I Quantum mechanics is not weird, unless presented as such

[A. Neumaier]

So in what sense is the thermodynamic limit of QFT deterministic?

In the sense that it results in 19th century classical thermodynamics. In the latter theory there are known, exact, nonrandom relations between the thermodynamic quantities, and one can predict (from a thermodynamic potential and the values of a few state variables) the results of all reversible changes with certainty. No thermodynamics textbook mentions randomness (unless it refers to an underlying microscopic picture, i.e., to statistical mechanics).

 

[A. Neumaier]

that sounds like a hidden-variables theory of the type that is supposed to not exist.

Well, I argued that it might be nonlocal hidden variables - namely all those that describe the neglected environment. No Bell-type theorem excludes this possibility, and statistical mechanics demands that these variables must be taken into account. The only open question is whether these abundant hidden variables are enough to explain everything random. My strong suspicion is that they do.

 

[stevendaryl]

Well, I argued that it might be nonlocal hidden variables - namely all those that describe the neglected environment. No Bell-type theorem excludes this possibility, and statistical mechanics demands that these variables must be taken into account. The only open question is whether these abundant hidden variables are enough to explain everything random. My strong suspicion is that they do.

I had to leave the discussion for a while, because I was overly busy with my paying job, so I may have missed something, but it seems to me that taking into account the environment can't possibly resolve the nondeterminism using only unitary evolution. My argument is pretty simple:

Let |\psi_U\rangle be a state (including an electron, a stern-gerlach device, and the environment) which leads to measurement outcome "spin-up" for a spin measurement. Let |\psi_D\rangle be a state which leads to measurement outcome "spin-down". Then the state |\psi_?\rangle = \alpha |\psi_U\rangle + \beta |\psi_D\rangle would be a state that would lead to an undetermined outcome to the measurement. Maybe you can argue that there is no way to produce state |\psi_?\rangle, but it certainly exists in the Hilbert space, and it's not at all obvious to me that it would be unachievable.

 

[A. Neumaier]

it seems to me that taking into account the environment can't possibly resolve the nondeterminism using only unitary evolution. My argument is pretty simple:

Let |\psi_U\rangle be a state (including an electron, a stern-gerlach device, and the environment) which leads to measurement outcome "spin-up" for a spin measurement. Let |\psi_D\rangle be a state which leads to measurement outcome "spin-down". Then the state |\psi_?\rangle = \alpha |\psi_U\rangle + \beta |\psi_D\rangle would be a state that would lead to an undetermined outcome to the measurement. Maybe you can argue that there is no way to produce state |\psi_?\rangle, but it certainly exists in the Hilbert space, and it's not at all obvious to me that it would be unachievable.

This is a well-known argument, used already long ago by Wigner, I believe.

But it is not valid in my setting: Here, in the algebra of linear operators of some huge, universal Hilbert space, there is a unique density matrix of the universe that describes reality, and all systems that are observable are described by the projections of this universal density matrix to the algebra of linear operators of the tiny Hilbert space describing the observable system under investigation.
Most of the superpositions, while they exist in the tiny Hilbert space, have no relation to the universal density matrix, hence cannot be used to make an argument.

 

[stevendaryl]

This is a well-known argument, used already long ago by Wigner, I believe.

But it is not valid in my setting, where, in some huge, universal Hilbert space, there is a unique density matrix of the universe that describes reality, and all systems that are observable are projections of this universal density matrix to the tiny Hilbert space describing the microscopic system under investigation.
Most of the superpositions, while they exist in the tiny Hilbert space, have no relation to the universal density matrix, hence cannot be used to make an argument.

I think I understand your point, but it still seems like a tremendous leap. The same argument I made earlier can be lifted up to the level of universal density matrix, I would think. Why does the universal density matrix necessarily lead to definite outcomes to all possible experiments? Is there a way to prove this for a typical density matrix, or are your assuming some kind of "fine-tuning" of the initial density matrix to insure that it's true?

