Sure, within the limits of applicability the Classical Mechanics has shining clarity. But it does not work for either very small objects, like elactrones, or for very large object, which Universe is. And so, scientists developed QM for small objects and General Relativity for large objects and scales.

A human being lives on Earth, his instincts are developed within applicability of CM. For this reason alone, CM perfectly fits our instincts, which we accept as CLARITY.

Nice question Demetris! I thing yes, it is subordinate! The reason as I see it, is that one can form non-standard (infinitesimal, Boolean, etc.) models of CM, and the expects that these behave like a QM model. Especially if you substitute inCM reals by Boolean-valued reals with respect to a projection algebra in a Hilbert space, the you may have QM measurements.

Sure, within the limits of applicability the Classical Mechanics has shining clarity. But it does not work for either very small objects, like elactrones, or for very large object, which Universe is. And so, scientists developed QM for small objects and General Relativity for large objects and scales.

A human being lives on Earth, his instincts are developed within applicability of CM. For this reason alone, CM perfectly fits our instincts, which we accept as CLARITY.

QM is working in a totally different part of the world, the atomar physics. CM has been developed for our macroscopic impressions and experience. So I don´t want to decide subordinate or higher priority. What the aim of this question?

Demetris, I agree with Hanno Krieger. Why do you need a hierarchy?

Demetris,

there exists p-adic calculus (QM and CM), where some of mentioned by You problems disappear.

With best regards,

Eugene.

Gerard 't Hooft has deviating views on the physical interpretation of quantum theory. He believes that there should be a deterministic theory underlying quantum mechanics. Using a toy model he has argued that such a theory could avoid the usual Bell inequality arguments that would disallow such a local hidden variable theory.

http://arxiv.org/pdf/0908.3408v1.pdf

I agree with Mr. Hooft: In a finite universe, quantum mechanics may only refer to approximations, not to an exact theory. I have followed this ideal to deduce a cosmological model with variable constants.

@Hanno and @Galina, if you measure the $billions that we have spent on CERN and the 'particle of ...' you will see that, when in some countries there is no job, no electricity, no food, no..., then we have to make a hierarchy and stop playing with our toys. Ok, when it was necessary the concept of quantum was inserted, but since then there exist a huge speculation of the term "quantum this, quantum that", so we have to return to initial point. Otherwise we will continue playing intellectual games, like the double slit experiment and zombi cats and we will state that ...we are working with a theory that nobody cannot understand...I think it is something like an intellectual ... (was censored by me due to my polite education).

@Costas, when I was trying in the year 1988 to find a 'quantum chaotic behaviour in quantum field theories' I was forced to study in deeper level all the classical apparatus (which by the way @Mohammad is not Newtonian but Hamiltonian and Lagrangian - like QED -) and then I had the biggest scientific disappointment in my whole scientific life:

*Oh, yes, my net friends, there existed NOTHING at all in QM to remind chaos.

*Although I spent an enormous amount of time, my conclusion was that we have to define everything from scratch in order to be able to start studying the possibility of candidate systems, to try find ways to chaos ...Oh my God, a simple disaster...

*After that I stopped working in Physics and I studied Economics.

So, if I start again working in this field I will not allow my self working in a "dead end way".

=====

Another big issue is this:

-->We are always start from a classical concept, Lagrangian, normal modes, circular motion (De Broglie) and then we are doing the 'quantization process': we are cutting the meat or like Procrustes we fit the reality to a linear algebrraic procedure.

Sorry, but one thing I am sure and you can fight against me as long as you want is this:

Nature IS NOT linear.-

If we are trying to explain the Nature by eigenvectors, eigenvalues and other (nice, I like them) mathematical tools, then the Nature simply will not be explained!

Dear Demetris,

I´ve no problems to discuss the hierarchy for spending money either for science or for the wellfare of the people and nations. But that was not your question. And QM is no intelectual game, it´s a wonderful and at the moment the only serious and scientifically accepted explanation of the microscopic world.

I would like to use common terms and say this: CM is the comprehension of the macroscopic world. Any time one wants to study some microscopic level of reality, has to use non-Cantorian, Non-standard mathematics! Full stop.

