Quantum Field Theory Constrains Traversable Wormhole Geometries

Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable.Comment: 26 pages, plain LaTe

The Quantum Interest Conjecture

Although quantum field theory allows local negative energy densities and fluxes, it also places severe restrictions upon the magnitude and extent of the negative energy. The restrictions take the form of quantum inequalities. These inequalities imply that a pulse of negative energy must not only be followed by a compensating pulse of positive energy, but that the temporal separation between the pulses is inversely proportional to their amplitude. In an earlier paper we conjectured that there is a further constraint upon a negative and positive energy delta-function pulse pair. This conjecture (the quantum interest conjecture) states that a positive energy pulse must overcompensate the negative energy pulse by an amount which is a monotonically increasing function of the pulse separation. In the present paper we prove the conjecture for massless quantized scalar fields in two and four-dimensional flat spacetime, and show that it is implied by the quantum inequalities.Comment: 17 pages, Latex, 3 figures, uses eps

Variational Principle for Mixed Classical-Quantum Systems

An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical variables are expressed in the form of a quantum state vector which includes the action of the classical subsystem in its phase factor. It is shown that the statistical ensemble of Brownian state vectors for a quantum particle in a classical thermal environment can be described by a density matrix evolving according to a nonlinear quantum Fokker-Planck equation. Exact solutions of this equation are obtained for a two-level system in the limit of high temperatures, considering both stationary and nonstationary initial states. A treatment of the common time shared by the quantum system and its classical environment, as a collective variable rather than as a parameter, is presented in the Appendix.Comment: 16 pages, LaTex; added Figure 2 and Figure

Motion of Inertial Observers Through Negative Energy

Recent research has indicated that negative energy fluxes due to quantum coherence effects obey uncertainty principle-type inequalities of the form |\Delta E|\,{\Delta \tau} \lprox 1\,. Here $|\Delta E|$ is the magnitude of the negative energy which is transmitted on a timescale $\Delta \tau$. Our main focus in this paper is on negative energy fluxes which are produced by the motion of observers through static negative energy regions. We find that although a quantum inequality appears to be satisfied for radially moving geodesic observers in two and four-dimensional black hole spacetimes, an observer orbiting close to a black hole will see a constant negative energy flux. In addition, we show that inertial observers moving slowly through the Casimir vacuum can achieve arbitrarily large violations of the inequality. It seems likely that, in general, these types of negative energy fluxes are not constrained by inequalities on the magnitude and duration of the flux. We construct a model of a non-gravitational stress-energy detector, which is rapidly switched on and off, and discuss the strengths and weaknesses of such a detector.Comment: 18pp + 1 figure(not included, available on request), in LATEX, TUPT-93-

Fluctuations of the Retarded Van der Waals Force

The retarded Van der Waals force between a polarizable particle and a perfectly conducting plate is re-examined. The expression for this force given by Casimir and Polder represents a mean force, but there are large fluctuations around this mean value on short time scales which are of the same order of magnitude as the mean force itself. However, these fluctuations occur on time scales which are typically of the order of the light travel time between the atom and the plate. As a consequence, they will not be observed in an experiment which measures the force averaged over a much longer time. In the large time limit, the magnitude of the mean squared velocity of a test particle due to this fluctuating Van der Waals force approaches a constant, and is similar to a Brownian motion of a test particle in an thermal bath with an effective temperature. However the fluctuations are not isotropic in this case, and the shift in the mean square velocity components can even be negative. We interpret this negative shift to correspond to a reduction in the velocity spread of a wavepacket. The force fluctuations discussed in this paper are special case of the more general problem of stress tensor fluctuations. These are of interest in a variety of areas fo physics, including gravity theory. Thus the effects of Van der Waals force fluctuations serve as a useful model for better understanding quantum effects in gravity theory.Comment: 14 pages, no figure

