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.

/pdf/the-cosmological-constant-and-dark-energy-1w78acsak0.pdf

The Cosmological Constant and Dark Energy

Meeting the Universe Halfway is an ambitious book with far-reaching implications for numerous fields in the natural sciences, social sciences, and humanities. In this volume, Karen Barad, theoretical physicist and feminist theorist, elaborates her theory of agential realism. Offering an account of the world as a whole rather than as composed of separate natural and social realms, agential realism is at once a new epistemology, ontology, and ethics. The starting point for Barad’s analysis is the philosophical framework of quantum physicist Niels Bohr. Barad extends and partially revises Bohr’s philosophical views in light of current scholarship in physics, science studies, and the philosophy of science as well as feminist, poststructuralist, and other critical social theories. In the process, she significantly reworks understandings of space, time, matter, causality, agency, subjectivity, and objectivity.

In an agential realist account, the world is made of entanglements of “social” and “natural” agencies, where the distinction between the two emerges out of specific intra-actions. Intra-activity is an inexhaustible dynamism that configures and reconfigures relations of space-time-matter. In explaining intra-activity, Barad reveals questions about how nature and culture interact and change over time to be fundamentally misguided. And she reframes understanding of the nature of scientific and political practices and their “interrelationship.” Thus she pays particular attention to the responsible practice of science, and she emphasizes changes in the understanding of political practices, critically reworking Judith Butler’s influential theory of performativity. Finally, Barad uses agential realism to produce a new interpretation of quantum physics, demonstrating that agential realism is more than a means of reflecting on science; it can be used to actually do science.

Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black hole explosions

Modified Gravity and Cosmology

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

/pdf/decoherence-einselection-and-the-quantum-origins-of-the-5c70dshgfi.pdf

Decoherence, einselection, and the quantum origins of the classical

Following an historical introduction, the conventional canonical formulation of general relativity theory is presented. The canonical Lagrangian is expressed in terms of the extrinsic and intrinsic curvatures of the hypersurface ${x}^{0}=\mathrm{constant}$, and its relation to the asymptotic field energy in an infinite world is noted. The distinction between finite and infinite worlds is emphasized. In the quantum theory the primary and secondary constraints become conditions on the state vector, and in the case of finite worlds these conditions alone govern the dynamics. A resolution of the factor-ordering problem is proposed, and the consistency of the constraints is demonstrated. A 6-dimensional hyperbolic Riemannian manifold is introduced which takes for its metric the coefficient of the momenta in the Hamiltonian constraint. The geodesic incompletability of this manifold, owing to the existence of a frontier of infinite curvature, is demonstrated. The possibility is explored of relating this manifold to an infinite-dimensional manifold of 3-geometries, and of relating the structure of the latter manifold in turn to the dynamical behavior of space-time. The problem is approached through the WKB approximation and Hamilton-Jacobi theory. Einstein's equations are revealed as geodesic equations in the manifold of 3-geometries, modified by the presence of a "force term." The classical phenomenon of gravitational collapse shows that the force term is not powerful enough to prevent the trajectory of space-time from running into the frontier. The as-yet unresolved problem of determining when the collapse phenomenon represents a real barrier to the quantum-state functional is briefly discussed, and a boundary condition at the barrier is proposed. The state functional of a finite world can depend only on the 3-geometry of the hypersurface ${x}^{0}=\mathrm{constant}$. The label ${x}^{0}$ itself is irrelevant, and "time" must be determined intrinsically. A natural definition for the inner product of two such state functionals is introduced which, however, encounters difficulties with negative probabilities owing to the barrier boundary condition. In order to resolve these difficulties, a simplified model, the quantized Friedmann universe, is studied in detail. In order to obtain nonstatic wave functions which resemble a universe evolving, it is necessary to introduce a clock. In order that the combined wave functions of universe-cum-clock be normalizable, it turns out that the periods of universe and clock must be commensurable. Wave packets exhibiting quasiclassical behavior are constructed, and attention is called to the phenomenological character of "time." The innerproduct definition is rescued from its negative-probability difficulties by making use of the fact that probability flows in a closed finite circuit in configuration space. The article ends with some speculations on the uniqueness of the state functional of the actual universe. It is suggested that a viewpoint due to Everett should be adopted in its interpretation.

