How Does Environmentally Induced Decoherence Affect Quantum State Reduction?

[rkastner]

...
So to me, orthodox QM just doesn't make sense. Maybe one of the other interpretations--objective collapse, or many-worlds, or Bohmian mechanics--makes sense, but the orthodox interpretation doesn't. It seems like people are willfully fooling themselves.

I hope you will consider the transactional interpretation for a true solution of the measurement problem. (Cf. http://www.cambridge.org/9780521764155); and
http://transactionalinterpretation....tivistic-and-non-relativistic-quantum-theory/

 

[bhobba]

one has to put in classicality to get classicality out

That I am not sure of.

Regarding Zurek it boils down to the typical modelling thing - there are hidden assumptions in Zurek for sure - but if they are 'benign' or not is the debate. An example is the decision theoretic approach of Wallace. I have read his book and its pretty tight if you accept using decision theory is a valid approach. For some (me include) its rather obvious - for others - it makes no sense. Personally I find Zurek just another interpretation - and not my favoured one.

Thanks
Bill

 

[vanhees71]

What vanhees71 is claiming is that there is no measurement problem, no classical/quantum cut in a minimal interpretation - ie. without BM or MWI. Vanhees71's claim is extremely controversial, and as far as I can tell, it is wrong, and not a matter of taste. The book by Haroche and Raimond rebuts vanhees71's position that decoherence solves the measurement problem.

Where can I find this? I've only looked into the online version of the book a bit. The formula-to-text ratio is a bit too small to make it attractive enough for me to buy it yet. Is it nevertheless good? Of course Haroche is a Nobel Laureat, but that doesn't neceessarily imply that he writes good textbooks ;-)).

 

[rubi]

Fair enough. I can't pretend that I understand the mathematical intricacies of the paper I cited, and I obviously don't expect you to give me a definitive description of ontological "reality". Yet, my general impression was that the authors had claimed to have demonstrated that the quantum wave function is actually "something", or at least represents "something", and is not simply a mathematical tool. Perhaps I was mistaken, or perhaps the paper was rubbish, as Bill has suggested.

The paper discusses the question, whether the specification of some hidden variables determines the quantum state uniquely. It's a mathematical condition, but it doesn't doesn't answer any question about reality. That's just weird terminology, which unfortunately gets used a lot.

But do you believe that the experimental results are real?

Well, I believe that experimenters can provide us with a bunch of numbers, but I don't really commit to anything beyond that. Apparently, something is really odd about nature, since the idea that we can assign numbers to all properties of its parts in a consistent way must be given up, and I have no idea what that implies for the interpretation of the measurement results. This is of course an interesting philosophical question, but physicists must accept it as a fact, just like they must accept the constancy of the speed of light.

 

[vanhees71]

It was von Neumann who in his 1932 book, where he made QM mathematically fully respectable, also made the collapse (then called state reduction) definite and prominent. Bohm then coined 1951 the name collapse for state reduction. Many people from the quantum optics community finally observed in 1986+ the collapse as quantum jumps in certain continuous measurements of single atoms in an ion trap, so that it is now in various quantum optics books; see, e.g., Section 8.2 of Gerry & Knight 2005.

It is not appropriate to blame Heisenberg for all this - I don't even know what Heisenberg contributed.

Don't listen to their words... Einstein's dictum is the more right when it comes to quantum theory. What I couldn't figure out previously when I looked at the papers you quoted in connection with "quantum jumps" is, where is a clear proof for the non-validity of quantum dynamics when measuring an object. I know that nowadays you can observe the transition of atomic states emitting/absorbing photons/em radiation. What I'm not aware of is that there's an unambigous proof that quantum dynamics as provided by standard quantum theory is disproved. As long as this is not the case, I don't buy the notion of "quantum jumps". There are rapid transitions (rapid compared to the typical macroscopic time scales of observations of such transitions) but no "quantum jumps". One of the greatest achievements of the modern QT (Heisenberg 1925 worked out by Born, Jordan, and Heisenberg thereafter ("Dreimännerarbeit"), which is his most important contribution to (real) physics, Schrödinger 1926, Dirac 1926/27) is to have overcome the ad-hoc assumption of "quantum jumps" in the old (Bohr-Sommerfeld-)theory.

Von Neumann's book is great in providing a mathematical rigorous treatment in terms of the Hilbert-space formulation. The physics part is a bit questionable, leading to extremely weird interpretations which are close to solipsism ;-)).

 

[Demystifier]

How do you distinguish (by observations) between case 2 and 3? According to standard quantum theory there is no possibility to distinguish the two cases!

