Elihu Lubkin is widely known for his early (1963) paper in
which the earliest generalization of Dirac's magnetic monopole to other gauge
fields (Yang-Mills, gravity), appears. This and a subsequent paper are among the
first to describe the geometrical nature of Yang-Mills theory -- a theory built
from a connection on a fiber bundle. Motivating much of Lubkin's work is the
task of interpreting quantum mechanics, and it has led him to several roughly
distinct lines of resarch. One, in some ways parallel to current work on
decoherence, is a study of the entropy of an n-dimensional subsystem of a pure
state. A second involves the Everett multi-world interpretation. Lubkin
independently conceived a similar viewpoint, and a more recent version can be
found in his condensed book, "Schrödinger's Cat" (International Journal of
Theoretical Physics, 1979). Lubkin's strikingly original suggestion of an
experiment based on the Necker cube may well be the forerunner of experimental
attempts to detect a quantum component of consciousness. A third line of
research involves an attack on superselection rules; an assault in progress
couples quantum mechanics based on real and complex Hilbert spaces, to chip at
the invisibility of a phase factor.
Professor Lubkin has also been working on
the extension of statistical mechanics to noncommuting observables. This has
developed into a blend of thermodynamics and matrix mechanics, "physics without
time". His solution -- entropy of erasure -- to "where the entropy of
measurement goes when the outcome is known", may help in the ontology of
physics. His extension of the tests of quantum mechanics ("extraneous tests,
b-plexes"), parallel to the density-matrix extension of the wave function, dates
from the 1970's. He is eager to form an ontological group, dealing with quantal
theory of measurement. Lubkin's interest in thermodynamics includes a piece
(1987) on self-adsorption and possible negative entropy, for fluid-fluid
boundaries, and others (1993, 1997) on "heat without heat"': how quantum
mechanics supports the second law of thermodynamics with a new kind of
semipermeable membrane for isolating systems thermodynamically yet not
mechanically.
