Duda Jarek

Cold fusion is generally classified as fringe science and so I wasn't treating it seriously, but there was recently PhysOrg article about public demonstration of generating 12kW for half an hour from nickel+hydrogen by device in which such amount of chemical energy just wouldn't fit ... it's difficult not to be skeptical about such absolutely revolutionary claims, but it motivated me look closer at this field and so I became aware that there are thousands of papers about cold fusion, hundreds of groups reported excessive heat: http://www.lenr-canr.org/index.html If it's not just a massive scum of hallucinations, there is needed some theoretical explanation of such eventual low energy nuclear reactions - one of reasons of rejecting such possibilities was lack of theoretical understanding: used directly quantum mechanics says that probability of tunneling through such repelling barrier between nucleuses is completely negligible. But what if we can sharpen a bit quantum mechanical probability cloud of electron - try to imagine some movement of localized electron behind this picture ... Imagine such free-fall electron's trajectories which nearly pass nucleus - its electric field could pull proton behind ... straight to hit the nucleus - localizing electrons make cold fusion much more likely... And so Gryzinski write in his book that a few days after the Pons&Fleishmann announcement, he explained such phenomena as naturally appearing in his model and it was published in Nature a month later (April 1989). He was enthusiast of cold fusion, had a few papers about it and two patents. The main reason of reluctance to imagine particles as quite localized entities as seen while scatterings, seems to be the interference phenomenon. But QM doesn't have monopoly for interference - it's completely natural also in classical physics like on water surface ... or I've just found PRL paper reporting interference of macroscopic droplet: http://prl.aps.org/abstract/PRL/v97/i15/e154101 If we accept particles as shape/structure maintaining localized construct of the field (solitons), there is still interference expected for them - just decompose them into plane waves using Fourier transform and (in linear approximation) plane waves interfere. It's just that soltions are far from the concept of (various number of) classical particles - there is also extremely complicated communication between them going through the field causing e.g. interference effects. Generalizing this picture into more trajectories leads to Feynman's path integral formulation of quantum mechanics. Classical trajectories can be seen as some useful approximation, for example the base of semiclassical approximation or ... stochastic perturbation - alternative view on such practically randomly perturbed trajectory is that in such case the safe is to assume Boltzmann distribution among possible paths, what as in euclidean paths integrals, leads to transformation of classical trajectories into 'near' (overlapping) quantum eigenstates (presentation) What do you think about the possibility of cold fusion and of localized particles?

I defended my PhD in computer science (now in progress in physics ), which half was was about this new approach to data correction - basically it's extended convolutional codes concept to use much larger states (which require working not on the whole space of states as usual, but only on used tree of states and allows to practically complete repair in linear time) and using entropy coder to add redundancy (simultaneous data compression and rate can be changed fluently). The thesis is the paper from arxiv with a few small improvements ( can be downloaded from http://tcs.uj.edu.pl/graduates.php?degree=1〈=0 ) Here is presentation I've used - with a few new pictures which should make understanding concepts (and asymmetric numeral systems) easier and e.g. some comparison to LDPC.

