:24:07 +0000theory of flightgreenhouse effectclimate sciencemathematics educationmyth of backradiationquantum mechanicsclimate politicsRoyal Swedish Academy of Sciencesblack body radiationAIAADLRKTH-gateclimate simulationmatematik-ITclimate sensitivityQuantum ContradictionsKTH-gate3physicsscienceengineering education reformtheory of relativitysimulation technologyKammarrättenmathematicsthermodynamics of global climateBodyandSoulPlanck's LawStefan-Boltzmann's LawIPCCLennart BengtssonHögsta FörvaltningsdomstolenCO2KTH-gate2Schrödinger's equationphysical quantum mechanicsradiative heat transfercosmologyemissivity2nd law of thermodynamicsSky DragongravitationEinsteinKVAinterviewsMattelyftetPlanck's constantfluid mechanicsclimategateStandard CaculusFalse-SBOLRfinite precision computationradiating atomCFDFundamental Theorem of CalculusKTHOffentlighetsprincipenbig bluffmysticism of modern physicsmany-minds relativitysvensk klimatpolitikclay probleminfrared thermometerpyrgeometermodtranIPCC TrickNew View on gravitationphotonsphysics illusionsroy spencerturbulenceJudy CurryPrandtlStefan Lövenfred singerradiative forcinguncertainty principleclimate modelsNADAPrandtl Medalbolometerlapse rateresonanceCERESKVAs klimatuttalandeMuir Russell Inquirylindzenmany-minds physicssecret of separationteknikdelegationentheory of sailingIR cameraMSTdAlembertgatedark energyfinite element quantum mechanicsphotoelectric effectDr FaustusFEniCSFakultetsnämnden KTHLaplace demonRoyal SocietySVTSvenska Mekanikdagararrow of timeclimate skepticeconomical crisisfree willBert Bolin Centre for Climate ResearchCMBGlenn Research CenterKirchhoff's lawSvenska Matematikersamfundetazarcensorshipcosmological principledark matteribookkollegialt lärandephlogistonthermal imaging3rd Nobel SymposiumAcademic Rights WatchAnders ÅngströmFreedom FestHubble's LawKlimatupplysningenOckham's razorPenguin logicRiksbankenSchwarzschildboundary layerconstructive physicscrisis in physicsdefinition vs physical factdirection of timeiducationperiodic tablepiano acousticsprinciple of least actionrepo rateshorttime vs longtime accuracyChandrasekharFinal SolutionHans RoslingHelmholtz ReciprocityHiggs mechanismLorentz transformationMichelson-MorleyPopperQEDSMHISULFZeno's arrow paradoxfaint sun paradoxlord moncktonnobel prizenumerical analysisrelativitystellar aberrationstring instrumentswave-particle dualityCJ70DNDiracDiscussion ForumEquivalence PrincipleFeynmanGoogle BooksHeisenbergKTH-studenterKnut ÅngströmMOOCMagnus effectMaxwell's equationsNewton's 2nd lawSRSagnac effectUlf DanielssonUnicornWien's displacement lawaeroacousticsaniconismatmosphere spectrumbigbrunobutterfly effectconduction vs radiationcopernicuscritical thinkingdark age of sciencedefinition as factdynamical systememissvityentropyfinite elementgalileohäggströmmillikanpeer reviewpokerprypyrgeomterscientific methodseminarsstability-wellposednessstring theorysvarta håltyndallvon NeumannwellposednessÖppna GöteborgClaes Johnson on Mathematics and Sciencetowards understanding by critical constructive inquiryhttp://claesjohnson.blogspot.com/noreply@blogger.com (Claes Johnson)Blogger1455125tag:blogger.com,1999:blog-1500584444083499721.post-1677981075659783502Wed, 02 Sep 2015 06:44:00 +00002015-09-04T15:24:07.451+02:00finite element quantum mechanicsphysical quantum mechanicsFinite Element Quantum Mechanics 5: 1d Model in Spherical SymmetryThe new Schrödinger equation I am studying in this sequence of posts takes the following form, in spherical coordinates with radial coordinate $r\ge 0$ in the case of spherical symmetry, for an atom with kernel of charge $Z$ at $r=0$ with $N\le Z$ electrons of unit charge distributed in a sequence of non-overlapping spherical shells $S_1,...,S_M$ separated by spherical surfaces of radii $0=r_0<r_1<r_2<...<r_M=\infty$, with $N_j>0$ electrons in shell $S_j$ corresponding to the interval $(r_{j-1},r_j)$ for $j=1,...,M,$ and $\sum_j N_j = N$:<br /><br />Find a complex-valued differentiable function $\psi (r,t)$ depending on $r≥0$ and time $t$, satisfying for $r>0$ and all $t$,<br /><ul><li>$i\dot\psi (r,t) + H(r,t)\psi (r,t) = 0$ (1)</li></ul><div>where $\dot\psi = \frac{\partial\psi}{\partial t}$ and $H(r,t)$ is the Hamiltonian defined by</div><div><ul><li>$H(r,t) = -\frac{1}{2r^2}\frac{\partial}{\partial r}(r^2\frac{\partial }{\partial r})-\frac{Z}{r}+ V(r,t)$,</li><li>$V(r,t)= 2\pi\int\vert\psi (s,t)\vert^2\min(\frac{1}{r},\frac{1}{s})R(r,s,t)s^2\,ds$,</li><li>$R(r,s,t) = (N_j -1)/N_j$ for $r,s\in S_j$ and $R(r,s,t)=1$ else,</li></ul><div>and </div><ul><li>$4\pi\int_{S_j}\vert\psi (s,t)\vert^2s^2\, ds = N_j$ for $j=1,...,M$. (2)</li></ul><div>Here $-\frac{Z}{r}$ is the kernel-electron attractive potential and $V(r,t)$ is the electron-electron repulsive potential computed using the fact that the potential $V(s)$ of a spherical uniform surface charge distribution of radius $r$ centered at $0$ of total charge $Q$, is given by $V(s)=Q\min(\frac{1}{r},\frac{1}{s})$, with a reduction for a lack of self-repulsion within each shell given by the factor $(N_j -1)/N_j$.<br /><br />The $N_j$ electrons in shell $S_j$ are thus homogenised into a spherically symmetric charge distribution of total charge $N_j$.<br /><br />This is a free boundary problem readily computable on a laptop, with the $r_j$ representing the free boundary separating shells of spherically symmetric charge distribution of intensity $\vert\psi (r,t)\vert^2$ and a free boundary condition asking continuity and differentiability of $\psi (r,t)$. </div><div><br /></div><div>Separating $\psi =\Psi +i\Phi$ into real part $\Psi$ and imaginary part $\Phi$, (1) can be solved by explicit time stepping with (sufficiently small) time step $k>0$ and given initial condition (e.g. as ground state):<br /><ul><li>$\Psi^{n+1}=\Psi^n-kH\Phi^n$, </li><li>$\Phi^{n+1}=\Phi^n+kH\Psi^n$, </li></ul><div>for $n=0,1,2,...,$ where $\Psi^n(r)=\Psi (r,nk)$ and $\Phi^n(r)=\Phi (r,nk)$, while stationary ground states can be solved by the iteration</div><div></div><ul><li>$\Psi^{n+1}=\Psi^n-kH\Psi^n$, </li><li>$\Phi^{n+1}=\Phi^n-kH\Phi^n$, </li></ul><div>while maintaining (2).<br /><br />A remarkable fact is that this model appears to give ground state energies as minimal eigenvalues of the Hamiltonian for both ions and atoms for any $Z$ and $N$ within a percent or so, or alternatively ground state frequencies from direct solution in time dependent form. Next I will compute excited states and transitions between excited states under exterior forcing.<br /><br />Specifically, what I hope to demonstrate is that the model can explain the periods of the periodic table corresponding to the following sequence of numbers of electrons in shells of increasing radii: 2, (2, 8), (2, 8, 8), (2, 8, 18, 8), (2, 8, 18, 18, 8)... which to be true lacks convincing explanation in standard quantum mechanics (<a href="http://www.chem.ucla.edu/dept/Faculty/scerri/">according to E. Serri</a> among many others).<br /><br />The basic idea is thus to represent the total wave function $\psi (r,t)$ as a sum of shell wave functions<br />with non-overlapping supports in the different in shells requiring $\psi (r,t)$ and thus $\vert\psi (r,t)\vert^2$ to be continuous across inter-shell boundaries as free boundary condition, corresponding to continuity of charge distribution as a classical equilibrium condition.<br /><br />I have also with encouraging results tested this model for $N\le 10$ in full 3d geometry without spherical shell homogenisation with a wave function as a sum of electronic wave functions with non-overlapping supports separated by a free boundary determined by continuity of wave function including charge distribution.<br /><br />We compare with the standard (Hartree-Fock-Slater) Ansatz of quantum mechanics with a multi-dimensional wave function $\psi (x_1,...,x_N,t)$ depending on $N$ independent 3d coordinates $x_1,...,x_N,$ as a linear combination of wave functions of the multiplicative form<br /><ul><li>$\psi_1(x_1,t)\times\psi_2(x_2,t)\times ....\times\psi_N(x_N,t)$, </li></ul><div>with each electronic wave function $\psi_j(x_j,t)$ with global support (non-zero in all of 3d space). Such multi-d wave functions with global support thus depend on $3N$ independent space coordinates and as such defy both direct physical interpretation and computability, as soon as $N>1$, say. One may argue that since such multi-d wave function cannot be computed, it does not matter that they have no physical meaning, but the net output appears to be nil, despite the declared immense success of standard quantum mechanics based on this Ansatz.</div></div></div></div>http://claesjohnson.blogspot.com/2015/09/finite-element-quantum-mechanics-5-1d.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-4756902202746545033Sun, 30 Aug 2015 12:07:00 +00002015-09-01T14:47:04.807+02:002nd law of thermodynamicsarrow of timefinite element quantum mechanicsfinite precision computationphysical quantum mechanicstheory of flightQuantum Information Can Be Lost<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-POwX2OE3svI/VeLvbulKPPI/AAAAAAAA6hc/QS5bl4XzODc/s1600/Fil-2015-08-24-19-51-26.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="http://1.bp.blogspot.com/-POwX2OE3svI/VeLvbulKPPI/AAAAAAAA6hc/QS5bl4XzODc/s400/Fil-2015-08-24-19-51-26.png" width="400" /></a></div><br /><a href="http://www.extremetech.com/extreme/212968-stephen-hawking-may-have-finally-solved-the-black-hole-information-problem">Stephen Hawking claimed in lecture at KTH in Stockholm last week</a> (watch the lecture <a href="https://www.kth.se/en/aktuellt/nyheter/hawking-offers-new-solution-to-black-hole-mystery-1.586546">here</a> and check <a href="https://www.kth.se/en/aktuellt/nyheter/hawking-conference-takes-aim-at-paradox-of-black-hole-theory-1.585138">this announcement</a>) that he had solved the "black hole information problem":<br /><ul><li><i>The information is not stored in the interior of the black hole as one might expect, but in its boundary — the event horizon,” he said. Working with Cambridge Professor Malcolm Perry (who spoke afterward) and Harvard Professor Andrew Stromberg, Hawking formulated the idea hat information is stored in the form of what are known as super translations.</i></li></ul><div>The problem arises because quantum mechanics is viewed to be reversible, because the mathematical equations supposedly describing atomic physics formally are time reversible: a solution proceeding in forward time from an initial to a final state, can also be viewed as a solution in backward time from the earlier final state to the initial state. The information encoded in the initial state can thus, according to this formal argument, be recovered and thus is never lost. On the other hand a black hole is supposed to swallow and completely destroy anything it reaches and thus it appears that a black hole violates the postulated time reversibility of quantum mechanics and non-destruction of information.</div><div><br /></div><div>Hawking's solution to this apparent paradox, is to claim that after all a black hole does not destroy information completely but "stores it on the boundary of the event horizon". Hawking thus "solves" the paradox by maintaining non-destruction of information and giving up complete black hole destruction of information.</div><div><br /></div><div>The question Hawking seeks to answer is the same as the fundamental problem of classical physics which triggered the development of modern physics in the late 19th century with Boltzmann's "proof" of the 2nd law of thermodynamics: Newton's equations describing thermodynamics are formally reversible, but the 2nd law of thermodynamics states that real physics is not always reversible: Information can be inevitably lost as a system evolves towards thermodynamical equilibrium and then cannot be recovered. Time has a direction forward and cannot be reversed. </div><div><br /></div><div>Boltzmann's "proof" was based an argument that things that do happen do that because they are "more probable" than things which do not happen. This deep insight opened the new physics of statistical mechanics from which quantum borrowed its statistical interpretation.</div><div><br /></div><div>I have presented a different new resolution of the apparent paradox of irrreversible macrophysics based on reversible microphysics by viewing physics as analog computation with finite precision, on both macro- and microscales. A spin-off of this idea is a new resolution of d'Alemberts's paradox and a new theory of flight to be published shortly.</div><div><br /></div><div>The basic idea here is thus to replace the formal infinite precision of both classical and quantum mechanics, which leads to paradoxes without satisfactory solution, with realistic finite precision which allows the paradoxes to be resolved in a natural way without resort to unphysical statistics. See the listed categories for lots of information about this novel idea.</div><div><br /></div><div>The result is that reversible infinite precision quantum mechanics is fiction without physical realization, and that irreversible finite precision quantum mechanics can be real physics and in this world of real physics information is irreversibly lost all the time even in the atomic world. Hawking's resolution is not convincing.<br /><br />Here is the key observation explaining the occurrence of irreversibility in formally reversible systems modeled by formally non-dissipative partial differential equations such as the Euler equations for inviscid macroscopic fluid flow and the Schrödinger equations for atomic physics:<br /><br />Smooth solutions are strong solutions in the sense of satisfying the equations pointwise with vanishing residual and as such are non-dissipative and reversible. But smooth solutions make break down into weak turbulent solutions, which are only solutions in weak approximate sense with pointwise large residuals and these solutions are dissipative and thus irreversible. <br /><br />An atom can thus remain in a stable ground state over time corresponding to a smooth reversible non-dissipative solution, while an atom in an excited state may return to the ground state as a non-smooth solution under dissipation of energy in an irreversible process. </div><div><blockquote class="tr_bq"><br /></blockquote></div>http://claesjohnson.blogspot.com/2015/08/quantum-information-can-be-lost.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-4500265746627749540Fri, 28 Aug 2015 14:47:00 +00002015-09-01T15:06:01.795+02:00finite element quantum mechanicsphysical quantum mechanicsPlanck's LawQuantum ContradictionsFinite Element Quantum Mechanics 4: Spherically Symmetric Model<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-3wZT8tA0wh0/VeC3U3X6dnI/AAAAAAAA6hM/I5CaVoQvnU8/s1600/017_orbital.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-3wZT8tA0wh0/VeC3U3X6dnI/AAAAAAAA6hM/I5CaVoQvnU8/s200/017_orbital.gif" width="200" /></a></div><br />I have tested the new atomic model described in a<a href="http://claesjohnson.blogspot.se/2015/05/physical-quantum-mechanics-time.html"> previous post</a> in setting of spherical symmetry with electrons filling a sequence of non-overlapping spherical shells around a kernel. The electrons in each shell are homogenized to spherical symmetry which reduces the model to a 1d free boundary problem with the free boundary represented by the inter-shell spherical surfaces adjusted so that the combined wave function is continuous along with derivates across the boundary. The repulsion energy is computed so as to take into account that electrons are not subject to self-repulsion, by a corresponding reduction of the repulsion within a shell.<br /><br />The remarkable feature of this atomic model, in the form of a 1d free boundary problem with continuity as free boundary condition and readily computable on a lap-top, is that computed ground state energies show to be surprisingly accurate (within 1%) for all atoms including ions (I have so far tested up to atomic number 54 and am now testing excited states).