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

I Relativity in the Making- The Search for Gravitational Absorption in the Early Twentieth Century- Minkowski, Mathematicians, and the Mathematical Theory of Relativity- Heuristics and Mathematical Representation in Einstein's Search for a Gravitational Field Equation- Rotation as the Nemesis of Einstein's Entwurf Theory- II Relativity at Work- Einstein, Relativity and Gravitation Research in Vienna before 1938- Controversies in the History of the Radiation Reaction Problem in General Relativity- The Penrose-Hawking Singularity Theorems: History and Implications- III Relativity at Large- The Cosmological Woes of Newtonian Gravitation Theory- Genesis and Evolution of Weyl's Reflections on De Sitter's Universe- Milne, Bondi and the 'Second Way' to Cosmology- Steady-State Cosmology and General Relativity: Reconciliation or Conflict?- IV Relativity in Debate- Larmor versus General Relativity- Kretschmann's Analysis of Covariance and Relativity Principles- Point Coincidences and Pointer Coincidences: Einstein on the Invariant Content of Space-Time Theories- Contributors

The expanding worlds of general relativity

Field equations in teleparallel space–time: Einstein's Fernparallelismus approach toward unified field theory

Gravitational lensing, now taken as an important astrophysical consequence of the general theory of relativity, was found even before this theory was formulated but was discarded as a speculative idea without any chance of empirical confirmation. Reconstruction of some of Einstein's research notes dating back to 1912 reveals that he explored the possibility of gravitational lensing 3 years before completing his general theory of relativity. On the basis of preliminary insights into this theory, Einstein had already derived the basic features of the lensing effect. When he finally published the very same results 24 years later, it was only in response to prodding by an amateur scientist.

The origin of gravitational lensing: a postscript to Einstein's 1936 Science paper.

L'A. analyse la note et les travaux de recherche de D. Hilbert sur les fondements de la physique par rapport a la theorie de la relativite et les equations de la gravitation d'Einstein

The Relativity of Discovery: Hilberts First Note on the Foundations of Physics

A historical account of Einstein's 'Fernparallelismus' approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a space-time characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appeared in the period from summer 1928 until spring 1931. In the historical analysis special attention is given to the question of how Einstein tried to find field equations for the tetrads. We claim that it was the failure to find and justify a uniquely determined set of acceptable field equations which eventually led to Einstein's abandoning of this approach. We comment on some historical and systematic similarities between the 'Fernparallelismus' episode and the 'Entwurf' theory, i.e. the precursor theory of general relativity pursued by Einstein in the years 1912-1915.

Tilman Sauer

Papers

The expanding worlds of general relativity

Field equations in teleparallel space–time: Einstein's Fernparallelismus approach toward unified field theory

The origin of gravitational lensing: a postscript to Einstein's 1936 Science paper.

The Relativity of Discovery: Hilberts First Note on the Foundations of Physics

Field equations in teleparallel spacetime: Einstein's Fernparallelismus approach towards unified field theory