MINNOWBROOK SYMPOSIUM  ON   THE STRUCTURE OF SPACE-TIME  MAY 28 - 31, 1999  to maps  Phone Numbers

 
 Organizing Committee:                                                Advisory Committee:
 

Mark Bowick  Don Marolf  Kameshwar Wali (Chair)	Abhay Ashtekar  Giovanni Landi  Alain Connes  Fedele Lizzi  Ali Chamseddine Rafael Sorkin

Opening Remarks - Kamesh Wali

Session I    9:30 AM - 1:00 PM
Relativists' View of Space-time
Moderator:  Jurgen Ehlers

(9:30 AM - 10:30 AM)
John Stachel
Generally covariant space-times: What is the point?

I will review the various space-time structures associated with Galileian, Minkowskian, generally non-relativistic and generally relativistic theories, and show why generally covariant space-times are fundamentally different from their predecessors (hole argument). this difference puts into question the usual starting point of space-time theories: a fixed manifold composed of distinguishable points. I will show that this basic feature of generally covariant theories does not depend on the presence of a differentiable or even a topological structure, but can be generalized to any set subject to certain relations. Some proposals to use mathematical structures that do not start with point sets to describe space-time structures will be reviewed.

(10:30 AM - 11:30 AM)
Ted Newman
Characteristic Surfaces and General Relativity

The general theory of relativity (GR), a theory of the geometry of physical space-tine, is usually (or at least often) considered as a classical field theory with the basic field being the (pseudo-Riemannian) metric tensor along with its associated connection field and curvature tensor with many similarities (e.g. a Cauchy evolution) to that of most field theories. In this work we will present an alternate point of view or reformulation of GR (with new variables) that appears not to have any analogous reformulation in other field theories. In this reformulation, the fundamental variables are families of surfaces and a scalar function; the standard variables, i.e., the metric tensor, etc., now become derived concepts. These surfaces, which are described by partial differential equation, become the characteristic surfaces of a conformal metric which is obtained directly from the surfaces themselves. The scalar function is a conformal factor turning the conformal metric into an Einstein metric. We emphasize that though, neither the presentation nor the final equations resemble the standard version of GR, the final results are identical to GR.

We briefly mention several technical difficulties working with these equations and then speculate on their usefulness in both "practical" problems and in fundamental issues.

11:30 AM - 12:00 Noon
Break

(12:00 Noon - 1:00 PM)
Roger Penrose
Quantum State Reduction as a Gravitational Phenomenon: Theory and Experiment

The problem of quantum state-vector reduction is addressed in many different ways by the various schools of thought in quantum mechanics. To support my own particular viewpoint that reduction is an actual fundamental conflict between the basic principles of general relativity and those of quantum mechanics. This leads to the conclusion that a quantum superposition - i.e. a "Schrodinger's cat" - is unstable and will decay into one or the other of the two states in quantum superposition in a period of time that can be calculated from the gravitational energies involved. For a real cat, this time would be a tiny fraction of a second, which is why we do not actually see quantum-superposed Schrodinger's cats. But for a small enough object, like a very small crystal, this predicted effect should be measurable. A specific space-based experiment to detect this effect (now being actively investigated) will be described. Some recent theoretical developments will also be presented.

1:30 PM
Lunch

Session II    4:00 PM - 6:30 PM
Lessons from Blackhole Thermodynamics
Moderator:  John Madore

(4:00 PM - 5:00 PM)
Ted Jacobson
Entropy and Gravity: horizons, entanglement and the holographic bound

This talk is intended to provide an overview of some results and open questions concerning the meaning of black hole entropy and the nature of the holographic bound on the entropy contained within a surface of given area. In particular I will address issues such as the role of internal states, entanglement, species independence, renormalization of G, the hoop conjecture, the second law, and the thermodynamic derivation of the Einstein equation from the proportionality of area and entropy.

