Schrӧdinger equation is only an appriximation. In general, there is the system of equations for particles and fields. This system is nonlinear because particles and fielda are connected with each other.

That's the general answer with decoherence. Unfortunately, that doesn't work. Decoherence is just built out of measurement processes, and then can't solve the measurement problem. The same was true of the Heisenberg microscope, which during a long time was thought to explain the Heisenberg uncertainty principle. The wave collapse being intrinsically non local, no local process can explain it, be it non linear, irreversible etc.

I think that this is not decoherence itself. It can be shawn that quantum mechanics is nonlinear and this nonlinearity gives us an unswer. Nonlinearity of quantum mechanics is a consequense of system of equations for particles and fields.

``It can be shown that quantum mechanics is nonlinear and this nonlinearity gives us an answer.''

Can it really? I believe there are, on the one hand, theoretical arguments that most kinds of nonlinearity lead to the possibility of superluminal communication, and on the other, that there is substantial experimental evidence yielding rather strict upper bounds on nonlinearity in quantum mechanics. See S. Weinberg, PRL 62 (5) 485 (1989).

I think that nonlinearity of QM is not connected with superluminal communications. It is the consequense of nonlinear system of equations for particles and fields. In general, fields are quantized and this fact should be taken into account.

Schrӧdinger equation only works before and after scattering (accompanied by the creation or annihilation of particles).

Decoherence is just one part of the answer. We have also come to know about recoherence. There no 100% classical systems, as well as there are not 100% quantum systems.

All systems are quantum, classical system is only limiting case

It depends what you mean by nonlinearity: the Schrodinger equation for the time evolution of the states is linear in usual QM. Weinberg has shown that, if you introduce a nonlinear variation for this time evolution of the states, then very stringent limitations can be found from experiment. Further, it has been argued rather cogently that, if such a modification exists, then some kind of superluminal communication might well be possible, or else communication between different macroscopic branches of the Everett universe wave function. .

On the other hand, one can always write quantum mechanical equations in some nonlinear way. But that does not affect the basic problem of QM, which is given by the fact that linear superpositions cannot disappear.

But Schrӧdinger equation can not describe inelastic scattering processes: it only works before and after scattering (accompanied by the creation or annihilation of particles).

The Schroedinger equation, or appropriate gener- alisations, describes the state evolution for all systems. I do not think you will find evidence for nonlinear evolution in the state evolution. 

Simple example is the Compton scattering. Solution of this problem is only possible in the frame of Quantum Field Theory.

Fair enough, but I do not think quantum field theory will give you what you want. In effect, it is non-trivial to define a state in QFT (because it must contain superpositions of different states involving various numbers of particles) but it is not impossible in principle. In that case, the evolution equation for the state will doubtless be linear. Similarly, no matter how convoluted the internal dynamics may be, the scattering matrix is always linear, showing well enough that the intermediate evolution is linear as well.

Dear colleague

According to the Copenhagen interpretation,the superposition principle is a major positive postulate of quantum mechanics. Quantum mechanics contains classical mechanics as a limiting case but simultaneously requires it as its justification because the available measuring instruments to test the predictions of quantum mechanics are assumed to be classical. Thus, the measurements are irreversible, although the Schr¨odinger equation, which describes the motion of a particle prior to the measurement, is reversible. It appears that because quantum mechanics is a more general theory than classical mechanics, the measurement apparatus can also be described based on quantum mechanics, i.e., one can assume that it is in a superposition of its states. However, in that case, the entire system (particle + measurement apparatus) is also in a superposition of states and there is no reason to believe that they must behave in another manner.

Regards 

Schrӧdinger equation is only an appriximation. In general, there is the system of equations for particles and fields. This system is nonlinear because particles and fielda are connected with each other.

 By the way in S matrix exponent is considered in terms of a series, each member of which corresponds to the creation (or annihilation) of particles and can be described using the corresponding Feynman diagrams. In this case, the dependence of the series members on the wave functions in the S-matrix decomposition is also essentially nonlinear.

`` This system is nonlinear because particles and fielda are connected with each other.''

True in the Heisenberg picture. *Observables* evolve nonlinearly, even in nonrelativistic QM. *Wave functions*, or states, evolve linearly. It is just not the usual way to describe relativistic systems.