<br /><br />Recall that the wave function $\psi (x,t)$ solving the free boundary problem, has the form<br /><ul><li>$\psi (x,t) =\psi_1(x,t)+\psi_2(x,t)+...+\psi_S(x,t)$ (1)</li></ul><div>with $(x,t)$ a common space-time coordinate, where $S$ is the number of shells and $\psi_j(x,t)$ with support in shell $j$ is the wave function for the homogenized wave function for the electrons in shell $j$ with $\int\vert\psi_j(x,t)\vert^2\, dx$ equal to the number of electrons in shell $j$.</div><div><br /></div><div>Note that the free boundary condition expresses continuity of charge distribution across inter-shell boundaries, which appears natural.</div><div><br /></div><div>Note that the model can be used in time dependent form and then allows direct computation of vibrational frequencies, which is what can be observed. </div><div><br /></div><div>Altogether, the model in spherical symmetric form indicates that the model captures essential features of the dynamics of an atom, and thus can useful in particular for studies of atoms subject to exterior forcing. </div><div><br /></div><div>I have also tested the model without spherical homogenisation for atoms with up to 10 electrons, with similar results. In this case the the free boundary separates diffferent electrons (and not just shells of electrons) with again continuous charge distribution across the corresponding free boundary. </div><div><br /></div><div>In this model electronic wave functions share a common space variable and have disjoint supports and can be given a classical direct physical interpretation as charge distribution. There is no need of any Pauli exclusion principle: Electrons simply occupy different regions of space and do not overlap, just as in a classical multi-species continuum model.</div><div><br /></div><div>This is to be compared with standard quantum mechanics based on multidimensional wave functions $\psi (x_1,x_2,...,x_N,t)$ typically appearing as linear combinations of products of electronic wave functions<br /><ul><li>$\psi (x_1,x_2,...,x_N,t)=\psi_1(x_1,t)\times \psi_2(x_2,t)....\times\psi_N(x_N,t)$ (2)</li></ul>for an atom with $N$ electrons, each electronic wave function $\psi_j(x_j,t)$ being globally defined with its own independent space coordinate $x_j$. Such multidimensional wave functions can only be given statistical interpretation, which lacks direct physical meaning. In addition, Pauli's exclusion principle must be invoked and it should be remembered that Pauli himself did not like his principle since it was introduced ad hoc without any physical motivation, to save quantum mechanics from collapse from the very start...<br /><br />More precisely, while (1) is perfectly reasonable from a classical continuum physics point of view, and as such is computable and useful, linear combination of (2) represent a monstrosity which is both uncomputable and unphysical and thus dangerous, but nevertheless is supposed to represent the greatest achievement of human intellect all times in the form of the so called modern physics of quantum mechanics.<br /><br />How long will it take for reason and rationality to return to physics after the dark age of modern physics initiated in 1900 when Planck's "in a moment of despair" resorted to an ad hoc hypothesis of a smallest quantum of energy in order to avoid the "ultra-violet catastrophe" of radiation viewed to be impossible to avoid in classical continuum physics. But with <a href="http://claesjohnson.blogspot.se/search/label/finite%20precision%20computation">physics as finite precision computation</a>, which I am exploring, there is no catastrophe of any sort and Planck's sacrifice of rationality serves no purpose.<br /><br /><b>PS</b> Here are the details of the spherical symmetric model starting from the following new formulation of a Schrödinger equation for an atom with $N$ electrons organised in spherical symmetric form into $S$ shells: Find a wave function<br /><ul><li>$\psi (x,t) = \sum_{j=1}^N\psi_j(x,t)$</li></ul>as a sum of $N$ electronic complex-valued wave functions $\psi_j(x,t)$, depending on a common 3d space coordinate $x\in R^3$ and time coordinate $t$ with non-overlapping spatial supports $\Omega_1(t)$,...,$\Omega_N(t)$, filling 3d space, satisfying<br /><ul><li>$i\dot\psi (x,t) + H\psi (x,t) = 0$ for all $(x,t)$, (1)</li></ul>where the (normalised) Hamiltonian $H$ is given by<br /><div><ul><li>$H(x) = -\frac{1}{2}\Delta - \frac{N}{\vert x\vert}+\sum_{k\neq j}V_k(x)$ for $x\in\Omega_j(t)$,</li></ul><div>where $V_k(x)$ is the potential corresponding to electron $k$ defined by </div><ul><li>$V_k(x)=\int\frac{\vert\psi_k(y,t)\vert^2}{2\vert x-y\vert}dy$, for $x\in R^3$,</li></ul><div>and the wave functions are normalised to correspond to unit charge of each electron:</div><div><ul><li>$\int_{\Omega_j}\vert\psi_j(x,t)\vert^2 =1$ for all $t$ for $j=1,..,N$.</li></ul><div><div>Assume the electrons fill a sequence of shells $S_k$ for $k=1,...,S$ centered at the atom kernel with $N_k$ electrons on shell $S_k$ and </div><div><ul><li>$\int_{S_k}\vert\psi (x,t)\vert^2 =N_k$ for all $t$ for $k=1,..,S$,</li><li>$\sum_k^S N_k = N$.</li></ul></div></div></div><div>The total wave function $\psi (x,t)$ is thus assumed to be continuously differentiable and the electronic potential of the Hamiltonian acting in $\Omega_j(t)$ is given as the attractive kernel potential together with the repulsive kernel potential resulting from the combined electronic charge distributions $\vert\psi_k\vert^2$ for $k\neq j$, with total electronic repulsion energy<br /><ul><li>$\sum_{k\neq j}\int\frac{\vert\psi_k(x,t)\vert^2\vert\psi_k(y,t)\vert^2}{2\vert x-y\vert}dxdy=\sum_{k\neq j}V_k(x)\vert\psi_k(x)\vert^2\, dx$.</li></ul><div>Assume now that the electronic repulsion energy is approximately determined by homogenising the $N_k$ electronic wave function $\psi_j$ in each shell $S_k$ into a spherically symmetric "electron cloud" $\Psi_k(x)$ with corresponding potential $W_k(y)$ given by</div><ul><li>$W_k(y)=\int_{\vert x\vert <\vert y\vert}R_k\frac{\vert\Psi_k(x)\vert ^2}{\vert y\vert}\, dx+\int_{\vert x\vert >\vert y\vert}R_k\frac{\vert\Psi_k(x)\vert ^2}{\vert x\vert}\, dx$,</li></ul><div>and $R_k(x)=\frac{N_k-1}{N_k}$ for $x\in S_k$ is a reduction factor reflecting non self-repulsion of each electron (and $R_k=1$ else): Of the $N_k$ electrons in shell $S_k$, thus only $N_k-1$ electrons contribute to the value of potential in shell $S_k$ from the electrons in shell $S_k$. We here use the fact that the potential $W(x)$ of a uniform charge distribution on a spherical surface $\{y:\vert y\vert =r\}$ of radius $r$ of total charge $Q$, is equal to $Q/\vert x\vert$ for $\vert x\vert >r$ and $Q/r$ for $\vert x\vert <r$.<r p=""></r></div><div><r div=""></r><br /><div>Our model then has spherical symmetry and is a 1d free boundary problem in the radius $r=\vert x\vert$ with the free boundary represented by the radii of the shells and the corresponding Hamiltonian is defined by the electronic potentials computed by spherical homogenisation in each shell. The free boundary is determined so that the combined wave function $\psi (x,t)$ is continuously differentiable across the free boundary. </div><br /><br /></div></div><br /></div></div>http://claesjohnson.blogspot.com/2015/08/finite-element-quantum-mechanics-4.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-7796438867141066143Thu, 27 Aug 2015 12:13:00 +00002015-08-27T14:13:54.358+02:00finite element quantum mechanicsperiodic tablephysical quantum mechanicsFinite Element Quantum Mechanics 3: Explaining the Periodicity of the Periodic Table<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-D1b3F_Dp1b0/Vd7-0XPqBvI/AAAAAAAA6g4/PjzUGm9eya4/s1600/PeriodicTable-NoBackground2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="360" src="http://2.bp.blogspot.com/-D1b3F_Dp1b0/Vd7-0XPqBvI/AAAAAAAA6g4/PjzUGm9eya4/s640/PeriodicTable-NoBackground2.png" width="640" /></a></div><br /><a href="http://www.tp.umu.se/~dion/atmol/Slides/QDT.pdf">According to Eric Scerri,</a> the periodic table is not well explained by quantum mechanics, contrary to common text book propaganda, not even the most basic aspect of the periodic table, namely its periodicity:<br /><ul><li><i>Pauli’s explanation for the closing of electron shells is rightly regarded as the high point in the old quantum theory. Many chemistry textbooks take Pauli’s introduction of the fourth quantum number, later associated with spin angular momentum, as the foundation of the modern periodic table. Combining this two-valued quantum number with the ear- lier three quantum numbers and the numerical relationships between them allow one to infer that successive electron shells should contain 2, 8, 18, or $2n^2$ electrons in general, where n denotes the shell number. </i></li><li><i>This explanation may rightly be regarded as being deductive in the sense that it flows directly from the old quantum theory’s view of quantum numbers, Pauli’s additional postulate of a fourth quantum number, and the fact that no two electrons may share the same four quan- tum numbers (Pauli’s exclusion principle). </i></li><li><i>However, Pauli’s Nobel Prize-winning work <b>did not provide a solution to the question which I shall call the “closing of the periods”—that is why the periods end, in the sense of achieving a full-shell configuration, at atomic numbers 2, 10, 18, 36, 54, and so forth. This is a separate question from the closing of the shells.</b> For example, if the shells were to fill sequentially, Pauli’s scheme would predict that the second period should end with element number 28 or nickel, which of course it does not. Now, this feature is important in chemical education since it implies that quantum mechanics can- not strictly predict where chemical properties recur in the periodic table. It would seem that quantum mechanics does not fully explain the single most important aspect of the periodic table as far as general chemistry is concerned. </i></li><li><i>The discrepancy between the two sequences of numbers representing the closing of shells and the closing of periods occurs, as is well known, due to the fact that the shells are not sequentially filled. Instead, the sequence of filling fol- lows the so-called Madelung rule, whereby the lowest sum of the first two quantum numbers, n + l, is preferentially oc- cupied. As the eminent quantum chemist Löwdin (among others) has pointed out, this filling order has never been derived from quantum mechanics. </i></li></ul><div>On the other hand, in the new approach to atomic physics I am exploring, the periodicity directly connects to a basic partitioning or packing problem, namely how to subdivide the surface of a sphere in equal parts, which gives the sequence $2n^2$ by dividing first into two half spheres and then subdividing each half spherical surface in $n\times n$ pieces, in a way similar to dividing a square surface into $n\times n$ square pieces. With increasing shell radius an increasing number of electrons, occupying a certain surface area (scaling with the inverse of the kernel charge), can be contained in a shell. </div><div><br /></div><div>In this setting a "full shell" can contain 2, 8, 18, 32,.., electrons, and the observed periodicity 2, 8, 8, 18, 18, 32, 32, with each period ended by a noble gas with atomic numbers 2 (He), 10 (Neon), 18 (Argon), 36 (Krypton), 54 (Xenon), 86 (Radon), 118 (Ununoctium, unkown), with a certain repetition of shell numbers, can be seen as a direct consequence of such a full shell structure, if allowed to be repeated when the radius of a shell is not yet large enough to house a full shell of the next dignity. </div><div><br /></div><div>Text book quantum mechanics thus does not explain the periodicity of the periodic table, while the new approach am I pursuing may well do so in a very natural way. Think of that. </div>http://claesjohnson.blogspot.com/2015/08/finite-element-quantum-mechanics-3.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-1809435468232507010Tue, 25 Aug 2015 17:55:00 +00002015-08-25T19:58:49.733+02:00svarta hålUlf DanielssonUlf Danielsson om Klimathot, Hawking och Svarta Hål. <div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-Dl8zdTFubjI/Vdyseo2_K6I/AAAAAAAA6gk/UDA1NVpEnTM/s1600/ulddanielson.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="212" src="http://1.bp.blogspot.com/-Dl8zdTFubjI/Vdyseo2_K6I/AAAAAAAA6gk/UDA1NVpEnTM/s320/ulddanielson.jpg" width="320" /></a></div><br /><a href="http://ulfdanielsson.com/">Strängfysikern Ulf Danielsson har startat en blogg </a>med Stephen Hawking's besök vid KTH och föreläsning på Stockholm Waterfront som initiellt dragplåster. Ulf skriver gärna om svarta hål, som han verkar tro inneha verklig fysisk existens som "singularitet" till lösningar till Einstein's ekvationer. Ulf verkar även tro på kimatalarmismen som den predikas av IPCC:<br /><ul><li><i>När det gäller människogenererad klimatpåverkan är huvudslutsatsen klar: den finns där, och risken att den får betydande följder för den mänskliga civilisationen om inget görs är överhängande. Den senaste <a href="http://www.ipcc.ch/">IPCC-rapporten</a> gör det omöjligt att dra någon annan generell slutsats.</i></li></ul><div>Vi skeptiker som granskat vetenskapen bakom IPCCs klimatalarmism, vet att Ulf i denna fråga blivit helt vilseförd. Frågan är om samma sak gäller för svarta hål? </div><div><br /></div><div>Om det nu är så att man kan hitta singulariteter hos lösningar till Einstein's ekvationer, vilket i sig kan diskuteras eftersom dessa ekvationer är hart när omöjliga att lösa, betyder det att dessa singulariteter också har fysisk realitet? </div><div><br /></div><div>Även om det finns massa i centrum på galaxer som man inte kan se, vilket observationer av galaxers dynamik verkar tyda på, så betyder det väl inte nödvändigtvis att denna osynliga massa utgörs av svart hål? </div><div><br /></div><div>Kan det vara så att IPCCs (farligt tjocka enligt Ulf) rapport utgör ett svart hål ur vilken ingen sann information förmår utstråla?</div>http://claesjohnson.blogspot.com/2015/08/ulf-danielsson-om-klimathot-hawking-och.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-5847338775684808708Tue, 25 Aug 2015 13:14:00 +00002015-08-28T21:03:08.578+02:00finite element quantum mechanicsphysical quantum mechanicsQuantum Contradictionsquantum mechanicsSchrödinger's equationFinite Element Quantum Mechanics 2: Questions without Answers<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-CjSItRiphmE/VdxmG4G7iZI/AAAAAAAA6gM/T6l4uWkDzbU/s1600/9783642693670.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="http://1.bp.blogspot.com/-CjSItRiphmE/VdxmG4G7iZI/AAAAAAAA6gM/T6l4uWkDzbU/s200/9783642693670.jpg" width="138" /></a></div><a href="http://4.bp.blogspot.com/-V2Gk6fCoLdc/VdxnGi-jtZI/AAAAAAAA6gU/qaGcE3n1RYw/s1600/10.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-V2Gk6fCoLdc/VdxnGi-jtZI/AAAAAAAA6gU/qaGcE3n1RYw/s200/10.jpg" width="171" /></a><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Hans Primas formulates in Chemistry, Quantum Mechanics and Reductionism, the following basic questions left without answers in textbook quantum mechanics:<br /><ol><li><i>Do isolated quantal systems exist at all?</i></li><li><i>Is the Pauli Principle a universal and inviolable fact of nature?</i></li><li><i>Does quantum mechanics apply to large molecular systems?</i></li><li><i>Is the superposition principle universally valid?</i></li><li><i>Why do so many stationary states not exist?</i></li><li><i>Why are macroscopic bodies localised?</i></li><li><i>Why does quantum mechanics fail to account for chemical systematics?</i></li><li><i>Why can approximations be better than the exact solutions?</i></li><li><i>Why is the Born-Oppenheimer picture so successful?