5:00 PM - 5:30 PM
Break

(5:30 PM - 6:30 PM)
Robert Wald
Issues in Black Hole Thermodynamics

The validity of the laws of classical black hole mechanics, the existence of the Hawking effect, and the apparent validity of the generalized second law of thermodynamics have established beyond any reasonable doubt that a deep relationship exists between black holes and thermodynamics. Yet, some major issues remain unresolved, such as whether the entropy of a black hole should be viewed as "residing" in its deep interior, on its horizon, or in its "thermal atmosphere". I will review some of the main established results in black hole thermodynamics and discuss some of the open issues.

7:00 PM
Dinner

Session III    8:30 PM - 10:30 PM
Panel Discussion:
(To include the day's sessions and other pertinent topics)
Moderator:  Lee Smolin
Amanda Peet, Don Marolf, Holger Nielsen, David Lowe
 

SATURDAY, MAY 29, 1999

Session IV     9:00 AM - 12:30 PM
String Theory and String Theorists' View of Space-time
Moderator:  Donald Marolf

(9:00 AM - 10:00 AM)
Joseph Polchinski
Field Theory / String Theory Duality and Spacetime

The recent Maldacena and Matrix Theory dualities, between various field theories and string theory, have given for the first time a nonperturbative formulation of string theory.  I review these developments, with particular attention to the nature of spacetime.

(10:00 AM - 11:00 AM)
Brian Greene
Some Reflections on Spacetime from String Theory

Although Riemannian geometry is a powerful framework for analyzing classical properties of spacetime on large distance scales, a quantum mechanical formulation of gravity in the context of string theory shows that new geometrical ideas must be incorporated. Over the past few years, research has shown that some of these new ideas involve various dualities, mirror symmetry, topology change, and non-commutative geometry. Together, these geometrical structures are part of the evolving discipline of "quantum geometry" or "stringy geometry". In this talk, I will discuss some of these developments in quantum geometry, highlight some of their physical and mathematical implications, and indicate our current state of understanding.

11:00 AM - 11:30 AM
Break

(11:30 AM - 12:30 PM)
Michael Douglas
D-Geometry, Matrix theory and Noncommutative Geometry

Our understanding of the nature of space-time in M theory is best likened to the proverbial blind men studying an elephant. In this talk we survey a more recently developed aspect -- the nature of space-time as seen by D-branes.
 
 

1:00 PM
Lunch (and a visit to the Adirondack Museum}

Session V   4:00 PM - 6:30 PM
Quantum Geometry
Moderator:  J. Wess

(4:00 PM - 5:00 PM)
Abhay Ashtekar
Glimpses of quantum geometry

Features of quantum geometry will be illustrated through examples. Specifically, we will consider: i) Einstein-Maxwell theory in 2+1 dimensions; and, ii) quantum geometry of black hole horizons in 3+1 dimensions. In the first case, one can completely solve the model, write the quantum metric operator and analyze its properties. The analysis brings out some unforeseen limitations of the classical and semi-classical theory. In the second case, the horizon geometry is captured by the quantum Chern-Simons theory on a punctured 2-sphere. These states account for the black hole entropy.  The horizon resembles a ``pinned balloon''. At each puncture there is an effective deficit angle and all these angles add up to 4?.  Both treatments are non-perturbative and quantum effects are associated with "Coulmobic'' rather than "radiative'' modes of the gravitational field.

5:00 PM - 5:30 PM
Break

5:30 PM - 6:30 PM
John Baez
Spin networks, spin foams, and quantum gravity

A spin network is a graph with edges labeled by representations of some group and vertices labeled by intertwining operators. Thanks in part to the introduction of spin network techniques, we now have a mathematically rigorous and intuitively compelling picture of the kinematical aspects of loop quantum gravity. Indeed, since spin networks form a convenient basis of kinematical states, they have largely replaced collections of loops as our basic model for 'quantum 3-geometries'. But to better understand the dynamical aspects of quantum gravity, we would also like a model for 'quantum 4-geometries'. In other words, we want a truly quantum-mechanical description of the geometry of spacetime. Recently the notion of 'spin foam' has emerged as an interesting candidate. A spin foam is a 2-dimensional cell complex with faces labeled by representations and edges labeled by intertwining operators; generically, any slice of a spin foam gives a spin network.

