When Quantum Mechanics is thrashed by non-physicists #1

[atyy]

My question was what it means to say that a macroscopic device measures observable $X$. As I said, that seems to necessarily involve making a macroscopic/microscopic distinction that goes beyond the mathematics of quantum mechanics.

Can't we understand macroscopic and microscopic to be fundamental undefined concepts that are part of the mathematics? So macroscopic is a synonym for observable, and microscopic is a synonym for quantum state.

 

[kith]

I don't know a way to say that a device measures a particular observable without invoking the macroscopic/microscopic distinction, which isn't part of the mathematics of quantum mechanics.

I think this is the only part of the problem which is widely considered to be solved.

As far as I can see, there are three problems associated with the preferred basis:
1) the factorization problem
2) the actual problem of the preferred basis
3) the problem of outcomes

The factorization problem notes that in order to picture the measurement as a quantum interaction between the system and the apparatus leading to entanglement between the two, you need to decompose the big Hilbert space in a certain way. If you have only the big Hilbert space and the full Hamiltonian, there are always bases where you only have simple phase rotations. So you don't get the picture of interacting subsystems by these two entities alone. I think this is what Demystifier is talking about when he says "MWI has a well-known preferred basis problem". There's a paper on all this by Schwindt.

The actual problem of the preferred basis is the question if and how the eigenstates of an observable are singled out dynamically in a measurement. This is what you are referring to and I think this is what Zurek's environmental induced superselection or decoherence explains by using only quantum dynamics (and certain approximations) for the composite system. A device measures a particular observable because its Hamiltonian and its thermodynamical properties lead to a maximal and robust entanglement between the eigenstates of the observable for the system and the states of the pointer of the device.

The problem of outcomes is the question why a single outcome is observed although the final state after decoherence is a mixed state.

 

[TrickyDicky]

The states do not depend on the basis and they do not say they do. What they show is that physics depends on the basis, implying that the state by itself is not physics.

Right, the state mentioned in the first QM postulate is supposed according to its wording to be basis-independent and to be physical. They show that is contradicted by the math, and therefore the physics, that is in practice basis-dependent in the way you explain( but they use a different path to prove their theorem).

 

[dextercioby]

So just that I'm clear, there's a certain value to the paper, but not with respect to a valid critique to the PBR theorem. So they would have 100% accurate, had they formulated the conclusion in a less daring way.
Thanks,

 

[TrickyDicky]

So just that I'm clear, there's a certain value to the paper, but not with respect to a valid critique to the PBR theorem. So they would have 100% accurate, had they formulated the conclusion in a less daring way.
Thanks,

I agree they didn't elaborate much their conclusions about the consequences of their theorem on PBR, many-worlds, BM, etc, so that part even if it may be correct comes across as weak and bold.

 

[vanhees71]

First, by saying that you exchange something with the environment contains a preferred basis problem. Namely, the split of the whole system into "you" and "environment" depends on the choice of basis for the whole system.

Second, you say that
i) you are a quantum state, and
ii) you have an ability to choose another state
Is that consistent? If so, then a state has ability to choose another state. But how that ability is realized? Can it be described by the Schrödinger equation alone? If yes, then you are probably assuming a many-world interpretation, for which it is well-known to lead to the preferred basis problem. If not, then you probably need some other equation, but then what that other equation is, and are you sure that it is basis independent? These are all non-trivial questions, and whatever your answer is, I claim that the preferred basis problem emerges. If you do not see it, try to answer all these questions; depending on your answer I will tell you how the preferred basis problem then emerges.

Third, note that Ballentine would not agree that you are the quantum state.

Hm, that would mean that quantum theory is incomplete in saying that at least an experimental physicist, who plans and performs an experiment cannot be described by quantum theory. But then immediately the question arises, what are the validity boundaries of quantum theory.

To make it clear, I'm pretty sure that all our physical theories are incomplete. At least we can't prove completeness, but so far we haven't found any observation that contradicts quantum theory. Since you can never empirically prove a theory to be complete, the claim QT is complete is not a scientific statement.

Of course, our experience shows that our experimental colleagues are very able to plan and conduct experiments with quanta, which so far all turned out in accordance with the predictions of QT. Of course, this doesn't solve your metaphysical/philosophical problems but "for all practical purposes" it's a great success of QT.

