Alain homers with Ali and Slava on base : further thoughts

[Jimster41]

Just some crazy talk...

...but I am curious if there may be testable expectations, at the end of the day, for quantization/discretization of classical entropies. If space-time geometry is made up of discrete spin foam, and 4d spacetime emerges from it's evolution, a fitness function based on distributable $\lambda$ (or something like it), could be the source of microscopic path-entropy-differences. And if entropy scales up from this mechanism in a discretely scale-invariant way (say with powers of $i$) - that might explain why entropy builds such weird repetitive s_____.

 

[wabbit]

Assuming I got that (well I know nothing of distributed lambdas so that's a pretty big assumption, but anyway...) - I don't think so, scaling behaviours usually play their magic between two limiting scales, and if anything QG stops that from extending below the Planck scale : )

 

[Jimster41]

Assuming I got that (well I know nothing of distributed lambdas so that's a pretty big assumption, but anyway...) - I don't think so, scaling behaviours usually play their magic between two limiting scales, and if anything QG stops that from extending below the Planck scale : )

Hey @wabbit, thanks for trying anyway! Can you elaborate on what you mean by "scaling behaviors usually play their magic between two limiting scales"

I got all excited about how (someone posted in a thread) the Imirzzi parameter, in some LQG theory, worked out nicely with a guess of $i$. I had a cartoon of that parameter as a sort of "counting constant" defining the number of little Planck holes in a region of spin foam, or the number of vertices in the network, and relating that to the scale of the gravitational field in that region.

No idea what that means really, but that's what I interpreted naively. I have this image I can't get out of my head, of the fluctuation theorem (as expressed by Galvin Crooks) relating system path selection to heat exchange and initial and final state entropy. Problem is, that whole theorem feels circular unless you give either the entropy of the final and initial states, or the probability of the system taking the path between them "causal" status. Since the probability of path is really only an observation, then maybe it is the state entropy - that is really just a label placed over the previously unaccounted for causal driver - which may be QM spacetime geometry evolution, and real properties thereof. If regions of spin foam of different "total number of Planck volumes" scale gravitationally as powers of the complex plane, iterations on which show discrete scale invariance (fractals etc) there seems to be a potential mechanism for the discrete-scale invariance we see macroscopically (tree branches and bronchioles, etc) The path selection surface, created by discrete QG, scaled as a repeating pattern, could create complex Hamiltonian contours, and act as the source of "free energy" from system path selection in spacetime. The huge(est) empty gap in this cartoon I would expect to give pause is how the SM or SUSY or whatever, in turns out to be with QG supports the extension of features from the realm of the (discrete) Quantum spacetime process, up to macroscopic harmonics.

The G. Crooks paper. There are a lot that talk a out his F.T. I would love to know more about what they say. He's a main source for that bio-physicist Jeremy England.

http://arxiv.org/abs/cond-mat/9901352

 

[wabbit]

About the limiting scales : nothing fancy, just the observation that scaling behaviours in nature are always limited - in practice by the range of scales at which it is observed, and in theory by the range in which the relevant effects generating it are dominant or significant. Scaling in turbulent fluids limited below by the atomic scale, above by the system scale ; branching in growth is limited below by the elementary structure scale, above by some limit like gravity, a container, etc. - and these limits are no hindrance to such effects, there is no need for an effect to be valid at all scales for it to "play its magic".

The rest I'm afraid is way above the poor rabbit's head : )

 

[Jimster41]

About the limiting scales : nothing fancy, just the observation that scaling behaviours in nature are always limited - in practice by the range of scales at which it is observed, and in theory by the range in which the relevant effects generating it are dominant or significant. Scaling in turbulent fluids limited below by the atomic scale, above by the system scale ; branching in growth is limited below by the elementary structure scale, above by some limit like gravity, a container, etc. - and these limits are no hindrance to such effects, there is no need for an effect to be valid at all scales for it to "play its magic".

The rest I'm afraid is way above the poor rabbit's head : )

That clarifies your statement for me. My confusion though is when the magic observed is across widely different scales, is that a meaningless coincidence (too rare to be meaningful) or is there a mathematical description that both have in common, regardless of the perceived physical domain of "cause"? I think that the research into emergence suggests there is and there there are lots of examples up and down the scale, and in time as well. (I know I need to support that statement, and not that this does, I am currently reading a book called "Sync" by a researcher named Steven Strogatz)

If there is a none too rare commonality to phenomena at widely different scales, then does the existence of that common description require explanation? I believe it does. Does it imply something physical? What else, if not, excluding pure anthropocentrism projection? And If that mechanism exists, by definition it has to operate in some scale invariant way. The fact that all the "magic" across all scales is not the same, meaning the universe is not just one big simple pattern but a collection of very diverse things, and, a lot of repeating patterns, suggests it is not continuously scale invariant, but would be consistent with a system built from a discrete-scale invariant mechanism.

Feel like I should apologize for veering off into personal theorizing, just can't help wondering aloud... And it fun to try and guess

 

[wabbit]

Maybe another thread would be a better place to discuss this, this is interesting but I'm afraid we're straying quite far from Conne's work here : )
Perhaps you could ask a mod to move these posts to a new thread ?