Can a conscious observer collapse the probability wave?

Killtech

as you correctly write the basis that arises from an observable determines what is being measured. so you will have to find a relation between the hamiltonian and your basis and postulate that this relation is responsible for the decoherence (for all systems). finding this relation is a real addition to the theory and could complete it in the sense that it provides a first vague (but somewhat defined) mechanism to determine when the collapse actually happens and what causes it.

for example in the simple case of a hydrogen atom you could argue that only energy eigenstates have a time independent charge density. so if you classically couple the EM-field to the charge you find that only those are no source for EM-waves (although they have an angular momentum ;)). mixed states of two energy states oscillate periodically with a frequency proportional to their energy difference. all mixed states lose energy in this way thus must be unstable. this distinguishes the energy eigenstates from all other basis and could be a hint of how the above mentioned relation could look like.


the other option i see would be to try to construct a justification of measurement from the equations of motion (EOM). but one finds that these yield unphysical results in systems where a wave function interacts with multiple objects that are macroscopic far away because the EOM describe quantum objects as pure waves with no particle nature whatsoever. thus they are wrong in general and relay on the measurement postulate as a supplement for macroscopic interactions. a possibility of generalizing them to yield better results at macro level is to add non-linear terms that change the macro behavior. it makes sense to go for non-linear dynamics because they are know to produce results astonishingly similar to QM predictions. for example they provide a source of randomness arising from chaos (sensitivity to initial conditions), collapse behavior and may have soliton solutions that behave like waves microscopically but as particles macroscopically. finally the QED is a linearization (2nd quantization) of naturally non-linear field theory (dirac-maxwell, EM-field classically coupled to the charge density of wave function).

however non-linear dynamics are way more complex and much much harder to solve. in case of dirac-maxwell little is known about any solutions even in the simplest free case. on the other hand a non-linear QM must provide a derivation of the measurement postulate because the usual probability interpretation breaks apart when the wave function is no more normed to 1. due to the current lack of a mechanism to decide when the collapse happens it is very difficult to guess the form of the non linear interactions to reproduce it.

in any case you need to extend QM by something to solve the measurement problem.

Ken G

We never "use" an initial macro state, it would be way too difficult in any interpretation. The interpretation is around what we imagine the initial state is. None of the interpretations involve usage, everything we actually use is the same in every interpretation and that's why they all get the same answers.
Decoherence can be used to show that a closed system evolving unitarily can project onto a density matrix of a subsystem that evolves, over time, to be diagonal. So we get that subsystem density matrices can be diagonal, so projections of pure states can be mixed states. But we never know the quantum state of the measuring device, so we simply don't know if it even has one-- this is purely a choice of our imagination to make. Decoherence allows us avoid contradiction when we imagine that macro systems have a quantum state, but it is not evidence that they do. And above all, it begs the key issue in the measurement problem-- how does a diagonal density matrix for the substate turn, unitarily or otherwise, into a definite measured outcome? We can never find any initial state for the whole, if a measurement is involved. There is never any measurement that has a well defined initial state for the environment, that's why we need an interpretation of the environmental interaction. Copenhagen just says that part of the interaction in the measurement creates a "collapse" which need not involve unitary evolution of the entire system. It is close to the ensemble interpretation, in that neither asserts there is a unitarily evolving quantum state for the whole, but the ensemble interpretation does not take the "collapse" literally because the whole mathematical structure applies only to the ensemble, whereas Copenhagen suggests that something inherently non-deterministic is occuring.I'd say there are two very different "measurement problems" that tend to get confused. One is, how does a unitarily evolving quantum state of the whole project into a diagonal density matrix for a subspace, and the other is, how does a diagonal density matrix turn into a definite outcome. The various interpretations hinge on the answer to the latter question, and I don't see any progress on that issue at all-- I see it as entirely a subjective choice for the philosopher/physicist. Decoherence has made interesting progress on the former question, but in my view that was always the easy question.

Killtech

excuse my naive approach but i didn't dig into decoherence so far. but whenever you have an operator on a subspace there exists a basis that diagonalizes it (AoC assumed). the question for me always was which basis will that be / which operators will become diagonalized and what determines it. isn't that the interesting question regarding the first part of the measurement problem?

Ken G

The operator that corresponds to the measurement is diagonalized in the basis corresponding to the eigenstates of the measurement, but that's not what is getting diagonalized in decoherence. It's the density matrix, which does not characterize the measurement, it characterizes the state of the system. The connection to the measurement is that an environment capable of doing a given measurement is an environment that will also diagonalize the density matrix in the eigenbasis of the measurement, but the key point is, diagonalizing the density matrix is not a mathematical operation, it is a physical change.I think the problem with that question is it goes away when it is not framed backwards. We don't wonder why a given operator diagonalizes with respect to some observational basis, we say that that operator corresponds to whatever measurement has the eigenbasis it is that diagonalizes the operator. In other words, the fact that we have a given measurement is because we have that diagonalization, not the other way around.

audioloop

from a nonlinear process ? to which part ? process 1 or process 2 ?

kith

Well, that's my main point: we don't have to postulate anything here. In principle, we can derive decoherence and the basis it occurs in from the unitarian dynamics of the combined system using its full Hamiltonian. I think this is called environment-induced superselection ("einselection").

The Schrödinger equation is wrong for open systems, but new equations can be derived from the unitarian evolution of the larger (isolated) system. So beeing wrong doesn't necessarily mean that they rely on the measurement postulate.

I'm not familiar with nonlinear QM and the like. But I don't see the necessity for such things.

kith

Yes, this sounds logical. So probably, I should refine my view a bit. Copenhagen is special in the way that the assumption of unitarian evolution of the whole system doesn't explain collapse.

Yes, I agree. At this point, we need an interpretation. But Jazzdude and Killtech think we haven't done enough, if we derive the mixed state of the system from unitarian evolution of the whole and then explain the question of definite outcomes by an interpretation.

Ken G

There's no need for nonlinearity in process 1, as decoherence accomplishes that linearly. But process 2 is another story. Some might invoke nonlinearity that is outside quantum mechanics to get the final stage of the "collapse", others might say it just happens and cannot be described in any theory, still others say it doesn't happen at all, it is merely an illusion of our perception. We just don't know which one is right at this stage, but I wager that the future of physics will be guided by the answer.

Ken G

I think it's fair to say that interpretations often have to fill in for missing physics. The problem is, the physics is indeed missing, so the interpretation is the best we can do at present. It might always be missing-- we've been lucky so far that we rarely reach a "dead end" beyond which physics can go no further. Collapse might be too fundamentally wrapped up in the functioning of the observer to be reduced to fundamental physics, in which case it might be that dead end that will always have to be relegated to interpretation. Or, it might be resolved, and set the stage for the next big revolution in physics.

Killtech

actually this is no non-linear QM. as far as i know dirac-maxwell and alike are pure classical field theories that just behave very much like corresponding quantum field theories except for the measurement which simply isn't described within such theories.

however there are non-linear theories that can reproduce the collapse and even derive born's rule in some form. they are an extension to usual QM and show another solution to the measurement problem's 2nd part - collapse to a well defined measured value.