Your logic is the following: A and B cannot be distinguished by observation, therefore A and B are the same.

But that's wrong. Theoretical physics is full of things that cannot be distinguished by observation, yet they are not the same. For instance, your claims in https://www.physicsforums.com/threads/why-are-the-gamma-matrices-invariant.859144/ differ from those by samalkhaiat, yet the difference cannot be distinguished by observation. (By the way, I am on your side on that thread.)

 

[vanhees71]

If the spin state of a particle is that of an unpolarized particle it's theoretically uniquely described by the statistical operator $\hat{\rho}=1/2 \hat{1}$. No matter, how you prepared this state, that's its description, and it cannot be distinguish different ways to have it prepared. You cannot distinguish whether unpolarized particles are prepared by extracting them from a thermal bath or by tracing over the 2nd particle in the entangled spin state. The latter simply means that Alice sends one of the entangled particles to Bob without telling him that it is part of an entangled pare. Bob just finds unpolarized particles when measuring an ensemble. He cannot distinguish it from unpolarized particles coming out of an oven, where they are in (near) thermal equilbrium.

I don't think that my claims differ from samalkhaiat. He agrees with my math but not with my semantics concerning "transformation behavior of spinors". There is no difference even in the mathematics, only in our talk about it ;-)). How should it, it's standard textbook knowledge as old as Dirac's discovery of his spinors.

 

[stevendaryl]

I hope you will consider the transactional interpretation for a true solution of the measurement problem. (Cf. http://www.cambridge.org/9780521764155); and
http://transactionalinterpretation....tivistic-and-non-relativistic-quantum-theory/

Most of my misgivings about quantum mechanics are really about the standard interpretation. The alternative interpretations don't suffer from the same problems. I have read about the transactional interpretation (which seems to me very much like retrocausal and time-symmetric interpretations). They sound promising, but I haven't spent as much time thinking about them as I ought to.

 

[stevendaryl]

Almost all modern texts include the collapse. I still recall your derivation of the conditional wave function - I am not sure it is right, but it looks pretty good. However, you are simply deriving the collapse. Unless you forbid the Schroedinger picture, the collapse is required as a consistency condition.

For me, both halves of the measurement assumption are about equally problematic: (1) That a measurement returns an eigenvalue of the observable, with probabilities given by the Born rule, and (2) that afterward, the system is in an eigenstate of that observable with that eigenvalue. The "minimal interpretation" includes just the first, and not the second. But to me, the hard part about the measurement problem is understanding how definite outcomes arise in the first place.

 

[stevendaryl]

What do you say to the answer given in the discussion in posts #83 - #109 of another thread?

I'm not sure I understand the discussion there. But I will read the paper being discussed (Concepts and methods in the theory of open quantum systems http://arxiv.org/pdf/quant-ph/0302047v1.pdf)

 

[Demystifier]

I don't think that my claims differ from samalkhaiat. He agrees with my math but not with my semantics concerning "transformation behavior of spinors". There is no difference even in the mathematics, only in our talk about it ;-)). How should it, it's standard textbook knowledge as old as Dirac's discovery of his spinors.

Fine, but then the difference between proper and improper mixture is also in the semantics, in the way of talk if you like, because the mathematics and physics of mixed states is as old as the Landau's discovery of mixed states. My point is, the fact that we all (including you) discuss semantics here and there shows that the difference in semantics is not irrelevant.

 

[naima]

Quantum mechanics is a theory that predicts relative frequencies for certain events. It provides us with a probability distribution for each observable. In fact, we could get rid of the Hilbert space and operators completely and reformulate QM purely as a bunch of evolution equations for these probability distributions.

I think now that you are right. I have long believed that this point of view was hiding interferences under the carpet.
When we have |dead> and |alive> in the Hilbert space most problem come from our belief that the general possible way to mix them is with a linear combination.
If we consider that we have |dead><dead| and|alive><alive| can we get an inner composition law thar generalises the superposition law?
Ranko shows that the answer is yes.
We are accustomed in interferometry to follow vectors along the paths and to add them when they meet. It becomes less obvious when there there is a partial visibility of the fringes. When we have a partial decoherence.
Look at the link. You will see that it solve many problems. But not the output problem, of course

 

[stevendaryl]

If the spin state of a particle is that of an unpolarized particle it's theoretically uniquely described by the statistical operator $\hat{\rho}=1/2 \hat{1}$. No matter, how you prepared this state, that's its description, and it cannot be distinguish different ways to have it prepared. You cannot distinguish whether unpolarized particles are prepared by extracting them from a thermal bath or by tracing over the 2nd particle in the entangled spin state. The latter simply means that Alice sends one of the entangled particles to Bob without telling him that it is part of an entangled pare. Bob just finds unpolarized particles when measuring an ensemble. He cannot distinguish it from unpolarized particles coming out of an oven, where they are in (near) thermal equilbrium.