Brownian motion requires relatively large 'walker', which is constantly being pushed in random directions (no memory) - it's derived as infinitesimal limit of Generic Random Walk (GRW) on a graph(lattice), in which each outgoing edge is equally probable. But let's imagine we want to estimate probability density of positions of some entity which doesn't just constantly 'stop and make new independent decision', but make some concrete trajectory, which for example could depend on the past (by e.g. velocity) - in such situations the safer than taking statistical ensemble among single edges as in GRW/Brownian motion, should be using statistical ensemble among whole possible paths. The simplest such model is Maximal Entropy Random Walk (MERW) on graph, it can be defined in a few ways: - stochastic process on given graph which maximizes average entropy production, or - assuming uniform probability distribution among possible paths on graph, or - for each two vertices, each path of given length between them is equally probable. Obtained formulas are: P(a->b ) = [math] \frac{M_{ab}}\lambda \frac {\psi_b}{\psi_a} [/math] where M is graph's adjacency matrix ([math]M_{ij}\in{0,1}[/math]) lambda is its dominant eigenvalue with psi eigenvector (real, positive because of Frobenius-Perron theorem) [math]M \psi=\lambda \psi [/math] stationary probability distribution is: P(a) is proportional to [math](\psi_a)^2[/math] This stochastic process is Markovian - depends only on the last position, but to calculate these transition probabilities we just have to know the whole graph - we should think about this probabilities not as that 'the walker' uses them directly, but that they are only used by us to propagate our knowledge while estimating probability density of his current position. (Minus adjacency matrix) occurs to correspond to discrete Hamiltonian, so while GRW/Brownian motion spreads probability density almost uniformly, MERW has very similar localization properties as quantum mechanics. While adding potential: changing statistical ensemble among paths into Boltzmann distribution and making infinitesimal limit of lattice constant, we get stationary probability density exactly as quantum mechanical ground state (similar to Feynman's euclidean path integrals). Here is PRL paper about MERW localization properties: http://prl.aps.org/abstract/PRL/v102/i16/e160602 Here is my presentation with e.g. 2 intuitive derivations of MERW formulas and some connection to quantum chaos: http://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B7ppK4I%20yMhisYmI3YTAzNzYtMDkyNy00ZDAxLTg1NGEtOTg4NWNkYzU3M%20jQ1&hl=en Here is simulator which allows to compare conductance models using GRW and MERW: http://demonstrations.wolfram.com/preview.html?draft/93373/000008/ElectronConductanceModelUsingMaximalEntropyRandomWalk Here are more formal derivations: http://arxiv.org/abs/0710.3861 Here is a trial to expand this similarity to quantum mechanics: http://arxiv.org/abs/0910.2724 I'm currently working on my PhD thesis in physics on this subject and so I would really gladly discuss about it.

Basically this classical-quantum correspondence we were talking about is the region of so called quantum chaos - I believe MERW-based model is what they were missing to understand it - in this presentation are for example its 2 intuitive derivations and connection with quantum chaos. If someone is interested, here has developed discussion about MERW: http://www.sciforums.com/forumdisplay.php?f=33

But Heisenberg's quantum uncertainty also doesn't mean that there is no internal dynamics - it only restricts practical aspect: measurement. Taking further implications based on Bell's inequalities assumes that probabilistic models on local deterministic Lagrangian (field) mechanics should be also local - such assumption about models representing our knowledge is just wrong (see maximal entropy random walk). In not standard: idealistic, but practical classical mechanics we also have to have in mind that we cannot have infinite measurement precision, full information - we have to work on probability clouds ... what through chaos, ergodicity leads to practical picture far from the idealistic one ...

Lagrangian mechanics conserve volume, so indeed practically any nonlinearity have also repelling direction, making that we lose information exponentially with time. But is it really necessary for information loss? For example linear one? Let's imagine the simplest situation: you have a single particle in empty space (no interactions) and you know its initial velocity with finite precision - how does you knowledge about its position evolve with time? (or your knowledge about position along magnetic field from the topic...) ps. And in practice we should also remember that e.g. electron have magnetic momentum, what complicates the dynamic through precessive motion - adding nonlinearities ... ps2. I see that since QM, even if it imply classical mechanics (Ehrenfest theorem), physicists are no longer interested in it, so I would like to advertise one of the best books I've studied and the only good one in classical mechanics I've seen - giving not only standard for physicist tool to shut up and calculate, but really deep understanding, showing its beauty - Arnold's books.

No - I'm saying that classically we also don't have infinite precision - we know parameters with some unavoidable uncertainty - and it often grows with time (along directions with positive Lyapunov exponents) ... for example even in idealized situation from the topic, we still have decrease of knowledge (with time) about the current state of system ... Or in other words - butterfly effect doesn't need quantum mechanics ... Radiation decay is succeeding complication - we can rather only predict probability of such phenomenas - so while considering statistical ensemble among all possible scenarios for our knowledge of initial conditions, we should add to this set scenarios with decay using proper probability density ... Classical mechanics may look simpler than quantum ... but it's misleading - to do it seriously, we just have to consider that we don't have full information and so use some probabilistic/thermodynamical models - making calculations quite similar to quantum ...

