What does it take to solve the measurement problem? (new paper published)

[Demystifier]

The problem is that one has to bound the errors in the classical approximation, and the bounds obtainable by the standard techniques are usually exponential in the duration.

But the errors due to chaos are also exponential in the duration, so the ratio of two errors (one due quantum uncertainty, the other due to chaos) should remain constant. Do I miss something?

 

[A. Neumaier]

Far from being rigorous, my argument is roughly $\Delta E \Delta t \sim \hbar$, so for larger $\Delta t$, $\Delta E$ is smaller i.e. more classical.

Why is a smaller energy uncertainty more classical?? In an eigenstate of a quantum system, the energy uncertainty is zero, but nothing classical appears.

And the uncertainty in time for long living astronomic objects can be assumed to be tiny,

 

[A. Neumaier]

But the errors due to chaos are also exponential in the duration, so the ratio of two errors (one due quantum uncertainty, the other due to chaos) should remain constant. Do I miss something?

To prove that the classical chaotic motion is followed for larger and larger times you need smaller and smaller error bounds, since otherwise all you can prove is that the system is somewhere in the chaotic attractor.

 

[Demystifier]

otherwise all you can prove is that the system is somewhere in the chaotic attractor.

Isn't that enough?

 

[A. Neumaier]

Isn't that enough?

No. One can observe classical chaotic motion of planets to far higher accuracy. Just as we can resolve a Lorenz attractor quite well, not only say that the motion is somewhere in the blob.

 

[Demystifier]

No. One can observe classical chaotic motion of planets to far higher accuracy. Just as we can resolve a Lorenz attractor quite well, not only say that the motion is somewhere in the blob.

OK, but that's not how the Hossenfelder's argument works. Her argument is something like this: To explain the motion of Hyperion, which is in agreement with classical chaotic mechanics, we need first need to solve the measurement problem for the Hyperion. My objection is that here "Hyperion" and "chaotic" are red herrings, because we can put the whole problem into a more familiar form: To explain the motion of cat, which is in agreement with classical non-chaotic mechanics, then we need first need to solve the measurement problem for the cat.

 

[A. Neumaier]

OK, but that's not how the Hossenfelder's argument works. Her argument is something like this: To explain the motion of Hyperion, which is in agreement with classical chaotic mechanics, we need first need to solve the measurement problem for the Hyperion.

That's not her argument. Her argument is:
The long term motion of Hyperion is in agreement with classical chaotic mechanics. Thus to explain it by quantum mechanics we need to show that quantum mechanics reproduces the classical motion for these long time scales, which has not been done so far. This, in turn, is related to the measurement problem.

 

[atyy]

OK, but that's not how the Hossenfelder's argument works. Her argument is something like this: To explain the motion of Hyperion, which is in agreement with classical chaotic mechanics, we need first need to solve the measurement problem for the Hyperion. My objection is that here "Hyperion" and "chaotic" are red herrings, because we can put the whole problem into a more familiar form: To explain the motion of cat, which is in agreement with classical non-chaotic mechanics, then we need first need to solve the measurement problem for the cat.

Oh, is that what the paper is about. She had a YouTube video about it which was completely wrong (see also QuantumBrick's comments under the video).
https://blog.jessriedel.com/2017/07...cs-part-7-quantum-chaos-and-linear-evolution/

 

[PeterDonis]

Her argument is something like this

No, her argument is like this: QM predicts that the motion of an object like Hyperion should only show classical chaotic behavior on a time scale comparable to the Ehrenfest time; but Hyperion's actual observed motion shows classical chaotic behavior on a longer time scale than that. So QM can't explain the observed motion of Hyperion.

This is different from the usual arguments about Schrodinger's cat because in the latter scenario the Ehrenfest time does not come into play.