 

[atyy]

Hm, that would mean that quantum theory is incomplete in saying that at least an experimental physicist, who plans and performs an experiment cannot be described by quantum theory. But then immediately the question arises, what are the validity boundaries of quantum theory.

Not exactly. The experimentalist can be described by a wave function, but then there must be another experimentalist with classical apparatus to measure the probabilities predicted by his wave function, otherwise quantum theory makes no predictions. At some stage, one has to introduce the notion of classical apparatus distinct from the quantum system, which is why the classical/quantum cut is part of standard quantum theory, as described in Landau & Lifshitz, Weinberg, and Susskind. To escape it, one needs a more complete theory like Bohmian Mechanics or an interpretation like Many-Worlds.

Of course, this doesn't solve your metaphysical/philosophical problems but "for all practical purposes" it's a great success of QT.

It is not a metaphysical/philosophical problem. The "for all practical purposes" theory makes no predictions without a classical/quantum cut, so quantum theory with only unitary evolution of the wave function has had no successes (unless MWI is a coherent framework). It is because one uses a cut that quantum theory is said to be "for all practical purposes". You have often mentioned coarse-graining, as Peres does. If coarse-graining works, it is equivalent to introducing a classical/quantum cut, because Peres envisages the coarse graining as changing a Wigner function with negative portions into a classical probability distribution, which means that classical particles with simultaneous position and momentum exist.

 

[atyy]

I agree with you, it's not a correct criticism of PBR. What they seem to miss is that their identification
real = basis independent
is not a true fact, but merely a convenient definition.

So just that I'm clear, there's a certain value to the paper, but not with respect to a valid critique to the PBR theorem. So they would have 100% accurate, had they formulated the conclusion in a less daring way.

I think so, but I am not sure exactly why PBR or Bohmian Mechanics escapes. Here's a try. The invariance they would like to have would mean that non-commuting observables have simultaneous reality, and is meant to provide counterfactual definiteness (the uncertainty is due to a probability distribution over definite classical events). So "counterfactual definiteness" is the more general definition of "real" or "physical" that they wish to consider (as they mention on p9). However, counterfactual definiteness can be provided by contextuality, as PBR and Bohmian Mechanics allow for.

 

[atyy]

Hm, that would mean that quantum theory is incomplete in saying that at least an experimental physicist, who plans and performs an experiment cannot be described by quantum theory. But then immediately the question arises, what are the validity boundaries of quantum theory.

Just to add to post #37, here is Asher Peres's criterion for the measuring apparatus.

http://arxiv.org/abs/quant-ph/9906023 (p8): "A valid measuring apparatus must admit a classical description equivalent to its quantum description [22] and in particular it must have a positive Wigner function."

A positive Wigner function means that the apparatus has a classical description.

 

[vanhees71]

Usually you need to do some coarse graining to make a positive semidefinite phase-space distribution out of the Wigner function. The classical description is valid if the macroscopic observables are well described within the accuracy by the coarse-graining procedure. The important point is that there is an "overlap" between the validity of the classical (coarse-grained) description and the full quantum dynamics. There's no invalidity of quantum theory involved somewhere. So FAPP the measurement problem is solved.

 

[atyy]

Usually you need to do some coarse graining to make a positive semidefinite phase-space distribution out of the Wigner function. The classical description is valid if the macroscopic observables are well described within the accuracy by the coarse-graining procedure. The important point is that there is an "overlap" between the validity of the classical (coarse-grained) description and the full quantum dynamics. There's no invalidity of quantum theory involved somewhere. So FAPP the measurement problem is solved.

The coarse graining is essentially a collapse. One cannot coarse-grain too early, because coarse graining loses coherence, which can in principle be detected. So one has to coarse-grain at the end of the measurement, which is when one obtains an irreversible outcome. In traditional QM, one says that after a measurement, the state collapses. In Peres's version, one says that after a measurement, the Wigner function of the apparatus is coarse-grained. So there are still two time evolutions - reversible unitary evolution and irreversible (collapse = coarse-graining).

 

[vanhees71]

I avoid collapse. The coarse-graining procedure is way more than a simple ad-hoc assumotion and way more convincing than an instantaneous collapse. It explains the classical behavior of macroscopic objects, particularly measurement apparati, which are indeed necessarily classical in the sense that the classical description suffices to describe it's macroscopic observables. By definition a measurement apparatus must be constructed such that the macroscopic observables ("pointer state") are accurate enough to resolve the observable of the measured quantum system.