Yes. And it's also striking that an equal mixture of spin-up and spin-down in the z-direction leads to the same mixed state as an equal mixture of spin-up and spin-down in the x-direction.

 

[bhobba]

If we consider that we have |dead><dead| and|alive><alive| can we get an inner composition law thar generalises the superposition law?

That's impossible - utterly impossible. A cat can never - never be alive and dead. Cats are decohered to have definite position. The position of the constituent parts of a cat are different for alive and dead cats.

Thanks
Bill

 

[A. Neumaier]

What I'm not aware of is that there's an unambigous proof that quantum dynamics as provided by standard quantum theory is disproved.

Unitary dynamics for small quantum systems is extremely well disproved - people in quantum optics always have to work with dissipative, nonunitary dynamics to describe their small systems quantitatively. Thus it is an experimental fact that small quantum systems cannot be described by unitary evolution.
The reason is that they are almost never isolated enough to justify the unitary approximation. The state reduction or collapse accounts for that.

On the other hand, if one makes a quantum system big enough that its interaction with the neglected environment can be ignored (which is often the case in macroscopic situations) or can be described by classical external interaction terms then unitary dynamics is valid to a very good approximation.

Thus state reduction (= collapse) is not in contradiction with the unitary dynamics of an isolated system.

 

[naima]

Bhobba, I see that we agree! there is another composition law that the addition of vectots.

 

[stevendaryl]

That's impossible - utterly impossible. A cat can never - never be alive and dead. Cats are decohered to have definite position. The position of the constituent parts of a cat are different for alive and dead cats.

There's a gap in the formalism of quantum mechanics, in my opinion, when it comes to how to describe macroscopic systems, such as cats. The Dirac bra-ket notation doesn't actually make sense for macroscopic objects. There is no such thing as a complete set of states for a cat, because if you perturb a cat too greatly, it's no longer a cat, but a collection of particles. So a notation such as |dead\rangle\langle dead| doesn't mean much.

What it seems to me that decoherence tells us is that it only makes sense to talk about a wave function in the very small--systems that are small enough that they can be said to have a state--and the very large--the wave function of the entire universe (which is what MWI and Bohmian mechanics deals with). At the intermediate scale of cats, I'm not sure what formalism is appropriate. Maybe the ad hoc use of a combination of quantum and classical is the best we can do.

 

[bhobba]

The Dirac bra-ket notation doesn't actually make sense for macroscopic objects.

Good point. A cat is entangled with all sorts of things.

Thanks
Bill

 

[stevendaryl]

Unitary dynamics for small quantum systems is extremely well disproved - people in quantum optics always have to work with dissipative, nonunitary dynamics to describe their small systems quantitatively. Thus it is an experimental fact that small quantum systems cannot be described by unitary evolution.

I'm a little unclear as to what you mean by this. Are you just saying that because the system of interest is constantly interacting with the environment (the electromagnetic field), you can't use unitary evolution, because that only describes an isolated system?

 

[A. Neumaier]

I'm a little unclear as to what you mean by this. Are you just saying that because the system of interest is constantly interacting with the environment (the electromagnetic field), you can't use unitary evolution, because that only describes an isolated system?

Yes, exactly. And if it is not constantly but temporarily interacting with a measurement device, one can't use unitary evolution either, because that only describes an isolated system. The simplest (though somewhat approximate and often too rigid) remedy is to replace the unitary evolution by a collapse during the brief moment of interaction (in the second case) and by many collapses at random times during continuous interaction (in the first case). In many instances (and especially in most simple textbook instances) this was good enough throughout the 83 years since von Neumann to make it into the majority of textbooks. But for higher accuracy (quantitatively accounting for losses) one needs explicit nonunitary dynamics, most typically of Lindblad type.

 

[A. Neumaier]

At the intermediate scale of cats, I'm not sure what formalism is appropriate.

That of statistical mechanics, of course!

 

[Mentz114]

I'm a little unclear as to what you mean by this. Are you just saying that because the system of interest is constantly interacting with the environment (the electromagnetic field), you can't use unitary evolution, because that only describes an isolated system?

I found this paper recently and it seems to address this issue in an understandable way.