I agree that the concept of wavefunction collapse is a consequence of Newtonian thinking where non-quantum observer exist. I think that observer should not be classical.

The measuring apparatus can't be described in quantum mechanics. Classical mechanics isn't a limiting case of quantum mechanics either. Those are mere beliefs that have never been proven, for the simple reason they are wrong. They consistently pop up and prevent any sound reasoning.

Kralj

Tell us where the common sense is in Newtonian logic

Mass? Force?

And Newton did not invent differential calculation to describe his abstract ideas?

A state vector does not describe the state of a system. It describes what is currently known about the probabilities of various results that might arise when we make a particular measurement/observation. It is determined not only by the system itself but by the measurements/observations that a particular observer has made or intends to make. This applies to cats just as it applies to elementary particles. The state vector for an observer who does not look in the box (or who has not yet looked in the box) is a superposition. It concerns his current knowledge about the cat. It isn't about the cat "as it is in itself".

"superposition of states" only belongs to the Göttingen-København mythology. But nothing in the real world corresponds to that.

"Collapse of the wave function" too, is strictly internal to this hegemonic mythology.

If you do not know more the position of the submarine, you pretend that the submarine "is in a superposed state".

:-D

Complete edition of the transactionnal physics, in french at https://www.researchgate.net/publication/313309517_La_microphysique_que_l'on_vous_conte_est-elle_bien_la_bonne_La_physique_quantique_transactionnelle_expliquee_pour_tous

Just the fifteen anti-transactionist postulates, in french :

http://jacques.lavau.deonto-ethique.eu/Physique/quinze_postulats.html

Abridged and bilingual :

http://jacques.lavau.deonto-ethique.eu/Physique/postulates.html

We use the Fermat-Fresnel principle : all the real paths come in phase. That's all !

Book La microphysique que l'on vous conte est-elle bien la bonne ...

@ Eric: ``The state vector for an observer who does not look in the box (or who has not yet looked in the box) is a superposition.''

Here I would, somewhat hesitatingly, express a different opinion: there is an essential difference between knowing that the probability of the cat's being alive is 1/2 (with another 1/2 for the other alternative), and knowing that the cat is in the state

L + D

(where I leave out normalisation factors.) Indeed, both this state and the state

L - D

lead to the same conclusions concerning the cat's survival probabilities. Yet the existence of a + sign in the relative phase is a basic feature of this state, so much so that L+D and L-D are a dichotomy which could be taken to be equally basic as the L versus D dichotomy.

So yes, the outside observer, before looking inside the box, sees a ``superposition'' of the L and D states, but it is an incoherent superposition, whereas the paradox implied in Schrodinger's argument refers rather, I think, to the maintenance of coherent superposition.

My favourite argument for the impossibility of measuring the phase between macroscopic objects, draws from the 2nd law: suppose you could measure the phase, by an apparatus called P. Also suppose you have a dead cat, that is, prepared in the state D. Now use P to measure whether this state D is in fact in the state

L + D

or in the state

L - D

You will get one of the two as a result, by the definition of a measurement. Now measure the resulting state to know whether it corresponds to a dead or alive cat. With probability 1/2, the dead cat has resuscitated.

Unfortunately, of course, this is more of a proof that such phases cannot be measured practically, than an effective way of bringing cats back to life.

@Melkikh A.V.

Compton scattering. Solution of this problem was given in 1930 by Erwin Schrödinger.

Mention of it by P.A.M. Dirac in his Nobel Lecture, though Schrödinger himself was intensely demoralized, and did not mention his own results.

Intensely demoralized by ? By ? By whom ? Cui bono ?

I had rediscovered this result in 2011 :

http://jacques.lavau.deonto-ethique.eu/Physique/Zitterbewegung_Bragg_Compton_english.html

Of course they can-only that just certain elements of the possible superpositions survive the ``macroscopic'' limit. That's part of the definition of what's meant by ``macroscopic''.

The wavefunction isn't a classical notion and the probability density it defines isn't either. Imposing certain conditions on the ``quantum'' probability density leads to the ``classical'' probability density, which has support on a subset of the states of the quantum system.