</i></li><li><i>Is temperature an observable? </i></li></ol><div>Despite now almost 100 years of giant efforts by giant scientific minds, no satisfactory answers to these basic questions have been delivered. There is no reason to believe that 100 more years will give any answers and the question must be posed if there is something fundamentally wrong with textbook quantum mechanics which prevents progress? </div><div><br /></div><div>Yes, I think so: The origin of all these questions without answers is the starting point of textbook quantum mechanics with a wave function </div><div><ul><li>$\psi (x_1,....,x_N,t)$ depending on $3N$ space coordinates and time,</li><li>satsifying a linear scalar wave equation in $3N$ space dimensions and time, </li></ul></div><div>for an atom with $N$ electrons as particles, with $\vert\psi (x_1,...,x_N,t)\vert^2$ interpreted as the probability that particle $j$ is at position $x_j$ at time $t$ for $j=1,...,N$. </div><div><br /></div><div>Such a wave function is both uncomputable (because of the many spatial dimensions) and unphysical (because an atom is not an insurance company computing probabilities, as little as an individual person paying an insurance). The fact that textbook quantum mechanics still after almost hundred years is stuck with such a hopeless scientific misconception, is nothing less than a scientific tragedy.<br /><br />Hans Primas gives the following devastating verdict:<br /><ul><li><i>There is no general agreement about the referent (physical meaning) of pioneer (textbook) quantum mechanics.</i></li><li><i>Pioneer quantum mechanics has an agonising shortcoming: It cannot describe classical systems. </i></li><li><i>From a fundamental point of view the only adequate interpretation of quantum mechanics is an ontic (realistic) interpretation.... Bohr's epistemic interpretation expresses merely states of knowledge and misses the point of genuine scientific inquiry...If we assume that pioneer quantum mechanics is a universal theory of molecular matter, then an ontic interpretation of this theory is impossible.</i></li><li><i>The Bohr Copenhagen (textbook) interpretation is not acceptable as a fundamental theory of matter. </i></li></ul><div>In other words, pioneer (textbook) quantum mechanics is a failed scientific project, and it is an open problem to find an ontic description of atomic physics by "genuine scientific inquiry", that is, in the spirit of the device of this blog, "by critical constructive inquiry towards understanding". </div></div>http://claesjohnson.blogspot.com/2015/08/finite-element-quantum-mechanics-2.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-2811176649955478039Tue, 25 Aug 2015 11:50:00 +00002015-08-25T19:23:44.569+02:00finite element quantum mechanicsphysical quantum mechanicsQuantum Contradictionsquantum mechanicsSchrödinger's equationFinite Element Quantum Mechanics 1: Listening to Bohm<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-zMA12OczGE0/VdxVyOsLYlI/AAAAAAAA6f0/T_iww9ysGdo/s1600/david_bohm_quantum_theory_book.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-zMA12OczGE0/VdxVyOsLYlI/AAAAAAAA6f0/T_iww9ysGdo/s320/david_bohm_quantum_theory_book.jpg" width="201" /></a></div><a href="http://2.bp.blogspot.com/-9RJkCIwYPLA/VdxWDJ_eh9I/AAAAAAAA6f8/WLlAc74fLHQ/s1600/david_bohm-2.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-9RJkCIwYPLA/VdxWDJ_eh9I/AAAAAAAA6f8/WLlAc74fLHQ/s320/david_bohm-2.jpg" width="211" /></a><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />David Bohm discusses in the concluding chapter of Quantum Theory the relationship between quantum and classical physics, stating the following charcteristics of classical physics:<br /><ol><li><i>The world can be analysed into distinct elements.</i></li><li><i>The state of each element can be described in terms of dynamical variables that are specified with arbitrarily high precision.</i></li><li><i>The interrelationship between parts of a system can be described with the aid of exact casual was that define the changes of the above dynamical variables with time in terms of their initial values. The behavior of the system as a whole can be regarded as the result of the interaction by its parts.</i></li></ol><div>If we here replace, "arbitrarily high precision" and "exact" with "finite precision", the description 1-3 can be viewed as a description of </div><div><ul><li>the finite element method </li><li>as digital physics as digital computation with finite precision</li><li>as mathematical simulation of real physics as analog computation with finite precision.</li></ul><div>My long-term goal is to bring quantum mechanics into a paradigm of classical physics modified by finite precision computation, as a form of computational quantum mechanics, thus bridging the present immense gap between quantum and classical physics. This gap is described by Bohm as follows:</div><div><ul><li><i>The quantum properties of matter imply the indivisibility unity of all interacting systems. Thus we have contradicted 1 and 2 of the classical theory, since there exist on the quantum level neither well defined elements nor well defined dynamical variables, which describe the behaviour of these elements.</i></li></ul><div>My idea is thus to slightly modify classical physics by replacing "arbitrarily high precision" with "finite precision" to encompass quantum mechanics thus opening microscopic quantum mechanics to a machinery which has been so amazingly powerful in the form of finite element methods for macroscopic continuum physics, instead of throwing everything over board and resorting to a game of roulette as in the text book version of quantum mechanics which Bohm refers to.</div></div><div><br /></div><div>In particular, in this new form of computational quantum mechanics, an electron is viewed as an "element" or a "collection of elements", each element with a distinct non-overlapping spatial presence, with an interacting system of $N$ electrons described by a (complex-valued) wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ of the form </div><div><ul><li>$\psi (x,t) = \psi_1(x,t) + \psi_2(x,t)+...+\psi_N(x,t)$, (1)</li></ul></div><div>where the electronic wave functions $\psi_j(x,t)$ for $j=1,...,N$, have disjoint supports together filling 3d space, indicating the individual presence of the electrons in space and time. The system wave function $\psi (x,t)$ is required to satisfy a Schrödinger wave equation including a Laplacian </div><div>asking the composite wave functions $\psi (x,t)$ to be continuous along with derivatives across inter element boundaries. This a is a free boundary problem in 3d space and time and as such readily computable. </div><div><br /></div><div><a href="http://claesjohnson.blogspot.se/search/label/physical%20quantum%20mechanics">I have with satisfaction observed</a> that a spherically symmetric shell version of such a finite element model does predict ground state energies in close comparison to observation (within a percent) for all elements in the periodic table, and I will report these results shortly.</div><div><br /></div><div>We may compare the wave function given by (1) with the wave function of text book quantum mechanics as a linear combination of terms of the multiplicative form:</div><div><ul><li>$\psi (x_1,x_2,...x_N,t)=\psi_1(x_1,t)\times\psi_2(x_2,t)\times ...\times\psi_N(x_N,t)$,</li></ul><div>depending on $N$ 3d space coordinates $x_1,x_2,...,x_N$ and time, where each factor $\psi_j(x_j,t)$ is part of a (statistical) description of the global particle presence of an electron labeled $j$ with $x_j$ ranging over all of 3d space. Such a wave function is uncomputable as the solution to a Schrödinger equation in $3N$ space coordinates, and thus has no scientific value. Nevertheless, this is the text book foundation of quantum mechanics.</div><div><br /></div><div>Text book quantum mechanics is thus based on a model which is uncomputable (and thus useless from scientific point of view), but the model is not dismissed on these grounds. Instead it is claimed that the uncomputable model always is in exact agreement to all observations according to tests of this form: </div><div><ul><li>If a computable approximate version of this model (such as Hartree-Fock with a specific suitably chosen set of electronic orbitals) happens to be in correspondence with observation (due to some unknown happy coincidence), then this is taken as evidence that the exact version is always correct. </li><li>If a computable approximate version happens to disagree with observation, which is often the case, then the approximate version is dismissed but the exact model is kept; after all, an approximate model which is wrong (or too approximate) should be possible to view as evidence that an exact model as being less approximate must be more (or fully) correct, right? </li></ul><div><b>PS</b> The fact that the finite element method has been such a formidable success for macroscopic problems as systems made up of very many small parts or elements, gives good hope that this method will be at least as useful for microscopic systems viewed to be formed by fewer and possibly simpler (rather than more complex) elements. This fits into a perspective (opposite to the standard view) where microscopics comes out to be more simple than macroscopics, because macroscopics is built from microscopics, and a DNA molecule is more complex than a carbon atom, and a human being more complex than an egg cell. </div></div></div><div><br /></div></div>http://claesjohnson.blogspot.com/2015/08/finite-element-quantum-mechanics-1.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-9184474965000521549Sat, 15 Aug 2015 13:50:00 +00002015-08-15T21:21:09.123+02:00physical quantum mechanicsPopperQuantum ContradictionsPopper vs Physics as Finite Precision Computation<div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-H0SsB4oWdkY/Vc8_5dQT-CI/AAAAAAAA6fU/n4tl1m4zXnI/s1600/popper1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-H0SsB4oWdkY/Vc8_5dQT-CI/AAAAAAAA6fU/n4tl1m4zXnI/s320/popper1.jpg" width="240" /></a></div><div><i>Today, physics is in a crisis....it is a crisis of understanding...roughly as old as the Copenhagen interpretation of quantum mechanics...</i>(in 1982 Preface to Quantum Theory and the Schism in Physics)</div><div><br />Karl Popper's vision expressed in <a href="http://www.criticalrationalism.net/2013/09/22/postscript-to-the-logic-of-scientific-discovery-after-50-years/">The Postscript to the Logic of Scientific Discovery</a> (with the above book as Vol III), is a science of modern quantum physics which shares the following characteristics of classical physics:</div><div><ol><li>Realism</li><li>Determinism (A)</li><li>Objectivism.</li></ol><div>Popper compares this paradigm of rationality with the ruling paradigm of modern physics being the exact opposite as an irrationality characterised by:</div></div><div><ol><li>Idealism</li><li>Indeterminism (B)</li><li>Subjectivism.</li></ol><div>The crisis of modern physics acknowledged by all prominent physicists of today, can be viewed as an effect of (B). It is no wonder that (B) being an irrational opposite to a rational (A), has led to a crisis. </div><div><br /></div><div>The reason the paradigm (A) of classical macroscopic physics was replaced by (B) when Planck-Bohr-Born-Heisenberg shaped the ruling (Copenhagen) paradigm of modern physics, was a perceived impossibility to (i) explain the phenomena of black-body radiation by classical electrodynamics and (ii) to give the standard multi-dimensional (uncomputable) wave function of Schrödinger's equation describing microsopic atomic physics, a physical meaning. </div><div><br /></div><div>I have been led to a version of Popper's paradigm (A) viewing physics as</div><div><ul><li>finite precision computation </li></ul></div><div>where (i) and (ii) can be handled in a natural way and the resort to the extreme position (B) can be avoided. This paradigm is outlined as <a href="https://computationalblackbody.wordpress.com/">Computational Blackbody Radiation</a> and <a href="https://claesjohnsonmathscience.wordpress.com/">The World as Computation</a>. </div></div><div><br /></div><div>In particular I have explored a computable <a href="http://claesjohnson.blogspot.se/search/label/physical%20quantum%20mechanics">three-dimensional alternative version of Schrödinger's equation conforming to (A) </a>and I will present computational results in upcoming posts. In particular, it appears that this (computable) version explains the periodic table more directly than the standard (uncomputable) one. More precisely, an uncomputable mathematical model is useless and cannot be used to explain anything.<br /><br /><b>PS</b> The crisis in physics rooted in the Copenhagen interpretation has deepened after Poppers 1982 analysis, following a well known tactic to handle a pressing problem, which appears to be unsolvable: make the problem even more severe and unsolvable and thereby relieve the pressure from the original problem. Today we can observe this tactic in extreme form with physicists flooding media with fantasy stories about dark matter, dark energy, parallel worlds and cats in superposition of being both dead and alive, all phenomena of which nothing is known. The Dark Ages appears as enlightened against this background.</div>http://claesjohnson.blogspot.com/2015/08/popper-vs-physics-as-finite-precision.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-5984106768228248365Tue, 04 Aug 2015 14:17:00 +00002015-08-05T18:03:36.216+02:00KTH-gateKTH-gate2KTH-gate3simulation technologyDystert Resultat av KTH-Gate = Noll: SimuleringsTeknik Läggs Ner<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-HFEomyy-U64/VcEOv5oZTVI/AAAAAAAA6e0/aj5h8119qYw/s1600/einstein.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="218" src="http://2.bp.blogspot.com/-HFEomyy-U64/VcEOv5oZTVI/AAAAAAAA6e0/aj5h8119qYw/s320/einstein.jpg" width="320" /></a></div><br />KTH-gate är benämningen på på den aktion som KTH riktade mot mitt verk som innebar att min ebok<a href="http://www.nada.kth.se/~cgjoh/preview/bodysoul.pdf"> Mathematical Simulation Technology (MST) </a>avsedd att användas inom det nya kandidatprogrammet i Simuleringsteknik och Virtuell Design (STVD), mitt under pågående testkurs under HT10 förbjöds av KTH (för en fullständig redogörelse för detta drama, som saknar motsvarighet inom demokratisk stats akademi, se <a href="http://claesjohnson.blogspot.se/search/label/KTH-gate">här</a>, <a href="http://claesjohnson.blogspot.se/search/label/KTH-gate2">här</a>, <a href="http://claesjohnson.blogspot.se/search/label/KTH-gate3">här</a> och <a href="http://claesjohnson.blogspot.se/search/label/simulation%20technology">här</a>).<br /><br />Resultatet av censuringripandet blev att kandidatprogrammet separerades från den grupp av lärare som initierat programmet med avsikt att driva detsamma och för detta fått KTHs stöd. Sålunda startade STVD HT12 på en grund av gamla kurser i numerisk analys under ledning av en annan grupp lärare i numerisk analys, detta utan marknadsföring och resultatet blev därefter: Noll intresse, noll söktryck, noll intagningsbetyg, noll aktualitet = noll resultat.<br /><br />KTH insåg efter två år att det var totalt meningslöst att driva ett sådant program och HT14 fattade så Leif Kari, skolchef på skolan för Teknikvetenskap och huvudansvarig för censureringen av MST, det helt följdriktiga beslutet att lägga ner STVD (eller med omskrivning låta det vara "vilande") enligt <a href="http://www.csc.kth.se/~cgjoh/STVD1.pdf">denna offentliga handling</a> (som registrator vänligt nog grävt fram då varken Leif Kari eller någon annan inblandad velat svara på mina upprepade frågor om status för STVD). Man kan i denna skakande rapport läsa:<br /><div class="separator" style="clear: both; text-align: center;"></div><ul><li><i>väldigt lågt söktryck</i></li><li><i>stora svårigheter för studenterna att klara studierna</i></li><li><i>förkunskaper alldeles för svaga</i></li><li><i>mindre an 20% klarar uppflyttningskraven. </i></li></ul>Så har då KTH lyckats med sitt uppsåt att stoppa ett alltför lovande initiativ från en alltför internationellt stark gruppering på KTH, under uppvisande av komplett inkompetens på alla nivåer. KTH har således genom censur förstört ett potentiellt högt värde och ersatt det med noll. Bra jobbat enligt KTHs rektor Peter Gudmundson, som aktivt deltog i bokbränningen 2010; när böcker bränns återstår bara aska.