Three two-century-old problems and a senior citizen

Is there life after 70, one may ask? Is there a second wind for a septuagenarian? There might be, as I now attempt to introduce three old problems in physics and mathematics.

The first problem is considered a mathematical problem, although I view it more as a physics and engineering problem, the so-called Navier Stokes Equation (NSE), whose solution has eluded mathematicians for 200 years.  The equation is the fundamental basis of aerodynamics, blood flow and even high-energy collisions in the so-called quark-gluon plasma, produced by smashing heavy nuclei against each other. It was even proposed that there is no solution to it, although by now my existence proof for its solution stands unchallenged, but perhaps not understood. Could life go on without a universally accepted solution? Of course, mostly through brute force computer solutions, else progress in technology would be forever hampered. Airplanes, submarines and rockets do not await the solution, only an intellectual justification for a solution was missing. How did I find a solution? By starting with what is called a time-evolution equation (Institute for Advanced Study, Princeton) which then produced the solution. There was no frontal attack, as I said, one could solve NSE by not solving NSE directly.  Mathematicians are still puzzled by my solution, but the top four mathematicians in the field are aware of my solution. More tolerant physicists tacitly accept it and I am now applying it to practical problems, like climate modeling, demonstrating what I call an analytic speed up of modeling by orders of magnitude. There will be no wait for universal agreement as applications multiply.

The second problem is Loschmidt’s Paradox, also about 200 years old, the apparent contradiction between the reversibility of dynamical laws, and the nearly universal irreversibility of natural phenomena. There have been partial resolutions of the paradox, but my own resolution of the paradox appears rigorous, leading to a definitive conclusion: if the initial condition, or specification of givens, as students put it, contains an asymmetry in velocities — no matter how small — then the system is irreversible in time. If the initial data is symmetric in velocities, then the system is reversible. Of the two problems mentioned so far, a solution of the Navier-Stokes Equation, and Loschmidt’s Paradox, I regard the latter as more significant, to a philosophical point. The Navier-Stokes Equation solution is simply technical, even if it has more applications. But my resolution of the Loschmidt’s Paradox categorically proves that NSE is irreversible, that is, evolves only in one direction of time for most physical situations. The problem remains, interesting as well, what unique initial data results in reversible behavior?
The above studies have led me to ask: why is life irreversible? Could one extend conclusions from dynamical systems to life itself? This is a far more ambitious effort!

The third problem, as old as the Navier-Stokes Equation, is the origin of turbulence. For almost 200 years, it has been suggested that the problem of turbulence will be solved by finding irregular, chaotic, turbulent solutions of NSE. For as long as NSE was unsolved, this was a convenient way to postpone the resolution of the problem of turbulence. My solution of NSE contains no turbulence, every time-dependent variable is smooth and regular, as mathematicians describe it. Will turbulent solutions from NSE appear later? I doubt it. I have cultivated the view that turbulence is a quantum manifestation of matter, that when the internal degrees of freedom, such as molecular rotations, are awakened by internal or external energy, the fluid, that is the aggregate of molecules, becomes turbulent. There is no need for much of classical mathematics, it is enough to use quantum mechanics. Now quantum mechanics was developed only after the early 1900s. There was no way that continuum mechanics or the mechanics of classical gases and liquids, could ever come up with quantum mechanics. Traditional researchers of turbulence are not equipped to use quantum mechanics. It will require at least a generation of engineers trained in quantum mechanics to understand the quantum theory of turbulence, my third problem.

All three problems, NSE, Loschmidt’s Paradox and turbulence required my time evolution approach, the common thread in the resolution of the problems, but the quantum mechanical theory of turbulence could also use a lot of new theoretical and experimental concepts, for which I have written the Quantum Nature of Turbulence, and Quantum Theory of Turbulence, the latter in proof stage.

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Amador Muriel returned to academia after 25 years of European information technology consultancies, all the while pursuing a continuous personal program of research on turbulence. His research had been hosted intermittently at the Institute for Advanced Study in Princeton, Max Planck Institute for Complex Systems in Dresden, and CERN, Geneva. The consultancies were organized by his company, Data Transport Systems (DTS), then based in Geneva, Switzerland. At Harvard, he found an exact solution to the 3D Navier-Stokes Equation, invited as the inaugural paper of Results in Physics, 2  (2011). In addition to an exact solution of the Navier-Stokes Equation, he has resolved a generalized version of Loschmidt’s Paradox about irreversible phenomena and reversible dynamics, to be published by Physics Letters A in 2013. His latest works on the Navier-Stokes Equation show that turbulence will be difficult to explain classically. In any case, in the past three years he has shifted more attention to classical fluid flow because of the climate modeling uses of his exact solution. He may be reached at [email protected].