So you also think that while considering (e.g. to predict something) classical trajectories, we can ignore the fact that we have limited knowledge/precision? Because for uncertainty you have QM and only QM? It for example says that practically never we will get perfect (classical) circulation from the topic ... and that our knowledge about particle's position along magnetic field decreases with time ... I thought that it's physicists who should be mainly worried about it ... while surprisingly it's only mathematicians who not only cares, but even treat this subject extremely seriously - we have chaos theory with Lyapunov exponents in the first approximation, then trajectories can ergodically cover some sets ... finally stabilizing density (time average) when bounded like in Penning trap...

What? I've understood your answer that the only picture in proton's potential you can tolerate is probabilistic one, because of its Planck scale size - so I've responded that it's nonsense - Schroedinger's probabilistic picture is universal - works also in macroscopic samples ... and it doesn't have to be guessed, but can be mathematically derived ... ... and yes - electron's behavior in semiconductor is also in EM field - of concrete lattice of atoms ... and as you could see - I've returned in my post to classical picture - as you've been taught for this situation ... But I should get used to that you are not capable to discuss, but only to present your faith ... I apology for bothering you. bye

Matter of size? Really? So how would you explain stationary probability density of electrons in macroscopic semiconductor sample? I would say that it's Schroedinger's ground state probability density ... (?) And I would gladly finally heard which quantum effect are you referring to, to reject quantum superposition of classical trajectories picture ... or how do you understand corpuscular half of duality ... but I agree it's not for this thread ... Returning to simple 'classical' situation from the topic - it's you who should said that it can be also described in Schroedinger's picture ... but I think such wavefunction would be thickening - it's not like in atoms that we have orbital of fixed wavefunction amplitudes, but it would be rather seen as continuously decohering ... (?) It's one of reasons I didn't want to go into QM here - I agree that classical picture is more convenient here. But still in classical picture we have unavoidable uncertainty, which through different kind of chaos leads to that for example in such macroscopic Penning trap, the most convenient picture could be thermodynamical one - it should reach some thermodynamical equilibrium and what we should work on are time averages of trajectories probability density, do you disagree? And I would say that natural thermodynamical assumption in such 'prisoned trajectories' situation is Boltzmann distribution among possible ones - there is a funny coincidence that it leads exactly to Schroedinger's ground state stationary probability density ... so I would conclude that it's not true that Schroedinger's picture works only in Planck's scales, but is just universal - works in proton's potential, but also in macrosopic Penning trap, semiconductor ... do you disagree?

I apology for misunderstanding - I'm not satisfied with the reason you gave, but I had no intention to take this discussion here - I also generally wanted by the way to understand your way of thinking in which classical trajectories are fine, unless we are considering EM field of proton, where the only description you tolerate is probabilistic(?). My intention was to point jerryyu to Penning trap for deeper understanding of the situation he was asking for and to remind to be careful about such classical (hard) descriptions - that in practice we don't/cannot have full information, so we should rather use probabilistic (soft) descriptions like Schroedinger's picture. To be more concrete - let's look at the topic: imagine we want to place a single particle on circulatory orbit perpendicular to magnetic field... Our particle sources are not perfect - we probably can assume some Gaussian of its initial momentum and time/position - we could predict well let say a few first periods, but the initial uncertainty becomes more and more essential (so called chaos) - especially on the axis along magnetic field: we can only assume wider and wider Gaussian there - the amount of information we have is decreasing with time (so called 2nd law of thermodynamics). How would you predict results of such experiment? Do you think we can ignore our lack of knowledge while considering such classical trajectories? peace

I disagree - classically we often also haven't full knowledge and to cope with it we use thermodynamical models which represent our knowledge, do you disagree? For example assuming Boltzmann distribution among possible scenarios: trajectories, what leads exactly to stationary probability distributions from Schroedinger's picture (like Feynman path integrals in imaginary time http://www.worldscibooks.com/etextbook/4443/4443_chap3_2.pdf ). ... and generally I would like to understand why when I've tried to discuss results claiming good agreement with experiment from dozens of peer-reviewed papers (with hundreds of citings) about such classical systems in e.g proton's EM field, you've classified it as speculations? http://www.scienceforums.net/topic/51199-any-comments-about-gryzinski-free-fall-atomic-model/ ! Moderator Note split from charged particle in magnetic field thread