Quantum Theory of Gravity. I. The Canonical Theory

Quantum field theory in curved spacetime

Dynamical theory of groups and fields

Contrary to the situation which holds for the canonical theory described in the first paper of this series, there exists at present no tractable pure operator language on which to base a manifestly covariant quantum theory of gravity. One must construct the theory by analogy with conventional $S$-matrix theory, using the $c$-number language of Feynman amplitudes when nothing else is available. The present paper undertakes this construction. It begins at an elementary level with a treatment of the propagation of small disturbances on a classical background. The classical background plays a fundamental role throughout, both as a technical instrument for probing the vacuum (i.e., analyzing virtual processes) and as an arbitrary fiducial point for the quantum fluctuations. The problem of the quantized light cone is discussed in a preliminary way, and the formal structure of the invariance group is displayed. A condensed notation is adopted which permits the Yang-Mills field to be studied simultaneously with the gravitational field. Generally covariant Green's functions are introduced through the imposition of covariant supplementary conditions on small disturbances. The transition from the classical to the quantum theory is made via the Poisson bracket of Peierls. Commutation relations for the asymptotic fields are obtained and used to define the incoming and outgoing states. Because of the non-Abelian character of the coordinate transformation group, the separation of propagated disturbances into physical and nonphysical components requires much greater care than in electrodynamics. With the aid of a canonical form for the commutator function, two distinct Feynman propagators relative to an arbitrary background are defined. One of these is manifestly covariant, but propagates nonphysical as well as physical quanta; the other propagates physical quanta only, but lacks manifest covariance. The latter is used to define external-line wave functions and non-radiatively-corrected amplitudes for scattering, pair production, and pair annihilation by the background field. The group invariance of these amplitudes is proved. A fully covariant generalization of the complete $S$ matrix is next proposed, and Feynman's tree theorem on the group invariance of non-radiatively-corrected $n$-particle amplitudes is derived. The big problem of radiative corrections is then confronted. The resolution of this problem is carried out in steps. The single-loop contribution to the vacuum-to-vacuum amplitude is first computed with the aid of the formal theory of continuous determinants. This contribution is then functionally differentiated to obtain the lowest-order radiative corrections to the $n$-quantum amplitudes. These amplitudes split automatically into Feynman baskets, i.e., sums over tree amplitudes (bare scattering amplitudes) in which all external lines are on the mass shell. This guarantees their group invariance. The invariance can be made partially manifest by converting from the noncovariant Feynman propagator to the covariant one, and this leads to the formal appearance of fictitious quanta which compensate the nonphysical modes carried by the covariant propagator. Although avoidable in principle, these quanta necessarily appear whenever manifestly covariant expressions are employed, e.g., in renormalization theory. The fictitious quanta, however, appear only in closed loops and are coupled to real quanta through vertices which vanish when the invariance group is Abelian. The vertices are nonsymmetric and always occur with a uniform orientation around any fictitious quantum loop. The problem of splitting radiative corrections into Feynman baskets becomes more difficult in higher orders, when overlapping loops occur. This problem is approached with the aid of the Feynman functional integral. It is shown that the "measure" or "volume element" for the functional integration plays a fundamental role in the decomposition into Feynman baskets and in guaranteeing the invariance of radiative corrections under arbitrary changes in the choice of basic field variables. The "measure" has two effects. Firstly, it removes from all closed loops the non-causal chains of cyclically connected advanced (or retarded) Green's functions, thereby breaking them open and ensuring that at least one segment of every loop is on the mass shell. Secondly it adds certain nonlocal corrections to the operator field equations, which vanish in the classical limit $\ensuremath{\hbar}\ensuremath{\rightarrow}0$. The question arises why these removals and corrections are always neglected in conventional field theory without apparent harm. It is argued that the usual procedures of renormalization theory automatically take care of them. In practice the criteria of locality and unitarity are replaced by analyticity statements and Cutkosky rules. It is virtually certain that the "measure" may be similarly ignored (set equal to unity) in gravity theory, and that attention may therefore be confined to primary diagrams, i.e., diagrams which contain Feynman propagators only, with no noncausal chains removed. A general algorithm is given for obtaining the primary diagrams of arbitrarily high order, including all fictitious quantum loops, and the group invariance of the amplitudes thereby defined is proved. Essential to all these derivations is the use of a background field satisfying the classical "free" field equations. It is never necessary to employ external sources, and hence the well-known difficulties arising with sources in a non-Abelian context are avoided.

Bryce S. DeWitt

Papers

Quantum Theory of Gravity. I. The Canonical Theory

Quantum Theory of Gravity. I. The Canonical Theory

Quantum field theory in curved spacetime

Dynamical theory of groups and fields

Quantum Theory of Gravity. II. The Manifestly Covariant Theory