117805675
Entropy Defined, Entropy Increase and Decoherence Understood, and Some Black-Hole Puzzles Solved
Statistical mechanics explains thermodynamics in terms of (quantum) mechanics by equating the entropy of a microstate of a closed system with the logarithm of the number of microstates in the macrostate to which it belongs, but the question `what is a macrostate?' has never been answered except in a vague, subjective, way. However Hawking's discovery of black hole evaporation led to a formula for black hole entropy with no subjective element. In this letter, we argue from this result, together with the assumption that `black hole thermodynamics is just ordinary thermodynamics applied to black holes', that a macrostate for a general (quantum gravitational) closed system is an equivalence class of matter-gravity microstates with the same expectation values for the matter degrees of freedom alone. Not only does this finally answer the question `what is entropy?', but it also predicts the equality of the thermodynamic entropy of a black hole with the matter and the gravity entropy-like quantities derived from the Euclidean path integral. Furthermore it gives us a clear glimpse of an ultimate synthesis of quantum theory and gravity in which we see that (a) gravity acts as a universal environment, thus predicting that, if the initial state of the universe is unentangled, its entropy must go on increasing forever, (b) the gravitational field has degrees of freedom, but no observables, thus enabling gravity to perform the trick of providing an objective continual process of decoherence. All the above rests on the validity of unitarity. The `information-loss puzzle' had raised doubts about that. But we suggest a resolution for this puzzle.
123597708
A uniqueness result in the Segal–Weinless approach to linear Bose fields
We prove a theorem, which, while it fits naturally into the Segal–Weinless approach to quantization seems to have been overlooked in the literature: Let (D,σ) be a symplectic space, and T (t) a one parameter group of symplectics on (D,σ). Let (H, 2Im〈⋅ ‖ ⋅〉) be a complex Hilbert space considered as a real symplectic space, and U(t) a one‐parameter unitary group on H with strictly positive energy. Suppose there is a linear symplectic map K from D to H with dense range, intertwining T (t) and U(t). Then K is unique up to unitary equivalence.
16748405
The robustness of a many-body decoherence formula of Kay under changes in graininess and shape of the bodies
In "Decoherence of macroscopic closed systems within Newtonian quantum gravity" (Kay B S 1998 Class. Quantum Grav. 15 L89-L98) it was argued that, given a many-body Schrodinger wave function ψ(x1, . . . , xN) for the centre-of- mass degrees of freedom of a closed system of N identical uniform-mass balls of mass M and radius R, taking account of quantum gravitational effects and then tracing over the gravitational field amounts to multiplying the position-space density matrix
123297693
Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space–times with horizons
Let ω be a state on the Weyl algebra over a symplectic space. We prove that if either (i) the ‘‘liberation’’ of ω is pure or (ii) the restriction of ω to each of two generating Weyl subalgebras is quasifree and pure, then ω is quasifree and pure [and, in case (i) is equal to its liberation, in case (ii) is uniquely determined by its restrictions]. [Here, we define the liberation of a (sufficiently regular) state to be the quasifree state with the same two point function.] Results (i) and (ii) permit one to drop the quasifree assumption in a result due to Wald and the author concerning linear scalar quantum fields on space–times with bifurcate Killing horizons and thus to conclude that, on a large subalgebra of the field algebra for such a system, there is a unique stationary state whose two point function has the Hadamard form. The paper contains a number of further related developments including: (a) (i) implies a uniqueness result, e.g., for the usual free field in Minkowski space. We compare and contra...
120058153
Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate killing horizon
Abstract This paper is concerned with the study of quasifree states of a linear, scalar quantum field in globally hyperbolic spacetimes possessing a one-parameter group of isometries with a bifurcate Killing horizon. Some results on the uniqueness and thermal properties of such states are well known in the special cases of Minkowski, Schwarzschild, and deSitter spacetimes, and our main aim is to present new stronger results and to generalize them to this wide class of spacetimes. As a preliminary to proving our theorems, we develop some aspects of the theory of globally of hyperbolic spacetimes with a bifurcate Killing horizon, we give some new results on the structure of Bose quasifree states of linear fields (the class which includes all the usual “Fock vacua”), and we clarify and further develop the notion of a “Hadamard state”. We then consider the quasifre e states on these spacetimes which have vanishing one-point function, are invariant under the one-parameter isometry group, and are nonsingular in a neighborhood of the horizon in the sense that their two-point function is of the Hadamard form there. We prove that, on a large subalgebra of observables (which are determined by observables localized in compact regions of the horizon) such states are unique and pure. Furthermore, if the spacetime admits a certain discrete “wedge reflection” isometry (as holds automatically in the analytic case) we prove that this state - if it exists - must be a KMS state at the Hawking temperature T = κ /2 π when restricted to those observables in our subalgebra which are localized in one of the (“right” or “left”) wedges of the spacetime where the Killing orbits are timelike near the horizon. Here, κ denotes the surface g ravity of the horizon. Under the further assumption that the nonsingularity of the state holds globally and that there are no “zero modes” in the one-partic le Hilbert space belonging to the state, we extend the uniqueness result to all observables localized in the full “domain of determinacy” of the hori zon. However, existence of states satisfying the hypotheses of our theorems does not hold in general and, indeed, we prove the nonexistence of any stationary (not necessarily quasifree) Hadamard state on the Schwarzschild-deSitter and Kerr spacetimes. We remark that nowhere in the analysis do we need to assume any form of Einstein's equations.
117120091
A uniqueness result for quantum field theory on spacetimes with bifurcate Killing horizons
118976996
One-neutron knockout in the vicinity of the N=32 sub-shell closure: Be-9(Cr-57,Cr-56+gamma)X
Gade, A. Janssens, R. V. F. Bazin, D. Brown, B. A. Campbell, C. M. Carpenter, M. P. Cook, J. M. Deacon, A. N. Dinca, D. -C. Freeman, S. J. Glasmacher, T. Horoi, M. Kay, B. P. Mantica, P. F. Mueller, W. F. Terry, J. R. Tostevin, J. A. Zhu, S.
41288355
Spectroscopy of the odd-odd fp-shell nucleus Sc-52 from secondary fragmentation
The odd-odd fp-shell nucleus {sup 52}Sc was investigated using in-beam {gamma}-ray spectroscopy following secondary fragmentation of a {sup 55}V and {sup 57}Cr cocktail beam. Aside from the known {gamma}-ray transition at 674(5) keV, a new decay at E{sub {gamma}}=212(3) keV was observed. It is attributed to the depopulation of a low-lying excited level. This new state is discussed in the framework of shell-model calculations with the GXPF1, GXPF1A, and KB3G effective interactions. These calculations are found to be fairly robust for the low-lying level scheme of {sup 52}Sc irrespective of the choice of the effective interaction. In addition, the frequency of spin values predicted by the shell model is successfully modeled by a spin distribution formulated in a statistical approach with an empirical, energy-independent spin-cutoff parameter.