 

[Demystifier]

No, her argument is like this: QM predicts that the motion of an object like Hyperion should only show classical chaotic behavior on a time scale comparable to the Ehrenfest time; but Hyperion's actual observed motion shows classical chaotic behavior on a longer time scale than that. So QM can't explain the observed motion of Hyperion.

That's only the first part of her argument. The second part is something like: Since QM can't explain the observed motion of Hyperion, we need to find something which will make the motion classical, and to find it we have to solve the measurement problem.

 

[PeterDonis]

That's only the first part of her argument. The second part is something like: Since QM can't explain the observed motion of Hyperion, we need to find something which will make the motion classical, and to find it we have to solve the measurement problem.

Ok, but the first part alone is enough, if correct, to undermine claims that QM can explain the behavior of systems that exhibit classical dynamics on time scales longer than the Ehrenfest time. If you go on to criticize the second part of her argument, aren't you agreeing with the claim of the first part that I have just stated?

 

[PeterDonis]

The second part is something like: Since QM can't explain the observed motion of Hyperion, we need to find something which will make the motion classical, and to find it we have to solve the measurement problem.

I would not state it this way, because if we believe that QM can't explain the observed motion of Hyperion, and by extension of any system that shows classical dynamics beyond the Ehrenfest time, then why would we describe what we are looking for to take its place as "solving the measurement problem", since the measurement problem itself is a problem of QM, and if we accept the first part of her argument, we are discarding QM?

 

[Demystifier]

If you go on to criticize the second part of her argument, aren't you agreeing with the claim of the first part that I have just stated?

Yes I do.

 

[Demystifier]

I would not state it this way, because ...

Neither would I, but I think this is what she did.

 

[PeterDonis]

Yes I do.

Isn't Bohmian mechanics QM? Doesn't it have the same problem that is described in the first part of her post?

 

[Demystifier]

Isn't Bohmian mechanics QM? Doesn't it have the same problem that is described in the first part of her post?

QM has the problem in the first part only if one does not take into account the standard QM theory of quantum measurements, e.g. in the form of von Neumann theory of measurement combined with the collapse postulate. When one takes this into account, then the problem in the first part goes away. Likewise, when BM takes into account von Neumann theory of measurement combined with Bohmian trajectories that lead to an apparent effective collapse, the problem in the first part goes away. The standard and Bohmian QM make the same predictions only when one does take the theory of quantum measurements into account, i.e. only when the problem in the first part is removed.

 

[PeterDonis]

QM has the problem in the first part only if one does not take into account the standard QM theory of quantum measurements, e.g. in the form of von Neumann theory of measurement combined with the collapse postulate.

How does this fix the issue with the Ehrenfest time?

 

[Demystifier]

How does this fix the issue with the Ehrenfest time?

The classical limit corresponds to a wave packet which is narrow in the phase space. Ehrenfest time is the time after which the unmeasured wave packet is no longer narrow, due to the wave packet spreading. The measurement induces something like a wave function collapse, which prevents too much spreading i.e. keeps the wave packet narrow for an arbitrarily long time.

 

[PeterDonis]

The classical limit corresponds to a wave packet which is narrow in the phase space. Ehrenfest time is the time after which the unmeasured wave packet is no longer narrow, due to the wave packet spreading. The measurement induces something like a wave function collapse, which prevents too much spreading i.e. keeps the wave packet narrow for an arbitrarily long time.

Ok, but this only works if we adopt an interpretation in which collapse is a real physical process. On such an interpretation wave packets for something like Hyperion never get a chance to expand for any significant time at all, let alone for a time comparable to the Ehrenfest time, because Hyperion is constantly interacting with other stuff. Similar remarks would apply to any macroscopic object.

Such an interpretation probably doesn't bother you, since your preferred interpretation is Bohmian mechanics, where the "collapse" is already built in, so to speak, because particle positions (or something roughly equivalent--I note that in your paper you adopt a model in which a bosonic field is the fundamental ontic object) are always definite. But it's still just one interpretation, and one which many physicists find problematic.

