Hi Juan
Thanks for your comments and for carefully reading my essay. I'm really glad and thankful for that. So I have the chance to clarify things.
You say: "...this would imply that the universe as a whole does not have properties."
Not necessarily. The question here is a bit, what concepts do we use, to describe the universe. Usually we do it by imaging the universe consisting of things, that we are able to describe as isolated systems (atoms, electrons, photons etc.) But you are right, there is a problem from a positivist view to talk about the size of the universe or about the wavefunction of the universe.
You say: "I would mention that a measurement of position essentially consists on comparing the absolute positions of the object being measured and the measurement apparatus."
I'm not so sure what you intend to say here by saying "absolute positions". I did not what to go to much into the interesting topic of how measure distances. I belief this more complicated as one might think. I just wanted to refer to the dispute between Leibniz and Newton about the existence of the absolute space.
You say: "But both viewpoints are not equivalent."
You are right. They are not. I just wanted to say, that if you ask different people what an observation or and observational evidence is, you would get different answers, and that it would not be sure, if the people ever could agree. Only if they would have a common realistic theory of how the information from a thing outside me enters my senses, they could agree.
You say: "...Bohr's appeal to classical concepts to explain quantum measurements does have anything to do with sense impressions, but it is related to the need to break the superposition principle."
Maybe I should not have said sense impression. What I intended to say was, that at the end, we have to be able to read out some numbers or marks from a measurement apparatus and we have to be able to describe how a machine is build etc. This is done by a classical language. I do not think , that the fact that we are bound to classical concepts is "related to the need to break the superposition principle." But you are right, the reference to Bohr creates more confusion than clarity.
You say: "The laws of Newton are not only valid for closed systems."
Yes and no. But I will take more time to reply to this comment and do it later.
You say: "There are a problem, a sheep is an open system and its quantum state is not described by any wavefunction."
I new it: I should have been more explicit! The sheep has really no other properties than having the two colors. The colors should stand for properties like spin or location. I really only use the sheep, so we can imagine something concrete in the box with specific properties.
You say: "I guess by closed you really mean isolated. Well, this statement cannot be correct, at any instant systems interact with the environment."
I should have been more clear here, because I think it is an important point. If you have two systems in quantum mechanics and a Hamiltonian describing an interaction between the two systems, the two systems usually get entangled. So there is an exchange of information, between the two systems. And the two systems cannot be describe as two separated closed system. If one wants to describe the dynamic of only one subsystem, it would have been described as open system with a non unitary dynamic. But, and here comes the important point: there might exist a state in system 2, such that the two system do not get entangled independently of the state of system 1. (I gave an example in the essay, where this is in fact the case: when the field of flower is in the state |p1,p2>). So the dynamics of system 1 can be described by a unitary dynamic as if it was a closed or isolated system, although it is not.
I belief, but this certainly has to be worked out more clearly, that you need closed systems to define physical properties. For instance in Newtonian mechanics. You have to have first a force free system. Here you can define, what you mean by distances and velocity. Only then you can the describe, what happens, when forces are applied to the system (ie. you have an open system). This corresponds I think a bit to Poincaré's role of conventions.
You say: "Decoherence is an irreversible processes, but it is not needed to solve the time-arrow problem."
You might be right here. The arrow of time is certainly a difficult problem.
You say: "Fundamental properties of fundamental particles like mass do not require a Lorenz invariant environment. ..."
Well, this also has to be worked out more clearly. Certainly we can only only define masses of a particle as in a way fundamental property of the particle that does not change and is independent of the perspective, if the laws are Lorenz invariant. Then mass is a Casimir operator and commutes with all other observables. So to conclude in a way, that the environment is also in Lorenz invariant state is not directly clear and needs to be shown. In quantum field theories in a way I imagine the vacuum state could be the environment of the free electron and there the vacuum is Lorenz invariant.
Thanks again for you comment,
Luca