I think Peres explains all this very well in his book Quantum Theory, Concepts and Applications.

 

[Demystifier]

Hm, that would mean that quantum theory is incomplete in saying that at least an experimental physicist, who plans and performs an experiment cannot be described by quantum theory.

The truth of this claim depends on what exactly one means by "quantum theory". One way to make this claim more precise is to quote Sheldon Goldstein who said that "either the wave function is not all or Schrödinger equation is not always true".

 

[Demystifier]

I think Peres explains all this very well in his book Quantum Theory, Concepts and Applications.

This is probably the best book to understand the instrumental operational view of QM, but that is certainly not the only way to view QM.

 

[atyy]

I avoid collapse. The coarse-graining procedure is way more than a simple ad-hoc assumotion and way more convincing than an instantaneous collapse.

Whether it is ad-hoc or more convincing that collapse is a matter of taste. Coarse-graining, if it works, is like collapse in that it says that we do not know how to make sense of a wave function of the universe, and that quantum dynamics requires more than unitary evolution.

I think Peres explains all this very well in his book Quantum Theory, Concepts and Applications.

This is probably the best book to understand the instrumental operational view of QM, but that is certainly not the only way to view QM.

I like Peres's book very much. However, I do not think it is the best book for understanding the instrumental or operational view of QM. The formulation by Landau and Lifshitz or Weinberg with a classical/quantum cut and collapse has the advantage of making clear that quantum theory is only FAPP, even though it has never been falsified. In that sense, Landau and Lifshitz and Weinberg make clear that there is a measurement problem, whereas Peres is reluctant to admit that quantum theory has a serious problem and tries to disguise it by his notion of coarse-graining.

 

[vanhees71]

Hm, that's why I like Peres's book so much :-).

 

[Demystifier]

Landau and Lifshitz and Weinberg make clear that there is a measurement problem

Can you specify where exactly Landau and Lifshitz say that?

 

[stevendaryl]

The truth of this claim depends on what exactly one means by "quantum theory". One way to make this claim more precise is to quote Sheldon Goldstein who said that "either the wave function is not all or Schrödinger equation is not always true".

There is sense in which what Goldstein says seems right. While MWI tries to get away with nothing but the wave function, and nothing but unitary evolution, I'm not completely convinced that it is satisfactory because of (1) the basis problem--how do we get "alternative worlds" out of the wave function without a picking a preferred basis, and (2) the probability problem--how does the appearance of probabilistic evolution come from the deterministic Schrödinger equation? Besides MWI, all the other formulations or interpretations of QM have something--measurements or observers or definite positions of particles or something--that goes beyond wave function + Schrödinger equation.

But there's another sense in which Goldstein's claim is a little strange. If it were the case that the Schrödinger equation is not always true, then shouldn't there be instances of observable violations of Schrödinger's equation? I don't think there are any. The apparent wave function collapse seems to be such a violation, but if we treat the measurement process quantum-mechanically, there doesn't seem to be any need for a collapse hypothesis. (Or more precisely, there is no specific moment where the collapse needs to happen--it can always be moved into the future, to some observer of the observer.)

If it's the case that there is something more than the wave function, you would think that there would be some experimental evidence for it. But there isn't.

So the weirdness about Goldstein's claim is that even if you can plausibly argue that wave function + unitary evolution can't be all there is, you can also argue that whatever else there is has no physical effect. It is affected by quantum mechanical processes, but it doesn't affect them.

 

[atyy]

Can you specify where exactly Landau and Lifshitz say that?

No, I can't, but it seemed obvious to me once there is a classical/quantum cut, which they do make explicit. They do however, say something about quantum mechanics being strange, since it cannot be formulated without classical physics, even though classical physics is a limit of quantum theory.

 

[Demystifier]

Or more precisely, there is no specific moment where the collapse needs to happen--it can always be moved into the future, to some observer of the observer.

I disagree. From my point of view, even if it can be moved to the time at which I observe it, it certainly cannot be moved to a later time at which somebody else observes me.

 

[stevendaryl]

I disagree. From my point of view, even if it can be moved to the time at which I observe it, it certainly cannot be moved to a later time at which somebody else observes me.

Why can't it? Because you have a memory of observing something definite? But it seems consistent to me (although very strange) to believe that when you make a measurement, your own brain state enters a superposition of different memories, and then at some later time, a collapse happens that eliminates all but one of those memories.

