That is exactly where you need to be and you have got everything factual that science knows.

I am going to borrow the general conclusions that we currently "know" because you have now arrived where everyone else has that followed the evidence and you should be able to tick off the twelve statements some may appear technical but I am confident you can work out what is meant.

They are a statement of twelve observational science facts you accepted in your journey although probably not consciously. They are however the observational facts as we sit here in 2014 and you would need new evidence to overturn any of them. What no one will be able to tell you is why those 12 observational facts occur that is outside our current understanding.

Quote:

1. Quantum mechanics is valid everywhere, for small and large systems, for intelligent and unintelligent objects; and all quantities that were thought to be "real" classical observables in the ignorant era of classical physics become linear operators on the Hilbert space with their eigenstates, eigenvalues, and their probabilities that can be predicted from the amplitudes (but never deterministically); there is no segregation of contextual and real observables

2. Classical physics is always just an approximation, and can be derived to be a good one under certain circumstances

3. Only probabilities may be predicted by quantum mechanics (i.e. in the real world) and classical determinism only occurs when the probabilities become negligibly small everywhere except for a small vicinity of the "correct" classical history

4. The boundary between the quantum and classical realms occurs when the interference effects get suppressed; this loss of coherence (the loss of information about the relative phases of complex amplitudes) is the only effect that universally occurs to produce a limit that is well described by classical physics in our quantum world

5. The suppression of quantum interference is called decoherence, and is caused by the interactions with the environment (i.e. degrees of freedom that we can't and don't want to keep track of); in this process, the off-diagonal elements of the density matrix plummet and the diagonal entries may be interpreted as classical probabilities; in this regime when the interference is gone, Bell's inequalities (and other manifestations of the classical intuition) become approximately valid

6. Quantum mechanics fully determines where this boundary occurs, and the required inequalities depend on the physical system, its Hamiltonian, the density of the environment, the strength and speed of interactions, and many other things: the emergence of the classical limit is a dynamical question and there is no "universal" answer to the questions e.g. "how many atoms or how long time one needs for classical physics to emerge"; everyone should calculate or review at least five order-of-magnitude estimates of the "critical" quantities where the classical limit becomes valid, in order to see the huge diversity of these scales in different contexts; these calculated boundaries are obviously correct on theoretical grounds and in many cases, the quantum-classical transition can actually be observed (at the predicted place)

7. In a classical regime, the preferred basis vectors of the Hilbert space are those that can imprint themselves into the environment (in Zurek's jargon, these states pass the einselection which makes them immune against decoherence); bizarrely non-local Schrödinger's cat superpositions are not in this category, and one can show, e.g. in the consistent history framework, that they don't allow us to formulate consistent histories (for which the probabilities add as expected from logic); it is fully understood what's wrong with Schrödinger cat superpositions and the derivation of the preferred states depends on the Hamiltonian

8. There is no room for a physical collapse or, on the contrary, for an ad hoc privileged role of conscious observers; the wave functions only predict the probabilities but they can be calculated for any set of consistent histories, regardless of whether the systems look conscious, unconscious, macroscopic, or microscopic; the only "collapse" that occurs is the rapid diagonalization of the density matrix in the preferred basis by the interactions with the environment; however, the "unrealized" diagonal entries of the matrix (probabilities of outcomes that won't come true) are never "physically" set to zero because their interpretation always remains probabilistic, even when the classical approximation becomes acceptably accurate

9. There cannot be any deterministic description that would allow one to know the outcomes non-probabilistically, such as "pilot waves" or "hidden variables", not even in principle, and questions attempting to know "more" than what quantum mechanics predicts are unphysical; the Conway-Kochen Free will theorem is a way to prove that the microscopic outcomes can't be deterministically determined

10. From all practical points of view, Niels Bohr and his friends in the Copenhagen school were right on the money and decoherence may be interpreted as a justification, derivation, or a proof of their assumption that the classical intuition is fine for (mostly) large objects and quantum mechanics is crucial for (mostly) microscopic objects; they didn't know the modern derivation of decoherence but they understood its qualitative implications

11. Decoherence is a process with an inherent arrow of time that makes it analogous to friction, heat dissipation, and other thermodynamic processes with an arrow of time; the effects are related, the arrows inevitably agree with one another, and decoherence is as real as the other processes (that increase the entropy); the time-reversal asymmetry of decoherence is inevitable because the environment can't be assumed to be non-locally entangled with the system in the far past, but it can be shown to be correlated in the future because of the evolution (and one can't ever assume anything about the future or impose "final" boundary conditions by the very definition of the future which is yet to be seen)

12. On the other hand, consistent histories are just a particular convenient framework to formulate physical questions in a certain way; the only completely invariant consequence of this formalism is the Copenhagen school's postulate that physics can only calculate the probabilities, they follow the laws of quantum mechanics, and when decoherence is taken into account, to find both the quantum/classical boundary as well as the embedding of the classical limit within the full quantum theory, some questions about quantum systems follow the laws of classical probability theory (and may be legitimately asked) while others don't (and can't be asked)

Last edited by Orac; 05/30/14 07:53 AM.

I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.