A Effective Dynamics of Open Quantum Systems: Stochastic vs Unitary Models

[vanhees71]

What about treating the observer's consciousness as the classical system and the whole universe minus the observer's consciousness as the quantum system? This makes it obvious that the collapse (of the universe) is a subjective process, since we can remove from the universe the consciousness of any single observer without changing the physics.

Define "consciousness" and have a lot of fun ;-).

 

[A. Neumaier]

Define "consciousness" and have a lot of fun ;-).

I defined it already:

Continuing this process as long as possible I end up with a quantum system that comprises essentially the whole universe - even the brain, since it can be observed by the observer if he puts enough electrodes into his head and watches the responses on a screen. According to the Copenhagen interpretation (in von Neumann's specific form) the final quantum system develops unitarily except for the moments where the observer makes his observation of the system, causing its collapse.

Only very little remains that observes the now huge quantum system - whatever this is, this is commonly called the observer's mind or consciousness.

 

[vanhees71]

Well, that's what the defenders of the European Human Brain Project want us to believe. I don't think that you can grasp what "consciousness" is by sticking only enough electrodes in ones head and observe the response on the screen. It's not even clear to me whether consciousness is something you can grasp with natural science at all or who has consciousness at all. Has a non-human primate like a Bonobo consciousness (I'd pretty say yes), a dog (I'm not that sure but it looks plausible), a single-cell organism, a bacterium? I don't know, and I don't know how to figure it out by scientific means. In other words, what specific pattern of signals from the electrodes in ones head tells me "that's consciousness"?

Fortunately, I also think that consciousness, whatever it is, is relevant to measure quantum systems. For that you need much simpler means than a human or any other creature's brain, let alone the state of the entire universe, which is a notion at least as questionable as consciousness.

 

[ddd123]

Fortunately, I also think that consciousness, whatever it is, is relevant to measure quantum systems. For that you need much simpler means than a human or any other creature's brain, let alone the state of the entire universe, which is a notion at least as questionable as consciousness.

Did you miss a "not" somewhere in this paragraph?

 

[vanhees71]

Sure, it must read

Fortunately, I also DON'T think that consciousness, whatever it is, is relevant to measure quantum systems. For that you need much simpler means than a human or any other creature's brain, let alone the state of the entire universe, which is a notion at least as questionable as consciousness.

 

[A. Neumaier]

I don't think that you can grasp what "consciousness" is by sticking only enough electrodes in ones head and observe the response on the screen. It's not even clear to me whether consciousness is something you can grasp with natural science at all or who has consciousness at all.

I claimed neither of it:

• I had moved the observble part to the quantum system and declared only what remins as the mind,
• I had acknowledged that what remains might not be describable by physics.
• I had allowed for animal or even inanimate observers.

Noticing that the observer can observe part of himself I include these parts of the observer into the quantum system and remove it from the observing system. [...]
Only very little remains that observes the now huge quantum system - whatever this is, this is commonly called the observer's mind or consciousness. Given the failure of intense efforts to relate it to physics proper, it may well be immaterial and not describable by physics. [...]
One can repeat the procedure with any of the many (now male, female, animal, or inanimate) observers populating the universe, and finds that the collapse is a property of the corresponding (male, female, animal, or inanimate) mind, whatever the latter may be.

 

[A. Neumaier]

the state of the entire universe, which is a notion at least as questionable as consciousness.

Why should that be the case?

The state of the universe is needed and used for studying the first few fractions of a second of existence of the universe. The whole point of a unification of quantum physics with gravitation (apart from its theoretical desirability) is to be able to study cosmology and black holes under quantum conditions where observation is impossible.

My answer in post #199 fully explains in which sense it is a perfectly legitimate quantum object even in the Copenhagen interpretation.

 

[secur]

I continue this until the quantum system includes everything in the universe except the observer himself.

- Note "everything in the universe" includes other minds.

Given the failure of intense efforts to relate it to physics proper, it may well be immaterial and not describable by physics.