Dear Demetris,

CM, as well as QM were not guilty of “in some countries there is no job, no electricity, no food, no...”. It is just economic inevitable law fault. You will drive to despair much more, acquainting with that closely.

Dear Galina,

Dear Hanno,

Of course my main argument is not the financial cost of CERN play-ground, but you can forgive me due to my long-term financial suffering in Greece.

The main problem is that we have stacked with QM: nothing is moving neither to the future nor to the past.

We are enjoying passion conversations about many intriguing objects, but can you show me a ray of light or the end of the tunnel? I am afraid no.

Since I don't believe that I am an old (scientifically) man, I want to continue the story of Physics since the early 20th century in order to catch the train we have lost.

There are many unexplained phenomena.

Linear Algebra has reached its limits, we need further investigation to proceed.

I don't care about a curve fitting process where by using splines you can make a perfect fit: But even then nobody has claimed that those splines are living entities, just like QM argues for its Fourier fitting process!

Rather than putting CM and QM in some hierarchical position (relative to each other), what if we connect them?

The connection would be along an existing continuum we refer to as 'scale'. This continuum is not accounted for in a 3-D model of space - since in a 3-D model we should be able to measure the distance between any two objects in that space (how can we measure the distance between a book on a table and a molecule of a pen next to the book on the table - a measurement across scale?)

The 3-D volume of an object (say our body) at the macro scale (with organs and a skeleton) does not hold the same objects as the 3-D volume at the molecular scale (with molecules and proteins). The 3-D volume of our body is the same at both scales, but contianing different objects. Do these two 3-D volumes (let alone the 'space' in between) comprise the exact same space? In a 3-D model, a single 3-D volume is all you get. How can different objects occupy the same volume? Maybe they are not the same 3-D volume and are separated by the continuum of scale. Can this physical observable continuum of scale really be accounted for by a strict 3-D model of space?

If we take a 3-D set of axes at our macro scale, can we not 'slide' these axes 'down' along the continuum of scale - note this would be in a direction mutually perpendicular to all 3 axes. So is not the continuum of scale a 4th physical dimension sitting right under our noses - which could connect the large scale with our macro scale with the very small scale?

What we need is to alter our model of space to include this already existing already acknowledged physical continuum of scale.

This is how we can connect the levels of CM with the levels of QM...

Well, we might need some new mathematical tools as well - like a means of measuring and calculating across scale (which might change those linear equations of QM).

As a summary of discussions relative to this question:

*The sinusoidal solution of Schroedinger here:

https://www.researchgate.net/post/Is_modern_quantum_field_theory_like_geometrical_optics_was_for_describing_diffraction

*The action assumption of Feynman's QED here:

https://www.researchgate.net/post/What_is_the_legitimation_of_the_basic_Feynman_and_Hibbs_assumption

*About Sturm-Liouville theory:

https://www.researchgate.net/post/What_is_your_opinion_about_the_Sturm-Liouville_theory

*General discussion about Linear Science:

https://www.researchgate.net/post/Are_you_satisfied_with_our_linear_science

*The mythology about probability:

https://www.researchgate.net/post/Is_Probability_a_self-existent_concept_quantity_or_whatever

It is supposed that a superior theory can give the subordinate theory by suitable adjusting a set of its parameters. For example Special Relativity (SR) is superior to Newtonian Mechanics (NM) since by just taking a Taylor series expansion of the relativistic kinetic energy K we can obtain the corresponding Newtonian one, see here:

https://www.researchgate.net/file.PostFileLoader.html?id=516ed219d3df3ef16a00000b&key=50463516ed219d3192

But what about QM?

1)Why this theory cannot give us even a smell of a chaotic behaviour?

2)Why even if take the limit h-->0 we cannot obtain CM?

(See here: http://arxiv.org/pdf/1201.0150.pdf )

So, if we want to find a 'theory of everything' hierarchy plays a critical role.