<br /><div><br /></div>Ironiskt nog har Leif Kari och Skolan för Teknikvetenskap dock inte låtit sig nedslås av detta dystra resultat utan arbetar nu aktivt för att uppgradera det havererade kandidatprogrammet i Simuleringsteknik till ett nytt <a href="https://people.kth.se/~dary/tm/tm-application_2015-03-02.pdf">civilingenjörsprogram i Teknisk Matematik</a> enligt <a href="http://www.csc.kth.se/~cgjoh/STVD2.pdf">detta tilläggsbeslut. </a>Fakultetsrådet har naturligtvis inte tillstyrkt inrättandet av detta program (se<a href="https://intra.kth.se/polopoly_fs/1.575615!/FR%202015-06-09%20protokoll.pdf"> här 13d</a>), då logiken saknas: Om KTH inte är kapabelt att driva en kandidatutbildning inom teknisk matematik/simuleringsteknik, är KTH (som landets främsta tekniska högskola) än mindre kapabelt att driva ett civilingenjörsprogram med samma inriktning.<br /><br /><b>PS</b> <a href="http://www.studentum.se/Kandidatprogram_simuleringsteknik_och_virtuell_design_EJ_aak_1_endast_till_aak_2_eller_3_senare_del_av_program_334189.htm">Så här</a> beskrevs programmet av KTH när det startade 2012:<br /><ul><li><i>Simuleringsteknik och virtuell design är ett nytt program på KTH som utvecklats för att möta det ökande behovet av datorsimulering. </i></li><li><i>Utbildningen ger dig karriärmöjligheter inom många branscher, från verkstads- och processindustri, miljö- och energisektorn, via dataspel och animering, medicin och bioteknik till finansbranschen. </i></li><li><i>Du kan exempelvis jobba som beräkningskonsult, expert på visualisering och informationsgrafik eller som programdesigner. </i></li><li><i>Det nya kandidatprogrammet bygger på <b>en mycket stark forsknings- och utbildningsmiljö inom detta område på KTH och är unikt i Sverige.</b></i></li></ul><div>Ja, det är sannerligen unikt med sådan missskötsel, trots (eller kanske på grund av) KTHs priviligierade position. </div><div><br /></div><div></div>http://claesjohnson.blogspot.com/2015/08/dystert-resultat-av-kth-gate-noll.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-8827761514398483969Sat, 25 Jul 2015 12:20:00 +00002015-07-27T20:14:50.795+02:00Quantum ContradictionsFrank Wilczek: Ugly Answer to Ugly Question<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-2RbJS0L_eeo/VbN7t8R7uyI/AAAAAAAA6dE/2WKCrVdTxSQ/s1600/wilczek.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-2RbJS0L_eeo/VbN7t8R7uyI/AAAAAAAA6dE/2WKCrVdTxSQ/s320/wilczek.jpg" width="212" /></a></div><br />In his new book <a href="http://www.amazon.com/Beautiful-Question-Finding-Natures-Design/dp/1594205264">A Beautiful Question: Finding Nature's Deep Design, Frank Wilczek</a> (Nobel Prize in Physics 2004) starts out stating the questions (or paradoxes) which motivated the development of modern physics:<br /><i><br /></i><i>In the quantum world of atoms and light, Nature treats us to a show of strange and seemingly impossible feats. Two of these feats seemed, when discovered, particularly impossible:</i><br /><div><ul><li><i>Light comes in lumps. This is demonstrated in the photoelectric effect, as we’ll discuss momentarily. It came as a shock to physicists. After Maxwell’s electromagnetic theory was confirmed in Hertz’s experiments (and later many others), physicists had thought they understood what light is. Namely, light is electromagnetic waves. But electromagnetic waves are continuous.</i></li><li><i>Atoms have parts, but are perfectly rigid. Electrons were first clearly identified in 1897, by J. J. Thomson. The most basic facts about atoms were elucidated over the following fifteen years or so. In particular: atoms consist of tiny nuclei containing almost all of their mass and all of their positive electric charge, surrounded by enough negatively charged electrons to make a neutral whole. Atoms come in different sizes, depending on the chemical element, but they’re generally in the ballpark of</i> $10^{-8}$ <i>centimeters, a unit of length called an angstrom. Atomic nuclei, however, are a hundred thousand times smaller. The paradox: How can such a structure be stable? Why don’t the electrons simply succumb to the attractive force from the nucleus, and dive in.</i></li><li><i>These paradoxical facts led Einstein and Bohr, respectively, to propose some outrageous, half-right hypotheses that served as footholds on the steep ascent to modern quantum theory. </i></li><li><i>After epic struggles, played out over more than a decade of effort and debate, an answer emerged. It has held up to this day, and its roots have grown so deep that it seems unlikely ever to topple.</i></li></ul><a href="http://frankwilczek.com/">Wilczek</a> then proceeds to prepare us to accept the answers offered by the modern physics of quantum mechanics as the result of<i> epic struggles:</i><br /><ul><li><i>The framework known as quantum theory, or quantum mechanics, was mostly in place by the late 1930s. </i></li><li><i>Quantum theory is not a specific hypothesis, but a web of closely intertwined ideas. I do not mean to suggest quantum theory is vague—it is not. </i></li><li><i>With rare and usually temporary exceptions, when faced with any concrete physical problem, all competent practitioners of quantum mechanics will agree about what it means to address that problem using quantum theory. </i></li><li><i>But few, if any, would be able to say precisely what assumptions they have made to get there. Coming to terms with quantum theory is a process, through which the work will teach you how to do it.</i></li></ul><div>We learn that quantum mechanics is not built on specific hypotheses or assumptions, but nevertheless <i>is not vague</i>, and instead rather is<i> a process </i>monitored by <i>competent practitioners. </i>In any case, Wilczek proceeds to give us a glimpse of the basic hypothesis:</div><div><ul><li><i>In quantum theory’s description of the world, the fundamental objects are ....wave functions.</i></li><li><i>Any valid physical question about a physical system can be answered by consulting its wave function.</i></li><li><i>But the relation between question and answer is not straightforward. Both the way that wave functions answer questions and the answers they give have surprising—not to say weird—features.</i></li></ul><div>OK, so we are now enlightened by understanding that the answers that come out are weird. Wilczek continues:</div><ul><li><i>I will focus on the specific sorts of wave functions we need to describe the hydrogen atom: </i></li><li><i>We are interested, then, in the wave function that describes a single electron bound by electric forces to a tiny, much heavier proton.</i></li><li><i>Before discussing the electron’s wave function, we’ll do well to describe its probability cloud. The probability cloud is closely related to the wave function. The probability cloud is easier to understand than the wave function, and its physical meaning is more obvious, but it is less fundamental. (Those oracular statements will be fleshed out momentarily).</i></li><li><i>Quantum mechanics does not give simple equations for probability clouds. Rather, probability clouds are calculated from wave functions.</i></li><li><i>The wave function of a single particle, like its probability cloud, assigns an amplitude to all possible positions of the particle. In other words, it assigns a number to every point in space. </i></li><li><i>To pose questions, we must perform specific experiments that probe the wave function in different ways.</i></li><li><i>You get probabilities, not definite answers.</i></li><li><i>You don’t get access to the wave function itself, but only a peek at processed versions of it.</i></li><li><i>Answering different questions may require processing the wave function in different ways.</i></li><li><i>Each of those three points raises big issues.</i></li></ul></div></div><div><div>Wilczek then tackles these issues by posing new questions, or lacking question by retreating to an admirable attitude of <i>humility in a lesson of wisdom</i>: </div><div><ul><li><i>The first raises the issue of determinism. Is calculating probabilities really the best we can do?</i></li><li><i>The second raises the issue of many worlds. What does the full wavefunction describe, when we’re not peeking? Does it represent a gigantic expansion of reality, or is it just a mind tool, no more real than a dream?</i></li><li><i>The third raises the issue of complementarity....It is a lesson in humility that quantum theory forces to our attention. To probe is to interact, and to interact is potentially to disturb.</i></li><li><i>Complementarity is both a feature of physical reality and a lesson in wisdom.</i></li></ul><div>We see that Wilczek sells the usual broth of <i>strange and seemingly impossible feats, weird features</i>, and <i>outrageous half-right hypotheses, </i>all <i>raising big issues. </i>Wilczek sums up by the following quote of Walt Whitman under the headline<i> COMPLEMENTARITY AS WISDOM:</i></div></div></div><div><div><br /></div><div> <i>Do I contradict myself?</i></div><div><i> Very well, then, I contradict myself,</i></div><div><i> I am large, I contain multitudes.</i></div><div><br /></div><div>But physics is not poetry, and contradictory poetry does not justify contradictory physics. Contradictory mathematical physics cannot be true real physics, not even meaningful poetry. To get big by contradiction is a trade of politics, which is ugly and not beautiful.<br /><br />Nevertheless, Wilczek started his Nobel lecture as follows:<br /><ul><li><i>In theoretical physics, paradoxes are good. That’s paradoxical, since a paradox appears to be a contradiction, and contradictions imply serious error. But Nature cannot realize contradictions. When our physical theories lead to paradox we must find a way out. Paradoxes focus our attention, and we think harder.</i></li></ul><div>We understand that to Wilczek/modern physicists, contradictions are good rather than catastrophical and the more paradox the better, since it makes physicists <i>focus attention to think harder. </i> Beautiful. For more excuses, see <a href="http://frankwilczek.com/Wilczek_Easy_Pieces/317_What_Is_Quantum_Theory.pdf">What Is Quantum Theory</a>. Wilczek here retells the story of the Father (or Dictator) of Quantum Mechanics, Niels Bohr:<br /><ul><li><i>How wonderful that we have met with a paradox. Now we have some hope of making progress.</i></li></ul><div>The paradox presented itself in 1925, but what happened to the hope of progress? Is paradoxical physics the physics of our time? Does light come in lumps? Why are atoms stable? Despite paradoxes, no real progress for 90 years!!??</div></div><div class="page" title="Page 1"><div class="section"><div class="layoutArea"><div class="column"></div></div></div></div><b><br /></b><b>PS1</b> Here is the question killing the probability interpretation of the wave function: Since the wave function for the ground state of Hydrogen is non-zero even far away from the kernel, does it mean that there is a non-zero chance of experimentally detecting a Hydrogen ground state electron far away from the kernel it is associated with? Or the other way around, since the wave function is maximal at zero distance from the kernel, does it mean that one will mostly find the electron hiding inside the kernel?<br /><br /><b>PS2</b> Beauty is an expression of order and <i>deep design,</i> not of disorder and lack of design. An atomistic world ruled by chance can be beautiful only to a professional statistician obsessed by computing mean values.<br /><br /><b>PS3</b> <a href="http://www.math.columbia.edu/~woit/wordpress/?p=7881">Not Even Wrong</a> presents the book as follows: <i>Frank Wilczek’s new book, <a href="http://thepenguinpress.com/book/a-beautiful-question-finding-natures-deep-design/">A Beautiful Question</a>, is now out and if you’re at all interested in issues about beauty and the deep structure of reality, you should find a copy and spend some time with it. As he explains at the very beginning:</i><br /><ul><li><i>This book is a long meditation on a single question:</i></li><li><i>Does the world embody beautiful ideas?</i></li></ul><i>To me (and I think to Wilczek), the answer to the question has always been an unambiguous “Yes”. The more difficult question is “what does such a claim about beauty and the world mean?” and that’s the central concern of the book.</i><br /><i><br /></i><b>PS4 </b>Wilczek expresses a tendency shared by many modern physicists of pretending to know all of chemistry "in principle", simply by writing down a Schrödinger equation on a piece of paper, however without actually being able to predict anything specific because solutions of the equation cannot by computed: </div><div><ul><li><i>Wave functions that fully describe the physical state of several electrons occupy spaces of very high dimension. The wave function for two electrons lives in a six-dimensional space, the wave function for three electrons lives in a nine-dimensional space, and so forth. The equations for these wave functions rapidly become quite challenging to solve, even approximately, and even using the most powerful computers. This is why chemistry remains a thriving experimental enterprise, even though in principle we know the equations that govern it, and that should enable us to calculate the results of experiments in chemistry without having to perform them.</i></li></ul><div>In this illusion game, the uncomputability of the Schrödinger's many-dimensional equation relieves the physicist from the real task of explaining the actual physics of chemistry, while the physicist can still safely take the role of being in charge of principal theoretical chemistry underlying a "thriving experimental enterprise", which "in principle" is superfluous. Beautiful? </div></div><div><br /><br /></div><div></div></div>http://claesjohnson.blogspot.com/2015/07/wilczek-ugly-answers-to-ugly-questions.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-63841630381889006Mon, 13 Jul 2015 17:44:00 +00002015-07-25T14:31:15.678+02:00climate scienceJohan Rockström: CO2 Global Warming May Prevent New Ice Age<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-tQ31GbqONfg/VaP4SBihrRI/AAAAAAAA6cQ/5049H778Jfg/s1600/JR_1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="238" src="http://3.bp.blogspot.com/-tQ31GbqONfg/VaP4SBihrRI/AAAAAAAA6cQ/5049H778Jfg/s400/JR_1.jpg" width="400" /></a></div><br /><br /><a href="http://sverigesradio.se/sida/avsnitt/571827?programid=2071">Johan Rockström,</a> Executive Director of <a href="http://www.stockholmresilience.org/21/contact/staff/1-16-2008-rockstrom.html">Stockholm Resilience Centre</a> and leading Swedish CO2 global warming alarmist, <a href="http://sverigesradio.se/sida/avsnitt/576264?programid=1637">admits that emission of CO2 may prevent new ice age</a> (1.24 into news program):<br /><ul><li><i>Paradoxically this appears to be a positive effect of global warming.</i></li></ul><div>This adds another paradox to the already long list of paradoxes of CO2 global warming.</div>http://claesjohnson.blogspot.com/2015/07/johan-rockstrom-co2-global-warming-may.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-3614111181938133374Sat, 04 Jul 2015 07:17:00 +00002015-07-05T11:39:54.053+02:00climate politicscrisis in physicsQuantum ContradictionsCollapse of Modern Physics: Mainau Declaration 2015 on Climate Change<div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-aGZERqfJoQ8/VZeITsOCrII/AAAAAAAA6bg/RS2pG_xfTM4/s1600/mainaudec_slider.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="152" src="http://4.bp.blogspot.com/-aGZERqfJoQ8/VZeITsOCrII/AAAAAAAA6bg/RS2pG_xfTM4/s400/mainaudec_slider.jpg" width="400" /></a></div><br /><a href="http://www.lindau-nobel.org/the-mainau-declaration-2015-on-climate-change/">The Mainau Declaration 2015 on Climate Change</a> made at the 65th Lindau Nobel Laureate Meeting on Mainau Island at Lake Constance and signed by the following physicists, among 35 other Laureates, Stephen Chu, Peter Doherty, David Gross, Brian Schmidt and George Smooth, states that (with my numbering an comments added):</div><div><ol><li><i>We believe that our world today faces another threat (global warming) of comparable magnitude to that of nuclear weapons. </i>(Comparable in what sense?)