Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

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The Cosmological Constant and Dark Energy

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

2005년 대한 생화학·분자생물학회 하계학술대회를 다녀와서

A colloquium-style introduction to two electronic processes in a carbon monolayer (graphene) is presented, each having an analog in relativistic quantum mechanics. Both processes couple electronlike and holelike states, through the action of either a superconducting pair potential or an electrostatic potential. The first process, Andreev reflection, is the electron-to-hole conversion at the interface with a superconductor. The second process, Klein tunneling, is the tunneling through a $p\text{\ensuremath{-}}n$ junction. The absence of backscattering, characteristic of massless Dirac fermions, implies that both processes happen with unit efficiency at normal incidence. Away from normal incidence, retro-reflection in the first process corresponds to negative refraction in the second process. In the quantum Hall effect, both Andreev reflection and Klein tunneling induce the same dependence of the two-terminal conductance plateau on the valley isospin of the carriers. Existing and proposed experiments on Josephson junctions and bipolar junctions in graphene are discussed from a unified perspective.

Colloquium: Andreev reflection and Klein tunneling in graphene

The Genesis of General Relativity

This contribution gives an overview of Einstein's work on unified field theory. It characterizes this work from four perspectives, by looking at its conceptual, representational, biographical, and philosophical dimensions.

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Einstein’s Unified Field Theory Program

Heuristics and Mathematical Representation in Einstein's Search for a Gravitational Field Equation

The Stern-Gerlach-Experiment (SGE) performed in 1922 is a seminal benchmark experiment of quantum physics providing evidence for several fundamental properties of quantum systems. Based on the knowledge of today we illustrate the different benchmark results of the SGE for the development of modern quantum physics and chemistry. The SGE provided the first direct experimental evidence for angular momentum quantization in the quantum world and therefore also for the existence of directional quantization of all angular momenta in the process of measurement. Furthermore, it measured for the first time a ground state property of an atom, it produced for the first time a fully “spin-polarized” atomic beam, and it also revealed the electron spin, even though this was not realized at the time. The SGE was the first fully successful molecular beam experiment where the kinematics of particles can be determined with high momentum-resolution by beam measurements in vacuum. This technique provided a kind of new kinematic microscope with which inner atomic or nuclear properties could be investigated. Historical facts of the original SGE are described together with early attempts by Einstein, Ehrenfest, Heisenberg, and others to reveal the physical processes creating directional quantization in the SGE. Heisenberg’s and Einstein’s proposals of an improved multi-stage SGE are presented. The first realization of these proposed experiments by Stern, Phipps, Frisch and Segre is described. The experimental set-up suggested by Einstein can be considered as an anticipation of a Rabi-apparatus with varying fields. Recent theoretical work by Wennerstrom and Westlund, by Devereux and others, is mentioned in which the directional quantization process and possible interference effects of the two different spin states are investigated. In full agreement with the results of the new quantum theory directional quantization appears as a general and universal feature of quantum measurements. One experimental example for such directional quantization in scattering processes is shown. Last not least, the early history of the “almost” discovery of the electron spin in the SGE is revisited.

The Stern-Gerlach experiment revisited

We investigate the properties of two standard energy estimators used in path-integral Monte Carlo simulations. By disentangling the variance of the estimators and their autocorrelation times we analyze the dependence of the performance on the update algorithm and present a detailed comparison of refined update schemes such as multigrid and staging techniques. We show that a proper combination of the two estimators leads to a further reduction of the statistical error of the estimated energy with respect to the better of the two without extra cost.

Tilman Sauer

Papers

The Genesis of General Relativity

Einstein’s Unified Field Theory Program

Heuristics and Mathematical Representation in Einstein's Search for a Gravitational Field Equation

The Stern-Gerlach experiment revisited

Optimal Energy Estimation in Path-Integral Monte Carlo Simulations