@Demetris: Demetris, if you are really want to see something new, along the lines I suggested, then star with:

Regarding your initial impulse, Demetris. Remember, please, England on the eve of capitalism: struggle of people with machines. Read, please, Adam Smith and Karl Marx. The elites of the world will done only that they would like for themselves, nothing of the kind that would be useful for everybody.

@ G.Ustinova. Marx pisal temno. Ya chital v izlozhenii Stalina.

Read, please, his "Capital".

Once we realize we will not be able to travel even close to the speed of light, then we will understand that it will take enclosed societies across generations to traverse space. The social structure of an enclosed society will not survive the exploitive or repressive nature of current societal structures. New structures will be needed - and new societal structures take generations to produce. We are likely to be stuck on this planet for a long time - it becoming an enclosed society and forcing us to adjust accordingly.

@Costas, I started reading it.

I have a wonder: Have we think about that such a desirable concept of 'quantum gravity' simply does not exist?

Because as I am searching more I am finding theories that tend to accept many transcendent assumptions.

OK, this is intellectually and sci-fi nice. But is it reality?

I will add a comment on the item 1. of the "question" regarding the term "Quantum chaos" . The term is widely used in the current literature for effects in some manybody quantum systems which exhibit chaos in their classical limit . Namely, highly excited spectra of atomic nuclei, hydrogen atom in microwave or in a magnetic field, Rydberg atoms in crossed electric and magnetic fields, or typically, energy spectra of the Anderson model, all those are nonintegrable systems which exhibit typical irregularities called "quantum chaos ". These are characterized e.g. by probabilistic distributions of spacings of the nearest neighbour energy levels. These distributions exhibit maxima at finite values of the spacings and can be distinguished to pertain into one of three classes of universality: according to the symmetry of the underlying Hamiltonian. These distributions start a zero at \delta E=0, i.e. the levels never cross. On the contrary, the levels always avoid each other because of strong quantum repulsion at small spacings. Once there was proposed to use rather the term "quantum chaology" , but in spite of possible misunderstandings the term "quantum chaos " survived and now it is standard name for "the symptoms of chaos at a quantum level " for systems which become chaotic at classical limit .

It is to be noted that when making the semiclassical limit, before taking the limit \hbar-.> 0 there is to be averaged the observables and after that to take the limit. Namely there are strong oscillations because of the expression 1/\hbar which must be removed by averaging before taking the limit \hbar->0. .

Demetris, you wrote:

"I want to continue the story of Physics since the early 20th century in order to catch the train we have lost."

I agree with you that Nature is non-linear, contrary to QM. However, I wonder how QM might look like if the idea of wavelets was well known to its creators. Perhaps this is "the missed train"?

@Denetris: Demetris, I am not an expert in QM, you can judge if this formalization leads anywhere. What leads me to suggest to you this book is my constant believe that if you have something which holds for macro-world, and you want to generalize it to some level of microworld then you have to use nonstandard (Boolean or infinitesimal) or even topos theoretic models.

Ther are also these works which might interset you:

Chris J. Isham , 2011: Dirac Medal for his works on quantum gravity, may be what you were looking for!

@Marek, just think this: What if we could generally solve the microscopic problems with all possible functional basis available and not only the sinusoidal one?

Oh yes, wavelets and why not solitons? I can guarantee you that solitons have nothing to jealous from typical sinusoidal wavepacket. The way is to create a new Schroedinger equation, of general form. How do you find this idea?

@Costas, your suggestions are rigorous but they need time to be read!

Can you give me a 'soft mathematical' description of topos (τόπος! μεγαλείο...) and category (κατηγορία!) in two paragraphs?

I shall read them, but time, time...

@Costas, you had right for the second article of Isham: it was easier readable.

Demetris, download my book ΘΕΜΕΛΙΩΔΕΙΣ ΕΝΝΟΙΕΣ ΚΑΙ ΘΕΜΕΛΙΑ ΤΩΝ ΜΑΘΗΜΑΤΙΚΩΝ, to find a conceptual introduction to Categories. As for topos I will choose for you a down to earth introduction.

Some nice introductions to categories and topoi:

And topos:

No. Classical mechanics is a limiting case of quantum mechanics.