 

[Demystifier]

Ok, but this only works if we adopt an interpretation in which collapse is a real physical process. On such an interpretation wave packets for something like Hyperion never get a chance to expand for any significant time at all, let alone for a time comparable to the Ehrenfest time, because Hyperion is constantly interacting with other stuff. Similar remarks would apply to any macroscopic object.

Such an interpretation probably doesn't bother you, since your preferred interpretation is Bohmian mechanics, where the "collapse" is already built in, so to speak, because particle positions (or something roughly equivalent--I note that in your paper you adopt a model in which a bosonic field is the fundamental ontic object) are always definite. But it's still just one interpretation, and one which many physicists find problematic.

My point is, if one does not accept the existence of some kind of physical "collapse" (i.e. one does not accept any of the interpretations such as Copenhagen, Bohmian, or many worlds), then Hyperion is not the first problem that sticks out. The Schrodinger cat problem is a much more obvious problem. And when one solves the Schrodinger cat problem (whatever the solution is, including the Hossenfelder's superdeterministic hidden variables), then the Hyperion problem is automatically solved as well. So my point is, yes, there is a deep fundamental problem to solve, but no, the Hyperion is not a very good example to explain what the problem is.

 

[PeterDonis]

if one does not accept the existence of some kind of physical "collapse" (i.e. one does not accept any of the interpretations such as Copenhagen, Bohmian, or many worlds)

Shouldn't it be "does" accept (instead of "does not")? Many worlds specifically denies that collapse is a physical process. Copenhagen is agnostic about it. And Bohmian says that the apparent "collapse" is just a result of our ignorance of initial conditions (i.e., it's similar to the ignorance interpretation of classical statistical models), so it also says that collapse isn't a real physical process.

 

[PeterDonis]

when one solves the Schrodinger cat problem (whatever the solution is, including the Hossenfelder's superdeterministic hidden variables), then the Hyperion problem is automatically solved as well

I think that would depend on the proposed solution of the Schrodinger's cat problem. Hossenfelder's superdeterministic solution would of course solve both problems, but that's to be expected. A model in which collapse was an actual physical process that violated unitary dynamics would also of course solve both problems. And in Bohmian mechanics, of course, these problems don't even exist in the first place, because Bohmian mechanics is perfectly deterministic (it just uses explicitly non-relativistic non-local dynamics for the pilot wave to address the issues that Hossenfelder prefers to address with superdeterminism).

But I'm not sure those exhaust all the possibilities for a proposed solution to the Schrodinger's cat problem. For one thing, proponents of other interpretations, such as many worlds, claim that their interpretations solve the Schrodinger's cat problem. But it's not clear to me that they also solve the Hyperion problem.

 

[Demystifier]

Shouldn't it be "does" accept (instead of "does not")? Many worlds specifically denies that collapse is a physical process. Copenhagen is agnostic about it. And Bohmian says that the apparent "collapse" is just a result of our ignorance of initial conditions (i.e., it's similar to the ignorance interpretation of classical statistical models), so it also says that collapse isn't a real physical process.

No, it shouldn't. Many worlds also have an apparent effective (not true) collapse, similar to Bohmian mechanics. Many versions of Copenhagen talk about collapse very explicitly, as @atyy will confirm. And Bohmians definitely do not say that collapse is a result of ignorance of initial conditions, it is a result of particles entering only one branch of the wave function. It is the randomness of collapse, not the collapse itself, that results from ignorance of initial conditions in Bohmian mechanics.

 

[Demystifier]

For one thing, proponents of other interpretations, such as many worlds, claim that their interpretations solve the Schrodinger's cat problem. But it's not clear to me that they also solve the Hyperion problem.

It's clear to me.

 

[Demystifier]

And in Bohmian mechanics, of course, these problems don't even exist in the first place, because Bohmian mechanics is perfectly deterministic (it just uses explicitly non-relativistic non-local dynamics for the pilot wave to address the issues that Hossenfelder prefers to address with superdeterminism).

