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Is decoherence a resolution to the issue of measurement? I have read arguments on both sides.
I think this is where decoherence is really supposed to help, but I'm not sure I agree with all of this. The result of decoherence is that the eigenstates of the system gets entangled with certain states of the environment. These states are called "pointer states". I don't know the details, but these pointer states are supposed to be records of the result of the interaction, which are stable in the sense that they will stick around at least for a while. Since the well-defined states of your memory appear to be somewhat stable records of the result of the measurement you've just performed, I think that when the physicist performing the experiment is considered part of the environment, the pointer states will be states in which the physicists memory isn't a superposition.According to the projection postulate, at measurement, the state collapses into an eigenstate in a probabilistic way, and since it *is* an eigenstate, the relevant sharp values obtain. So the problem of how sharpness arises, definite properties, out of superpositions, is also an outcome of the collapse postulate.
I don't think decoherence does solve *this* problem. There is no collapse on decoherence, there is just S's equation, and all decoherence does is show that system+environment too gets into a superposition. If there's a problem with how things can have sharp values when they're in a superpositional state, then I don't see how decoherence helps.
But at this point a mwi interpretation is being invoked. If the question. is `how to solve prob of sharp values given we're in a superposition', then it's mwi rather than decoherence that's doing the work. Interpreting the terms as different worlds, one where the cat is dead and the other alive, was always a way getting sharpness from a superposition.Now each of the remaining terms is interpreted as a "world" in which a particular result happened, and "you" (a different you in each world) remember that it happened.
MWI is not the only non-collapse interpretation. In BM, for example, hidden variables (particle trajectories) define what world REALLY exists. But I agree, MWI is the most logical one.But at this point a mwi interpretation is being invoked. If the question. is `how to solve prob of sharp values given we're in a superposition', then it's mwi rather than decoherence that's doing the work. Interpreting the terms as different worlds, one where the cat is dead and the other alive, was always a way getting sharpness from a superposition.
yossell said:But at this point a mwi interpretation is being invoked. If the question. is `how to solve prob of sharp values given we're in a superposition', then it's mwi rather than decoherence that's doing the work. Interpreting the terms as different worlds, one where the cat is dead and the other alive, was always a way getting sharpness from a superposition.
Incidentally, can I ask you - or anyone - a technical question about decoherence? The slogan is: in decohering systems, the off diagonal terms tend to zero incredibly quickly. Does this mean that the off-diagonal terms *do* reach zero at some point, or just hover near zero after a very short amount of time? I took it to be the latter, but I'm not certain.
The way I see it, QM as defined by the Dirac-von Neumann axioms (the usual stuff about Hilbert spaces and the probability rule) either describes what actually happens, or it doesn't. The assumption that it doesn't is the ensemble interpretation, and the assumption that it does is the MWI...unless you impose additional axioms just to get rid of the other worlds. You described one such additional axiom, the idea that "collapse" is a mysterious physical process that eliminates superpositions. I recently came across another one. David Mermin's "Ithaca interpretation" is essentially the MWI with the additional idea that QM somehow doesn't apply to consciousness, and that this gets rid of the other worlds.But at this point a mwi interpretation is being invoked. If the question. is `how to solve prob of sharp values given we're in a superposition', then it's mwi rather than decoherence that's doing the work.
But that's not what we're doing, or at least not what we should be doing. I think I made a mistake in my previous post. Instead of considering the evolution of the state vector, I should have considered the evolution of the density matrix (or statistical operator, or whatever you prefer to call it). It changes from a pure state (the one corresponding to the state vector on the left in my previous post) to a very good approximation of a mixed state (a mix of pure state operators corresponding to the terms on the right). So what decoherence does is to make the other terms in the density matrix (not in the expansion of a state vector in terms of basis vectors) insignificant, and now the remaining terms can be interpreted as worlds. Without decoherence, I don't think the MWI even makes sense, because there would be nothing to separate the terms that describe the sort of correlations we actually observe from the sort of correlations that are never observed.Interpreting the terms as different worlds, one where the cat is dead and the other alive, was always a way getting sharpness from a superposition.
