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bg032
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Many physicists claim that decoherence determines the emergence of the worlds in the Many World Interpretation (MWI). I have always found such a claim elusively proved and actually wrong. Recently I wrote a paper: http://arxiv.org/abs/1008.3708 addressing such a subject, and I sent it to Foundation of Physics for publication. The reports of the two referees were not totally negative, and the criticisms of the two referees were completely different. Anyway the paper has been rejected. As usual, some points that I thought to be clearly expressed and almost evident were not so for the readers. It would be very useful for me to discuss with the referees, but unfortunately this is not possible. Therefore I have thought to present synthetically the main points of the paper in this forum, hoping that a discussion could help me in better formulating them or alternatively in convincing myself to be wrong. For shake of simplicity and clarity, I will subdivide the presentation of my paper into three threads, namely:
1) Minimal elements of a MWI and the preferred basis problem
2) Does decoherence solve the preferred decomposition problem?
3) Does permanent spatial decomposition (PSD) solve the preferred decomposition problem?
Point 1 is the present thread, and the following threads will be open successively in the case in which a useful discussion develops in this thread and my claims are understood and accepted.
I think that at least the two following minimal postulates have to be part of a MWI:
A) A wave function subjected to unitary time evolution: \Psi(t)=U(t)\Psi_0 is associated with the universe.
B) A criterion exists for defining, possibly in an approximate way, a preferred decomposition \Psi(t)= \Phi_1 + \ldots + \Phi_n for every t, where the elements of the decomposition are approximately orthogonal.
Remarks: the elements of the decomposition correspond to the different worlds. Their number has been assumed to be finite for simplicity; it could also be infinite, thought at most countable. The fact that the definition of the decomposition is allowed to be approximate does not mean that it can be elusive. For example, if two decompositions \{\Phi_1, \ldots, \Phi_n\} and \{\Phi'_1, \ldots, \Phi'_n\} of \Psi(t) are compatible with the approximation, we must however have that ||\Phi_i - \Phi'_i|| \approx 0 for i=1, \ldots n, and if the two decompositions have different numbers of elements they can be appropriately grouped to obtain two decompositions having the same number of elements and satisfying the above property.
I formulate
The preferred decomposition problem (PDP): what is the criterion defining the preferred decomposition of point B?
I prefer the name "preferred decomposition problem" rather than the usual "preferred basis problem" because I find the latter to be misleading; in fact what we need here is to define a decomposition of a given vector, and not to define the whole basis for the Hilbert space of the universe.
It is well known that decoherence theory is based on the subdivision System-Environment, and that this subdivision is problematic when the whole system is the universe. However, since my claim (in the paper and in the next thread) is that decoherence does not solve the PDP even if this subdivision is given, I formulate
The facilitated PDP: assuming that a subdivision in System and Environment is given in some way for the universe, what is the criterion for defining the decomposition of point B?
In the next thread, if it will be open, I will argue that decoherence does not solve the Facilitated PDP.
1) Minimal elements of a MWI and the preferred basis problem
2) Does decoherence solve the preferred decomposition problem?
3) Does permanent spatial decomposition (PSD) solve the preferred decomposition problem?
Point 1 is the present thread, and the following threads will be open successively in the case in which a useful discussion develops in this thread and my claims are understood and accepted.
I think that at least the two following minimal postulates have to be part of a MWI:
A) A wave function subjected to unitary time evolution: \Psi(t)=U(t)\Psi_0 is associated with the universe.
B) A criterion exists for defining, possibly in an approximate way, a preferred decomposition \Psi(t)= \Phi_1 + \ldots + \Phi_n for every t, where the elements of the decomposition are approximately orthogonal.
Remarks: the elements of the decomposition correspond to the different worlds. Their number has been assumed to be finite for simplicity; it could also be infinite, thought at most countable. The fact that the definition of the decomposition is allowed to be approximate does not mean that it can be elusive. For example, if two decompositions \{\Phi_1, \ldots, \Phi_n\} and \{\Phi'_1, \ldots, \Phi'_n\} of \Psi(t) are compatible with the approximation, we must however have that ||\Phi_i - \Phi'_i|| \approx 0 for i=1, \ldots n, and if the two decompositions have different numbers of elements they can be appropriately grouped to obtain two decompositions having the same number of elements and satisfying the above property.
I formulate
The preferred decomposition problem (PDP): what is the criterion defining the preferred decomposition of point B?
I prefer the name "preferred decomposition problem" rather than the usual "preferred basis problem" because I find the latter to be misleading; in fact what we need here is to define a decomposition of a given vector, and not to define the whole basis for the Hilbert space of the universe.
It is well known that decoherence theory is based on the subdivision System-Environment, and that this subdivision is problematic when the whole system is the universe. However, since my claim (in the paper and in the next thread) is that decoherence does not solve the PDP even if this subdivision is given, I formulate
The facilitated PDP: assuming that a subdivision in System and Environment is given in some way for the universe, what is the criterion for defining the decomposition of point B?
In the next thread, if it will be open, I will argue that decoherence does not solve the Facilitated PDP.