The basic "axioms" of QM Hilbert space, eigen value...) do not specify a "scale" (the Schrödinger equation is the only one which involves the Planck constant and is a consequence of the Wigner's theorem), so they are not at the heart of the problem. The key issue is that the usual concepts of classical mechanics are not pertinent to represent the motion of bodies (say particles or atoms) without internal structure in the relativist geometry. Which leads to the introduction of spinors and "matter fields".

Actually the principle of least action and lagrangians (which are the basis of mechanics) still apply (or are assumed to apply) at the atomic scale, and they do not require any linearity, even in a perturbative approach. However they state only the necessary conditions that must be met at equilibrium, so they cannot easily be used in the discontinuous phenomena, such that those involved in "chaotic situations". They require different tools, such as the Fock spaces representations, which are similar to the kinetic of gas.

@Demetris: yes, solitons are even more tempting than wavelets. Both kinds of objects are much more intuitive than plane waves. Think about electron just separated from an atom (ionization): it instantly becomes a plane wave, present in entire space, everywhere. Isn't it strange? On the other hand we have a famous two-slit experiment ...

In addition, the nonlinearity seems (at least to me) to be an inherent feature of solitons. The problem is, however, can we build a base from solitons? This would be great, if done, but what about the undeniable discretness of our world then? Anyway, exotic quasi-particles, like phonons, magnons, etc., could become more 'real'. The classical mechanics would easily survive such an revolution, but would the QM?

I hope somebody, some day, will try soliton-based alternative.

Some references:

http://www.scholarpedia.org/article/Soliton

http://personalpages.to.infn.it/~boffetta/Papers/osbc91.pdf

http://en.wikipedia.org/wiki/Inverse_scattering_transform

http://people.maths.ox.ac.uk/trefethen/pdectb/kdv2.pdf

http://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation

My thought is this:

"Can we present a directly observable alternative to sinusoidal ansatz, but with the additioanal ability to produce also the soliton solutions?"

Demetris,

No. Sinusoidal ansatz is linear, but soliton solutions are nonlinear. Unfortunately, now effective nonlinear theory is absent.

With best regards,

Eugene.

Johan,

all this is linear, but life is nonlinear.

With best regards,

Eugene.

Several points: first, the difference between linear and non-linear problems is, in the case of quantum versus classical mechanics, a bit a question of the formalism: Koopman developed a way to descibe classical mechanics in terms of linear PDE's, very similar to the Schroedinger equation, though with important differences. On the other hand, if we do quantum mechanics in the Heisenberg picture, the observables obey infinite hierarchies of non-linear equations, which in some approximation (Ehrenfest theorem) actually reduce to the classical equations.

So the linearity issue is a bit moot. On the other hand there is a real difference: bounded quantum systems have discrete spectrum, leading eventually to quasiperiodic behaviour, whereas all chaotic classical systems, which are generally bounded as well, have continuous spectrum. This means that classical systems can display irreversible behaviour, whereas quantum bounded systems cannot. What happens in the classical limit, is simply that the time scale on which quasiperiodicity becomes apparent diverges as the scale of the system's typical actions becomes large with respect to hbar. An additional issue needed to obtain the classical limit is the following: at some point, if a state corresponding to a large system spreads out too much in space, it will become very sensitive to external effects (dephasing and decoherence). This leads to loss of the characteristically quantum properties and the system then does behave like a classical system.

So the classical limit of QM is possible, even in the chaotic case. As far as QED is concerned, I admit to not having very much expertise, but it is clear enough (read Jackson's chapter 17 on radiation reaction for details) that the classical theory of an electron interacting with the electromagnetic field is far more messy and filled with contradictions, than the corresponding quantum mechanical theory, which has provided some of the most precise measurement of physics in general (Lamb shift, g-2). So even if the quantum theory is a bit murky, it does something which the corresponding theory cannot do in any way. And from the point of view of logical consistency, as I said, classical electrodynamics of point charges is in a far worse state than QED.

F. Leyvraz,

point charges remains in QM and QED with all their contradictions (see Feynman).