Mathematically, I think what you're saying might be something along the lines of the following:

Let \rho be the density matrix of the universe at some time (let's pick a frame/coordinate system so that we can talk about the state at one time). Then the claim might be that there is a decomposition of \rho into the form \rho = \sum_j p_j |\psi_j\rangle \langle \psi_j | where \psi_j is an orthonormal basis such that for each j, all macroscopic quantities (such as the outcomes of measurements) have definite values. I don't see why that should be the case.

(You can always write \rho = \sum_j p_j |\psi_j\rangle \langle \psi_j | , but you can't always be guaranteed that your favorite set of observables---the macroscopic values of measurement results--will be diagonal in the basis \psi_j)

 

[A. Neumaier]

Why does the universal density matrix necessarily lead to definite outcomes to all possible experiments? Is there a way to prove this for a typical density matrix, or are your assuming some kind of "fine-tuning" of the initial density matrix to insure that it's true?

I only need to assume that the observed part of the universe is approximately in local equilibrium. This is amply corroborated by experiment, and provides a very strong constraint on the universal density matrix. Indeed, local equilibrium is just the assumption needed to derive fluid mechanics or elasticity theory from quantum field theory, and for more than a century we describe every macroscopic object in these terms. Thus only those density matrices qualify as typical that satisfy this experimental constraint.
In my book (see post #2 of this thread), I call the corresponding states Gibbs states.

Let \rho be the density matrix of the universe at some time (let's pick a frame/coordinate system so that we can talk about the state at one time). Then the claim might be that there is a decomposition of \rho into the form \rho = \sum_j p_j |\psi_j\rangle \langle \psi_j | where \psi_j is an orthonormal basis such that for each j, all macroscopic quantities (such as the outcomes of measurements) have definite values. I don't see why that should be the case.

This is obviously not the case but this was not my claim. We do not need definite values but only values accurate enough to match experimental practice. This is a much less severe condition.

We all know from classical nonequilibrium thermodynamics that the macroscopic local observables are a small set of fields (in the simplest case just internal energy density and mass density). We also know from statistical mechanics in the grand canonical ensemble that these are given microscopically not by eigenvalues but by certain well-defined expectations. Under the assumption of local equilibrium, the fluctuations of the corresponding averaged quantum fields around the expectations are negligible. Thus the values of the macroscopic effective fields (obtained by corresponding small-scale averaging in the statistical coarse-graining procedure) are sharp for all practical purposes.

Mathematically, this becomes exact only in the thermodynamic limit. But for observable systems, which have finite extent, one can estimate the uncertainties through the standard fluctuation formulas of statistical mechanics. One finds that for macroscopic observations at the human length and time scale, we typically get engineering accuracy. This is the reason why engineering was already successful long before the advent of quantum mechanics.

 

[stevendaryl]

I only need to assume that the observed part of the universe is approximately in local equilibrium. This is amply corroborated by experiment, and provides a very strong constraint on the universal density matrix. Indeed, local equilibrium is just the assumption needed to derive fluid mechanics or elasticity theory from quantum field theory, and for more than a century we describe every macroscopic object in these terms. Thus only those density matrices qualify as typical that satisfy this experimental constraint.
In my book (see post #2 of this thread), I call the corresponding states Gibbs states.

But to me, the question is about quantum theory, not empirical observations. Does QM predict those observations?

 

[vanhees71]

So in what sense is the thermodynamic limit of QFT deterministic?

Don't ask me. I don't understand this claim at all.

 

[stevendaryl]

This is obviously not the case but this was not my claim. We do not need definite values but only values accurate enough to match experimental practice. This is a much less severe condition.

I think that's just a clarification of what I mean by "macroscopic quantities". I like your suggestion of giving coarse-grained descriptions of the mass-energy density, and field values. If the description is coarse enough, then the uncertainty principle doesn't get in the way of knowing the "macroscopic state of the universe" to that level of accuracy.

