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The Gravity Probe B Relativity Mission was successfully launched on April 20, 2004 from Vandenberg Air Force Base in California, a culmination of 40 years of collaborative development at Stanford University and NASA. The goal of the GP-B experiment is to perform precision tests of two independent predictions of general relativity, the geodetic effect and frame dragging. On-orbit cryogenic operations lasted 17.3 months, exceeding requirements. Analysis of the science data is now in progress with a planned announcement of results scheduled for December 2007. [ABSTRACT FROM AUTHOR]

A new eaa in fundamental physics began with the discovery of pulsars 1967, the discovery of the first binary pulsar in 1974 and the first millisecond pulsar in 1982. Ever since, pulsars have been used as precise cosmic clocks, taking us beyond the weak-field regime of the solar-system in the study of theories of gravity. Their contribution is crucial as no test can be considered to be complete without probing the strong-field realm of gravitational physics by finding and timing pulsars. This is particularly highlighted by the discovery of the first double pulsar system which was discovered by our team in 2003. The double pulsar is unique in that both neutron stars are detectable as radio pulsars. This, combined with significantly higher mean orbital velocities and accelerations when compared to other binary pulsars, suggested that the system would become the best available testbed for general relativity and alternative theories of gravity in the strong-field regime. Indeed, this has been achieved only three years after its discovery with four independent strong-field tests of GR, more than has been obtained for any other system. Use of the theory-independent mass ratio of the two stars makes these tests uniquely different from all preceding studies. Ourresults confirm the validity of GR at the 0.05% level, which is by far the best precision yet achieved for the strong-field regime. Remarkably, the transverse velocity of the systems center of mass is extremely small, a result which is important for future GR. tests and evolutinary studies. [ABSTRACT FROM AUTHOR]

Despite the impotant experimental success of General Relativity, there are several theoretical reasons indicating that gravitational phenomena may change radically from the predictions of Einstein's theory at very short distances. A main motivation comes from studies of unifying all fundamental forces in the framework of a consistent quantum theory, called string theory. This theory introduces a new physical constant, the string length, under which a new elementary structure shows up, changing drastically all physical laws of nature. In particular, lowering the string scale in the TeV region provides a theoretical framework for solving the so-called mass hierarchy problem: the apparent weakness of gravity can then be accounted by the existence of large internal dimensions, in the submillimeter tegion, and transverse to a braneworld where our obserbed universe is confined. I review the main properties of this scenario and its implications for new travitational phenomena that can be obserbed at both particle colliders, and in non-accelerator experiments searching for new short range forces at submillimeter distaces. I also discuss the warped metric case and possible localization of gravity in the presence of infinite size extra dimensions that cal modify Newton's law at cosmoligical distance scales. [ABSTRACT FROM AUTHOR]

After recalling the coceptual foundations and the vasic sturcture of general relativity, we review some of its main modern developments (apart from cosmology): ( i ) the post-Newtonian limit and weak-field tests in the solar system, (ii) strong gravitationl feelds and black holes, (iii) strong-field and radiative tests in binary pulsar observations, (iv) gravitational waves, (v) general relativity and quantum theory. [ABSTRACT FROM AUTHOR]

This is a report on our joint work with A. Chamseddine and M. Marcolli. This essay gives a short introduction to a potential application in physics of a new type of geometry based on spectral considerations which is convenient when dealing with non-commutative spaces, i.e., spaces in which the simplifying rule of commutativity is no longer applied to the coordinates. Starting from the phenomenological Lagrangian of gravity coupled with matter one infers, using the spectral action principle, that space-time admits a fine structure which is a subtle mixture of the usual 4-dimensional continuum with a finite discrete structure F. Under the (unrealistic) hypothesis that this structure remains valid (i.e., one does not have any "hyperfine" modification) until the unification scale, one obtains a number of predictions whose approximate validity is a basic test of the approach. [ABSTRACT FROM AUTHOR]

Heisenberg spin-1/2 chains are the archetype of quantum integrable one-dimensional models describing magnetic properties of a wide range of compounds (like the KCuF3 crystal), which can be probed experimentally through neutron scattering experiments, while being at the same time at the root of the invention of Bethe ansatz and Yang-Baxter structures that led in turn to quantum groups discovery. The aim of this contribution is to describe these algebraic ingredients and to show how to obtain from them (using combined analytical and numerical analysis) dynamical correlation functions of integrable Heisenberg spin-1/2 chains, the Fourier transform of which, the so-called dynamical structure factors, being directly measured in inelastic neutron scattering experiments. Our method is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem. It leads to recent progress in the computation of integrable Heisenberg spin-1/2 chains correlation functions that we review here. [ABSTRACT FROM AUTHOR]

We review the connection between non-commutative gauge theory, matrix models and fluid mechanical systems. The non-commutative Chern-Simons description of the quantum Hall effect and bosonization of collective fermion states are used as specific examples. [ABSTRACT FROM AUTHOR]

A new version of scale analysis and renormalization theory has been found on the non-commutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external fields. The good news is that quantum field theory is better behaved on non-commutative than on ordinary space: indeed it has no Landau ghost. We review this rapidly growing subject. [ABSTRACT FROM AUTHOR]

