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The Ninth Course of the International School of Cosmology and
Gravita tion of the Ettore Majorana Centre for Scientific Culture
is concerned with "Topological Properties and Global Structure of
Space-Time." We consider this topic to possess great importance.
Our choice has also been influenced by the fact that there are many
quest ions as yet unre solved. Standard general relativity
describes space-time as a four-dimensional pseudo-Riemannian
manifold, but it does not prescribe its large-scale structure.
Inorderto attempt answers to some topological questions, such as
whether our universe is open or closed, whether it is orientable,
and whether it is complete or possesses singularities, various
theoretical approaches to global aspects of gravitational physics
are presented here. As topological questions playa role in
non-standard theories as weIl, it will be found that some of the
lectures and seminar talks in this volume adopt the point of view
of standard relativity, whereas others are based on different
theories, such as Kaluza-Klein theories, bimetric theories, and
supergravity. We have found it difficult to organize these papers
into classes, say standard and non-standard theory, or models with
and without singularities. One paper, by R. Reasenberg, is
experimental. Its purpose was to give the theorists present an
inkling of the opportunities, as weIl as the pitfalls, of
experimental research in gravitational physics. Accordingly, we
have arranged all contributions alphabetically, by first-named)
author."
For the Sixth Course of the International School of Cosmology and
Gravitation of the "Ettore Maj orana" Centre for Scientific Cul-
ture we choose as the principal topics torsion and supergravity,
because in our opinion it is one of the principal tasks of today's
theoretical physics to attempt to link together the theory of ele-
mentary particles and general relativity. Our aim was to delineate
the present status of the principal efforts directed toward this
end, and to explore possible directions of work in the near future.
Efforts to incorporate spin as a dynamic variable into the
foundations of the theory of gravitation were poineered by E.
Cartan, whose contributions to this problem go back half a century.
Accord- ing to A. Trautman this so-called Einstein-Cartan theory is
the sim- plest and most natural modification of Einstein's 1916
theory. F. Hehl has contributed a very detailed and comprehensive
analysis of this topic, original view of non-Riemannian space-time.
Characteristic of Einstein-Cartan theories is the enrichment of
Riemannian geometry by torsion, the non-symmetric part of the
otherwise metric-compatible affine connection. Torsion has a impact
on the theory of elementary particles. According to V. de Sabbata,
weak interactions can be based on the Einstein-Cartan geometry, in
that the Lagrangian describing weak interactions and torsion
inter-- action possess analogous structures, leading to a
unification of weak and gravitational forces.
In this XVII Course of the International School of Cosmology and
Gravitation devoted to "ADVANCES IN THE INTERPLAY BETWEEN QUANTUM
AND GRAVITY PHYSICS" we have considered different aspects of the
influence of gravity on quantum systems. In order to achieve this
aim, in many lectures, seminars and discussions we have
strengthened the interplay between gravity and quantum systems
starting from the situation in the early universe based on
astrophysical observations, up to the earthly based experiments
with atom interferometry for probing the structure of space-time.
Thus we have had timely lectures on the quantum field and horizon
of a black hole including reviews of the problem of black holes
thermodynamics and entropy, quantum information, quantum black
holes, quantum evaporation and Hawking radiation, recent advances
in stockastic gravity. We have also discussed quantum fluctuations
in inflationary universe, quantum effects and reheating after
inflation, and superplanckian energies in Hawking radiation. In
this regard the subject of spinors in purely affine space-time and
Dirac matter according to Weyl in the generalized theory of
gravitation were developed . The dualism between space-time and
matter has been deeply analyzed in order to see why, for general
relativity, this is an obstacle for quantization of the theory.
Also canonical Gravity and Mach's principle, torsion and curvature
as commutator for Quantum Gravity and Dirac Geometry of real
space-time were analysed, together with the problem of
5-Dimensional Projective Unified Field theory and Multidimensional
Gravity and Cosmology.
In this XVII Course of the International School of Cosmology and
Gravitation devoted to "ADVANCES IN THE INTERPLAY BETWEEN QUANTUM
AND GRAVITY PHYSICS" we have considered different aspects of the
influence of gravity on quantum systems. In order to achieve this
aim, in many lectures, seminars and discussions we have
strengthened the interplay between gravity and quantum systems
starting from the situation in the early universe based on
astrophysical observations, up to the earthly based experiments
with atom interferometry for probing the structure of space-time.