 

[vanhees71]

Precisely the apparently "deterministic" behavior of macroscopic systems is due to a "blurred" enough view on them. One way is to derive semiclassical transport models from QFT. The Kadanoff-Baym equations (fully quantum) become a Boltzmann equation in the quasiparticle limit applying leading-order gradient expansion.

 

[stevendaryl]

I think that's just a clarification of what I mean by "macroscopic quantities". I like your suggestion of giving coarse-grained descriptions of the mass-energy density, and field values. If the description is coarse enough, then the uncertainty principle doesn't get in the way of knowing the "macroscopic state of the universe" to that level of accuracy.

The question is: Can the universe be in a superposition of states that have different macroscopic states? If not, why not?

 

[A. Neumaier]

But to me, the question is about quantum theory, not empirical observations. Does QM predict those observations?

Quantum theory is derived from empirical observations and organizes these into a coherent whole. Quantum field theory predicts - under the usual assumptions of statistical mechanics, which include local equilibrium - hydrodynamics and elasticity theory, and hence everything computable from it.

Of course it predicts only the general theoretical structure, since all the detail depends on the initial conditions. But it predicts in principle all material properties, and quantum chemists are doing precisley that. All these are essentially exact predictions of QFT, with errors dominated by the computational techniques available rather than the uncerainty due to the averaging. Together with prepared or observed initial conditions it predicts the values of the macroscopic observables at later times. For example, computational fluid dynamics is an essential tool for the optimization of modern aircrafts.

Local equilibrium itself is usually justified in an ad hoc way assuming fast relaxation scales. These can probably be derived, too, but I haven't seen a derivation. But one knows when this condition is not satisfied in practice - namely if the mean free path lenth is too long. This happens for very dilute gases, where the Boltzmann equation must be used instead of hydrodynamic equations (and can be derived from QFT).

 

[A. Neumaier]

The question is: Can the universe be in a superposition of states that have different macroscopic states? If not, why not?

In the view I outlined above, the universe is not in a pure state but in a Gibbs state where local equilibrium holds to a good approximation. This is not a pure state but a mixture, $\rho=e^{-S/k}$ where $S$ is an entropy operator and $k$ the Boltzmann constant.

The more precise one wants to describe the state of the universe, the more complex is the form of $S$. Local equilibrium means that one considers the approximation where $S$ is an integral over local fields, and leads to hydrodynamics. The next, more accurate approximation is microlocal equilibrium, where
$S$ is an integral over local fields, and leads to kinetic theory (Boltzmann equation and Kadanoff-Baym equations). Critical point studies go even selectively beyond that ot make predctions of critical exponents.

 

[georgir]

Well, I argued that it might be nonlocal hidden variables - namely all those that describe the neglected environment. No Bell-type theorem excludes this possibility, and statistical mechanics demands that these variables must be taken into account. The only open question is whether these abundant hidden variables are enough to explain everything random. My strong suspicion is that they do.

Interesting how you imagine these "non-local hidden variables" and their effects... In particular, are they actual variables, i.e. do they get changed by some processes? I think this is critical for distinguishing from LHV models - because constant "variables", even if called "non-local" in some sense, can in my opinion always be modeled by local copies. Only their non-local change, or in other words spooky action at a distance, is what sets a model apart of LHV models and allows Bell violations.

 

[Hornbein]

This is a well-known argument, used already long ago by Wigner, I believe.

But it is not valid in my setting: Here, in the algebra of linear operators of some huge, universal Hilbert space, there is a unique density matrix of the universe that describes reality, and all systems that are observable are described by the projections of this universal density matrix to the algebra of linear operators of the tiny Hilbert space describing the observable system under investigation.
Most of the superpositions, while they exist in the tiny Hilbert space, have no relation to the universal density matrix, hence cannot be used to make an argument.

I'd like to have your expert opinion on the Conway-Kochen theorem. http://arxiv.org/pdf/quant-ph/0604079.pdf and http://arxiv.o rg/pdf/0807.3286.pdf

 

[A. Neumaier]

are they actual variables, i.e. do they get changed by some processes?