E.F.

Dear Johan,

all this linearity (true of course) contains no information. It is like empty space.

With best regards,

Eugene.

@Marek Gutowski:

"Think about electron just separated from an atom (ionization): it instantly becomes a plane wave, present in entire space, everywhere. Isn't it strange?"

It would indeed be exceedingly strange, but that is not really what actual computation yields. If you take the time-dependent Schroedinger equation and solve it, say starting with the system in an eigenstate of some fixed external potential V(x), and then apply an external time-dependent potential W(x) * cos(omega t) between time 0 and time T, say defined by 2*pi*k/omega, Then you turn off the potential.This is then a well-defined problem which you can solve analytically, if you take a simple enough V(x), say square well in one dimension, and W(x) smal enough so that you can apply perturbation theory, or numerically otherwise.

In this case, for starters, nothing is instantaneous: the function psi(x, t) always changes continuously. Further, the value of the integral of the modulus squared of psi(x, t) always remains equal to one, so psi(x, t) always remains, for all t, a function that goes to zero as x->infinity. The real difference, which is what, indeed, allows to speak of "ionization" is the following: the initial wave function is altogether orthogonal to the continuous eigenfunctions, that is, the ones involving plane waves. For this reason, the state is bound, that is, its position remains bounded for all t. On the other hand, after the perturbation, the resulting wave function is a linear combination of the original bound state with an integral over a continuum of states involving plane waves. This yields a wave packet, bounded in space, but which does indeed move to infinity as time increases. But this is exactly what we mean by ionization. The one thing that is, indeed, a bit peculiar is the following: the state is a combination (coherent superposition) of the bound state and the continuum states. So for large times, the particle will find itself with a certain amplitude bound to the original atom and with another amplitude moving freely. One then needs measurement (or some kind of decoherence process) to tell us whether the particle has in fact been ionized or not.

It took me a little time, but here it is, look the attachment.

We take the function:

f(x)=1/(1+x^2) at [-1,1]

and approximate some of its values with splines. The approximation is excellent.

If we try to expand the approximation outside the [-1,1] we see that this divergences.

So, by analogy to quantum mechanics:

*sinusoidal basis --> splines

*range of convergence --> renormalization problem of QED

We use splines, but:

1)we never argued that they are living entities, like the 'waves' of QM

2)we avoid using them outside the radius of convergence, while in QM/QED this is silently by-passed.

It's very simple - http://ikar.udm.ru/sb/sb51-1.htm, http://eng.ikar.udm.ru/sb/sb22e.htm

Dear Johan,

no problem to translate the article (http://ikar.udm.ru/sb/sb51-1.htm) or the book (http://eng.ikar.udm.ru/sb/sb22e.htm) using Google (http://translate.google.ru/#ru/de/ or http://translate.google.ru/#en/de/).

P.S. St. Valentines Day

Regards

Valentin Shironosov

14.02.14, Russia

@F. Leyvraz, a first issue is:

"is Schroedinger eq. the equation of everything?"

Personally I doubt, it is a convenient approximation, the Fourier series approximation of microscopic phenomena.

A second issue is this:

"...psi(x, t) always remains, for all t, a function that goes to zero as x->infinity"

Of course if we add more terms is a Fourier series expansion we have better approximation and there exists also the Parseval identity. But this does not mean that every additional term has a physical significance at all.

With QM interpretation we managed to give 'life' to approximatelly added terms in relevant series expansion, try to think about it (Look my splines figure above).

@Valentin, we have also Pappas ionization apparatus in Greece...

Dear Johan,

Do You know the sizes of electron?

With best regards,

Eugene.

Johan,

and what does it mean delta functions in QM and QED equations?

Best

Eugene.

Another big story is the double slit experiment: Because we don't want to accept the wave like nature of material things we have built a whole set of extreme answers. The situation is very simple: All those 'explanations' are being promoted and even people they do this, do not believe they are right. It is the industry of vagueness: Don't believe the obvious, follow us the gurus...