7:30 PM
Gala Dinner
Remarks by Eric A. Schiff
Chair, Syracuse University Department of Physics
 
 

SUNDAY, MAY 30, 1999

Session VI    9:00 AM - 12:30 PM
Non-Commutative Geometry
Moderator:  Arthur Jaffe

(9:00 AM - 10:00 AM)
Alain Connes
Space-time from a Non-Commutative Geometric Point of View

(10:00 AM - 11:00 AM)
Ali Chamseddine
Noncommutative Geometry and the Spectral Action

The relevance of noncommutative geometry to physical problems is
reveiwed. Examples of noncommutative spaces such as those appearing in
the standard model and string theory are given. The spectral action principle for noncommutative spaces is proposed. It is shown that when this principle is applied to the standard model,
internal symmetries are merged with space-time symmetry unifying gravity with the other forces.

11:00 AM - 11:30 AM
Break

(11:30 AM- 12:30 PM)
Dirk Kreimer
Hopf Algebra Structures in Radiative Corrections and Noncommutative Geometry

This talk will discuss recent developments in perturbative Quantum Field Theory, which show that theories as familiar as ordinary QED reveal a Hopf algebra governing their renormalization, which in turn is related to the Hopf algebra structure of diffemorphisms in the context of NCG.

1:00 PM
Lunch
 

Session VII    3:00 PM - 6:30 PM
Discrete Space-time
Moderator:  Mark Bowick

(3:00 PM - 4:00 PM)
Klaus Fredenhagen
Uncertainty relations for coordinates of space-time events, and noncommutative geometry

Fundamental physical principles imply some deviation from a smooth structure of space-time at small scales. These deviations can be modeled by a noncommutative space. Attempts for a formulation of physical laws on a fuzzy space time are discussed.

(4:00 PM - 5:00 PM)
Rafael Sorkin
A causal set dynamics of sequential growth

Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively accessible "half way house" to full quantum gravity that possibly contains the latter's classical limit (general relativity). Because they can be expressed in terms of state models for an assembly of Ising spins living on the relations of the causal set, these theories also illustrate how non-gravitational matter can arise dynamically from the causal set without having to be built in at the fundamental level.

5:00 PM - 5:30 PM
Break

(5:30 PM - 6:30 PM)
David Finkelstein
Spin, Statistics and Space-time Structure

Below the quark scale space-time, matter, measurement and the dynamical law can no longer be separated operationally but fuse into one variable, which we call the dynamic D of the system. D can be considered as an atomized and unified generalization of the s matrix. D acts on a composite of space-time-dynamic elements --chronons for short -- whose statistics is crucial. Each of the classical groups generates a unique natural quantum statistics. A groups generate Fermi-dirac statistics; C Bose-Einstein; and B and D, the newer Schur-Wilczek statistics, where the individual is described in a quadratic space and the composite in its spinor space. Of these on S-W is 2-valued and gives rise to spinors, so we infer that chronons have S-W statistics. This implies a large Clifford algebra Cliff(N₊, N_-)  of possible dynamics with one Clifford unit for each chronon, representing permutations. Now swaps are basic, not creation and annihilation or spin. The dynamic is maximally described by one element from which both space-time and the usual fields are to be constructed in the limit  . This theory links the period 8 of the chessboard of Clifford algebras to the dimension 4 of space-time, and accounts for the apparent Maxwell-Boltzman statistics of classical space-time points. Earlier we suggested that spin and statistics are correlated because  rotation is homotopic to a swap. Now they are correlated because rotations are swaps.

7:00 PM
Dinner

Session VIII    8:30 PM -
Panel Discussion
Moderator: Carlo Rovelli
Ctirad Klimcik, Renata Kallosh, Daniel Kastler, Eli Hawkins
 
 

There will be a phone number in your room or lodge, and during the conference
you can be reached at the following numbers:
        Main Lodge      518-352-7212
        Kitchen           518-352-7200
        Classroom        518-352-7209
        Fax                 518-352-7602

Penny Davis  315-443-5960
Kamesh Wali  315-443-9113  (home: 315-637-5978)
 
 
 

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