</li><li><i>Successive generations of scientists have helped create a more and more prosperous world. </i>(Physicists are helping mankind to prosperity) </li><li><i>This prosperity has come at the cost of a rapid rise in the consumption of the world’s resources. </i>(Poor people are consuming more and more)</li><li><i>If left unchecked, our ever-increasing demand for food, water, and energy will eventually overwhelm the Earth’s ability to satisfy humanity’s needs, and will lead to wholesale human tragedy. </i>(Ultimate doomsday scenario. Purpose?)</li><li><i>Already, scientists who study Earth’s climate are observing the impact of human activity. </i>(What impact?)</li><li><i>In response to the possibility of human-induced climate change, the United Nations established the Intergovernmental Panel on Climate Change (IPCC) to provide the world’s leaders a summary of the current state of relevant scientific knowledge. </i>(Scientists will tell what to do)</li><li><i>While by no means perfect, we believe that the efforts that have led to the current IPCC Fifth Assessment Report represent the best source of information regarding the present state of knowledge on climate change.</i> (Best source compared to what?)</li><li><i>We say this not as experts in the field of climate change, but rather as a diverse group of scientists who have a deep respect for and understanding of the integrity of the scientific process.</i> (Physicists know nothing about climate)</li><li><i>Although there remains uncertainty as to the precise extent of climate change, the conclusions of the scientific community contained in the latest IPCC report are alarming, especially in the context of the identified risks of maintaining human prosperity in the face of greater than a 2°C rise in average global temperature. </i>(Uncertainty as to precise extent? But alarming! Identified risks? Human prosperity to whom?)</li><li><i>The report concludes that anthropogenic emissions of greenhouse gases are the likely cause of the current global warming of the Earth. Predictions from the range of climate models indicate that this warming will very likely increase the Earth’s temperature over the coming century by more than 2°C above its pre-industrial level unless dramatic reductions are made in anthropogenic emissions of greenhouse gases over the coming decades. </i>(Effect of dramatic reduction? On climate? On people?)</li><li><i>Based on the IPCC assessment, the world must make rapid progress towards lowering current and future greenhouse gas emissions to minimize the substantial risks of climate change. </i>(Rapid progress? Minimize substantial risks?)</li><li><i>We believe that the nations of the world must take the opportunity at the United Nations Climate Change Conference in Paris in December 2015 to take decisive action to limit future global emissions. </i>(Decisive actions by whom? Limit future global emissions, for whom?) </li><li><i>This endeavor will require the cooperation of all nations, whether developed or developing, and must be sustained into the future in accord with updated scientific assessments. </i>(Physicists will tell the world what to do)</li><li><i>Failure to act will subject future generations of humanity to unconscionable and unacceptable risk. </i>(Failure to do what? What is unconscionable and unacceptable risk?</li></ol><div>The fact that Physics Nobel Laureates sign a political document like this can be seen as a logical consequence of the collapse in modern physics of the rationality of classical physics, a collapse into stupidity which will subject future generations of humanity to unconscionable and unacceptable risks. </div></div>http://claesjohnson.blogspot.com/2015/07/collapse-of-modern-physics-mainau.htmlnoreply@blogger.com (Claes Johnson)3tag:blogger.com,1999:blog-1500584444083499721.post-2337588141393646785Thu, 25 Jun 2015 20:07:00 +00002015-08-29T08:22:57.490+02:00finite precision computationmany-minds relativityphysical quantum mechanicsQuantum Contradictionstheory of relativityModern Physics: Meaningless Sacrifice of Causality, Rationality and Reality?<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-zfvzOiviKBM/VYz8X7PD5RI/AAAAAAAA6aM/lOLjZY5dI4Y/s1600/Helmholtzcrop.jpg" imageanchor="1"><img border="0" height="400" src="http://4.bp.blogspot.com/-zfvzOiviKBM/VYz8X7PD5RI/AAAAAAAA6aM/lOLjZY5dI4Y/s400/Helmholtzcrop.jpg" width="273" /></a></div>Hermann von Helmholtz in Conservation of Force (1862-63): <i>Reason we call that faculty innate in us of discovering laws and applying them with thought...there is a kind, I might almost say, of artistic satisfaction,when we are able to survey the enormous wealth of Nature as a regular-ordered whole--a cosmos, an image of the logical thought of our mind.</i><br /><br />Modern physics in the form of relativity theory and quantum mechanics was born from a perceived impossibility of solving the following "problems" using methods of classical deterministic continuum physics:<br /><ol><li>Second law of thermodynamics (irreversibility in formally reversible systems).</li><li>Blackbody radiation (including avoidance of an ultraviolet catastrophe).</li><li>Existence of a unique aether medium for propagation of electromagnetic waves. </li></ol><div>Boltzmann "solved" 1. by introducing statistical physics, thus giving up classical determinism or causality.<br /><br />Planck "solved" 2. introducing a smallest quantum of energy, thus giving up the classical continuum of rational mechanics.<br /><br />Einstein "solved" 3. by freeing electromagnetics from an aether, thus giving up classical coordinates of space and time describing reality. </div><div><br /></div><div>In each case the sacrifice of pillars classical physics was monumental and the grandness of the sacrifice was taken as a sign that it was inevitable and thus justified: No physicist would be willing the give up so much, unless it was absolutely necessary, as expressed by Planck excusing his introducing of the quantum:<br /><div class="page" title="Page 26"><div class="layoutArea"><div class="column"><ul><li><i>...the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be...</i></li></ul>But if one day it shows that 1-3 in fact can be handled using a mild extension of classical deterministic continuum physics, then the monumental sacrifices would be unnecessary and then without rationale.</div></div></div></div><div><br /></div><div>And yes, it may be that such a mild extension is possible in the form of <b>finite precision computation </b>exposed on <a href="https://claesjohnsonmathscience.wordpress.com/">The World as Computation.</a><br /><b><br /></b></div><div>This connects to Helmholtz' approach to 1. with heat as partly "incalculable" or "disordered" energy as energy with limited capability of being transformed to other forms of ("calculable") energy. This brings us back to the peak of classical physics represented by the mechanism of Helmholtz:<br /><ul><li><i>Natural phenomena should be traced back to the movements of material objects which possess inalterable motive forces that are dependent only on spatial relations.</i></li><li><i>Science, the goal of which is the comprehension of nature, must begin with the presupposition of its comprehensibility and proceed in accordance with this assumption until, perhaps, it is forced by irrefutable facts to recognise limits beyond it may not go.</i></li></ul><div>It thus appears to be possible to handle 1. and 2. by classical mechanism modified by finite precision computation. Further, 3. may be handled as suggested by the British physicist Ebenezer Cunningham (1881-1977) by viewing an aether is an immaterial space-time coordinate systems with the observed non-existence of a unique aether medium simply as an expression of the possibility of choosing many immaterial aethers/coordinate systems.</div><div><br /></div><div>It thus may be that the monumental sacrifices made by modern physicists in order to cope with 1-3, are not necessary, and as such represent human stupidity, rather than heroic victory of the power of the human mind as official truth of modern physics propagated by modern physicists. </div><br /></div>http://claesjohnson.blogspot.com/2015/06/modern-physics-meaningless-sacrifice-of.htmlnoreply@blogger.com (Claes Johnson)6tag:blogger.com,1999:blog-1500584444083499721.post-1511209004812306618Tue, 23 Jun 2015 07:12:00 +00002015-06-23T09:23:23.804+02:00physical quantum mechanicsQuantum Contradictionsquantum mechanicsQM on Shaky Ground, Still after 90 Years<a href="http://www.sciencedirect.com/science/referenceworks/9780125126663">Encyclopedia of Mathematical Physics</a> (2006) states in Introductory Article: Quantum Mechanics:<br /><ul><li><i>QM in its present formulation is a refined and and successful instrument for the description of the non relativistic phenomena at the Planck scale, <b>but its internal inconsistency is still standing on shaky ground.</b></i></li><li><i>In this section we describe some of the <b>conceptual problems which plague present day QM</b>...</i></li></ul><div>How is it possible that today 90 years after the formulation of Schrödinger's equation as the foundation of QM, this foundation is still inconsistent and shaky, plagued by conceptual problems. What have physicists been doing all these years?<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-ffweO3rmASA/VYkIMp2GIII/AAAAAAAA6Zs/3yd4w5W8i5Y/s1600/700px-Solvay_conference_1927.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="288" src="http://3.bp.blogspot.com/-ffweO3rmASA/VYkIMp2GIII/AAAAAAAA6Zs/3yd4w5W8i5Y/s400/700px-Solvay_conference_1927.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Solway Conference 1927</td></tr></tbody></table></div>http://claesjohnson.blogspot.com/2015/06/qm-on-shaky-ground.htmlnoreply@blogger.com (Claes Johnson)13tag:blogger.com,1999:blog-1500584444083499721.post-1110535932475464385Thu, 18 Jun 2015 20:05:00 +00002015-06-19T12:35:31.879+02:00fluid mechanicstheory of flightNew Theory of Flight Accepted for Publication in Journal of Mathematical Fluid MechanicsThe ground-breaking article <a href="http://www.csc.kth.se/~jhoffman/Johan_Hoffman_KTH/Pub_files/kth-ctl-4044.pdf">New Theory of Flight</a> is now accepted for publication in Journal of Mathematical Fluid Mechanics. The paralyzing spells of Prandtl, father of modern fluid mechanics, and Kutta and Zhukovsky, fathers of modern aerodynamics, are now finally broken after more than 100 years of misleading unphysical mathematics. A post-modern era of (computational mathematical) fluid mechanics and aerodynamics is now approaching...http://claesjohnson.blogspot.com/2015/06/new-theory-of-flight-accepted-for.htmlnoreply@blogger.com (Claes Johnson)3tag:blogger.com,1999:blog-1500584444083499721.post-1143942927723386558Sun, 14 Jun 2015 10:42:00 +00002015-06-14T20:07:33.045+02:00greenhouse effectpyrgeomterSpencer Struggles with The Greenhouse Effect and Dragons<a href="http://www.drroyspencer.com/2015/06/what-causes-the-greenhouse-effect/">Roy Spencer continues his long struggle</a> to convince the world that the Greenhouse Effect as the scientific foundation of CO2 global warming hysteria, is real physics:<br /><ul><li><i>I’ve had a request to (once again) go through an explanation of the (poorly-named) Greenhouse Effect (GHE). Hopefully there is something which follows that will help you understand this complex subject.</i></li></ul>Here is Roy's explanation:<br /><div><ul><li><i>The atmosphere DOES absorb IR energy. The IR absorption coefficients at various wavelengths, temperature, and pressures have been measured for water vapor, CO2, etc., in laboratories and published for decades.</i></li><li><i>This absorption means the atmosphere also EMITS IR energy, both upward and downward. And it is that DOWNWARD flow of IR energy (sometimes called “back radiation”) which is necessary for net warming of the surface from the greenhouse effect.</i></li></ul><div>Then Roy reveals the reason behind his irresistible urge to educate the world about the greenhouse effect:</div><div><ul><li><i>(Technical diversion: This is where the Sky Dragon Slayers get tripped up. They claim the colder atmosphere cannot emit IR downward toward a warmer surface below, when in fact all the 2nd Law of Thermodynamics would require is that the NET flow of energy in all forms be from higher temperature to lower temperature. This is still true in my discussion.)</i></li></ul></div><div>Roy's heavy weapon intended to kill those nasty Sky Dragon Slayers is:</div><ul><li><i>You can measure the greenhouse effect yourself with a <a href="http://www.drroyspencer.com/2013/05/imaging-the-greenhouse-effect-with-a-flir-i7-thermal-imager/">handheld IR thermometer pointed at the sky</a>, which measures the temperature change caused by a change in downwelling IR radiation. In a clear sky, the indicated temperature pointing straight up (“seeing” higher altitudes) will be colder than if pointed at an angle (measuring lower altitudes). This is direct evidence of the greenhouse effect…changes in downwelling IR change the temperature of a surface (the microbolometer in the handheld IR thermometer). That is the greenhouse effect.</i></li></ul>Then Roy shows that he is a humble and open-minded serious scientist: </div><div><ul><li><i>If I’ve make a mistake in the above, I’ll fix it. I realize some might not like the way I’ve phrased certain things. But I’ve been working in this field over 20 years, and the above is the best I can do in 1-2 hours time....you will find it is a complex subject, indeed.</i></li></ul><div>And yes Roy, you make a mistake by uncritically accepting a reading of a hand-held IR-thermometer, which being a thermometer measures temperature, as evidence of the reality of downward IR. You can read about your mistake under the<a href="http://claesjohnson.blogspot.se/search/label/pyrgeometer"> category "pyrgeometer"</a> including the following key posts:</div></div><div><ul><li><a href="http://claesjohnson.blogspot.se/2011/08/how-to-fool-yourself-with-pyrgeometer.html">How to Fool Yourself with a Pyrgeometer</a></li><li><a href="http://claesjohnson.blogspot.se/2013/01/ghe-fabricated-by-kipp.html">GHE Fabricated by Kipp&Zonen Pyrgeometer</a></li><li><a href="http://claesjohnson.blogspot.se/2013/02/big-bluff-of-pyrgeometer-dlr-as.html">The DLR-meter Formula behing CO2 Alarmism</a></li><li><a href="http://claesjohnson.blogspot.se/2013/02/big-bluff-of-pyrgeometer-dlr-as.html">BIG BLUFF: Pyrgeometer DLR as Bolometer OLR</a></li></ul><div>And so Roy, what is your reaction to the evidence I present?<br /><br /><b>PS</b> Roy appears to filter my comment to his post with a link to the above. Of course, it is Roy's responsibility to guarantee that his readers and users/buyers (not to speak of manufacturers such as Kipp&Zonen) of hand-held IR-thermometers, are not reached by disturbing information: Nobody wants to get told that the reading of a thermometer is temperature, since that is so evident to anyone with slightest education in science. In particular, Roy does not want to get told that he has been cheated by Kipp&Zonen in believing that the thermometer he bought measures Downwelling Longwave Radiation (DLR) and not temperature , and accordingly will no respond to my question. Under the choice of saying something (and revealing ignorance), and saying nothing (only indicating ignorance), Roy chooses to say nothing. But nothing is nothing.