The interesting bit for me is part 4 "Formal Treatment of Decoherence"

Decoherence-Free Subspaces and Subsystems
Daniel A. Lidar and K. Birgitta Whaley

abstract :Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the problem have been proposed. Here we provide a detailed a review of the theory of decoherence-free subspaces and subsystems, focusing on their usefulness for preservation of quantum information.

http://arxiv.org/abs/quant-ph/0301032v1.pdf

I would like to know what @A. Neumaier thinks of the paper.

 

[vanhees71]

Unitary dynamics for small quantum systems is extremely well disproved - people in quantum optics always have to work with dissipative, nonunitary dynamics to describe their small systems quantitatively. Thus it is an experimental fact that small quantum systems cannot be described by unitary evolution.
The reason is that they are almost never isolated enough to justify the unitary approximation. The state reduction or collapse accounts for that.

On the other hand, if one makes a quantum system big enough that its interaction with the neglected environment can be ignored (which is often the case in macroscopic situations) or can be described by classical external interaction terms then unitary dynamics is valid to a very good approximation.

Thus state reduction (= collapse) is not in contradiction with the unitary dynamics of an isolated system.

Well, the non-unitary dynamics doesn't disprove quantum dynamics, because it's derived from it. That's not what I mean. I'm only against using the notion of "quantum jumps". Also in stochastic equations there are no jumps but fluctuating (generalized) forces. For me "quantum jumps" a la Bohr imply that there's no dynamical law covering these rapid transitions, but that's not what any dynamical equation, be it the fundamental unitary evolution of closed systems or effective deterministic or stochastic equations for open systems.

 

[vanhees71]

I'm a little unclear as to what you mean by this. Are you just saying that because the system of interest is constantly interacting with the environment (the electromagnetic field), you can't use unitary evolution, because that only describes an isolated system?

Of course the interaction with the electromagnetic field on the fundamental level is also described by unitary time evolution. QED is a QT as any other!

 

[vanhees71]

Yes. And it's also striking that an equal mixture of spin-up and spin-down in the z-direction leads to the same mixed state as an equal mixture of spin-up and spin-down in the x-direction.

Well, it's described by $\hat{\rho}=\hat{1}/2$. There's no direction whatsoever. That's why it's called "unpolarized" and thus the distribution must not contain any direction ;-)).

 

[A. Neumaier]

http://arxiv.org/abs/quant-ph/0301032v1.pdf
I would like to know what @A. Neumaier thinks of the paper.

It uses an unconventionally broad notion of decoherence - which is usually reserved for the very fast decay of off-diagonal entries in a density matrix given as matrix elements between pointer states.

Decoherence free subspaces (DFS) are what allows one e.g., to consider the position and spin degrees of freedom in a Stern Gerlach experiment to behave unitarily before the measurement. The experimental difficulty in quantum computing is constructing systems whose nonunitary evolution has huge-dimensional nearly DFS.

 

[Demystifier]

Where can I find this? I've only looked into the online version of the book a bit. The formula-to-text ratio is a bit too small to make it attractive enough for me to buy it yet. Is it nevertheless good? Of course Haroche is a Nobel Laureat, but that doesn't neceessarily imply that he writes good textbooks ;-)).

I think many will agree that the best textbook on decoherence is the one by Schlosshauer:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20
In particular, the formula-to-text ratio is higher than in Haroche. (After all, unlike Haroche, Schlosshauer is a theorist.) More importantly, the book explains why decoherence does not completely resolve the measurement problem, even though it significantly alleviates it.

 

[bhobba]

I think many will agree that the best textbook on decoherence is the one by Schlosshauer:
\

I have a copy - its my bible.

Thanks
Bill

 

[Demystifier]

I have a copy - its my bible.

It's one of my bibles too. (The only Bible for decoherence, anyway.)

But for those who do not want to read the whole Bible, there is a shorter (and free) version by the same author:
http://lanl.arxiv.org/abs/quant-ph/0312059
The shorter version is even more direct in explaining what exactly is wrong with arguments in the literature that decoherence completely resolves the measurement problem.

 

[A. Neumaier]

Also in stochastic equations there are no jumps but fluctuating (generalized) forces.

You seem to think that stochastic processes must always be given by stochastic differential equations. But this is not true.

Classically, there are two basic kinds of stochastic processes - jump processes and diffusion processes; then there are combinations of these, and by a theorem of Kolmogorov no other Markov processes are possible. A classical counting process is always a jump process. Thus it is no surprise that one has the same possibilities in the quantum case.