OP? It's a thread about classical trajectory of charged particle in magnetic field - without magnetic momentum, on exactly perpendicular plane, it would 'circulate continuously', but generally it remains its momentum along magnetic field, so finally it makes kind of helix ... To make such trajectory bounded, we use e.g. Penning trap - and I thing in such papers jerryyu will find satisfactory answers, untrue? But generally we cannot know precisely these conditions, so we just have to use some statistical ensemble among possible scenarios - use probabilistic picture like Schroedinger's one, do you disagree?

I can't believe - (classical) ion trajectories in EM ... and swansont doesn't move it to speculations, but take a part in it ... Very interesting this kind of considerations are so called 'geonium atoms' in Penning trap, used for example to measure g-factor: http://heart-c704.uibk.ac.at/LV/AtomMolekul/dehmelt86.pdf Don't worry - because of Heisenberg principle, we cannot fully know e.g. initial conditions - we have to assume some probability density among scenarios - all trajectories should finally stabilize in the trap, so propagating this probability we should finally assume some probability cloud of electron - which have magnetic moment, so there is precessive motion involved(zitterbewegung), so we should use some order parameter describing expected relative phases in different places of this periodic internal motion of electron (like in superconducting ring) - Schroedinger's picture

Ok - you probably agree that all experiments(???) can be seen as superposition of standard classical trajectories - governed by Coulomb and Lorentz law, that we have solitons in physics, that duality principle has two halves (that children are similar to parents) ... but accepting its logical consequence (natural selection) bites your 'misterium of quantum inconceivability' (creation) - you know that wavefunctions are not fundamental, but really trying to understand: see a deeper picture there, would be against the way of thinking you've built (sin). If you will accept some day that physics(creation) could be understandable, would the next step be removing superposition? No! Don't worry - we have it also in classical field theories with solitons! Evolution in classical field theories is governed by hyperbolic/'wavelike' differential operators - in linear theories eigenfunctions of this operator are plane waves and their coordinates 'rotates its phase' with time - evolution can be represented as superposition of independently 'rotating' waves - like on water surface, EM, gravitational waves - interference naturally appears there ... What happens while adding nonlinear potential to this field theory? You probably say - plane waves will start interact with each other - succeeding powers in its expansion add more complicated vertices to Feynman diagrams ... But now look at solitons like on this animation - perturbabtive picture would try to build it from plane waves through infinite set of graphs which need renormalization ... Maybe I'm strange, but personally I prefer to imagine them in standard - localized - classical way ... Now if we consider single soliton - its evolution is just moving with constant speed, often 'rotating own phase'/spinning (wave nature) - it correspond to eigenfunction of this nonlinear evolution operator. Now if we have two solitons in the space - until they collide, they practically not interact - evolve independently - we have superposition of move+rotations. How to see now that single soltion/electron can interfere with itself? The success of quantum mechanics is simplicity of the way it represents extremely complex systems like half-silvered mirrors ... We think that classical field theories are intuitive, but they aren't - our intuition is governed by past->future causality relations, while Lagrangian mechanics fulfills CPT conservation - it just optimize 4D action: solution in each point of spacetime is in equilibrium with its 4D neighborhood - minimizing stress in all 4D direction, also past and future - spacetime is kind of '4D jello' ... I don't want to discuss that in this 4D field theory picture, single soliton could synchronize atoms of both mirrors ... so I will use convenient: quantum picture - especially they are equivalent Let's use perturbative picture to decompose soliton into plane waves ... and voila - plane waves interfere and so against intuition in classical field theories single soliton can interfere with itself Cheers ps. Here are some papers about making quantum computers on quants of magnetics fields (fluxons) in superconductor - macroscopic solitons: http://www.rle.mit.edu/media/pr150/44.pdf ... look at EM field around electron - aren't they also singularities/solitons ?