They change according to the Schroedinger equation of the universe, which determiens how $\rho(t)$ depends on time. The Hamiltonian would be known if we had a common generalization of the standard model and gravitation.

 

[A. Neumaier]

I'd like to have your expert opinion on the Conway-Kochen theorem. http://arxiv.org/pdf/quant-ph/0604079.pdf and http://arxiv.o rg/pdf/0807.3286.pdf

I don't think the paper has any relevance. The will of the experimenter is not relevant for Bell-type experiments, as all choices can be made by automatic devices. (See https://www.physicsforums.com/posts/5347224/ , especially point 9.)

In particular, the assumption made in their theorem is highly unrealistic. The choices made by an automatic device always depend on its internal state and its input, hence are in some sense determined by the information available to the device.

There is also no reason to believe that things would be different with humans, although here the definition of ''free will'' is beset with philosophical difficulties.

 

[Hornbein]

I don't think the paper has any relevance. The will of the experimenter is not relevant for Bell-type experiments, as all choices can be made by automatic devices. (See https://www.physicsforums.com/posts/5347224/ , especially point 9.)

In particular, the assumption made in their theorem is highly unrealistic. The choices made by an automatic device always depend on its internal state and its input, hence are in some sense determined by the information available to the device.

There is also no reason to believe that things would be different with humans, although here the definition of ''free will'' is beset with philosophical difficulties.

Aha. So you are a superdeterminist, like t'Hooft? You are correct: the theorem does not exclude this possibility.

 

[ddd123]

I reckon (if I haven't misunderstood) 't Hooft's attempts predict the impossibility of quantum computing: https://physics.stackexchange.com/q...egorically-dismiss-some-simple-quantum-models . Shor's post there seems to provide a big challenge for determinists.

 

[rkastner]

I got a pingback on my blog from someone with a question/comment about my blog post concerning 'Wrong idea...' but I can't find the post and I don't know who asked the question. Please feel free to contact me through my blog (there's a 'contact me' option there) if you would like a reply. Thanks.

 

[ddd123]

I got a pingback on my blog from someone with a question/comment about my blog post concerning 'Wrong idea...' but I can't find the post and I don't know who asked the question.

Off topic but, I wouldn't post emails on a public forum, it's inviting spam doomsday. Today's services are filtered but you increase it tenfold if not more. I may be wrong.

 

[rkastner]

Off topic but, I wouldn't post emails on a public forum, it's inviting spam doomsday. Today's services are filtered but you increase it tenfold if not more. I may be wrong.

Thanks, fixed it

 

[A. Neumaier]

Here, in the algebra of linear operators of some huge, universal Hilbert space, there is a unique density matrix of the universe that describes reality, and all systems that are observable are described by the projections of this universal density matrix to the algebra of linear operators of the tiny Hilbert space describing the observable system under investigation.
Most of the superpositions, while they exist in the tiny Hilbert space, have no relation to the universal density matrix, hence cannot be used to make an argument.

Further discussion of this part (concerning reality described by a universal density matrix), if any, please in this new thread!

 

[A. Neumaier]

One offshoot of this discussion (and the twin discussion of an associated experimental setting) is that I arrived at a new, improved understanding of relativistic causality. This settles (for me) all problems with causality in Bell-type theorems, and reduces the weirdness of nonlocality experiments to a problem in the psychology of knowledge. The residual weirdness is only of the same kind as the weirdness of being able to know what happens if some object falls into a classical black hole and when it will hit the singularity, although no information can escape from a black hole.

Thus the quantum case is not really different from the classical case in this respect. This throws light on the true, social, role of weirdness in quantum mechanics.

People very experienced in a particular area of real life can easily trick those who don't understand the corresponding matter well enough into believing that seemingly impossible things can happen. This is true in the classical domain, amply documented by magic tricks where really weird things happen, such as rabbits being pulled out of empty hats, etc..

