Saturday June 12 2004 till Saturday June 19 2004
   

In a 1957 article, Hugh Everett III proposed that the foundation of quantum mechanics be regarded as providing a description of reality in exactly the same sense as the formation of classical mechanics was thought to do. A brief account will be given of the “many-worlds” picture to which this view leads and of the way it dovetails with the more recent “consistent-histories” interpretation, leading to an understanding of how the familiar “classical” world emerges.

Bryce S. DeWitt (1923-2004),

University of Texas, 

Austin:

The classical action, S of a system, or its Hamiltonian, H are usually the starting point of its quantization.There is another less known, but powerful method, which begins with a set of vector fields on a manifold. The key steps of the method are:

1.Identifying the manifold and the set of vector fields dictated by the system.

2.Constructing the corresponding functional integral.

3.Writing down the Schroedinger equation satisfied by the functional integral.Reading off the Hamiltonian.

4.The semiclassical approximation of the functional integral yields the classical action function.

There is a straightforward blue print for steps 2, 3, and 4, which will be presented briefly.Choosing the dynamical vector fields is an art, similar to the art of choosing the action dictated by the system.Two non-trivial examples of dynamical vector fields will be given - possibly three if time permits.

Elliot Lieb, 

Princeton University:

The relativistic "no pair" model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A - in the Coulomb gauge.There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, , of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, , of fixed nuclei with charges . If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground state energy ) if one uses the customary D(0) to definethe electron space, but is stable () if one uses D(A) itself (provided the fine structure constant and are not too large). This result is extended to quantized fields here, and stability is proved for and . This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons.This is joint work with Michael Loss.

John L. Challifour,

Indiana University:

The quantization of gauge theories using a local, covariant gauge field requires an indefinite metric and subsequent loss of Osterwalder-Schrader positivity on the Euclidean Hilbert space. For the case of Chern-Simons theories, it is shown how to define the Osterwalder-Schrader map, the Wightman-Garding framework and a positive, selfadjoint semigroup starting with a Euclidean framework. 

David Batchelor,

NASA Goddard Space Flight Center:

Heisenberg's Uncertainty Principle determines the lifetimes of the antiparticle pairs that arise in vacuum fluctuations. This presentation describes semiclassical models for the dynamics of these two-body systems (electron-positron, quark-antiquark, and the other elementary massive particles). The models yield pair lifetimes that equal the Heisenberg lifetimes, to good approximation in most cases.The success of the models at predicting Heisenberg's pair lifetimes enables us to derive good approximations for the unit of charge 'e' and the QCD coupling parameter . The author concludes that Heisenberg's Uncertainty Principle governs the strengths of the two strongest forces (the electromagnetic force and the QCD color force).Full details may be found in the author's paper in Foundations of Physics,v. 32, no. 1, pp. 51-76 (2002).

Netsivi Ben-Amots,

Haifa, Israel:

We give a relativistic treatment to the dynamics of spherical bodies rotating at very high speed. It is found that most of the mass of a homogeneous spherical quark with Franklin rotation, is due to the relativistic increase of the mass.

This paper deals with a relativistic theory of gravitation based on the assumption of variable rest mass, and explores some implications.

Amos Harpaz ,

Israel:

The equation of motion (EOM) for an electric charge includes a third time derivative of the position. Usually, an EOM includes only the second derivative of the position, which demands two initial conditions for the solution of the equation. The presence of the third time derivative in this EOM raised the question, what third initial condition should be implied, and why this EOM is different from the regular EOMs in classical mechanics.

We find that the third initial condition needed to complement the solution is the initial acceleration, which determines the stress force in the curved electric field of the accelerated charge, and this is why the third time derivative of the position appears in the EOM of a charged particle. This stress force acts as a reaction force on the accelerated charge, and the work done by the accelerating (external) force in overcoming this reaction force is the source of the energy carried by the radiation. The existence of this reaction force also solves the "energy balance paradox" that bothered physicists for a long time. 

The stress force density is given by:, where E is the electric field of the charge, and is the radius of curvature of the electric field. It is found that for the simple case of a charge accelerated in a hyperbolic motion, the radius of curvature is given by: , where is the acceleration of the charge and is the angle between the direction of motion and the initial direction of the field line. We consider as the characteristic radius of curvature of this motion, and it is clear that the acceleration plays a crucial role in determining the radius of curvature of the electric field of an accelerated charge in any accelerated motion. Hence the initial value of the acceleration is needed to define the parameters of the motion, and the appearance of the third derivative of the position in the EOM is not a sad accident, but a legal requirement. 

