Topological Torsion, Negative Pressure and the Internal Energy
of a Nonequilibrium Fluid in 4D
The thermodynamic Internal Energy of a closed, nonequilibrium, rotating fluid
or gas can have a classical component related to potential energy and a
nonclassical component related to the spiral helicity density,
(v,curl v), of the gas dynamics. The existence of nonzero helicity density
is a topological property (of topological, not affine, torsion)
not found in isolated equilibrium thermodynamic systems.
Experimental Evidence indicates that Physical 3D space is not necessarily
Euclidean
Conventional physical dogma, justified by the local success of Newtonian
dynamics for particles, assigns a Euclidean metric with signature (plus, plus,
plus) to the three spatial dimensions. However, experimental evidence now
indicates that the intransitive, nonaffine, (rotational) dynamics of a fluid
admits a better description in terms of a 3 dimensional space with a Lorentz
metric of signature (plus, plus, minus), or a Majorana metric of signature
(minus, minus, plus). Three dimensional spaces with such nonEuclidean metric
signatures admit what mathematicians have described as maximal surfaces of zero
mean curvature, with conical or isolated singularities. The zero mean curvature
surfaces in Majorana space have negative Gauss curvature (similar to minimal
surfaces in Euclidean space), while the zero mean curvature surfaces in Lorentz
space have a positive Gauss curvature (in contrast to minimal surfaces in
Euclidean space). Falaco Solitons, easily created as topological defects in a
swimming pool, are claimed to be experimental artifacts of zero mean curvatures
surfaces immersed into 3D spaces of nonEuclidean metric. The topological
defects, in the otherwise flat surface of fluid density discontinuity, appear as
a pair of zero mean curvature surfaces, with a conical (dimple) singularity at
each end. The two conical singularities of the Falaco Soliton pair appear to be
connected with a 1D topological defect, or string under tension. The singular
conical points are associated with rotation (not translation) about a rotational
axis or "a fixed point", and are not mapped globally by affine transitive
transformations. In particular, the metric signature of 3D space with matter,
and its resultant dynamics, need not be Euclidean. These surfaces of zero mean
curvature, which are dominated by rotation, are generated by macroscopic
spinors.
A Topological Theory of the Physical Vacuum
This article examines how the physical presence of field energy and particulate
matter could influence the topological properties of space time. The theory is
developed in terms of vector and matrix equations of exterior differential
forms. The topological features and the dynamics of such exterior differential
systems are studied with respect to processes of continuous topological
evolution. The theory starts from the sole postulate that field properties of a
Physical Vacuum (a continuum) can be defined in terms of a vector space domain,
of maximal rank, infinitesimal neighborhoods, that supports a Basis Frame as a 4
x 4 matrix of C2 functions with nonzero determinant. The basis vectors of such
Basis Frames exhibit differential closure. The particle properties of the
Physical Vacuum are defined in terms of topological defects (or compliments) of
the field vector space defined by those points where the maximal rank, or
nonzero determinant, condition fails. The topological universality of a Basis
Frame over infinitesimal neighborhoods can be refined by particular choices of a
subgroup structure of the Basis Frame, [B]. It is remarkable that from such a
universal definition of a Physical Vacuum, specializations permit the deduction
of the field structures of all four forces, from gravity fields to Yang Mills
fields, and associate the origin of topological charge and topological spin to
the Affine torsion coefficients of the induced Cartan Connection matrix [C] of
1forms. grqc/0602118
The topological perspective of thermodynamics defines the 1form of Work as the
interior product of the process direction field V with the antisymmetric 2form
F = dA generated by the exterior derivative of the 1form of Action, A, used to
define the physical system. The eigenvectors of the 2form are either vectors
of eigenvalue zero, or isotropic complex Spinors (E. Cartan) of imaginary
eigenvalues. If the process is such that the Work 1form vanishes, then the
evolution is Hamiltonian, conservative, and composed of eigenvectors of zero
eigenvalue. If the 1form of Work is not zero, then the process must contain
spinor components. It follows that topological fluctuations in kinematics are
generated by processes that have spinor components.
coslab
Falaco Solitons as Cosmic Strings in a swimming pool. (COSLAB  Bilbao, Spain,
2003)
Vigier3
Cosmology as a turbulent non equilibrium van der Waals gas near its critical
point. (Vigier III Conference  Paris 2003) Euromech448 Falaco Solitons in a stratified Fluid (Euromech 448  Paris 2004)
AMS_ABQ
Non Equilibrium Thermodynamics  from the perspective of Continuous Topological
Evolution. (AMS meeting  Albuquerque USA 2004)
WMV
A movie (3.5 MB) demonstrating the creation and evolution of the topological
defects known as the Falaco Soliton. (Mazan, France 2004)
More detail can be found in the POD books referenced above
Finally, a new bifurcation mechanism explains the creation of Falaco
Solitons.
Cosmology from the point of view of nonequilibrium thermodynamics.
Yet could it be that there is a much simpler model that could
account for the various "features" of the "new" Universe? In this
article the idea is presented that the universe is a nonequilibrium
thermodynamic system with topological features of a universal van der
Waals gas.
The turbulent nonequilibrium thermodynamic cosmology of a real
gas near its critical point yields an explanation for:
1.The granularity of the night sky as exhibited by stars and galaxies.
2.The Newtonian law of gravitational attraction proportional to 1/rē.
3.The expansion and irreversible dissipation of the universe (4th order
curvature effects).
All of the above are deduced without explicit mention of the geometric
features of metric or connection!!"