The art of a magician consists in studying particular potentially weird aspects of Nature and presenting them in a context that emphasizes the weirdness. Part of the art consists of remaining silent about the true reasons why things work rationally, since then the weirdness is gone, and with it the entertainment value.

The same is true in the quantum domain. Apart from being technically very versed experimental physicists, people like Anton Zeilinger are quantum magicians entertaining the world with well-prepared quantum weirdness. And the general public loves it! Judging by its social impact, quantum weirdness will therefore never go away as long as highly reputed scientists are willing to play this role.

 

[ddd123]

One offshoot of this discussion (and the twin discussion of an associated experimental setting) is that I arrived at a new, improved understanding of relativistic causality. This settles (for me) all problems with causality in Bell-type theorems, and reduces the weirdness of nonlocality experiments to a problem in the psychology of knowledge. The residual weirdness is only of the same kind as the weirdness of being able to know what happens if some object falls into a classical black hole and when it will hit the singularity, although no information can escape from a black hole.

Honestly, I didn't understand this argument at all. As I said in the thread, the weirdness is in the correlated results themselves. Sure, we can anticipate them due to past experiments, but how is this different from what maline was saying: "QM is not weird because it's correct"? That seems to be your argument, but then you say it isn't. I am at a loss.

 

[A. Neumaier]

the weirdness is in the correlated results themselves.

Similarly, in relativity, the weirdness is in that different observers measure different clock times. it is weird only until you have a good mental scheme to think about it. People coming across relativity for the first time find it weird (and therefore intriguing, since it seems like a magical part of reality), but after getting accustomed to it, it is considered common sense.

stevendaryl had complained...

The problem that I have with QM is that it is so unclear what its semantics are. Is the wave function a description of the state of the world, or is it a description of our knowledge about the world? Or somehow both? Neither alternative really fits all the facts comfortably. Then there is the discrepancy between the objects described by the mathematical formalism (amplitudes for different possibilities) and what is actually observed (definite values for whatever is measured). Special Relativity similarly shows up a huge difference between what the theory says and what our observations show, but in the SR case, what things look like to an observer can be derived from what they are, at an objective level. In QM, there seems to be a fundamental distinction between observations and the underlying equations of physics, which means that the former is not completely explained by the latter.

...that the weirdness in quantum mechanics is different since there is no good mental picture (''semantics''), and therefore people struggle with different interpretations for now nearly a century. I separated in the other thread subjective and objective, and clarified the semantics of what causality should mean, and how the subjective aspects of knowledge create the apparent causality problems. Unfortunately, it didn't seem to help him. But the discussion clarified a lot for me.

 

[ddd123]

Yes I understood the purpose of your argument, I just don't understand the argument.

 

[Drakkith]

Several argumentative and off-topic posts, and the responses to them, have been removed. I remind all members to please stay on topic and civil in your discussions. Please see PF Terms and Rules for more info.

 

[Dadface]

One implication of the title of this thread is that in some quarters QM is considered to be weird. Does this suggested weirdness apply to the subject as a whole or only to certain specific aspects of the subject? If the latter is the case then what parts of QM are supposed to be weird? I'm reasonably familiar with some aspects of so called quantum weirdness as reported in the non specialist literature but I would be interested to know if there are any specialist QM practitioners who find all or parts of the subject to be weird.
Thank you.

 

[A. Neumaier]

I would be interested to know if there are any specialist QM practitioners who find all or parts of the subject to be weird.

Popular quantum magicians are at the same time very experienced specialist QM practitioners in quantum optics. They at least like to create for their audience the impression that parts of quantum mechanics is weird. This is common to magicians in any field, and not specific to quantum mechanics.

But since they understand their profession, I don't think any of our quantum magicians thinks that quantum mechanics is truly weird. It is fully rational to the mind sufficiently trained in mathematics and theoretical physics. This is why I think (and expressed in the title of the thread) that it is only the presentation that makes quantum mechanics appear weird.