They don't ever reach zero. They just get really small. I see that I used language that suggested otherwise, but that was just an accident.The slogan is: in decohering systems, the off diagonal terms tend to zero incredibly quickly. Does this mean that the off-diagonal terms *do* reach zero at some point, or just hover near zero after a very short amount of time? I took it to be the latter, but I'm not certain.
I'll certainly go along with you on this!The way I see it, QM as defined by the Dirac-von Neumann axioms (the usual stuff about Hilbert spaces and the probability rule) either describes what actually happens, or it doesn't.
But...there are many attempts to interpret qm literally in a way that doesn't commit you to MWI. I can't see where, in the formalism, there's anything which explicitly talks about many worlds. We may ultimately agree that other attempts to take qm as a theory about what actually happens lead to problems, the notion that objects really are in superpositions before measurement is too problematic - but I can't see how this *just is* MWI.The assumption that it doesn't is the ensemble interpretation, and the assumption that it does is the MWI
The axiom I had in mind was simply the collapse postulate. Just to make sure we're on the same page here: this is an axiom originally explicitly formulated by von Neumann. I'm aware that there are different formulations of QM, but this one appears in most textbooks, and it's typically taken as a standard part of QM. It says that:You described one such additional axiom, the idea that "collapse" is a mysterious physical process that eliminates superpositions.
That's it - after a measurement, the state is different from what it is before, and it's into an eigenspace. Whereas before the system was in a superposition of different values, the state is now in an eigenspace and so the superposition of these values has been eliminated. This is part of the standard (it's from Schaum - which plays it pretty safe!) evolutionary story, and it's a different story from the Schrodinger one.Schaum; said:If measurement of a quantity A on a physical system in the state |\psi> gives the result a_n, immediately after the measurement, the state is given by the normalised projection of |\psi> onto the eigenspace e_n assoiated with a_n.
Is this a FAPP (for all practical purposes) argument? I think the FAPP argument is fine when we're trying to explain the first aspect of the measurement problem I mentioned - the problem about evolution. Turns out that decoherence shows that the density matrix is really very very close to what we would have got had we applied collapse - so, as far as the empirical evidence goes, we don't have to take the collapse postulate literally - it's a useful heuristic which gets close the right results, and so there's no need to invoke the process of measurement to explain failure of interference pattern in certain situations - the S equation does it single handedly. But it's not clear how the FAPP argument goes if we're dealing with the problem of sharp values, how we get a sharp value out of a superpositional state. Being close to an eigenstate is not being an eigenstate, and if we were working with the eigenstate-eigenvalue link, then we've got problems.So what decoherence does is to make the other terms in the density matrix (not in the expansion of a state vector in terms of basis vectors) insignificant, and now the remaining terms can be interpreted as worlds.
WowI recently came across another one. David Mermin's "Ithaca interpretation" is essentially the MWI with the additional idea that QM somehow doesn't apply to consciousness, and that this gets rid of the other worlds.
For example?But...there are many attempts to interpret qm literally in a way that doesn't commit you to MWI.
I'm talking about a QM that includes the projection postulate.For example?
probably, these attempts introduces additional axioms?
'Pure' QM + Quantum Decoherence = MWI.
You can add something else (hidden variables, for example) to get non-MWI theory
What makes MWI so special is the fact that it is minimalistic.
Yes, we dont know everything. However, when I read "... value of the observable..." I think - wait, why only ONE value? Why not a superposition? Just by saying "result fo the measurement" or "value of an observable" we already assume the existence of the collapse.I did not want to criticise the circularity of definitions (MWI also has some issues with circularity what we try to apply it to the real world). All I wanted to say was the projection postulate itself makes sense only if some "flavor" of CI had been accepted.Dmitry67,
you're welcome to use the words "magic" if you wish. I take this to be a very strong way of saying that you find interpretations that do not give definitions here non-circular. I may even agree with you. But I recognise that this is contentious. The questions about which terms of a theory can or should or need to be given non-circular definitions is delicate. All theories have their primitives. There's nothing in what's literally written in QM textbooks that literally introduces such things as worlds - at least, not as far as I can see.