Ignored????? I thought I've agreed with the essence of these experiments - quantum superposition, haven't I ? They present superposition of trajectories, untrue? Does these experiments neglect that orbital is quantum superposition of classical trajectories? - it's what you've promised ... If not, please give some experiment which do it ... or let's go deeper into this intermediate picture (ps. this post is the analogue of making creationist to admit that children are similar to parents to wake up a possibility of understanding against misterium - to reduce the shock, we have to allow the designer to help sometimes )

Where interference experiments neglect particle nature of particles? In Mach-Zehnder we have two paths, in double-slit we have more of usually straight classical trajectories ... fulfilling Coulomb and Lorentz law (like in Stern-Gerlach), untrue? Ok, let's start with intermediate picture ... 'intelligent design' analogue - Can we imagine quantum orbital as superposition of many classical trajectories like in these experiments? In other words - do you accept soliton models (like fluxons, optical vertices, skyrmions) as the basis: on which we introduce quantum mechanics by allowing quantum superposition of multiple scenarios? If yes - if we take such single trajectory ... how would it look like?

So are Schroedinger's orbitals fundamental (reason) or not (result)? Which experiments shows that they cannot be the result of accepting corpuscle part of duality - that there is some trajectory behind, for example free-falling? These large number of papers from the best journals, having hundreds of citations strongly suggest that classical scattering works well, do you disagree? Free-fall model are succeeding scatterings from stationary point nearby - natural consequence for which in succeeding peer-revived papers there is shown often better agreement than for quantum calculations ... Which experiments are you referring to?

I know - like believers can choose creationist philosophy: God created us literally as in the Bible - everything is explained ... or try to search for a deeper understanding by accepting the possibility that God created us through evolution Dear quantunist, please finally explain why you take Schroedinger's picture literally even when we know that there are more precise (Dirac, QFT,...)... and don't accept the particle half in duality, which could allow to see PROBABILITY cloud as a result, not reason?

Please show me where I was trying to deny it???? No! It was never my point! What I'm fighting with are its magical inconceivable interpretations! - that from the fact that it doesn't see dynamics behind wavefunction collapse, you conclude that there isn't any - it's the problem which lead to indeterminism, inconceivability, splitting universes etc. ... religion instead of understanding! And all the time I'm asking for these 'verified predictions as why they are not equivalent' - please give one? Ok, once more: do you accept wave-particle duality? - that they are both waves and corpuscles? Looking at Mach-Zehnder interferometer - photons goes through concrete trajectories (are spatially localized - corpuscular nature) and simultaneously they have some phase rotation for interference (wave nature) - in field theories it means that they are just 'spinning' solitons. What's your problem with this simple, natural, understandable picture???? And doesn't it say that there is hidden concrete trajectory behind idealized representation of this situation: probability cloud of orbital? And so these 20 attoseconds electrons 'waits' before photoemission observed in the Science article doesn't have to be interpreted by 'blind faith': that it's out of physics (supernatural creature is making decision?) or it's time needed to split universes ... but just electron makes some concrete dynamics! Do you accept wave-particle duality? If yes - what this 'particle' half means for you? And generally - what do you think about wavefunction collapses? Ps. I've just realized what this situation reminds me: trying to convince creationist that God created us ... through evolution And to accept it, simple natural arguments are not enough, but they expect proof as fossils of all intermediate forms ... on which they wouldn't even look at. The problem is the 'misterium' phenomenon religion creates - the overwhelming feeling that it's so amazing that even trying to understand it would be a sin ...