 

[Demystifier]

Why can't it? Because you have a memory of observing something definite?

No. It's because I observe something definite right now.

But it seems consistent to me (although very strange) to believe that when you make a measurement, your own brain state enters a superposition of different memories, and then at some later time, a collapse happens that eliminates all but one of those memories.

If not before, the collapse must have happened right now, because right now I am having some definite state of consciousness.

 

[stevendaryl]

No. It's because I observe something definite right now.

I don't see how that is something you can know. You experience a definite observation, but that doesn't imply the nonexistence of other, incompatible observations. If you were in a superposition of two different brain states, each of which is observing something different, how would you know? Due to the linearity of Schrödinger's equation, two elements of a superposition have no effect on each other.

 

[bhobba]

No. It's because I observe something definite right now..

Indeed. Either you believe things exist independent of us or you don't. If you don't you are led to the slippery slope of a very weird view of the world especially with the computer technology we have these days and recoding the outcome of observations into computer memory.

That why I take the observation as occurring directly after decoherence which avoids all these issues.

Thanks
Bill

 

[stevendaryl]

Indeed. Either you believe things exist independent of us or you don't.

I don't quite see the relevance of that remark. The possibility that a human brain might be in a superposition of states doesn't imply that there is nothing objective independent of us. It seems to me to the contrary, that there is nothing special about a human brain, when it comes to QM.

If you don't you are led to the slippery slope of a very weird view of the world especially with the computer technology we have these days and recoding the outcome of observations into computer memory.

I don't understand what you are claiming leads to a slippery slope: Assuming that there is no collapse?

That why I take the observation as occurring directly after decoherence which avoids all these issues.

To me, the only thing special about decoherence is that it explains the practical difficulty (we can put it stronger: the practical impossibility) of observing interference effects between macroscopically distinguishable states. But that doesn't actually avoid the conceptual difficulties, it just means that we can consistently ignore them. There is a sense in which decoherence is just a sanity check that the assumption in the Copenhagen interpretation that the macroscopic world can be treated classically is consistent with QM.

 

[TrickyDicky]

I don't see how that is something you can know. You experience a definite observation, but that doesn't imply the nonexistence of other, incompatible observations. If you were in a superposition of two different brain states, each of which is observing something different, how would you know? Due to the linearity of Schrödinger's equation, two elements of a superposition have no effect on each other.

If you believe in a universe independent of the observer you can ignore all those considerations about brain superpositions.

 

[stevendaryl]

If you believe in a universe independent of the observer you can ignore all those considerations about brain superpositions.

That's the same thing that Bill Hobba said, and I don't see how that follows. What you have to assume to get the conclusion that there are no superpositions of macroscopically different brain states is to assume, not just that there exists a universe independent of the observer, but that observations accurately tell us something about that universe. That's a natural thing to want to be true, but it doesn't follow from the assume that there is an objective universe. MWI is a counter-example: the state of the universe is objective, independent of observers. But observations don't tell us anything about the state of the universe. (If we observe an electron to have spin-up along some axis, that doesn't imply that the electron has a definite spin in that direction, because in a different branch of the wavefunction, the electron has spin-down.)

 

[Demystifier]

I don't see how that is something you can know. You experience a definite observation, but that doesn't imply the nonexistence of other, incompatible observations. If you were in a superposition of two different brain states, each of which is observing something different, how would you know? Due to the linearity of Schrödinger's equation, two elements of a superposition have no effect on each other.

Are you invoking the many-world interpretation here?

 

[bhobba]

That's the same thing that Bill Hobba said, and I don't see how that follows.

Go back to what Demystifier said.

No. It's because I observe something definite right now.

Did what he observe objectively exist prior to the observer of the observer?

Thanks
Bill

 

[stevendaryl]

Are you invoking the many-world interpretation here?

"Invoking many-worlds" makes it sound like an additional assumption, but I think that it's the other way around--that you need to make an additional assumption (about the relationship between subjective mental states and the universe) in order to rule out the possibility of superpositions of brain states. It doesn't follow from your observations alone. To connect observations with the objective state of the universe requires a theory.

To me, the claims you are making are exactly backwards. To say that you know that your brain can't be in a superposition of states is to assume something special about brains that makes them different from electrons or atoms or molecules.