Our aim is to introduce the ideas of non-commutative geometry through the example of the Quantum Hall Effect (QHE). We present a few concrete situations where the concepts of non-commutative geometry find physical applications. [ABSTRACT FROM AUTHOR]

The concept of motion in quantum theory is reviewed from a didactical point of view. A unitary evolution according to a Schrödinger equation has very different properties compared to motion in classical physics. If the phase relations defining unitary dynamics are destroyed or unavailable, motion becomes impossible (Zeno effect). The most important mechanism is dislocalization of phase relations (decoherence), arising from coupling of a quantum system to its environment. Macroscopic systems are not frozen, although strong decoherence is important to derive quasi-classical motion within the quantum framework. These two apparently conflicting consequences of strong decoherence are analyzed and compared. [ABSTRACT FROM AUTHOR]

The concept of decoherence is defined, and discussed in a historical context. This is illustrated by some of its essential consequences which may be relevant for the interpretation of quantum theory. Various aspects of the formalism are also reviewed for this purpose. [ABSTRACT FROM AUTHOR]

Solid state quantum bit circuits (qubits) are candidates for the implementation of quantum processors, which can in principle perform some computational tasks beyond reach of classical sequential processors. Decoherence is there a key issue since electrical circuits are more prone to decoherence than microscopic objects such as atoms. We introduce the different families of solid state qubits, which are either based on single particle states in semiconductor nanostructures, or on global quantum states of superconducting Josephson circuits. We treat more in detail the Cooper pair box Josephson circuit, and the quantronium circuit derived from it. In this device, a decoupling strategy of the circuit from the outside circuitry allows to improve quantum coherence. We expose results obtained on the manipulation of the qubit state in the quantronium. We develop a general framework for understanding decoherence in qubit circuits, and show how coherence time measurements allow to characterize noise sources coup. [ABSTRACT FROM AUTHOR]

In a ground breaking discovery in 1994, Shor has shown that quantum computers, if built, can factor numbers efficiently. Since then quantum computing has become a burgeoning field of research, attracting theoreticians and experimentalists alike, and regrouping researchers from fields like computer science, physics, mathematics and engineering. Quantum information is very fragile and prone to decoherence. Yet by the middle of 1996 it has been shown that fault-tolerant quantum computation is possible. We give a simple description of the elements of quantum error-correction and quantum fault-tolerance. After characterizing quantum errors we present several error correction schemes and outline the elements of a full fledged fault-tolerant computation, which works error-free even though all of its components can be faulty. We also mention alternative approaches to error-correction, so called error-avoiding or decoherence-free schemes. [ABSTRACT FROM AUTHOR]

Decoherence is an extremely fast and efficient environment-induced process transforming macroscopic quantum superpositions into statistical mixtures. It is an essential step in quantum measurement and a formidable obstacle for a practical use of quantum superpositions (quantum computing for instance). For large objects, decoherence is so fast that its dynamics is unobservable. Mesoscopic fields stored in a high-quality superconducting millimeter-wave cavity, a modern equivalent to Einstein's ‘photon box', are ideal tools to reveal the dynamics of the decoherence process. Their interaction with a single circular Rydberg atom prepares them in a quantum superposition of fields, containing a few photons, with different classical phases. The evolution of this ‘Schrödinger cat' state can be later probed with a ‘quantum mouse', another atom, assessing its coherence. We describe here the experiments performed along these lines at ENS, and stress the deep links between decoherence and complementarity. [ABSTRACT FROM AUTHOR]

The environment surrounding a quantum system can, in effect, monitor some of the systems observables. As a result, the eigenstates of these observables continuously decohere and can behave like classical states. [ABSTRACT FROM AUTHOR]

Truly man is a marvelously vain, diverse, and undulating object. It is hard to found any constant and uniform judgment on him. Michel de Montaigne, Les Essais, Book I, Chapter 1: “By diverse means we arrive at the same end”; in The Complete Essays of Montaigne, Donald M. Frame transl., Stanford University Press (1958). [ABSTRACT FROM AUTHOR]

We review Einstein’s epistemological conceptions, and indicate their philosophical roots. The particular importance of the ideas of Hume, Kant, Mach, and Poincaré is highlighted. The specific characteristics of Einstein’s approach to physics are underlined. Lastly, we consider the practical application of Einstein’s methodological principles to the two theories of relativity, and to quantum theory. We emphasize a Kantian approach to quantum theory. [ABSTRACT FROM AUTHOR]

This is a previously unpublished manuscript of the lecture given by A. Einstein on November 2, 1910 before the Zürich Physical Society. The original document can be found in the bequest of Heinrich Zangger, at the Manuscripts Department of the Central Library of Zürich. Transcribed with the permission of the Central Library by W. Hunziker and A. Schultze (Institute for Theoretical Physics, ETH Zürich), kindly transmitted by N. Straumann (Institute for Theoretical Physics, University of Zürich-Irchel). The notes are by B. Duplantier (Department of Theoretical Physics, Saclay). [ABSTRACT FROM AUTHOR]