The situation described here resembles the situation in which a charge is supported at rest in a gravitational field. The electric field of the charge falls in a free fall in the gravitational field, the electric field is curved, and the expression for the radius of curvature of the electric field includes , which is the gravitational acceleration that characterizes the gravitational field.

J. Brian Pitts,

St. Edward’s University, Austin, Texas:

If Einstein's equations are to describe a field theory of gravity in special relativity, then the curved metric must respect the flat background metric's null cone.We give a kinematic description of the problem using a generalized eigenvector formalism based on the Segre’ classification of symmetric rank 2 tensors with respect to a Lorentzian metric.Using the naive gauge freedom, plausibly one can enforce the proper null cone relationship by restricting the configuration space.Gauge transformations do not form a group, but rather a groupoid.The flat metric guarantees global hyperbolicity, which dissolves the Hawking black hole information loss paradox.

Matej Pavsic,

Josef Stefan Institute, 

Ljubljana, Slovenia:

A space (in particular, spacetime) consists of points (events). But besides points there are also lines, surfaces, volumes, etc… Description of such geometric objects has turned out to be very elegant if one employs multi-vectors, which are the outer products of vectors. All those objects are elements of Clifford algebra. Since in physics we do not consider point particles only, but also extended objects, it appears natural to consider Clifford algebra as an arena in which physics takes place. Instead of spacetime we thus consider a more general space, the so called, Clifford manifold or C-space.

This is a space of the oriented r+1-dimensional areas enclosed by r-loops. We show that the extended objects can be described by r-loops and that the r-loop coordinates are natural generalizations of the concept of the center of mass coordinates. Besides the center of mass velocity an extended object has also the area velocity, the volume velocity, etc. (called multi-vector or holographic velocities).

We generalize the theory of relativity from Minkowski space M to C-space and thus bring into the game the holographic velocities. Besides the speed of light afundamental length L has to be introduced. If we take L equal to the Planck length we find that the maximum holographic speed are very slow and this explains why on the macroscopic scale we do not observe them. For instance, the area (the 2-vector) speed is of the order of 10^-26 m²/sec.

The action for a “point particle” in C-space is analogous to the action for a point particle in M₄. It is equal to the length of the world line in C-space. This action constrains the polymomentum to the mass shell in C-space. If we reduce the C-space action with respect to the 4-volume (4-vector or pseudoscalar) variables = X⁰¹²³, then all other variables are independent and evolve with respect to s which assumes the role of evolution parameter (the true time). The action so reduced is precisely the (well known) Stueckelberg action of the relativistic dynamics. 

In the unconstrained, minimal length, action, the variables are functions of an arbitrary parameter . The 4 volume also changes with . This explains why the world lines (actually the world tubes, if particles are extended) in M₄ are so long along time-like directions, and have so narrowspace-like extension. This is just a very natural ``final" state of objects evolving in M₄. Initially the objects may have arbitrary shapes, but if their 2-vector and 3-vector speeds are of the right sign (so it is on average in half of the cases), then their extensions along time-like directions will necessarily increase for positive 4-vector speeds; increasing 4-volume necessarily implies increasing length of a world tube (whose effective 2-area and 3-volume are constant or decreasing). Long world lines are necessary in order to provide the observed electromagnetic fields. Finite extensions of world lines provide a cutoff to the electromagnetic interaction, which is predicted to change with time.

All the conservation laws are still valid, since the true physics is now in C-space. In C-space there is no ``flow of time'' at all: past, present and future coexist in the 16-dimensional “block” C-space, with objects corresponding to wordlines in C-space. On the contrary, in the 4-dimensional subspace M₄ objects are evolving with respect to the Lorentz invariant evolution parameter s. A reconciliation between two seemingly antagonistic views is achieved, namely between the assertion that there is no time, no flow of time, etc., and the view that there is evolution, passage of time, relativistic dynamics. Both groups of thinkers are right, but each in its own space.

Tomislav Ivezic, 

Rudjer Boskovic Institute, 

Zagreb, Croatia:

In the usual Clifford algebra formulation of electrodynamics the Faraday bi-vector field F is decomposed into the observer dependent sum of a relative vector E (corresponding to the three-dimensional electric field vector and a relative bi-vector e₅B corresponds to the three dimensional magnetic field vector and e₅ is the (grade-4 pseudo-scalar). In this paper we present an observer independent decomposition of F by using the vectors (grade-1) of electric E and magnetic B field and consequently develop the invariant formulation of relativistic electrodynamics (independent of the reference frame and of the chosen coordinatization for that frame). This formalism does not make use of the intermediate electromagnetic 4-potential A and thus dispenses with the need for the gauge conditions. Moreover we present an equivalent formulation of electrodynamics by using the multi-vector (Clifford aggregate)<!--[if gte