<br /><br /></div></div><div><br /></div>http://claesjohnson.blogspot.com/2015/06/spencer-struggles-with-greenhouse-effect.htmlnoreply@blogger.com (Claes Johnson)2tag:blogger.com,1999:blog-1500584444083499721.post-7430000438986448010Sat, 13 Jun 2015 18:43:00 +00002015-06-13T20:59:50.279+02:00Quantum Contradictionsquantum mechanicsThe Copenhagen Interpretation of Quantum Mechanics??If you ask a physicist today about the foundations of modern physics (the theory of relativity and quantum mechanics), you will get most likely get the answer that all basic questions were answered long ago and neither questions nor answers need to be repeated. In short, "science is settled", and the question now is simply how to advance physics further into the unknowns of dark matter, dark energy, string theory and multiversa.<br /><div><br /></div><div>In particular, the answer for quantum mechanics is the Copenhagen Interpretation coined by Heisenberg in the 1950s as an expression of the influence of the Danish physicist Niels Bohr during the formative years of modern physics following the introduction by Max Planck in 1900 of the smallest quantum of action $h$. </div><div><br /></div><div>One of the few who still worries about the foundations of quantum mechanics is Lubos Motl, who in a sequence of posts on <a href="http://motls.blogspot.se/2011/05/copenhagen-interpretation-of-quantum.html">The Reference Frame states his commitment to the Copenhagen Interpretation</a> based on the following postulates:</div><ol><li><i>A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)</i></li><li><i>The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)</i></li><li><i>It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)</i></li><li><i>Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.</i></li><li><i>Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.</i></li><li><i>The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)</i> </li></ol><div>Let us now analyze these postulates from scientific point of view. We find:</div><div><ol><li>The idea that the wave function represents the subjective knowledge of a system, makes quantum mechanics into a personal experience, which cannot be science.</li><li>The idea that nature "essentially is probabilistic" is an ad hoc assumption, which can never be experimentally tested and thus does not belong to science.</li><li>Impossibility of knowledge contradicts scientific principle: Why does certain knowledge make other knowledge impossible?</li><li>Wave-particle duality as contradictory reality, does no make sense.</li><li>Divison of physics into "classical" and "non-classical" is without reason. Physics is physics.</li><li>Without division between "classical" and "non-classical", the idea that "non-classical" will approximate "classical", lacks rationale. </li></ol><div>I leave to the reader to evaluate the scientific value and rationality of these postulates supposedly expressing the contribution to humanity and the science of physics from what is called "modern physics". </div><div><br /></div></div>http://claesjohnson.blogspot.com/2015/06/the-copenhagen-interpretation-of.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-8772978562281936503Sat, 13 Jun 2015 07:04:00 +00002015-06-13T09:16:06.648+02:00physical quantum mechanicsQuantum Contradictionsquantum mechanicsThe Creation of Quantum Mechanics: The True Story by J Hendry Part 1<a href="http://www.amazon.com/Creation-Quantum-Mechanics-Bohr-Pauli-Dialogue/dp/902771648X"><i>The Creation of Quantum Mechanics and the Bohr-Pauli Dialog </i>by John Hendry</a> is presented as<br /><ul><li>a<i> genuine "history" as opposed to a mere technical report or popular or semi-popular account.</i></li><li><i>My aims in making this attempt have been to satisfy the needs of historians of science and, more especially, to promote a serious interest in the history of science among physicists and physics students.</i></li></ul>Hendry states in the Introduction:<br /><ul><li><i>On one hand the quantum theory has continued in all its formulations to show a remarkable predictive power in respect of experimental observations. In this respect it must rank as an extraordinarily successful physical theory, and as one that will not easily be displaced.</i></li><li><i>On the other hand, however, <b>dissatisfaction with the conceptual foundations of the theory has also apparently endured. </b></i></li><li><i>Many working physicists are seemingly content to accept what Einstein referred to as the <b>"gentle pillow" of the Copenhagen interpretation without asking any further questions,</b> and this has long been accepted as an orthodox position.</i></li><li><i>But if we restrict our attention to physicists (or indeed philosophers) of the first rank, then we see immediately that such an orthodoxy is illusory. It was created in the late 1920s when many of the leading quantum physicists, among them Bohr, Born, Heisenberg, Pauli, Dirac, Jordan and von Neumann, sunk their more philosophical differences in an effort to repel the challenge of the semi-classical interpretations and get on with the job of developing quantum electrodynamics. </i></li><li><i>But those differences remained. <b>Copenhagenism was and is a generic term covering a whole range of related interpretations. </b>Even when these interpretations are taken together, they cannot be considered as an entirely dominant orthodoxy. Among their early opponents some physicists might arguably be dismissed as narrow-sighted conservatives. But such outright dismissal is very difficult to uphold in Einstein's case, and still more so in those of Schrödinger and de Broglie, neither of whose preferred interpretations could reasonably be labelled classical. </i></li><li><i>More recently attention has shifted from the physical interpretation of quantum mechanics towards the logical and mathematical consistency of quantum field theory, but the issues remain closely connected and<b> opposition to Copenhagenism remains strong. </b></i></li><li><i>However, and here lies the crux of the matter, <b>the opponents seem to be no nearer to providing a valid alternative than were their predecessors of the late 1920s. </b></i></li><li><i>Beyond the limited compromise of Copenhagenism <b>there is still no such thing as a consistent and generally acceptable interpretation of quantum mechanics,</b> and the evidence of the last fifty years points unerringly to the conclusion that <b>there will not be one until </b>either the structure of our physical conceptions, or our expectations of physical theory, or the <b>quantum theory itself should undergo radical changes more far-reaching than any yet seen.</b></i></li><li><i>Faced with this dilemma it is tempting to react as did Peter Debye to <b>the problem of electrons in the nucleus,</b> a problem that arose in the immediate wake of quantum mechanics, by treating it as<b> something best ignored, "like the new taxes". </b></i></li><li><i>And many physicists have indeed taken this course, either ignoring the interpretative problem altogether (paying the taxes without question) or proceeding stubbornly to seek fundamentally classical interpretations that are demonstrably not there (stalling the taxman). </i></li><li><i>But whereas such attitudes may be expedient in the short term they are <b>ultimately inconsistent </b>with the <b>very spirit of the scientific enterprise. </b></i></li><li><i><b>The interpretative problem of quantum theory is several orders more fundamental</b> than that of nuclear electrons, and has proved <b>immensely more resistant to attempts at a solution.</b> </i></li><li><i>But <b>a theory with innate inconsistencies,</b> whatever its present predictive success, cannot be expected to serve for ever. </i></li><li><i><b>If the problem, like the tax, does not bear thinking about, then that is the strongest indication we can possibly have that it needs thinking about.</b> </i></li><li><i>And while it may not be so easily solved we can at least try to understand how such an <b>extreme situation arose in the first place.</b> </i></li><li><i>One aim of this study, then, is to approach the history of the theory of quantum mechanics as a <b>means of exploring its philosophy.</b> </i></li></ul><div>What Hendry effectively says is that the foundations of quantum mechanics as physical theory was an inconsistent mess at start hundred years ago and has so remained until now. How is it then possible that this inconsistent mess "<i>has continued in all its formulations to show a remarkable predictive power in respect of experimental observations"? </i></div><div><br /></div><div>Well, the answer is that since quantum mechanics as a multi-dimensional inconsistent mess is uncomputable, it is impossible to make predictions from theory alone. This means that whatever observation is made, there is a version of quantum mechanical messy theory that can be made to conform with the observation. This is the reason why there is no observation in conflict with any quantum mechanical theory, even though the theory is inconsistent, which of course is used as evidence that the inconsistent messy theory is perfect and consistent and always in perfect consistent agreement with observation.</div><div><br /></div><div>In Part 2 I will summarize Hendry's account of the genuine "history" and then ponder Hendry's appeal:<i> <b>quantum theory itself should undergo radical changes more far-reaching than any yet seen.</b></i> </div>http://claesjohnson.blogspot.com/2015/06/the-creation-of-quantum-mechanics-true.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-5765304261614401279Fri, 12 Jun 2015 07:47:00 +00002015-06-13T09:06:06.464+02:00physical quantum mechanicsQuantum Contradictionsquantum mechanicsTragedy of Modern Physics: Born's Statistical Interpretation of Quantum Mechanics<div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-7ENxe49q0bU/VXqnaPRBW8I/AAAAAAAA5v4/OxgrsOXRDeM/s1600/Born.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-7ENxe49q0bU/VXqnaPRBW8I/AAAAAAAA5v4/OxgrsOXRDeM/s320/Born.jpg" width="248" /></a></div><div class="separator" style="clear: both; text-align: center;"><i>Max Born in 1926 just after violating principles of classical physics of reality and causality: </i></div><div class="separator" style="clear: both; text-align: center;"><i><a href="http://cds.cern.ch/record/141137/files/cer-000052203.pdf?version=1">"A way had to be found for reconciling particles and waves"</a>. </i></div><br />Max Born was awarded the Nobel Prize in physics in 1954 for his statistical interpretation of solutions of <i>Schrödinger's wave equation </i>named <i>wave functions.</i> Schrödinger formulated his equation, which has come to serve as the basic mathematical model of the modern physics of quantum mechanics, in a moment of heavenly inspiration in the Alps in 1926 (together with one of his many girl friends), with the objective of interpreting the modulus squared $\vert\psi\vert^2$ of a wave function $\psi$ as <i>charge distribution.</i> </div><div><br /></div><div>But there was a problem with this interpretation: For an atom with $N$ electrons, Schrödinger's wave function depends on $3N$ space coordinates, which allows a direct physical meaning only in the case of Hydrogen with $N=1$. Schrödinger could not get around this obstacle and his equation was instead hi-jacked by Heisenberg and Born supported by Bohr and was then twisted into the so-called Copenhagen Interpretation with the wave function a <i>probability distribution of particle positions</i> viewed to represent wave-particle duality as the incarnation of the new physics. </div><div><br /></div><div>Schrödinger could not accept this probabilistic destruction of causality, but was effectively marginalized (together with Einstein and Planck and Lorentz and others) by the Bohr Copenhagen school leading the world into a new modern physics of wave-particle duality and complementarity outside classical rationality. </div><div><br /></div><div>It did not help that grandfather Lorentz joined Schrödinger's protest:</div><div><ul><li> <i>I care little for the conception of </i>$\vert\psi^2\vert$ <i> as a probability...In the case of an H-atom there is for a given energy E, also a non-vanishing probability outside the sphere which electrons of energy E cannot leave.</i> </li></ul></div><div>The Copenhagen interpretation took the lead and today we can see the result as a tragedy of modern physics dominated by string theory and multiversa beyond any rationality.</div><div><br /></div><div><a href="http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf">Born describes in his Nobel lecture</a> the sacrifice of classical ideals (or crime) which a modern physicist must be willing to commit: </div><div><ul><li><i><b>It is necessary to drop completely the physical pictures of Schrödinger </b>which aim at a revitalization of the classical continuum theory, <b>to retain only the formalism and to fill that with new physical content.</b></i></li></ul></div><div>To commit a crime requires a motivation and to commit a big crime requires a strong motivation. The first step on this road of modern physics was taken by Planck in 1900:</div><div><div><ul><li><i>The whole procedure was <b>an act of despair</b> because a theoretical interpretation (of black-body radiation) <b>had to be found at any price</b>, <b>no matter how high that might be</b>…<b>I was ready to sacrifice any of my previous convictions about physics.</b>..For this reason, on the very first day when I formulated this law, I began to devote myself to the task of investing it with true physical meaning.</i></li></ul></div></div><div>Einstein followed up in 1905 with his special relativity asking humanity to sacrifice classical concepts of space and time. In both cases, the grandness of the sacrifice supported credibility. </div><div><br /></div><div>In describing his crime Born first gives credit to scientists following the law: </div><div><ul><li><i>Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. <b>Such weighty views cannot be ignored. </b></i></li></ul></div><div>Born then recalls the historic fact that Bohr was stronger, adding an excuse that the crime rather concerns philosophy than physics: </div><div><ul><li><i>Niels Bohr has gone to a great deal of trouble to refute the objections. I, too, have ruminated upon them and believe I can make some contribution to the clarification of the position. The matter concerns the borderland between physics and philosophy, and so my physics lecture will partake of both history and philosophy, for which I must crave your indulgence.</i></li><li><i>The work, for which I have had the honour to be awarded the Nobel Prize for 1954, contains no discovery of a fresh natural phenomenon, but rather the basis for a <b>new mode of thought in regard to natural phenomena.</b></i></li></ul><div>Next follows an excuse with reference to "intellectual crisis": </div></div><div><div><ul><li><i>The first point is this: the work at the Göttingen school, which I directed at that time (1926-I927), contributed to the solution of an <b>intellectual crisis into which our science had fallen as a result of Planck’s discovery of the quantum of action</b> in 1900.</i></li><li><i>At the beginning of the twenties, every physicist, I think, was convinced that Planck’s quantum hypothesis was correct. According to this theory energy appears in finite quanta of magnitude </i>$h\nu$<i> in oscillatory processes having a specific frequency </i>$\nu$ <i>(e.g. in light waves). <b>Countless experiments could be explained in this way</b> and always gave the same value of Planck’s constant </i><i>.</i></li></ul></div><div>Then Born puts the blame on Heisenberg, his assistant:</div><i></i><br /><ul><i><li><i>Heisenberg, who at that time was my assistant, brought this period to a sudden end. He cut the Gordian knot by means of a philosophical principle and replaced guess-work by a mathematical rule. <b>The principle states that concepts and representations that do not correspond to physically observable facts are not to be used in theoretical description. </b></i></li><li>I was as excited by this result as a sailor would be who, after a long voyage, sees from afar, the longed-for land...I was convinced from the start that we had stumbled on the right path.