Dear Eugene, please look up this:

http://mathfaculty.fullerton.edu/mathews/a2001/Animations/Interpolation/FourierSeries/FourierSeries/FourierSeries3/FourierSeriescc.html

As the number of added sinusoidals increases then the accuracy is increased.

By the way the Heaviside or step function can be expressed via the Delta function:

The Heaviside function is the integral of the Dirac delta function: H′ = δ.

see here:

http://en.wikipedia.org/wiki/Heaviside_step_function

So, what? Every being added term is a living entity? ie "there exist a probability that the 'particle' can be somewhere"? I don't think so.

We have mixed mathematical approximation with physical interpretation in a very messy way...

Demetris, Johan,

I agree, but we have no anything better.

Best

Eugene.

Dear Eugene, this is the chance, we can catch the train from the early 20th century and go Physics a step forward, Don't be pessimistic...

Dear Johan,

Since you have worked so much, next task is to indicate the proper experiments that are suitable for confirming your arguments.

Then, albeit what somebody want to believe, nobody will be able to reject them.

This is your chance, start from the solid physics (your expertise field).

Friendly,

Demetris

PS I think that first of all you have to write a detailed book about electron.

Johan,

1. Controlling theoretical physics is illusion (nobody can control, for example your, Johan, mind).

2. Four coordinates of Minkovski space are linearly independent by definition.

3. Maxwell equations are nothing else as mathematical properties of any vector field in Euclid space. They contain no information for free space. All information is in material parameters, wich can not be extracted from Maxwell's equations theirselfs.

4. Particles (matter) are singularities in Minkovski space (see Torsten Asselmeyer-Maluga and Brans).

Best

Eugene.

Dear Johan,

1. For everybody the reality it's own.

2. If not independent, then not Minkovski space, but something other.

3. Minkovski space can not manifest, but can describe.

4. If You want to propose something better, then propose. Be constructive!

Best

Eugene.

I think we need to be careful when making statements like: "Maxwell equations are nothing else as mathematical properties of any vector field in Euclid space. They contain no information for free space. All information is in material parameters, wich can not be extracted from Maxwell's equations theirselfs." Maxwell equations are equations, in the first place, and any equation is a statement. A statement is not the name of a property, but an assertion. Furthermore, Maxwell equations include derivatives with respect to time and Euclid's space is timeless.

As we all know, any field in Euclid's space that's regular at infinite distance, can be obtained from its sources (divergence) and its vortices (rotational). That's the content of Helmholtz Theorem. Maxwell equations state a relation between the time derivative of the electromagnetic fields, their sources and vortices, and the densities of electric charge and current, which is not trivial. (See my paper http://arxiv.org/pdf/quant-ph/0409012v3.pdf)

If the electromagnetic field is studied in four-dimensional space time, Maxwell equations are transformed into:

\partial^j F^{ij} = \frac{4\pi}{c} J^i

It is true that any vector field can be represented as the divergence of a second order tensor, but this is not all that there is to electrodynamics, there is also the density of four-force: f^i = \frac{1}{c} F^{ij} J_j. The problem with classical electrodynamics is that the connection between f^i and J^i (the connection between inertia and electric charge is not given ab initio). The idea that an electron is a state of the electromagnetic field leaves the difference between the mass of an electron and the mass of a proton, for example, without a rational explanation.

Let's not forget also that boundary conditions, unless they are imposed at an infinite distance, can only be justified on the assumption that we have information about the field at the boundary, or there are material systems whose presence is modeled by these boundary conditions, as is the case when we study the radiation produced by an antenna or diffraction.

Dear Johan,

Eugene=Eugeneios=Ευγένειος is from greek word 'eugeneia'='ευγένεια' which means politeness. As I have noticed Eugene is one of the most polite scientists I have met in RG, so please, even if you 100% disagree with him, be polite with him.

Dear Oscar, have you any kind of idea how the situation could be if we started by the adoption that matter is not exactly sinusoidal waves but in general wave-like entity?

I mean, if we don't adopt the classical exp(i*k*x-w*t) assumption.

Is there any constraint that prevents us from working in such a general way?

Is there any relativistic kind of constraint?

