I Does chaos amplify inherent quantum level randomness?

[Filip Larsen]

Another interesting paper that seems relevant to the discussion in this thread:

Exploring quantum chaos with a single nuclear spin​

Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of quantum systems whose classical counterparts are chaotic are expected to show some features that resemble chaotic motion. Among the many controversial aspects of the quantum-classical boundary, the emergence of chaos remains among the least experimentally verified. Time-resolved observations of quantum chaotic dynamics are particularly rare, and as yet unachieved in a single particle, where the subtle interplay between chaos and quantum measurement could be explored at its deepest levels. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of a nuclear quadrupole interaction. This system is exquisitely measurable and controllable, and possesses extremely long intrinsic quantum coherence times, allowing for the observation of subtle dynamical behavior over extended periods. We show that signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling.

 

[gentzen]

Our disagreement seems easiest to discuss in Bohmian mechanics:

Only if by "Bohmian mechanics" you mean a different theory from standard QM, not just an interpretation of standard QM. As an interpretation of standard QM, the nonlinearity of the guiding equation is irrelevant since ...

I don't get to your objection. I even explicitly started by acknowledging that the nonlinearity of the guiding equation is irrelevant:

their guiding equation is nonlinear, and ... But you say that this is not the relevant dynamic, and I even agree with this.

And I also explicitly stated where I see our disagreement:

You want to conclude from the linearity of that dynamics (of the wavefunction) that it cannot exhibit chaos, and "I don't think that this argument is valid".

My point of using Bohmian mechanics to discuss our disagreement was that it is closer to QM than the Liouville equations I mentioned in my initial comment, while still allowing essentially the same explanation where the chaos is hiding, and even with essentially the same omissions. (But I see that Jarvis323 now provided nice references where the chaos hides in infinite dimensional linear dynamical systems. I fully understand that those are preferable to my "hints" at explanations with their "intentional omissions".)

 

[PeterDonis]

It is almost by definition of what emergence means in general

General statements about emergence are not the same as a specific derivation of chaos as emergent from the particular dynamics of QM. The latter is what is relevant to this thread.

 

[PeterDonis]

I even explicitly started by acknowledging that the nonlinearity of the guiding equation is irrelevant

And then you contradicted yourself by arguing that it is. If it's irrelevant, then it's irrelevant and can't be used as the basis of any argument that is relevant. If it can be used as the basis of a valid argument for this topic, then it's not irrelevant.

In any case, Bohmian mechanics is an interpretation of QM, and interpretation discussions are off topic in this forum. They belong in the interpretations subforum.

 

[PeterDonis]

@Filip Larsen thanks for the references. I'll take a look at them.

 

[gentzen]

And then you contradicted yourself by arguing that it is.

Well, I still argued for the relevance of "normal 3D space" mentioned in my initial comment. Whether it is exactly "normal 3D space" (as "privileged" by Bohmian mechanics) or more diverse classical dynamical properties (like momentum) is not important, because our disagreement seems to be about something else.

In any case, Bohmian mechanics is an interpretation of QM, and interpretation discussions are off topic in this forum. They belong in the interpretations subforum.

I had the impression that you wanted to discuss the dynamics of the wavefunction. Using Bohmian mechanics seemed like the easiest way to me to achieve this in a scenario where the wavefunction is agreed to be relevant, and the relevant dimensions are still reasonably small (i.e. at least the number of particles stays fixed without an infinite regress to more and more "environment" or larger and larger Hilbert spaces).

 

[PeterDonis]

I had the impression that you wanted to discuss the dynamics of the wavefunction.

For the specific topic of this thread, that is what is relevant. More precisely, basic QM without adopting any interpretation is what is relevant, since the title question of this thread is posed independently of any interpretation. As I have said, discussions that involve specific interpretations belong in the interpretations subforum.

Using Bohmian mechanics seemed like the easiest way to me to achieve this

Not if the discussion is to be independent of any interpretation.

 

[Fra]

Do you have a good reference for this?

Prescription for experimental determination of the dynamics of a quantum black box​

"We give an explicit way to experimentally determine the evolution operators which completely describe the dynamics of a quantum-mechanical black box: an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible and illustrate the general theory by considering specifically one-and two-quantum-bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication and computation systems."
-- Journal of Modern Optics, Volume 44, 1997 - Issue 11-12
(preprint also available on https://arxiv.org/abs/quant-ph/9610001)

/Fredrik

 

[PeterDonis]

@Fra, thanks for the reference, I'll take a look.

 

[Physicist248]

In principle yes. If you have a chaotic system of, say, interacting quantum particles then in principle you cannot know the exact initial condition and hence, at some point the quantum uncertainty has grown to the level of the macroscopic scale to which the motion is bounded.

How about in reality?