Quantum Fluctuations of Radiation Pressure

Quantum fluctuations of electromagnetic radiation pressure are discussed. We use an approach based on the quantum stress tensor to calculate the fluctuations in velocity and position of a mirror subjected to electromagnetic radiation. Our approach reveals that radiation pressure fluctuations are due to a cross term between vacuum and state dependent terms in a stress tensor operator product. Thus observation of these fluctuations would entail experimental confirmation of this cross term. We first analyze the pressure fluctuations on a single, perfectly reflecting mirror, and then study the case of an interferometer. This involves a study of the effects of multiple bounces in one arm, as well as the correlations of the pressure fluctuations between arms of the interferometer. In all cases, our results are consistent with those previously obtained by Caves using different mehods.Comment: 23 pages, 3 figures, RevTe

Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric

Continuing our investigation of the regularization of the noise kernel in curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D {\bf 63}, 104001 (2001)] we adopt the modified point separation scheme for the class of optical spacetimes using the Gaussian approximation for the Green functions a la Bekenstein-Parker-Page. In the first example we derive the regularized noise kernel for a thermal field in flat space. It is useful for black hole nucleation considerations. In the second example of an optical Schwarzschild spacetime we obtain a finite expression for the noise kernel at the horizon and recover the hot flat space result at infinity. Knowledge of the noise kernel is essential for studying issues related to black hole horizon fluctuations and Hawking radiation backreaction. We show that the Gaussian approximated Green function which works surprisingly well for the stress tensor at the Schwarzschild horizon produces significant error in the noise kernel there. We identify the failure as occurring at the fourth covariant derivative order.Comment: 21 pages, RevTeX

k=0Magnetic Structure and Absence of Ferroelectricity in SmFeO3

SmFeO3 has attracted considerable attention very recently due to the reported multiferroic properties above room-temperature. We have performed powder and single crystal neutron diffraction as well as complementary polarization dependent soft X-ray absorption spectroscopy measurements on floating-zone grown SmFeO3 single crystals in order to determine its magnetic structure. We found a k=0 G-type collinear antiferromagnetic structure that is not compatible with inverse Dzyaloshinskii-Moriya interaction driven ferroelectricity. While the structural data reveals a clear sign for magneto-elastic coupling at the N\'eel-temperature of ~675 K, the dielectric measurements remain silent as far as ferroelectricity is concerned

Charge-transfer energy in iridates: A hard x-ray photoelectron spectroscopy study

We have investigated the electronic structure of iridates in the double perovskite crystal structure containing either Ir4+ or Ir5+ using hard x-ray photoelectron spectroscopy. The experimental valence band spectra can be well reproduced using tight-binding calculations including only the Ir 5d, O 2p, and O 2s orbitals with parameters based on the downfolding of the density-functional band structure results. We found that, regardless of the A and B cations, the A2BIrO6 iridates have essentially zero O 2p to Ir 5d charge-transfer energies. Hence double perovskite iridates turn out to be extremely covalent systems with the consequence being that the magnetic exchange interactions become very long ranged, thereby hampering the materialization of the long-sought Kitaev physics. Nevertheless, it still would be possible to realize a spin-liquid system using the iridates with a proper tuning of the various competing exchange interactions

Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space

A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that no gauge invariant perturbation should become unbounded in time. A self-consistent linear response analysis of these perturbations, based upon an invariant effective action principle, necessarily involves metric fluctuations about the mean semi-classical geometry, and brings in the two-point correlation function of the quantum energy-momentum tensor in a natural way. This linear response equation contains no state dependent divergences and requires no new renormalization counterterms beyond those required in the leading order semi-classical approximation. The general linear response criterion is applied to the specific example of a scalar field with arbitrary mass and curvature coupling in the vacuum state of Minkowski spacetime. The spectral representation of the vacuum polarization function is computed in n dimensional Minkowski spacetime, and used to show that the flat space solution to the semi-classical Einstein equations for n=4 is stable to all perturbations on distance scales much larger than the Planck length.Comment: 22 pages: This is a significantly expanded version of gr-qc/0204083, with two additional sections and two new appendices giving a complete, explicit example of the semi-classical stability criterion proposed in the previous pape