There isn't. What the formalism says is that a measurement of an observable A changes a pure state [itex]\rho=|\psi\rangle\langle\psi|[/itex] into a mixed state:But...there are many attempts to interpret qm literally in a way that doesn't commit you to MWI. I can't see where, in the formalism, there's anything which explicitly talks about many worlds.
I take this to be the definition of the MWI because of the above and because I haven't found any other definition that makes any kind of sense. Yes, there are people (e.g. Max Tegmark) who claim that the MWI is what you have left when you have removed the probability stuff from the axioms, but this is nonsense. All of these guys use another axiom, which is essentially equivalent to the probability rule, without admitting (or realizing) that this is what they're doing. The "essentially equivalent" axiom is that the Hilbert space of a system is the tensor product of the Hilbert spaces of the subsystems.but I can't see how this *just is* MWI.
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The motivation for MWI is normally trying to do QM by *dropping* von Neumann's postulate, by letting Schrodinger's equation be the complete evolutionary account.
We're on the same page, but the version you quoted is using language that suggests that only one of the terms that appear on the right in my version is real. A mixed state can be used both to describe a single system in a specific but unknown state, or an ensemble of systems in lots of different states. Why does Schaum choose the first option? Perhaps because he's following the tradition started by von Neumann, who speculated that the "collapse" is a mysterious physical process that has nothing to do with unitary time evolution and has something to do with consciousness.The axiom I had in mind was simply the collapse postulate. Just to make sure we're on the same page here: this is an axiom originally explicitly formulated by von Neumann. I'm aware that there are different formulations of QM, but this one appears in most textbooks, and it's typically taken as a standard part of QM. It says that:
I arrived at this view of the MWI while debating it in other threads recently, so if you're interested you could find those threads.In fact, I'm very surprised to see you adopt MWI in this context - makes me think I haven't understood you,
That's right. I'm using the decomposition of the Hilbert space of the universe into system+environment, plus the decoherence process to single out something that we can think of as "worlds". I'm defining the worlds to be certain correlations between subsystems, specifically those correlations that are described by the terms that aren't extremely small.I'm not sure what you're doing when you say 'the remaining terms can now be interpreted as worlds.' Is this a kind of gestalt thing? A heuristic? That, in certain situations, we can, if you like, think of there being worlds?
There's only one physical system. Penrose calls it "the omnium" rather than "the universe" because it contains all the worlds. Its time evolution is unitary and described by the Schrödinger equation. The entire history of the omnium is a curve in a Hilbert space. The omnium has subsystems, but the worlds aren't among them. The subsystems are things like "you", "this chair" and "everything else". The worlds are just correlations between the states of the subsystems.I don't quite follow the physical picture. Either there are many worlds or there are not. Or do you think that they kind of emerge in certain situations - situations where decoherence applies?
I was wondering if there's another aspect to the measurement problem in terms of what one defines as the environment. I don't think I totally get decoherence yet, but doesn't it suggest that the environment gets entangled with the system so that the system's superposition gets restricted to some values? If that's the case don't we end up with a sort of infinite regress in terms of an an ever expanding environment upon which the smaller environment must be entangled. Eventually we have the entire universe and what would the entire universe have to be entangled with to have specific values?The result of decoherence is that the eigenstates of the system gets entangled with certain states of the environment. These states are called "pointer states". I don't know the details, but these pointer states are supposed to be records of the result of the interaction,
I think this is essentially correct. I've been thinking the same thing myself. My only objection is that I think you should be talking about state operators (i.e. density matrices) instead of state vectors. (See e.g. my edit of my first post in this thread). For all practical purposes, decoherence destroys the superpositions and puts the system into a mixed state instead.I was wondering if there's another aspect to the measurement problem in terms of what one defines as the environment. I don't think I totally get decoherence yet, but doesn't it suggest that the environment gets entangled with the system so that the system's superposition gets restricted to some values? If that's the case don't we end up with a sort of infinite regress in terms of an an ever expanding environment upon which the smaller environment must be entangled. Eventually we have the entire universe and what would the entire universe have to be entangled with to have specific values?