Yes Johan, sinusoidal waves are the status quo ante, what I'd like to search is the possibility of a more general wave nature than sin() cos(), exp(i*theta).

I don't know if this is possible under the current knowledge, but I am strongly convinced that, since sinusoidal is the simplest kind of wave and since our science is linear, ie a first order approximation of reality, then the more general equations for light and matter (even if I accept your identity matter=a kind of EM) should not be Maxwell's equations, so equations for matter should not be Schroedinger.

This is the chance:

Forget Maxwell, forget Schroedinger.

Keep only de Broglie and search for a generalization of the concepts of λ, k, m, p, E under a more general wave behaviour.

Any idea?

I´m happy to learn that modern QM is supposed to be bull shit and Vodoo. Now finally I understand it, of course only after doing my homework. :-((

Oscar,

Euclid means metric, but not the number of dimensions. Euclid space may have as many dimensions as You want.

With best regards,

Eugene.

Do, dear Johan, your answer is that we cannot escape from Maxwell equations?

It seems a little bit pessimistic, but I respect your opinion, since it is grounded on many years of effort.

Probably what I want to do is a generalized theory of light:

Take this universe with those constraints and you will end up to Faraday's law and other concepts that will lead you to this kind of light equations (Maxwell).

Can you for a moment 'get out' of our universe and see the whole situation more abstract?

Then probably you will agree that what we deal is just observations of our local universe and we have not a general theory of light (and consequently of matter).

Johan,

in Russia such man as You is named "крутой". If You want people understand You, speak understandable for them language. I, for example, faithfully try to understand You.

With best regards,

Eugene.

Demetris,

sin, cos or other linearly independent systems of functions are only coordinates in functional space, as basis vectors in Euclid space. You may choose any basis You want. It is only the language.

With best regards,

Eugene.

Dear Eugene,

Have you any kind of example that came with another choice, different than sin(), in the study of microscopic phenomena?

I mean is there already any 'Schroedinger type' equation that came with such a different basis?

Thank you.

Demetris,

I shall answer later.

With best regards,

Eugene.

Johan,

now it is understandable what are You speaking about. But You are pushing an open door. Your pretensions to different mathematical languages are not essencial.

With best regards,

Eugene.

Dear Demetris,

there are a lot of examples. The choice of functions depends on the symmetry of considered by You problem. If You have rectangular coordinates, then You use sin and cos, if cilindrical, then You use Bessel functions, if spherical, then spherical harmonics and so on.

With best regards,

Eugene.

@Demetris

If you were to use a sinusoidal function you will have to drop Schrödinger theory, because sinusoidal functions are real then, in order to satisfy Schroedinger equation, because the imaginary unit multiplies the time derivative, you will need to have an amplitude of zero. It can also be proved, because de second derivative of sin is -sin, that you cannot satisfy Klein-Gordon equation.

The wave functions of stationary states can be chosen real, because the time independent Schroedinger equation is real. Such is the case of the stationary states of a harmonic oscillator.

Going back to the original question, quantum mechanics is, in a way subordinated to classical mechanics, because it refers to measurement and all measurements involve classical objects.

Dear Eugene,

I focus on time dependent Scroedinger equation solution, look here:

http://www.cobalt.chem.ucalgary.ca/ziegler/Lec.chm373/Lec3/Lecture3.pdf

It is obvious from the construction of Sch.Eq. that it will never have a time solution different than a sinusoidal one.

But, I insist: sin() is the linear approach of the reality.

Probably, after so many data sets of CERN experiments, to exist many of those sets that can be explained with a different, non linear equation.

But, main dogma explains anything like Procrustes:

Cut and push untill the data fits the linear theory!

(It is similar to the Holy Inquisition of Medial Times...)

Is quantum mechanics subordinate to classical mechanics?

Yes!

See - Resonance in physics, chemistry and biology.