Aaaaargh! Pilot wave does not obey non-local dynamics. It is particles that obey non-local dynamics. And perfect determinism has nothing to do with that. The Hyperion problem does not exist in Bohmian mechanics because particles are localized objects, it has nothing to do with the fact that equations of motion for particles are non-local and deterministic.

 

[PeterDonis]

Many worlds also have an apparent effective (not true) collapse, similar to Bohmian mechanics.

Calling these both by the same name seems to me to cause far more confusion than it could possibly solve.

 

[PeterDonis]

Pilot wave does not obey non-local dynamics. It is particles that obey non-local dynamics.

I think this is just a difference in choice of words. The pilot wave is how the non-local dynamics that the particles obey is realized: the pilot wave (or "quantum potential") term in the equation if motion is where the non-local dynamics of the particles resides.

 

[Demystifier]

Calling these both by the same name seems to me to cause far more confusion than it could possibly solve.

Well, I'm not responsible for that language, I'm just using standard terminology. Do you have a proposal for better terminology?

 

[PeterDonis]

The Hyperion problem does not exist in Bohmian mechanics because particles are localized objects

Particles are localized objects in standard QM, so I don't see how this helps.

it has nothing to do with the fact that equations of motion for particles are non-local and deterministic.

The fact that the equations of motion are deterministic means that the results of all measurements are predetermined; there is no actual randomness. As you note, the apparent randomness is entirely due to our ignorance of initial conditions--just as in a classical theory. And it is that specific similarity with classical theories that causes there to be no Hyperion problem in Bohmian mechanics, for exactly the same reason that there is no such problem in classical dynamics.

 

[Demystifier]

Particles are localized objects in standard QM

I'm not sure what do you mean by localized here. I mean pointlike, zero-size, which particles in standard QM are certainly not.

 

[PeterDonis]

No, it shouldn't.

I still don't see why not. See below.

Many worlds also have an apparent effective (not true) collapse, similar to Bohmian mechanics. Many versions of Copenhagen talk about collapse very explicitly, as @atyy will confirm. And Bohmians definitely do not say that collapse is a result of ignorance of initial conditions, it is a result of particles entering only one branch of the wave function. It is the randomness of collapse, not the collapse itself, that results from ignorance of initial conditions in Bohmian mechanics.

None of this contradicts the point I was making, which is that collapse is not a real physical process in any of these interpretations.

 

[PeterDonis]

I'm not sure what do you mean by localized here.

I mean that when we observe a "particle", we observe it as a localized thing. We don't observe an electron as "smeared out" over an arbitrary amount of space. We observe it as a dot on a detector screen or something equivalent.

I mean pointlike, zero-size, which particles in standard QM are certainly not.

Ok, this clarifies what "localized" means in the Bohmian interpretation. But I'm not sure what actual work the "pointlike" part does, over and above the weaker notion of "localized" that I described above.

 

[Demystifier]

None of this contradicts the point I was making, which is that collapse is not a real physical process in any of these interpretations.

That is true, but the point is that the collapse does not even need to be a real physical process in order to solve the Hyperion problem. Hossenfelder said that it does, but she was wrong. Effective (not real) collapse a'la Bohm or many worlds is enough.

 

[Demystifier]

Ok, this clarifies what "localized" means in the Bohmian interpretation. But I'm not sure what actual work the "pointlike" part does, over and above the weaker notion of "localized" that I described above.

It provides that the Bohmian particle cannot enter more than one branch of the wave function, which explains why only one branch looks "real", which explains the illusion of collapse.

 

[PeterDonis]

the point is that the collapse does not even need to be a real physical process in order to solve the Hyperion problem

In the Bohmian interpretation, that's true, as I've already said. And since that is your preferred interpretation, I can see why it seems this way to you. But there are other interpretations.