Precisely this is the reason that ALSO the problem of arrow of time is still unsolvedlalbatros said:Juan wrote:
I cannot agree with that statement, altough I recognize a conceptual difficulty there.
For me, this problem is similar to the problem of irreversibility seen from the classical mechanics point of view. Non-unitary evolution might be a good approximation (maybe even *exact*!) when an interaction with a huge system (huge freedom) is involved.
My favorite example is the decay of atomic states: clearly the interaction of the discrete atomic system with the continuum system of electromagnetic radiation brings the decay. This decay is very conveniently represented by a "non hermitian" hamiltonian: this allows modeling of an atom (for the Stark effect e.g.) without including the whole field. This represents correctly the reality, altough the fundamental laws are unitary.
It is simply false that a non-unitary evolution can be derived from an unitary evolution as a kind of "good approximation". It is mathematically imposible and physically wrong. This is the reason people seriouly working in arrow of time (specialists in the topic) is proponing nonunitary evolutions. For example Prigogine theory, CSM, etc.
That a non-unitary evolution cannot be obtained from an unitary evolution was already adressed many time ago. In words of specialist van Kampen: irreversibility cannot be obtained from reversibility except by an appeal to manthematical funambulism. He clearly emphasized the word funambulism. In fact all 'derivations' in literature beggining from unitary physics have wrong mathematical steps of kind "since 2 + 2 = 5 then A > B". People is doing is adding wrong mathematicals teps for deriving the corerct answer from a incorrect beggining. That is, NOBODY is deriving irreversibility from unitarity.
All supposed 'derivations' i know from literature are mathematically wrong and physically unsustainable.
Your example of decay of atomic states is simply wrong as is well-known in literature on the problem of time. There is a couple of mistakes in standard elementary textbook 'derivations' (i remark supposed derivations). Literature on why standard elementary approaches are wrong when one study details is excesively huge i can cite all relevant papers on the topic. But i can say some of typical errors.
First the use of a continuum of radiation does not introduce irreversiblity since QFT is time-simmetric. The quantum states are not defined in standard QM and QFT and one uses approximation that a state is described via Dirac kets, which is not true, because the Dirac state is valid only when interaction is EXACTLY zero. Some authors are exploring more general states like Gamov ones.
The use of a pure continuum is an approximation known like 'thermodynamic limit'. In standard approaches resonances between discrete spectra and that ill-defined continuum spectra are simply ignored. In rigor, standard QM does not work in that continuum. In fact, as proven by Prigogine and colleagues the Hilbert space structure of QM collapses and wavefunctions loose probabilistic interpretation, for example the norm of density matrices is NOT the unity -they solve this introducing a more general RHS-. The relationship between the non-hermitian 'Hamiltonian' and the original Hermitian one is NEWER addressed. One can prove that the solution choosed in textbooks is incomplete (in a similar manner like ignoring negative energy states in relativistic Schrödinger equation does not work). The total system atom + field continues to be reversible and production of entropy computed is zero, which is wrong, etc.
As said the derivation of the nonunitary law from the unitary one is mathematically wrong. People DOES is really substitute the unitary law by the nonunitary one at some specific point of the computation, but this is 'hidden' is usual presentations -however one can prove that is that people is really doing-. Etc, etc.
1) Precisely the problem with QM -as already noted by Einstein- is that QM is incompatible with classical mechanics. Precisely Born explicitely splitted universe into two parts, classical and quantum, with QM applying only to the latter. The problem of quantum measurement is that people is attmepting to derive measuremente from QM only when one needs introduce some classicality concept from outside of QM. 2) Precisely Prigogine approach is the construction of a generalization of QM ALSO applicable to classical systems. It is also Penrose approach who argues that GR cannot completely quantized and that classical residue is hidden element for explaining measurement.lalbatros said:Juan wrote:
For many people, the interaction with a 'classical' or 'macroscopic' system is all that is needed to derive the PP. I think this is the most probable explanation for the PP. Landau considered this so obvious that it comes in the first chapters in his QM book.
I think that both approaches (Prigogine and Penrose) are good but are not the final answer.