3. Resonance in non-linear systems.

3.1. Simple computational method for non-linear dynamic systems.

3.2. About a pendulum of Kapica outside and inside zone of a parametric resonance.

3.3. Dynamic stability of saddle points in autonomous systems.

3.4. About stability of unstable states, bifurcation, chaos of non-linear dynamic systems.

3.5. Discretization, chaos and evolution in non-linear dynamic systems.

http://eng.ikar.udm.ru/sb/sb22e.htm

@Demetris

I am not married to quantum mechanics. As it is the case for any mathematical representation or data structure, if you provide the means for an interpretation you can use whatever you want. Then, however, you need to match experiment.

@Johan

So, according to you, the potential of electromagnetic field acts on electromagnetic field. Which potential, can you tell me? Is it the scalar potential? Which one?

@Oscar, that's the main task: explanations of measurements. The problem is that we cannot even think an alternative way of interpreting data (not you, as I saw you have obtained many alternative results).

So, by accepting the general guidance that Nature is in principle not linear, but is locally linear (a situation similar to Euclidean and other Geometries), we are trying to find the 'holes' in the so arrogant building of linear physics (say it quantum physics, it is the same, since all physical quantities are eigenvalues of hermitian linear operators).

Have you thought about any such a 'hole'?

If physics is to provide an understanding of 'reality', then it will also need to provide an understanding of the connexion of the very large to the macro to the very small. Since physics has assumed reality works from the very small 'upward', how does the structure of sub-atomic particles impact the structure of molecules impact the metal surface and interior of a metal at the micro-level impact impact the macro metal fatigue at our level (fatigue being something which impacts us directly). And the structure of nuclear particles impact the structure of molecules impact the structure of proteins impact the structure of cells impact the structure of our organs and skeleton impact the structure of our bodies.

That we are considering a question of hierarchy of QM nd CM shows we very far off from an understanding of how reality works across scale - an implicit continuum of reality.

This continuum appears to us as an exponential (a non-linear) scale. So we have yet to address a (an apparent) non-linear component to reality. Linear movement in this continuum could appear to us as non-linear movement (a constant velocity in the direction of scale could appear to us as a constant acceleration). So where we have modeled reality in a non-linear way, could be modeled linearly from a different model perspective.

This suggests that 'linear' and 'non-linear' are as much a consequence of our modeling perspective as an 'actual' character of the underlying reality.

We are 'trapped' in our perspective of reality starting from our 'macro' level of scale. If perspectives are relative, then we will need to understand the relativity of scale. Thinking that reality will be understood by the wave front of an electron also suggests the impact of scale has not yet significantly entered the main stream concerns of modeling reality.

This will come, possibly in the next 25 years.

Dear all,

Several issues need to be discussed in connection with the original question.

(1) The traditional view is that all classical Newtonian mechanics is contained in QM as a special case through Ehrenfest's theorems.

In this sense, QM is super-ordinate to CM not sub-ordinate to it.

(2) In the Heisenberg formulation as well as in Bohr's correspondence principle CM is recovered as the h-bar going to zero limit of QM.

(3) QM starts with linear equations but does not preclude non-linearity and also the appearance of quantum chaos. One may search for these topics on Google or read books by experts. So it is not true that only CM has these features.

(4) Classical mechanics also has got its own share of infinities and unsolved problems and thus QM cannot be said to be inferior on this score.

This is sufficient to show that the the answer to the question is a BIG "NO"

Regards

Rajat

Thanks Rajat, a realy thorough answer! Thats what I learned during my studies.

I repeat: a clear NO.

Demetris,

there is no such reality as a time in QM. Observable "time" is absent in QM. In QM time is only a parameter, therefore You can choose any way You want to model it. Linearity is the simplest choice.

With best regards,

Eugene.

Johan,

it is mental gymnastic.

With best regards,

Eugene.

Dear Rajat,

(1) your argument is circular: see a small proof

http://en.wikipedia.org/wiki/Ehrenfest_theorem

If we do not accept Schroedinger linear picture then nothing exists at all

(2)There exist proofs of the opposite: CM cannot be derived as h-->0

(3)I have read books by experts but if you find me a period doubling bifurcation of a quantum character I will glory you!

(4)The fact that CM is not the best theory is not an argument against the hierarchy.

We disagree, try again to convince me.