By 'blind faith' I meant the belief that common classical picture cannot get near glorious quantum picture - it's not about saying that one of them is wrong, but just oppositely - that both are correct - just different pictures: - classical sees from corpuscular nature of particles, through concrete spatial situation and - quantum from wave nature - from eigenstates of evolution operator, which for linear theories are just plane waves (on water, EM, gravitational), while for nonlinear they are more complicated (like atomic orbitals, or solitons) - what is important is its 'internal periodic motion' with time passing - simultaneous rotation of phases for all coordinates - so called unitary evolution. And generally no - using just Coulomb+Lorentz force doesn't left place for any new fitted heuristic terms - and it looks that they are not needed. And if some original theory needs such fitted heuristic modifications, it should rather suggest that it's not so perfect ... But I will defend QM in this moment - for example in this hydrogen molecule calculations for only simple Coulomb force full calculations would already need computer simulations ... but they still ignore e.g. magnetic momentums, Lorentz law, nucleus distance oscillations, relativistic corrections etc. ... these fitted guessed corrections are just needed because QM picture requires nightmarish calculations - it's correct picture, but extremely inconvenient for such considerations ... When we accept that particles have also corpuscular nature (are solitons), we will see probability clouds of orbitals as mainly time average - that orbitals are idealized mathematical tool to represent complicated, energetically stable dynamical situation in simple way - in some situations classical (corpuscular) picture is just more convenient for calculations. And generally this free-fall model isn't mine - this thread is to discuss well documented somebody's work - so I wouldn't even try to disturb it with mine amateur simulations and all the time I ask to relate to peer-reviewed papers about it (not only single enigmatic words) - especially that there is plenty of them... I can concretely discuss what I've worked on - mathematical arguments showing that quantum picture and picture of classical theories with solitons has the same bases - there is equivalence between them - and so they lead to the same consequences. Please - I really don't and didn't want to hear defending QM! All the time I'm asking for concrete (counter)arguments against equivalence of these two pictures? That there is no duality and particles are waves only?

1) I've given you concrete way of thinking that both models have the same basis - doesn't it mean that their consequences are also the same? - please finally give me any concrete counterargument? or 2) Please give me any concrete comment to his papers/lecture in which he shows many situation in which classical picture gives straightforward good correspondence, while quantum calculations require introducing new heuristic fitted coefficients - doesn't it mean that this theory itself doesn't agree with experiment? or 3) Do you believe that particles have also corpuscular nature? Pleeeeeeese give me finally any concrete (counter)argument that these two worlds cannot be just equivalent? That this poor little electron just have to constantly worry to which kingdom he has to magically jump now? Please stop praising glorious QM, defending with blind faith presenting "We are the Quantum, you will be assimilated", but if you call yourself a scientist, start responding to concrete arguments I gave ... finally give me anything concrete I could finally discuss with (and better than with this angular momentum) ... You want agreement with all experiments - which precisely experiments you are referring to? - that can be understood not in both, but in quantum picture only? Please comment this sample: http://www.ipj.gov.pl/~gryzinski/hydrogen_atom%20html.htm We have interference on water, Mallus law ('squares') in classical electromagnetism ... maybe you are referring to the most 'quantum': computers? Such algorithms are working on fixed finite number of qbits, untrue? Quantum field theories are needed to work with potentially infinite number of quantum objects - to work with fixed finite number it's enough to work with classical field theories, like tensor product of Klein-Gordon equations - it's exactly the picture I would like to understand why you think it's not enough? Field theories governed by Lagrangian mechanics are about optimizing four-dimensional action - that each point of space-time is in equilibrium with its four-dimensional neighborhood ... this CPT conserving picture is different from our intuitive causality one and for example allow for 'quantum' computations: http://www.scienceforums.net/topic/49246-four-dimensional-understanding-of-quantum-computers/ About potentially infinite number - QFT is abstract completely general way to represent them ... but look at nice animation here: http://en.wikipedia.org/wiki/Topological_defect - in field theories with solitons, we automatically also get potentially infinite number of them in much simpler way not leading to infinities ... and they can have simultaneously corpuscular and wave nature ... Which experiments you are referring to - that cannot be understood using (nonlinear: soliton) classical field theory (like Klein-Gordon or skyrmion models of baryons), but needs something more? What will be always still missing here?

