Chaos, quantum gravity, theory of everything....

[MathematicalPhysicist]

How is chaos incorporated into quantum gravity theories, or in theories that incorporate all the known 4 interactions?

I don't believe I've seen a thread where chaos theory is discussed in relation to superstring theories or LQG.
I've seen some papers and dissertations on quantum chaos and cosmological models, but haven't read them thoroughly.

So what is the connection if there is one, I haven't yet started reading BSM papers, but my feeling is that there should be obviously if a theory should be a theory of everything.

 

[MarekKuzmicki]

And how is chaos incorporated in classical physics? Chaos is something that comes (sometimes) from equations after realising that little change in beginning can create variety of solutions on the end.

 

[MathematicalPhysicist]

And how is chaos incorporated in classical physics? Chaos is something that comes (sometimes) from equations after realising that little change in beginning can create variety of solutions on the end.

Correct, so do they appear also in equations of quantum gravity or superstring theories?

 

[MarekKuzmicki]

Don't know quantum gravity or superstrings, but anserw should be 'yes' due to mathematics (properties of sets of equations).
Even on Newton theory ona could make fraktals https://en.wikipedia.org/wiki/Newton_fractal
Quantum theories develop from classics and are more mathematicaly complex than them.

 

[MathematicalPhysicist]

Well, I read that some consider classical canonical pertubation theory more complicated than the quantum counterpart.

 

[Demystifier]

Chaos is a property of solutions of (some) classical equations of motion. Quantum theory contains classical solutions in the form of Ehrenfest theorem, but people who study quantum theory are usually concerned with other, less classical, aspects of quantum theory. For that reason you will not find much discussion of chaos in the quantum literature.

 

[Demystifier]

but my feeling is that there should be obviously if a theory should be a theory of everything.

This is a misinterpretation of the idea of "theory of everything". Theory of everything is supposed to be able to describe everything in principle, but it does not mean that it is very efficient in describing everything in practice. For instance, even if string theory can, in principle, describe motion of planets around the Sun, no physicist will try to actually do that in practice. For practical purposes, the good old classical Newtonian mechanics is much more efficient.

 

[Demystifier]

Well, I read that some consider classical canonical pertubation theory more complicated than the quantum counterpart.

Yes, in a certain sense quantum mechanics is simpler than classical mechanics. For instance, the classical counterpart of the quantum Schrödinger equation is the classical Hamilton-Jacobi equation. However, Schrödinger equation is simpler to solve than Hamilton-Jacobi equation because the former is linear while the latter is non-linear.

 

[MathematicalPhysicist]

This is a misinterpretation of the idea of "theory of everything". Theory of everything is supposed to be able to describe everything in principle, but it does not mean that it is very efficient in describing everything in practice. For instance, even if string theory can, in principle, describe motion of planets around the Sun, no physicist will try to actually do that in practice. For practical purposes, the good old classical Newtonian mechanics is much more efficient.

Well, doesn't it depend on the precision you are looking for?

I mean GR is more accurate than Newtonian mechanics, I assume string or LQG will be more accurate than GR; it really depends on the application you have in mind, right?

 

[Demystifier]

Well, doesn't it depend on the precision you are looking for?

I mean GR is more accurate than Newtonian mechanics, I assume string or LQG will be more accurate than GR; it really depends on the application you have in mind, right?

In principle, you are right. In practice, however, you usually cannot get a better precision by taking effects of string/LQG theory into account in description of motion of planets.

 

[mitchell porter]

The most prominent example right now would be the Sachdev-Ye-Kitaev (SYK) model, in which you have a collection of fermions on a point interacting with each other, with randomly distributed strengths. It appears to be holographically dual to a "black hole" in one space dimension. This is not a candidate for a fundamental theory, but it is considered a calculable toy model in which properties of real quantum black holes may be demonstrated in simplified form. Quantum black holes are believed (by Susskind and others) to be "fast scramblers" which scramble the quantum state at high speeds, and this is probably a kind of chaotic process.

One difference between classical chaos and quantum chaos, is that classical chaos involves a kind of mixing of trajectories which is obscured in quantum mechanics by the uncertainty principle. (I don't know what happens if you look at chaos in Bohmian mechanics.) However, one may find that energy levels in a quantum chaotic system have a random distribution resembling the eigenvalues of certain random matrices, and possibly the zeroes of the Riemann zeta function.

But in general chaos is regarded as a property of complex systems, rather than something fundamental in a reductionist sense.

 

[Fra]

In principle, you are right. In practice, however, you usually cannot get a better precision by taking effects of string/LQG theory into account in description of motion of planets.

I see some really deep connections here that imo are not explored, and I also think it would be a nice thing to explore from the bohmian perspectivce. In particular the new solipsist HV?

The possible connection is if you add another deep idea, that we can sniff from this

Quantum black holes are believed (by Susskind and others) to be "fast scramblers" which scramble the quantum state at high speeds, and this is probably a kind of chaotic process

If you see this from my perspective, this scrambling can be understood as the "computation" necessary for random walk, which is time evolution.

Now consider two such interacting systems, then its easy to understand that systems couple or decouple living in the deterministic chaos since the sensitivity of the deterministic chaos is smaller than the computational capacity. So a mechanism for hiding the solipsist variables is that it takes a certain computational resoures (processing power and memory) to see (infer) them from the "in principled deterministic chaos". This view can even EXPLAIN the breaking of the classical determinisim. A locality principle that suggests that the system responds to local info only, and the infer this requiers computation. Thus, information that in the above sens "in principle" exists, can not be inferred du to limits of internal scramling speeds. Actully this is also a possible potential way to introduce quantum mechanics by alternative axioms.

Somehow, from a pragmatic perspective, what's chaotic and what's not depends on your observational resolution and processing capacity. This is IMO potentially related tot foundations of QM. Something is chaotic if its "too complex" for the observer to decode. Also conceptually then a black hole is powerful enoug to decode and take control over anything getting accros the horizon. Only think that can beat it, is then a bigger black hole.

Analogies with the computational complexity of encryption are also clear here. In way, one can thus see matter as en encryption of its behaviour. Anyone that can decode this - fast enoug, can also take control of it.

This is roughly speaking, my extrapolated association from in between the lines to this paper
https://arxiv.org/abs/1112.2034

I am not sure if Demystifier would share this association but its the angle i liked, and the connection between deterministic chaos and solipsism and more "fundamental undertainty".

/Fredrik

 

[haushofer]

The most prominent example right now would be the Sachdev-Ye-Kitaev (SYK) model, in which you have a collection of fermions on a point interacting with each other, with randomly distributed strengths. It appears to be holographically dual to a "black hole" in one space dimension. This is not a candidate for a fundamental theory, but it is considered a calculable toy model in which properties of real quantum black holes may be demonstrated in simplified form. Quantum black holes are believed (by Susskind and others) to be "fast scramblers" which scramble the quantum state at high speeds, and this is probably a kind of chaotic process.

One difference between classical chaos and quantum chaos, is that classical chaos involves a kind of mixing of trajectories which is obscured in quantum mechanics by the uncertainty principle. (I don't know what happens if you look at chaos in Bohmian mechanics.) However, one may find that energy levels in a quantum chaotic system have a random distribution resembling the eigenvalues of certain random matrices, and possibly the zeroes of the Riemann zeta function.

But in general chaos is regarded as a property of complex systems, rather than something fundamental in a reductionist sense.

Not just complex systems. Think e.g. about the logistic difference equation.