Joseph Samuel

A Lagrangian basis for Ashtekar's formulation of canonical gravity

A manifestly covariant Lagrangian is presented which leads to the reformulation of canonical general relativity using new variables recently discovered by Ashtekar.

Is Barbero's Hamiltonian formulation a Gauge Theory of Lorentzian Gravity?

This letter is a critique of Barberos constrained Hamiltonian formulation of general relativity, on which current work in loop quantum gravity is based. While we do not dispute the correctness of Barberos formulation of general relativity, we offer some criticisms of an aesthetic nature. We point out that unlike Ashtekars complex SU(2) connection, Barberos real SO(3) connection does not admit an interpretation as a space-time gauge field. We show that if one tries to interpret Barberos real SO(3) connection as a space-time gauge field, the theory is not diffeomorphism invariant. We conclude that Barberos formulation is not a gauge theory of gravity in the sense that Ashtekars Hamiltonian formulation is. The advantages of Barberos real connection formulation have been bought at the price of giving up the description of gravity as a gauge field.

THE LENSE-THIRRING EFFECT AND MACH'S PRINCIPLE

Abstract We respond to a recent paper by Rindler [Phys. Lett. A 187 (1994) 235] on the “anti-Machian” nature of the Lense-Thirring effect. We remark that his conclusion depends crucially on the particular formulation of Machs principle used and that a different formulation can lead to the opposite conclusion.

Elasticity of semiflexible polymers

We present a method for solving the wormlike chain model for semiflexible polymers to any desired accuracy over the entire range of polymer lengths. Our results are in excellent agreement with recent computer simulations and reproduce important qualitatively interesting features observed in simulations of polymers of intermediate lengths. We also make a number of predictions that can be tested in a variety of concrete experimental realizations. The expected level of finite size fluctuations in force-extension curves is also estimated. This study is relevant to mechanical properties of biological molecules.

Euler buckling-induced folding and rotation of red blood cells in an optical trap

We investigate the physics of an optically-driven micromotor of biological origin. A single, live red blood cell, when placed in an optical trap folds into a rod-like shape. If the trapping laser beam is circularly polarized, the folded RBC rotates. A model based on the concept of buckling instabilities captures the folding phenomenon; the rotation of the cell is simply understood using the Poincar\`e sphere. Our model predicts that (i) at a critical intensity of the trapping beam the RBC shape undergoes large fluctuations and (ii) the torque is proportional to the intensity of the laser beam. These predictions have been tested experimentally. We suggest a possible mechanism for emergence of birefringent properties in the RBC in the folded state.We investigate the physics of an optically driven micromotor of biological origin. When a single, live red blood cell (RBC) is placed in an optical trap, the normal biconcave disc shape of the cell is observed to fold into a rod-like shape. If the trapping laser beam is circularly polarized, the folded RBC rotates. A model based on geometric considerations, using the concept of buckling instabilities, captures the folding phenomenon; the rotation of the cell is rationalized using the Poincaré sphere. Our model predicts that (i) at a critical power of the trapping laser beam the RBC shape undergoes large fluctuations, and (ii) the torque that is generated is proportional to the power of the laser beam. These predictions are verified experimentally. We suggest a possible mechanism for the emergence of birefringent properties in the RBC in the folded state.

Nonclassical Paths in Quantum Interference Experiments

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

Duality and conformal structure

In four dimensions, two metrics that are conformally related define the same Hodge dual operator on the space of two‐forms. The converse, namely, that two metrics that have the same Hodge dual are conformally related, is established. This is true for metrics of arbitrary (nondegenerate) signature. For Euclidean signature a stronger result, namely, that the conformal class of the metric is completely determined by choosing a dual operator on two‐forms satisfying certain conditions, is proved.

Gravitational instantons from the Ashtekar variables

Presents an ansatz, suggested by Ashtekars reformulation (1986) of general relativity, which exactly solves the field equations with a cosmological constant. These solutions are gravitational instantons, i.e. self-dual Euclidean solutions of the Einstein field equations.

Transport along null curves

Fermi transport is useful for describing the behaviour of spins or gyroscopes following non-geodesic, timelike worldlines. However, Fermi transport breaks down for null worldlines. We introduce a transport law for polarization vectors along non-geodesic null curves. We show how this law emerges naturally from the geometry of null directions by comparing polarization vectors associated with two distinct null directions. We then give a spinorial treatment of this topic and make contact with the geometric phase of quantum mechanics. There are two significant differences between the null and timelike cases. In the null case (a) the transport law does not approach a unique smooth limit as the null curve approaches a null geodesic and (b) the transport law for vectors is integrable, i.e. the result depends only on the local properties of the curve and not on the entire path taken. However, the transport of spinors is not integrable: there is a global sign of topological origin.

Classical light analogue of the non-local Aharonov-Bohm effect

We demonstrate the existence of a non-local geometric phase in the intensity-intensity correlations of classical incoherent light, that is not seen in the lower-order correlations. This two-photon Pancharatnam phase was observed and modulated in a Mach-Zehnder interferometer. Using acousto-optic interaction, independent phase noise was introduced to light in the two arms of the interferometer to create two independent incoherent classical sources from laser light. The experiment is the classical optical analogue of the multi-particle Aharonov-Bohm effect. As the trajectory of light over the Poincare sphere introduces a phase shift observable only in the intensity-intensity correlation, it provides a means of deflecting the two-photon wavefront, while having no effect on single photons.