Great ... this thread shows well social situation: Glorious inconceivable quantum mechanics is rightful fundamental theory if for each experiment we can find finite number of fitted modifications to get agreement. While Coulomb law + Lorentz law + Lagrangian mechanics is right if it straightforward agree with ALL experiments ... but still nobody would even read it ... So how such paper could say something bad about almighty QM, hurting feelings of its worshipers ... I can believe they will finally find a finite number of corrections and new exciting expansions to fit it to experiment ... I give up. Please wake me up if you finally have a tiny concrete argument that they cannot be just equivalent - different views on the same ... ? cheers

He continued this way you propose as long as he was alive: look e.g. here http://www.ipj.gov.pl/~gryzinski/hydrogen_atom%20html.htm I'm planning to start working on different 'classical' model in near future - soliton particle model like skyrmion, but modeling not only single particles, but with promising correspondence of structure of solitons and their interactions to the whole particle menagerie (natural expansion of quantum phase concept/stress tensor: ellipsoid field - between too abstract skyrmions and too simple optical vertices - 4th section of http://arxiv.org/abs/0910.2724 ) ... Such solitons are simultaneously spatially localized (corpuscular nature) and have 'internal periodic motion' (like precession of spin): wave nature - sometimes it's essential to be somewhere and sometimes to 'fit with own phase' for interference-like effects ... ... but I would also like to take a closer look, make simulations myself of these classical atomic models ... This way: reproducing ALL experiments seems as quite a lot of work and computer power, especially for small number of persons ... and honestly: would anybody really looked at it (if now nobody do it) ... As a mathematician you should know well that there is also much shorter way to show equivalence of two theories: compare their bases, not consequences! Ok, I will repeat myself (look at first posts for more details): For both quantum mechanics and field theories (linearized, in eigenbase of evolution operator), the basic evolution is unitary, untrue? But QM has additionally decoherence ... which in modern view is believed not to be out of unitary picture, but thermodynamical consequence of interaction with environment, untrue? Classical thermodynamics: that when we cannot trace particle, we should assume Boltzmann distribution among possible trajectories, leads to going to the lowest Hamiltonian eigenfunction (with nonzero projection) - similar calculus as Feynman path integrals for imaginary time - this simple, natural thermodynamical model has 'squres' against Bell's intuition ... It explains decoherence and for example makes that stable orbits while stochastic perturbation shifts toward the nearest quantum state... So again: What is still missing to get 'full QM' - equivalence of bases of both theories? And generally: doesn't the need of introducing heuristic fitted coefficients suggest that theory is far from perfect? Doesn't bother you the basic technique while quantum calculations: adding succeeding guessed terms with fitted coefficient? Would really fundamental theory need something like that?

Bignose, So let's look at Gryziński's lectures, for example in http://www.cyf.gov.pl/gryzinski/teor7ang.html there is compared both calculations for hydrogen molecule. Quantum calculations (H.Haken, H.Ch.Wolf, Molec. Phys. and Elem. of Quant. Chem. p. 45-51, Springer-Verlag Berlin, Heidelberg, 1995) need heuristically modifying standard approach, introducing fitted succeeding artificial coefficients to get agreement with experiment ... comparable with what is get straightforward using just Coulomb and Lorentz force ... how would you comment it? And generally look at first posts - it's not about saying that only one them is true! We know that QM imply classical picture (e.g. Ehrenfest theorem) ... it's about seeing them equivalent - as just different pictures of the same ... Like that we can see evolution of coupled pendulums through their positions (classical picture), or through their normal modes: eigenstates of evolution operator - in this eigenbase evolution is literally 'superposition of rotations of coordinates' - unitary (quantum picture). I've heard many things here, but still no concrete counterarguments - so I ask again: why do you believe that these pictures cannot be just equivalent? That quantum orbitals are not just simple mathematical representation of some stable dynamical state (like in nuclear shell model) - that these probability densities cannot be sharpened - became governed by physics: deterministic, like seen as made by concrete trajectories? What about corpuscular nature of particles? Extremely small size of electron as particle? Seeing double-slit, Stern-Gerlach through concrete trajectories governed by Coulomb, Lorentz law? DJBruce, His classical scattering theory was widely used (like 450 citings) and I haven't seen nonpositive comments about it (?) His atomic models are natural consequence - just succeeding scatterings from nearby .. and the only nonpositive comment I've found is this enigmatic 'unsatisfactory'. One of goal for this thread was to understand this situation - why these understandable, noncontroversial finally working modern successors of well known Bohr model are just unknown and not developed further? Doesn't this 'discussion' itself suggest that it's rather a sociological problem? - please give me one concrete argument why they cannot be just equivalent?