Thus we have had timely lectures on the quantum field and horizon
of a black hole including reviews of the problem of black holes
thermodynamics and entropy, quantum information, quantum black
holes, quantum evaporation and Hawking radiation, recent advances
in stockastic gravity. We have also discussed quantum fluctuations
in inflationary universe, quantum effects and reheating after
inflation, and superplanckian energies in Hawking radiation. In
this regard the subject of spinors in purely affine space-time and
Dirac matter according to Weyl in the generalized theory of
gravitation were developed . The dualism between space-time and
matter has been deeply analyzed in order to see why, for general
relativity, this is an obstacle for quantization of the theory.
Also canonical Gravity and Mach's principle, torsion and curvature
as commutator for Quantum Gravity and Dirac Geometry of real
space-time were analysed, together with the problem of
5-Dimensional Projective Unified Field theory and Multidimensional
Gravity and Cosmology.
The Ninth Course of the International School of Cosmology and
Gravita tion of the Ettore Majorana Centre for Scientific Culture
is concerned with "Topological Properties and Global Structure of
Space-Time." We consider this topic to possess great importance.
Our choice has also been influenced by the fact that there are many
quest ions as yet unre solved. Standard general relativity
describes space-time as a four-dimensional pseudo-Riemannian
manifold, but it does not prescribe its large-scale structure.
Inorderto attempt answers to some topological questions, such as
whether our universe is open or closed, whether it is orientable,
and whether it is complete or possesses singularities, various
theoretical approaches to global aspects of gravitational physics
are presented here. As topological questions playa role in
non-standard theories as weIl, it will be found that some of the
lectures and seminar talks in this volume adopt the point of view
of standard relativity, whereas others are based on different
theories, such as Kaluza-Klein theories, bimetric theories, and
supergravity. We have found it difficult to organize these papers
into classes, say standard and non-standard theory, or models with
and without singularities. One paper, by R. Reasenberg, is
experimental. Its purpose was to give the theorists present an
inkling of the opportunities, as weIl as the pitfalls, of
experimental research in gravitational physics. Accordingly, we
have arranged all contributions alphabetically, by first-named)
author."
Dort nun, bei den Helden, bei diesen wirklich vorbild- haften
Menschen erscheint uns das Interesse fur die Person, fur den Namen,
fur Gesiebt und Gebarde er- laubt und naturlich. H. Hesse, Das
Glasperlenspiei Im Jahre 1979 feiert die Welt den 100. Geburtstag
Albert Einsteins. Dies bietet Anlass zu einem Ruckblick auf sein
Leben und sein wissenschaft- liches Werk, zu einem uberblick uber
Einsteins Bedeutung fur unsere Zeit und zu einer Vorausschau auf
kommende Jahre naturwissenschaftlicher Entwicklung. Einstein war
zweifellos eine der Schlusselfiguren der Geistesgeschichte unseres
Jahrhunderts. Sein Einfluss auf Physik, Philosophie und Politik ist
unubersehbar. Eine der grossartigsten wissenschaftlichen Leistungen
unserer Zeit, die Schoepfung der allgemeinen Relativitatstheorie,
die wohl zugleich die Kroenung von Einsteins Lebenswerk bildet, hat
sich uns erst in den letzten Jahren in ihrer vollen Bedeutung fur
die Gesamtphysik erschlossen. Die Moeg- lichkeiten der
Weltraumforschung, die es uns gestatten, die Scheuklappen der
Erdatmosphare abzuwerfen und erstmals mit freiem Blick das All zu
er- forschen, haben zu bedeutenden neuen Erkenntnissen gefuhrt und
gezeigt, dass auch einige der weitreichendsten Folgerungen aus der
Einsteinschen Theorie der uberprufung standhalten. Die allgemeine
Relativitatstheorie, die bis vor kurzem in ihrer mathematischen
Schwierigkeit und Komplexitat ein Aussenseiter unter den
physikalischen Theorien war, erweist sich aber auch immer mehr zu
einem Vorbild, nach dem nunmehr auch Theorien der
Elementarteilchenphysik und sogar der Festkoerperphysik gestaltet
werden. Mit der Herausgabe dieses Bandes haben wir uns die Aufgabe
gestellt, Einsteins Einfluss auf das Denken des 20. Jahrhunderts
anhand von Beitragen namhafter Wissenschaftler aufzuzeigen.
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