- But if it were describable by physics, it would be observable (within QM formulation). So there would be a positive semidefinite Hermitian matrix associated with it. The Hermitian operator represents (hypothetically) everything we can say mathematically / scientifically about mind within the QM approach. Then we can call the "describable by physics" case "hermitian".

In {immaterial} case, the final quantum system comprises the whole universe; in {hermitian} case, the final quantum system is still an excellent approximation of the universe.

- Now, you've dealt with only one mind: the observer's.

- With your approach you're forced to assume other minds also collapse wavefunction by observation. Therefore universe wavefunction can't develop unitarily but is constantly subjected to probabilistic projection operators.

- Note that MWI approach and others are specifically designed to avoid this "collapse" problem, so they can evolve the universe by unitary schroedinger's eqn, (and similar equations / fields as appropriate - Dirac, Klien-Gordon, etc.)

The quantum dynamics of the whole universe, suitably approximated, leads to an objective, reduced dynamics of the single small system in terms of a piecewise deterministic process (with unitary dynamics interspersed by quantum jumps at random times) when a discrete variable is observed (e.g., when particles are counted or the energy level is monitored),

- the "quantum jumps at random times" are caused by many observers making measurements. Between these events (which we can optimistically suppose countable) are "piecewise deterministic" interludes when / where the universe is allowed to evolve unitarily. Fine, but solving (approximately) these piecewise equations is very difficult. Whereas in MWI, it's easy to solve the (one-piece) unitary Universe wavefunction equation.

- On the other hand MWI-type approach misses the meat of the matter, the collapse, so I prefer your approach.

Averaged over many subsystems, these stochastic processes lead to a deterministic dynamics for the density operator, given by a Lindblad equation.

- I'll have to look at it someday, no doubt it's pretty difficult. But, after all, evolution of entire universe is a non-trivial problem.

 

[StevieTNZ]

Is it not the case that there is an observable of system+apparatus+rest of universe that, if measured, would tell the observer whether the combination is in a superposition?

(Reference: 'Quantum Mechanics and Experience' by David Albert -- chapter 8)

 

[A. Neumaier]

Well, this strays too far from the purpose of the thread, so I am not continuing the discussion involving observers. Nothing before my post #193 (which I should have posted in a new thread) depends on an observer.

 

[Mentz114]

Landay and Lifshitz were perfectly aware that one can get classical behaviour in certain limits from quantum behaviour. They explicitly comment that that does not negate the need for a classical/quantum cut. Again this is all wrt to the orthodox or Copenhagen or minimal interpretation.

There are of course well respected approaches like Many-Worlds, Bohmian Mechanics or Consistent Histories which attempt to solve the measurement problem of Copenhagen. All of these have to add in assumptions (eg. multple outcomes, hidden variables, weaker reality) for the ones they remove (classical/quantum cut and/or observer-dependent collapse). The minimal interpretation without the cut and collapse that seem to be advocated by Ballentine and Peres are not consistent with the vast majority of physics textbooks from Landau and Lifshitz through Cohen-Tannoudji, Diu and Laloe through Nielsen and Chuang through Weinberg. Of course correctness is not based on mainstream physics, so the reader will have to decide for himself whether the opponents of mainstream physics like Ballentine and Peres are correct.

Since Weinberg has been mentioned in the wave function/collapse debate I thought it worthwhile to mention his 2014 offering here.
He seems to be advocating the density matrix formalism and dropping wave function reality. Hooray.

 

[A. Neumaier]

Since Weinberg has been mentioned in the wave function/collapse debate I thought it worthwhile to mention his 2014 offering here.
He seems to be advocating the density matrix formalism and dropping wave function reality. Hooray.

This has already been mentioned and discussed here. One remarkable fact I mentioned there is that in interacting quantum field theory, the notion of a pure state loses its meaning.

 

[Mentz114]

This has already been mentioned and discussed here. One remarkable fact I mentioned there is that in interacting quantum field theory, the notion of a pure state loses its meaning.

Thanks, I missed the discussion altogether. Very edifying as always ( and feeding my own inclinations ).