The Metafluid Dynamics

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This article intends to present the history, the definition, and the philosophical perspective of metafluid dynamics. It does not aim to provide detailed technical information; the latter can be found in the references to the scientific literature, which are provided as HTML links or in-line, Harvard style, references. It is written without adopting any position with regard to the merits, or otherwise, of the theory. Its purpose is to summarize the little progress that has been achieved in the last decade and the possibilities that lie ahead based on published scientific work.

If you notice any omissions or errors, please, do not hesitate to contact me (marmanis at computer dot org).

[edit] Brief history

The term metafluid dynamics appeared for the first time in a conference talk that the author delivered in the "International Symposium on Theoretical and Computational Fluid Dynamics" in Florida State University on November 7, 1996. This particular symposium was organized in honor of Sir James Lighthill, it was a tribute to his monumental contributions to applied mathematics and, in particular, to fluid mechanics. Sir James Lighthill enjoyed the following quote (Debnath 1999)

“... as Sir Cyril Hinshelwood has observed ... fluid dynamicists were divided into hydraulic engineers who observed things that could not be explained and mathematicians who explained things that could not be observed.”

It is hard to imagine a better occasion for presenting a new theory that is related to fluid dynamics than a panel that was composed by some of the most distinguished fluid dynamicists in the late 20th century.

The theory was published, in the [1]Physics of Fluids under the title Analogy between the Navier-Stokes and Maxwell's equations: Application to Turbulence (Marmanis 1998). A year later, the theory was presented in more detail in the thesis entitled Analogy between the Electromagnetic and Hydrodynamic Equations: Application to Turbulence (Marmanis 1999).

The last article by the same author, namely, Turbulence, electromagnetism, and quantum mechanics: A common perspective was published in the book "Photon: Old problems in light of new ideas" (Dvoeglazov 2000). The latter paper was an attempt to introduce a deeper, ontological, connection between the dynamics of fluids in turbulent motion, as described by the model of the Navier-Stokes, and the dynamics of the electromagnetic field, as described by the Maxwell equations. In other words, it was proposed that the dynamics of the electromagnetic field is highly non-linear when expressed in terms of the electromagnetic potentials -- Maxwell's equations being linear only due to the original modeling of charge and current. It should be stressed that this particular ontological interpretation has never been published in the past, although several fluid models have been presented as early as 1890, for the same purpose.

The metafluid dynamics was not created by trial-and-error of mechanical models of aether and is not an analogy that was revived; a mere juxtaposition of the fields that are involved in earlier models and those that are involved in the metafluid dynamics suffices as a proof. For historical references, see, the book by Whittaker (1951) which is as comprehensive as it is authoritative. The origin of metafluid dynamics was an effort to connect the ephemeral and statistical nature of quantum mechanical objects with the temporary and statistical, but yet stable, nature of "structures" in turbulent flows; that work was published as a research thesis (Marmanis 1993). Thus, the works that influenced more its conception were Einstein's insistence on a causal interpretation of quantum mechanics, De Broglie's mechanical models, and related work along these lines. The vast literature on the subject of aether models was discovered by the author upon completion of the theory's core ideas; during the academic years 1994 and 1995.

Since that time there have been several other publications that relate directly or indirectly to the metafluid dynamics. This article will refer only to those publications that are generalizations, extensions, or otherwise directly related to metafluid dynamics.

In 1999, R.M. Kirby, H. Marmanis and D.H. Laidlaw presented the first visualizations of turbulent charge -- the analog of the electric charge in electromagnetism -- in a conference paper entitled ``Visualizing Multivalued Data from 2D Incompressible Flows Using Concepts from Painting.

In 2000, A. C. R. Mendes, W. Oliveira and F.I. Takakura presented hydrodynamic turbulence as a constrained system from the point of view of metafluid dynamics in Turbulence as a constrained system. This is the first Lagrangian description of metafluid dynamics that the author is aware of.

In 2001, G. Rousseaux discussed the question of completeness for Maxwell's equations in "Les équations de Maxwell sont-elles incomplètes?" and the position of the metafluid dynamics on that matter.

In 2002, G. Rousseaux and É. Guyon presented a review of the metafluid dynamics in the paper À propos d’une analogie entre la mécanique des fluides et l’électromagnétisme.

In 2003, A. C. R. Mendes, C. Neves, W. Oliveira and F.I. Takakura presented the metafluid dynamics as a gauge field theory.

In 2003, L. Saul presented a kinetic theory of a space-time model that is endowed with spin. In that context, by following the analogy that forms the core of metafluid dynamics, the author shows how to derive (to first order) Maxwell’s equations of electromagnetism and Schrödinger’s equation for the electron.

In 2004, D. Bǎleanu presented the metafluid dynamics as a constrained system within fractional Riemann-Liouville derivatives.

In 2005, A. C. R. Mendes, C. Neves, W. Oliveira and F.I. Takakura applied the Dirac’s quantization to the metafluid dynamics on NC spaces.

In 2005, D. Bǎleanu published the "Metafluid dynamics and Hamilton-Jacobi formalism" and the existence of the hidden gauge symmetry was analyzed. The main point of this work is that the obtained results are in agreement with those of the Faddeev-Jackiw approach.

In 2005, Z. Akdeniz, P. Vignolo and M.P. Tosi published the paper "Shell structure in the density profile of a rotating gas of spin-polarized fermions". The authors of that paper study a Fermi gas of spin-polarized charged particles in a uniform magnetic field, under conditions such that the Coulomb interactions can be neglected, can be mapped into a rotating Fermi gas of neutral atomic particles in a state of complete spin polarization, where the atom-atom interactions are negligible on account of the Pauli principle suppressing s-wave scattering. The interesting part here is that the authors invoke the metafluid dynamics correspondence to establish the map.

In the historical context of turbulence research, or the historical context of a mechanical model of aether, the metafluid dynamics is in an embryonic stage.

[edit] References

Bǎleanu D. Czechoslovak Journal of Physics,Vol. 54, No. 11 (2004) pp. 1165-1170

Bǎleanu D. Czechoslovak Journal of Physics,Vol. 55, No. 4 (2005) pp. 473 - 478

Debnath L. Internat. J. Math. & Math. Sci., Vol. 22, No. 4 (1999) pp. 667–688

Marmanis H. On the nature of turbulence in the equilibrium range, Technical Report, Institute de Mecanique des Fluides de Toulouse (IMFT), France, (1993)

Marmanis, H. Phys. Fluids Vol. 10, No. 6, pp. 1428-1437

Marmanis H. Analogy between the Electromagnetic and Hydrodynamic Equations: Application to Turbulence, Ph.D. Thesis, Brown University (1999)

Marmanis, H. Photons: Old problems in light of new ideas, Ed. V.V. Dvoeglazov, Nova Science Publications (2000)

Mendes A.C.R., Oliveira W. and Takakura F.I. (2000) [2]

Mendes A.C.R., Neves C., Oliveira W. and Takakura F.I. Braz. J. Phys. Vol.33, No. 2 (2003)

Mendes A.C.R., Neves C., Oliveira W. and Takakura F.I. (2005) [3]

Saul, L. Spin Waves as Metric in a Kinetic Space-Time Physics Letters A 314 (2003) pp. 472–478