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1997

THE ADAMANTINE AETHER

David Ritz Finkelstein

[TeX][Postscript]

Abstract:

We describe the vacuum as a crystalline hierarchy of creations and
annihilations, without the usual underlying absolute set of spacetime points.
What goes on in nature according to this theory is the generation of quantum
spacetime points out of their immediate predecessors. The causal connections
among points are just their family tree: Topology is genealogy. The physical
fields and quanta are smoothed descriptions of these connections or of their
departure from the vacuum mode, ripples on the face of the vacuum. A
hypercubic unit cell provides the correct spacetime symmetries with the
correct internal quark symmetries. Thought experiments suggest that the main
limit to the precision of spacetime coordinates is a Compton time, not the
Planck time. This makes room for the fundamental quantum of time to appear at
presently accessible energies.

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REALIZATIONS OF CAUSAL MANIFOLDS BY QUANTUM FIELDS

Heinrich Saller

[TeX][Postscript]

Abstract:

Quantum mechanical operators and quantum fields are interpreted as
realizations of timespace manifolds. Such causal manifolds are parametrized
by the classes of the positive unitary operations in all complex operations,
i.e. by the homogenous spaces D(n)=GL(C^n_R)/U(n) with n=1 for mechanics and
n=2 for relativistic fields. The rank n gives the number of both the discrete
and continuous invariants used in the harmonic analysis, i.e. two
characteristic masses in the relativistic case. 'Canonical' field theories
with the familiar divergencies are inappropriate realizations of the real
4-dimensional causal manifold D(2). Faithful timespace realizations do not
lead to divergencies. In general they are reducible, but nondecomposable - in
addition to representations with eigenvectors (states, particle) they
incorporate principal vectors without a particle (eigenvector) basis as
exemplified by the Coulomb field.

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TOPOLOGY AT THE PLANCK LENGTH

John Madore, L.A. Saeger

[TeX][Postscript]

Abstract:

A basic arbitrariness in the determination of the topology of a manifold at
the Planck length is discussed. An explicit example is given of a "smooth"
change in topology from the 2-sphere to the 2-torus through a sequence of
noncommuting geometries. Applications are considered to the theory of
D-branes within the context of the proposed M(atrix) theory.

�

1996

BENEATH GAUGE

David Ritz Finkelstein, Heinrich Saller, and Zhong Tang

[TeX][Postscript]

Abstract:

Seeking a relativistic quantum infrastructure for gauge physics, we analyze
spacetime into three levels of quantum aggregation analogous to atoms, bonds
and crystals. Quantum spacetime points with no extension make up more complex
link units with microscopic extension, which make up networks with
macroscopic extension. Such a multilevel quantum theory implies
parastatistics for the lowest level entities without additional physical
assumptions. Any hypercubical vacuum mode with off-diagonal long-range order
that is covariant under POINCARE also has bonus internal symmetries somewhat
like those of the standard model. A vacuum made with the dipole link proposed
earlier has too much symmetry. A quadrupole link solves this problem.

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HYPERCRYSTALLINE VACUA

David Ritz Finkelstein, Heinrich Saller, and Zhong Tang

[TeX][Postscript]

Abstract:

Let a quantum network be a Fermi-Dirac assembly of Fermi-Dirac assemblies
of...of quantum points, interpreted topologically. The simplest
quantum-network vacuum modes with exact conservation of relativistic
energy-momentum and angular momentum also support the local non-Abelian
groups of the standard model, torsion and gravity. The spacetime points of
these models naturally obey parastatistics. We construct a left-handed vacuum
network among others.

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QUANTUM RELATIVITY

David Ritz Finkelstein

Summary:

The author presents a simple algebraic quantum language sharpening and
deepening that of Bohr, Heisenberg, and von Neumann, with its own
epistemology, modal structure, and connectives. The core of the language is
the semigroup of physical actions. The work extends quantum algebra from
first-order to higher-order propositions, classes and actions; from positive
to indefinite metrics; and from quantum systems to quantum sets, quantum
semigroups, and quantum groups. The author applies the extended quantum
theory to a spacetime structure, which was taken as a fixed part of the
classical framework of the original quantum theory. This leads to a simple
proposal connecting the internal variables of spin, color, and isospin with
the fine structure of spacetime.

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Koberlein. Contents and Images of submitted papers are copyright via their
respective authors. Contents and Images of Webpages �1997 Louisburg College

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