Waves At Very Different Scales, QFT, and Rare Events

[ Follow Ups ] [ Post Followup ] [ String and M Theory Duality IX ] [ FAQ ]

Posted by OsherDoctorow on April 01, 2003 at 17:25:23:

Professor George Papanicolaou of Stanford University Mathematics Department was interviewed by ScienceWatch, the interview entitled "Stanford University's George Papnicolaou Seeks Order in Turbulence," http://www.sciencewatch.com/interviews/george_papanicolaou.htm, the interview apparently in 2002 since the article concludes "Copyright 2002". He moved to Stanford in 1993 from the Institute for Advanced Study in Princeton.

He cites 2 key problems: 1. making numerical calculations that straddle many scales, and 2. chaos. His interest in the two problems derives from the study of turbulence, which Feynman regarded as the last great unsolved problem in classical physics but which is stil relatively not understood because of its lack of separation of scales, having to deal with many scales of irregularities, as wel as its nonlinearity, chaos, stochastic properties.

I am at the point in my probabilistic-statistical development of Rare Event Theory where I am asking myself some similar questions to Professor Papnicolaou but in relation to string/brane/M/duality theory and QFT and QM.

Is it possible for extremely widely separated scales like macroscopic astronomical or macroscopic human and quantum microscopic to yield results which are perceived by any observer within the larger scale universe or half-universe or sector as discrete even though they are "really" continuous in the perception of the smaller scale regime observer?

If I hadn't seen the Papanicolaou interview, I made have hesitated to once again bring up this question because I thought that pure physicists might know more about it than me. Maybe they do. But I suspect that they don't. Interestingly, the good Professor was director of the Division of Wave Propagation and Applied Mathematics at Courant Institute of NYU 1979-1990 (and has about 150 publications, which is not quite that relevant).

The field of very different (wave) scales is quite alive and well; for example, Kolmogorov's "five-thirds law" is still being investigated (it is actually a conjecture) actively in turbulence, chaos is related to the onset of turbulence, the renormalization group method of Kenneth Wilson at Cornell tried to deal with many scales interacting simultaneously but so far has only been understood for toy problems. One of Prof P's (I'll abbreviate his name for brevity) interesting points is that for turbulent flow around an airplane, to this day people mostly resort to entirely empirical theories (heuristic) with much fine tuning.

Another interesting question in relation to superstringtheory.com is whether it is merely the macroscopic measurement/observation/empirical "evidence" that comes out discrete or the actual interaction or "osmosis" (one-sided) from microscopic to macroscopic that is discrete even though inside the microscopic the regime is continuous. Or does it matter? Actually, it matters very much (see below).

Jerry Iuliano's recent posting to me which showed some incredible "coincidences" among Feigenbaum and chaos-to-order phase transitions and the Cheops construct and the fine structure constant has inspired an idea for me: suppose that the solar flares were "viewed" by ants under the surface of the earth in their hives, which have finite number of holes. They would get rather indirect viewing unless they were under the holes directly, but the idea can be extended to indicate that they could well conclude that discrete processes were involved rather than a continuous plasma body called the Sun. But what the ants receive from the Sun depends very much on the continuous plasma nature of the Sun. If the Sun were a bunch of discrete objects even on the macroscopic scale, something quite different could well occur.

Still, it is worth studying QM and QFT and trying to make sense of them from the viewpoint of Rare Events and some parts of Fairly Frequent and Very Frequent Events, and seeing whether we can fill in the holes with Knowledge.
But we should also proceed separately into Rare Events at full speed. A matter of different scales, you know.