</li></i></ul><i></i><br /><div>Next, the success in the case $N=1$ is taken as evidence that the theory is correct for $N>1$:</div><div><ul><li><i>The first non-trivial and physically important application of quantum mechanics was made shortly afterwards by W. Pauli who calculated the stationary energy values of the hydrogen atom by means of the matrix method and found complete agreement with Bohr’s formulae. From this moment onwards there could no longer be any doubt about the correctness of the theory . </i></li></ul><div>But some doubts presented themselves:</div></div><div><ul><li><i>What this formalism really signified was, however, by no means clear. <b>Mathematics, as often happens, was cleverer than interpretative thought. </b></i></li></ul><div>In any case, Schrödinger's wave equation was accepted as the right thing, but not Schrödinger's interpretation of $\vert\psi\vert^2$ as charge density:</div><ul><li><i>Wave mechanics enjoyed a very great deal more popularity than the Göttingen or Cambridge version of quantum mechanics. It operates with a wave function $\psi$, which in the case of one particle at least, can be pictured in space, and it uses the mathematical methods of partial differential equations which are in current use by physicists. Schrödinger thought that his wave theory made it possible to return to deterministic classical physics. <b>He proposed</b> (and he has recently emphasized his proposal anew’s), <b>to dispense with the particle representation entirely, </b>and instead of speaking of electrons as particles, to consider them as a continuous density distributions. </i></li></ul>And then Born's commits the crime:<br /><ul><li><i>I immediately took up Schrödinger's method and an idea of Einstein’s gave me the lead. He had tried<b> to make the duality of particle-light quanta or photons and waves comprehensible</b> by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. </i></li><li><i>This concept could at once be carried over to the $\psi$-function:<b> it ought to represent the probability density for electrons</b> (or other particles). </i></li><li><i>It was easy to assert this, <b>but how could it be proved?</b></i></li></ul><div>Here is Born's justification of the crime:</div><div><ul><li><i>To us in Göttingen Schrödinger's interpretation seemed unacceptable in face of well established experimental facts. At that time it was already <b>possible to count particles by means of scintillations or with a Geiger counter,</b> and to photograph their tracks with the aid of a Wilson cloud chamber. </i></li></ul><div>with more "proof" from Heisenberg's Uncertainty Principle:</div></div><div><ul><li><i>However, a paper by Heisenberg containing his celebrated uncertainty relationship, contributed more than the above-mentioned successes to the swift acceptance of the statistical interpretation of the $\psi$-function. </i></li><li><i>It showed that not only the <b>determinism of classical physics must be abandonded,</b> but also the naive concept of reality which looked upon the particles of atomic physics as if they were very small grains of sand.</i></li></ul></div></div><div>But Born still struggled with the skeptics of atoms as dice-games: </div><ul><li><i>How does it come about then, that great scientists such as Einstein, Schrödinger, and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. Two closely knitted points of view are to be distinguished: <b>the question of determinism and the question of reality. </b></i></li></ul><div>arguing that everything including classical physics is a dice-game,:</div><div><ul><li><i>The determinism of classical physics turns out to be an illusion, created by overrating mathematico-logical concepts....and cannot, therefore, be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.</i></li></ul></div><div><div>But finally the self-doubts take over and Born's Nobel lecture given 28 year after the commitment of the crime, ends with questions:</div><ul><li><i>Are we still justified in applying to the electron the concept of particle and therefore the ideas associated with it?</i></li><li><i>Somewhere in our doctrine is hidden a concept, unjustified by experience, which we must elim- inate to open up the road. </i></li><li><i>To come now to the last point: can we call something with which the concepts of position and motion cannot be associated in the usual way, a thing, or a particle? And if not, what is the reality which our theory has been invented to describe?</i><i> </i></li></ul><div><div>To sum up we see that Born's justification of giving up the basic principles of classical physics, boils down to the following shaky weak arguments:</div><div><ul><li><i>A perceived need to make the duality of particle-light quanta or photons and waves comprehensible. </i></li><li><i>Because a Geiger counter gives a "click", what caused the "click" must be a "particle".</i></li></ul><div>We understand following Schrödinger as inventor of the basic mathematical model of quantum mechanics, if the particle idea is given up, then there is no need to make wave-particle duality "comprehensible", since then waves are enough. What remains is to reformulate Schrödinger's multidimensional wave equation into a system of three-dimensional wave functions representing charge distribution. This is what I now explore as (Computational) <a href="http://claesjohnson.blogspot.se/search/label/physical%20quantum%20mechanics">Physical Quantum Mechanics.</a></div><div><br />But the sad truth today is that nobody cares if the fundamentals of physics make sense or not: Quantum mechanics and relativity, although incompatible, is "settled modern physics" with all questions answered once and for all by now dead and gone physicists, who took the answers along into the grave. </div></div><div><br /></div><b>PS </b>Note that Heisenberg received the Nobel Prize in physics in 1932 and Schrödinger shared the Prize with Dirac in 1933, while Born had to wait 20 years until the coining of the Copenhagen Interpretation by Heisenberg in the early 1950s as the official formulation of quantum mechanics.<br />Today, only a few hard core extremist like Lubos Motl claim that this is the final word to which nothing can be added. The historical dimension of this view is described by A. Pais in the opening of his Address to the Annual Meeting of the Optical Society in 1982 entitled <i>Max Born and the Statistical Interpretation of Quantum Mechanics</i> as follows:<br /><ul><li><i>The introduction of probability in the sense of quantum mechanics, probability as an inherent feature of physical law, may well be the most drastic scientific change yet effected in the twentieth century. </i></li></ul><div>In other words: A Big Lie is more credible than a small one, so if you are going to cheat, make it Big. CO2 global warming alarmism gives an example of this tactic, which is now threatening to throw Western civilization back to Stone Age: This is "settled science" which is so Big that it cannot be questioned! </div><br /> </div></div><div><b><br /></b></div><div><div class="page" title="Page 9"></div></div></div>http://claesjohnson.blogspot.com/2015/06/tragedy-of-modern-physics-borns.htmlnoreply@blogger.com (Claes Johnson)5tag:blogger.com,1999:blog-1500584444083499721.post-7726486602828629699Wed, 03 Jun 2015 06:14:00 +00002015-06-04T11:20:43.381+02:00physical quantum mechanicsThe Copenhagen Interpretation vs Leibniz' Sufficient ReasonThe article Inconsistency of the Copenhagen Interpretation in Foundations of Physics, Vol. 21, No. 5, 1991, by C. I. J. M. Stuart, argues that:<br /><div><ul><li><i>The Bohr-Heisenberg scheme, which forms the basis of any current version of the standard or Copenhagen interpretation of quantum mechanics, is shown to be internally inconsistent.</i></li></ul>with the following introduction:<br /><ul><li><i>The predictive success of quantum mechanics has always been accompanied by vigorous debate concerning the theory's physical content as specified by the Copenhagen interpretation, i.e., the Bohr-Heisenberg scheme. </i></li><li><i>Einstein at first thought the scheme inconsistent, but later concluded that it made quantum mechanics consistent but incomplete.</i></li><li><i>Since then, the question of completeness has persisted in connection with "hidden variable" theories; but Einstein's opinion as to the scheme's consistency has been generally accep- ted and perhaps overshadowed by concern with the completeness issue, though a widely held modern view is that the scheme is incoherent and perhaps incomplete. </i></li><li><i>The main objective in this paper is to show that incoherence is not the problem but, much more seriously, the scheme is internally inconsistent. </i></li></ul>The article starts out by identifying the following basic postulates of the Copenhagen Interpretation:<br /><ol><li>T<i>he completeness postulate requires that the quantum mechanical wave function gives a complete specification of what can be known concerning quantum states. </i></li><li><i>The superposition principle requires that a quantum state represented by a linear superposition of allowable quantum states is itself an allowable quantum state. </i></li><li><i>The Heisenberg uncertainty principle requires that observables represented by noncommuting operators cannot simultaneously be measured with equal exactness, the exactness of the one being inversely proportional to the exactness of the other. </i></li><li><i>The probability interpretation requires that the wave function does not correspond to a material wave; instead, its amplitude corresponds to a probability amplitude and its absolute square corresponds to a probability density. </i></li><li><i>The principle of inseparability requires that, in quantum mechanics, a physical system consists of the object-system under investigation inseparably from the experimental apparatus used to make measurements; and, moreover, the interaction between object and apparatus forms an inseparable part of quantum phenomena. </i></li><li><i>Bohr's principle of complementarity requires that complementary experimental arrangements wilt yield complementary quantum phenomena. </i></li><li><i>Bohr's correspondence principle requires that quantum mechanics must converge to classical mechanics in the limit where quantum effects can be disregarded.</i></li></ol><div>This is important information, since the Copenhagen Interpretation seldom is described in precise terms, which makes critical evaluation difficult. Let us subject postulates 1-7 to <a href="http://en.wikipedia.org/wiki/Principle_of_sufficient_reason">Leibniz' test of sufficient reason</a>:</div><div><ol><li>What is the reason to believe that the wave function gives a complete specification of what can be known of the physics of atoms?</li><li>What is the reason to believe that the physics of atoms is linear? </li><li>What is the reason that position and velocity cannot be measured simultaneously? </li><li>What is the reason to believe that the wave function cannot correspond to a material wave? What is the reason to believe that it instead corresponds to probability amplitude?</li><li>What is the reason to believe that a physical system consists of the object-system inseparably connected to experimental apparatus?</li><li>What is reason for complementarity?</li><li>What is the reason for requiring that quantum mechanics must converge to classical mechanics if quantum mechanics effects can be discarded?</li></ol><div>Let us thus seek the sufficient reason for each postulate and see what we can come up with:</div></div><div><ol><li>No reason found.</li><li>No reason found.</li><li>With matter as wave the answer is trivial. With matter as particle, no reason is found.</li><li>The reason is the spatial multi-dimensionality of the wave function.</li><li>No reason that a physical system must be connected to experimental apparatus.</li><li>No reason.</li><li>No reason to explicitly require something self-evident: quantum mechanics without quantum effects must be classical mechanics.</li></ol><div>We conclude that only one reason has been found: the spatial multi-dimensionality of the wave function makes direct physical interpretation impossible, since physics as we know it takes place in three space dimensions. No other reason has been identified. </div><div><br /></div><div>After this evaluation showing that the sole reason for the Copenhagen Interpretation is an ad hoc assumption about mathematical formalism, it is natural to ask if there is a quantum mechanics with wave functions depending on a common three-dimensional space variable plus time? </div><div><br /></div><div>In a sequence of posts the category "physical quantum mechanis" I seek to give a positive answer to this question. The reason for this form of quantum mechanics is the same as for classical mechanics, which may well be sufficient.<br /><br />We have not found any sufficient reason for the Copenhagen Interpretation which fits with Stuart's observation that the Copenhagen Interpretation is internally inconsistent: Of course, there can never be a sufficient reason for the validity of a scientific model which is internally inconsistent. Of course, there can never be a sufficient reason to view a scientific contradiction as a scientific truth. Only in the Copenhagen Interpretation is this possible, but that means that whatever it is, it is not science.</div></div><div><div><br /></div></div><div><i><br /></i></div></div>http://claesjohnson.blogspot.com/2015/06/the-copenhagen-interpretation-vs.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-1939456418914818737Thu, 28 May 2015 17:26:00 +00002015-06-02T18:43:26.861+02:00finite precision computationPhysics as Analog Finite Precision Computation vs Physics as Statistics<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-r2Lf2LEF6Fo/VWdPImtEfCI/AAAAAAAA5pQ/PPirutpQypE/s1600/diceman1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-r2Lf2LEF6Fo/VWdPImtEfCI/AAAAAAAA5pQ/PPirutpQypE/s320/diceman1.jpg" width="204" /></a></div><br />I am exploring an approach to physics as "analog finite precision computation" to be be compared with classical physics as "analog infinite precision physics" and modern physics as "physics of dice games" or "statistical physics".<br /><br />The step from classical to modern physics was forced upon physicists starting in the mid 19th century when it became clear that the 2nd law of thermodynamics could not be found in classical infinite precision physics of irreversible systems. The way to achieve irreversibility was to assume that atoms play dice games with the outcome of a throw of a dice inherently irreversible: To "unthrow" a dice was (correctly) understood to be impossible and thus irreversibility was introduced and the paralysis of reversible classical physics was broken. So far so good.<br /><br />But the fix came with severe side effects as real physics independent of human observation was replaced by statistical physics representing "human understanding", as if the world goes around just because some physicist is making observations and claim them to be understandable. Einstein and Schrödinger could never be convinced that atoms play dice, despite major pressure from the physics community. <br /><br />The unfortunate result of this collapse of rationality of deterministic physics, has led modern physics into wildly speculative physics of strings and multiverse, which nobody can understand.<br /><br />But there is a milder way of introducing irreversibility into classical reversible physics, and that is to view physics as analog computation with finite precision instead of infinite precision.<br /><br />This connects directly to a computer operating with finite decimal expansion of real numbers as a necessary restriction of infinite decimal expansion, in order to allow computations to be performed in finite time: In order to make the world go around, and it does go around, and thus not come into a halt, physical processes cannot be realised with infinite precision and thus finite precision computation is a must in a world that goes around. It is thus necessary, but it is also sufficient to introduce irreversibility into classical reversible physics.