Can you give a reasonably rigorous argument for this?Demystifier said:I would expect that for larger times the classical limit is even more valid.
For justifying an otherwise unsupported claim made by a contributor to the forum, only peer-review published work counts.drmalawi said:I thought only peer-review published work were allowed on this forum?
I don't understand what's puzzling.martinbn said:But that's the puzzling point. If there is chaos in classical mechanics, how can there be a classical limit!
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.A. Neumaier said:Can you give a reasonably rigorous argument for this?
All I said was that I think that this is the point she makes.Demystifier said:I don't understand what's puzzling.
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 said: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.
Why is a smaller energy uncertainty more classical?? In an eigenstate of a quantum system, the energy uncertainty is zero, but nothing classical appears.Demystifier said: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.
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 said: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?
Isn't that enough?A. Neumaier said:otherwise all you can prove is that the system is somewhere in the chaotic attractor.
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 said:Isn't that enough?
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 said: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.
That's not her argument. Her argument is:Demystifier said: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.
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).Demystifier said: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.
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.Demystifier said:Her argument is something like this
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 said: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.
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?Demystifier said: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.
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 said: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.
Yes I do.PeterDonis said: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?
Neither would I, but I think this is what she did.PeterDonis said:I would not state it this way, because ...
Isn't Bohmian mechanics QM? Doesn't it have the same problem that is described in the first part of her post?Demystifier said:Yes I do.
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 said:Isn't Bohmian mechanics QM? Doesn't it have the same problem that is described in the first part of her post?
How does this fix the issue with the Ehrenfest time?Demystifier said: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.
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 said:How does this fix the issue with the Ehrenfest 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.Demystifier said: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.
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 Schrödinger cat problem is a much more obvious problem. And when one solves the Schrödinger 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 said: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.
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.Demystifier said: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)
I think that would depend on the proposed solution of the Schrödinger'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).Demystifier said:when one solves the Schrödinger cat problem (whatever the solution is, including the Hossenfelder's superdeterministic hidden variables), then the Hyperion problem is automatically solved as well
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.PeterDonis said: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.
It's clear to me.PeterDonis said:For one thing, proponents of other interpretations, such as many worlds, claim that their interpretations solve the Schrödinger's cat problem. But it's not clear to me that they also solve the Hyperion problem.
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 said: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).