<br /><br />Finite precision computation thus solves the main problem which motivated the introduction of statistical physics, but in a much more gentle way and without the severe side effects of full-blown statistics based on dice games.<br /><br />Finite precision computational physics is represented by the modern computer, while statistical physics would correspond to a "dice computer" throwing a dice in every step of decision, just like the "dice man" created by the pseudonym Luke Rhinehart. The life of the "dice man" turned into misery, which can be compared with (reasonably) successful ordinary (reasonably controlled) life under finite precision, without a dice but with constant pressure to go onto the next day.<br /><br />So if you want to compare finite precision analog physics to modern statistical physics, make the thought experiment of comparing your usual finite precision computer, which you use to your advantage, to a "dice computer" which would be completely unpredicatable. This is the comparison between an experienced computer wiz often getting reliable results, to a totally inexperienced user pushing the keys randomely and getting garbage.<br /><br />Or make the comparison of getting married to a person which follows a principle of "finite precision" to a person like the "dice man" who is completely unpredictable. What would you prefer?<br /><br />Few ideas can change your view in the same way as "physics as analog finite precision computation". Try it!http://claesjohnson.blogspot.com/2015/05/physics-as-analog-finite-precision.htmlnoreply@blogger.com (Claes Johnson)2tag:blogger.com,1999:blog-1500584444083499721.post-2762455600215460668Thu, 28 May 2015 13:48:00 +00002015-06-02T18:37:21.631+02:00physical quantum mechanicsSchrödinger's equationPhysical Quantum Mechanics: Time Dependent Schrödinger EquationWe consider a Schrödinger equation for an atom with $N$ electrons of the normalized form: Find a wave function<br /><ul><li>$\psi (x,t) = \sum_{j=1}^N\psi_j(x,t)$</li></ul>as a sum of $N$ electronic complex-valued wave functions $\psi_j(x,t)$, depending on a common 3d space coordinate $x$ and time coordinate $t$ with non-overlapping spatial supports $\Omega_1(t)$,...,$\Omega_N(t)$, filling 3d space, satisfying<br /><ul><li>$i\dot\psi (x,t) + H\psi (x,t) = 0$ for all $(x,t)$, (1)</li></ul>where the (normalised) Hamiltonian $H$ is given by<br /><div><ul><li>$H(x) = -\frac{1}{2}\Delta - \frac{N}{\vert x\vert}+\sum_{k\neq j}\int\frac{\vert\psi_k(y,t)\vert^2}{2\vert x-y\vert}dy$ for $x\in\Omega_j(t)$,</li></ul><div>and the electronic wave functions are normalised to unit charge:</div><div><ul><li>$\int_{\Omega_j}\vert\psi_j(x,t)\vert^2 =1$ for all $t$ for $j=1,..,N$.</li></ul></div><div>The total wave function $\psi (x,t)$ is thus assumed to be continuously differentiable and the electronic potential of the Hamiltonian acting in $\Omega_j(t)$ is given as the attractive kernel potential together with the repulsive kernel potential resulting from the combined electronic charge distributions $\vert\psi_k\vert^2$ for $k\neq j$.<br /><br />The Schrödinger equation in the form (1) is a free-boundary problem where the supports $\Omega_j(t)$ of the electronic wave functions may change over time.<br /><br />We solve (1) by time-stepping the system<br /><ul><li>$\dot u + Hv = 0$, $\dot v - Hu = 0$ (2)</li></ul><div>obtained by splitting the complex-valued wave function $\psi = u+iv$ into real-valued real and imaginary parts $u$ and $v$ (and with $\vert\psi\vert^2 =u^2+v^2$.) </div><br />This is a free-boundary electron (or charge) density formulation keeping the individuality of the electrons, which can be viewed as a "smoothed $N$-particle problem" of interacting non-overlapping "electron clouds" under Laplacian smoothing. The model (1) connects to the study in <a href="http://claesjohnson.blogspot.se/search/label/Quantum%20Contradictions">Quantum Contradictions</a> showing a surprisingly good agreement with observations.<br /><br />In particular, the time-dependent form (2) is now readily computable as a system of wave functions depending on a common 3d space variable and time, to be compared to the standard wave equation in $3N$ space dimensions which is uncomputable.<br /><br />I am now testing this model for the atoms in the second row of the periodic table, from Helium (N=2) to Neon (N=10), and the results are encouraging: It seems that time dependent N-electron quantum mechanics indeed is computable in this formulation and the model appears to be in reasonable agreement with observations. This gives promise to exploration of atoms interacting with external fields, which has been hindered by uncomputability with standard multi-d wave functions.<br /><br /><b>PS </b>The formulation readily extends to electrodynamics with the Laplacian term of the Hamiltonian replaced by<br /><br /><ul><li> $\frac{1}{2}(i\nabla + A)^2$</li></ul><div>and the potential augmented by $\phi$, where $A=A(x,t)$ is a vector potential, $\phi =\phi (x,t)$ is a scalar potential with $E = -\nabla\phi -\dot A$ and $B=\nabla\times A$ given electric and magnetic fields $E=E(x,t)$ and $B=B(x,t)$ depending on space and time. </div></div></div><div><br /><br /></div>http://claesjohnson.blogspot.com/2015/05/physical-quantum-mechanics-time.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-4673168667024363017Thu, 28 May 2015 13:08:00 +00002015-05-28T15:34:08.186+02:002nd law of thermodynamicsmyth of backradiation"Back Radiation" as Violation of the 2nd Law of Thermodynamics<a href="http://hockeyschtick.blogspot.se/2015/05/new-paper-reviews-summarizes-nipcc.html">A new article by Martin Herzberg in Energy&Environment</a> reviews & summarizes the NIPCC Report Climate Change Reconsidered -Physical Science. In particular, Herzberg gives the following devastating review of the phenomenon of "back radiation" supposedly being the "heating mechanism" of the "greenhouse effect: <br /><ul><li><i>The most prevalent definition or heating mechanism involves what is referred to as “back radiation”. Greenhouse gases absorb some of the IR radiation that the Earth’s surface radiates toward free space after it is heated by solar radiation. According to the Environmental Protection Agency, ”reradiated energy in the IR portion of the spectrum is trapped within the atmosphere keeping the surface temperature warm.” </i></li><li><i>This mechanism has the colder atmosphere blithely and spontaneously emitting radiant energy toward the warmer surface. </i></li><li><i>That energy is supposed to be absorbed by the Earth’s surface and heat it further. </i></li><li><i>Thus the warmer surface should get even warmer by absorbing energy from a colder source: in direct violation of the Second Law of Thermodynamics.</i></li></ul><div><a href="https://www.blogger.com/blogger.g?blogID=1500584444083499721#editor/target=post;postID=3990384015599052131;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=4;src=postname">Advocates of CO2 alarmism work hard to meet this argument claiming that the violation of the 2nd Law is only apparent</a>: "Back radiation" always comes along with "forward radiation" and the net radiation is always from warm to cold and so the 2nd law is not violated. The trouble with this way of handling the objection expressed by Herzberg (and myself), is that "back radiation" and "forward radiation" are supposed to be independent physical processes as "two-way flow of infrared photons", and at the same dependent coupled processes guaranteeing the the 2nd laws is not violated. </div><div><br /></div><div>But independent processes which are dependent, is a contradiction and so the effort to save "back radiation" from joining phlogistons in the wardrobe of unphysical processes, comes to nil and so the "greenhouse effect" is "hanging in the air" without scientific basis. </div>http://claesjohnson.blogspot.com/2015/05/back-radiation-as-violation-of-2nd-law.htmlnoreply@blogger.com (Claes Johnson)0tag:blogger.com,1999:blog-1500584444083499721.post-8489140854000203600Tue, 26 May 2015 10:24:00 +00002015-05-28T18:28:21.438+02:00myth of backradiationradiative heat transferDoes an Undetectable "Greenhouse Effect" Exist?Vincent Gray seeks to clarify the physics of the "greenhouse effect" in a new <a href="http://theclimatescepticsparty.blogspot.se/2015/05/the-greenhouse-effect.html">blog post at </a><br /><div><a href="http://theclimatescepticsparty.blogspot.se/2015/05/the-greenhouse-effect.html">The Australian Climate Sceptics - Exposing the flaws in the greatest hoax inflicted on the human race:</a></div><div><ol><li><i>Greenhouse gases, predominantly water vapour, do absorb infra red radiation from the earth, radiate the additional energy in all directions, including downwards and so warm the earth. </i></li><li><i>So the greenhouse effect does exist. </i></li><li><i>This effect must be very small as it has not been detected, despite the enormous effort that has been applied to try and find it.</i></li></ol><div>We read that Vincent here puts forward the idea that the atmosphere by radiating heat energy downwards causes warming of the Earth surface in a process of two-way radiative heat transfer between the atmosphere and surface including "back radiation" from a cold atmosphere to a warm surface. Vincent thus accepts the picture painted by CO2 alarmism based on a "greenhouse effect" and thereby gives it a free ride. Vincent shares this view with many "skeptics".</div><div><br /></div><div>At the same time as Vincents claims that "the greenhouse effect exists", he informs us that it has not been detected, presumably then because "it must be very small". </div><div><br /></div><div>All this is unfortunate because the two-way heat transfer including back radiation which Vincent describes, is not true physics but fake physics, as I have argued in extended writing. </div><div>Vincent defends his position with a direct attack on my position with the following argument (in bold):</div><div><ul><li><i>Radiation energy is converted to heat if it is absorbed by any suitable object. </i></li><li><i>The temperature of that object is quite irrelevant. </i></li><li><i>The speculation by some that radiation cannot be absorbed by an object whose temperature is bigger than that of the radiant emitter requires the <b>absurd assumption that radiation, is capable of detecting the temperature of distant objects before deciding whether they are fit to receive absorption. </b></i></li><li><i>Such an assumption restores the need for a belief in the existence of an ether.</i></li></ul><div>But is it absurd that an absorber can detect if the temperature of an emitter is bigger than its own temperature? Not at all! That information is encoded in the spectrum of the emission as the high-frequency cut-off described in Wien's displacement law with the cut-off increasing linearly with temperature. The result is that emission from a certain temperature cannot be re-emitted by an absorber at lower temperature and thus must be absorbed and turned into heat causing warming. </div></div></div><div><br /></div><div>A stone put in the sun light, can thus very well detect that the sun light falling upon itself was emitted at a temperature higher than its own, because sun light contains frequencies above the cut-off frequency of the stone. The stone detects this by finding itself being unable to re-emit these frequencies and thus cannot prevent getting heated by the Sun. This is nothing the absorber "decides" to do in Vincent's vocabulary, because atoms have no free will "to decide", but simply something the absorber is unable to do, which involves no "decision" and thus can be physics.</div><div><br /> So in conclusion I pose the following question to Vincent (and other "skeptics"): Since the "greenhouse effect" cannot be detected experimentally and your theoretical argument in support of its existence has shown to be incorrect, wouldn't it be more rational to give up arguing that the "greenhouse effect exists" because there is "back radiation", thus giving support to CO2 alarmism?<br /><br />I have asked Vincent to respond to this post, but it may well be be that Vincent, like some other "skeptics", simply hides (and warms up) after making an attack on a skeptic position of a frequency above his own cut-off.<br /><br /><b>PS</b> Vincent's claim of existence of a phenomenon that is not detectable, connects to an (unfortunate) aspect of modern physics, as opposed to classical physics, rooted in the Bohr Copenhagen interpretation of quantum mechanics, where the wave function is not viewed to represent real physics independent of human observation, but instead represents human understanding in statistical terms limited to what can be observed by humans. Modern physicists following Bohr are thus allowed to speak about only physics which is observable and then in statistical terms. But this is too narrow, and has opened the possibility of a vast physical landscape beyond observation, which physicists are now eagerly exploring in the extreme forms of string theory and multiversa. The (unfortunate) result is that speaking about phenomena of physics which cannot be detected, which in the view of classical physics is nonsense, has now become mainstream modern physics. </div>http://claesjohnson.blogspot.com/2015/05/does-undetectable-greenhouse-effect.htmlnoreply@blogger.com (Claes Johnson)44tag:blogger.com,1999:blog-1500584444083499721.post-1904344146032659542Sun, 24 May 2015 08:42:00 +00002015-05-24T15:33:29.095+02:002nd law of thermodynamicsmyth of backradiationTwo-way Heat Transfer and 2nd Law: Contradiction!The discussion with edX in the previous post exhibits a "greenhouse effect" connected to "back radiation" or "Downwelling Longwave Radiation DLR" from a cold atmosphere to a warmer Earth surface, as a part of two-way radiative heat transfer between two bodies each supposed to emit independently of the other according to a Stefan-Boltzmann law of the form $Q=\sigma T^4$ with $T$ body temperature and $\sigma$ a positive constant.<br /><br />As the discussion shows, advocating two-way heat transfer requires an argument showing that what appears to be a violation of the 2nd law of thermodynamics with the colder body transfering heat to the warmer, is only apparent. The argument is then that the heat transfer is always bigger from the warmer and so the net transfer is always from warm to cold.<br /><br />However, this argument is contradictory: Each body is supposed to emit independently of the other, yet at the same time the two transfer processes must somehow be linked to guarantee that the net transfer always comes out right, even if they are nearly equal. The transfer processes are thus assumed to be both independent and dependent, which is a contradiction. And contradictory physics can only be non-physical illusion.<br /><br />Unfortunately, in modern physics contradictions such as wave-particle contradiction, have come to be accepted by Bohr sophistery as "complementarity" or "duality". A "round square" is thus in modern physics not a contradiction, but just expresses "complementary" or "dual" properties of some higher physical existence incomprehensible to human understanding but still physics. But sophistery is not science and contradictory physics is non-physics. <br /><br />In this context, recall that the idea of two-way heat transfer was used by Schwarzschild in 1906 to set up a simple model for radiative heat transfer allowing a simple analytical solution as a linear function. The unphysical aspect of Schwarzschild'd model is exposed in the recent post <a href="http://claesjohnson.blogspot.se/2015/04/unphysical-schwarzschild-vs-physical.html">Unphysical Schwarzschild vs Physical Model for Radiative Heat transfer.</a> What was unphysical in 1906 is still unphysical today.http://claesjohnson.blogspot.com/2015/05/two-way-heat-transfer-and-2nd-law.htmlnoreply@blogger.com (Claes Johnson)5