What is the effective stress energy of particles created from the vacuum?

When spontaneous particle creation occurs in a strong gravitational field, it seems clear on physical grounds that the particle creation must back-react on the gravitation field. It is generally believed that in the semiclassical approximation this effect can be described by assigning an effective stress energy to the created particles, which acts as a source of the gravitational field via Einstein's equation. In this essay, I discuss an axiomatic approach for determining the renormalized value of this effective stress energy.This essay was awarded the third prize for 1977 by the Gravity Research Foundation.     

What is the magnetic Weak Gravity Conjecture for axions?

The electric Weak Gravity Conjecture demands that axions with large decay constant f couple to light instantons. The resulting large instantonic corrections pose problems for natural inflation. We explore an alternative argument based on the magnetic Weak Gravity Conjecture for axions, which we try to make more precise. Roughly speaking, it demands that the minimally charged string coupled to the dual 2‐form‐field exists in the effective theory. Most naively, such large‐f strings curve space too much to exist as static solutions, thus ruling out large‐f axions. More conservatively, one might allow non‐static string solutions to play the role of the required charged objects. In this case, topological inflation would save the superplanckian axion. Furthermore, a large‐f axion may appear in the low‐energy effective theory based on two subplanckian axions in the UV. The resulting effective string is a composite object built from several elementary strings and domain walls. It may or may not satisfy the magnetic Weak Gravity Conjecture depending on how strictly the latter is interpreted and on the cosmological dynamics of this composite object, which remain to be fully understood. Finally, we recall that large‐field brane inflation is naively possible in the codimension‐one case. We show how string‐theoretic back‐reaction closes this apparent loophole of large‐f (non‐periodic) pseudo‐axions.     

What is the Partition Bundle?

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometrical data. We discuss the nature of the object in such a theory that generalizes the partition function of a more conventional quantum field theory.     

What is the Relativistic Volterra Lattice?

We develop a systematic procedure of finding integrable 6ldquo;relativistic” (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretization living in the same hierarchy. Second, one considers this discretization as a particular Cauchy problem for a certain 2-dimensional lattice equation, and then looks for another meaningful Cauchy problem, which can be, in turn, interpreted as a new discrete time system. Third, one has to identify integrable hierarchies to which these new discrete time systems belong. These novel hierarchies are called then “relativistic”, the small time step $h$ playing the role of inverse speed of light. We apply this procedure to the Toda lattice (and recover the well-known relativistic Toda lattice), as well as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the “relativistic” deformations were not known previously. Received: 1 April 1998 / Accepted: 21 July 1998     

What is the Cause of Inertia?

The question of the cause of inertial reaction forces and the validity of Mach's principle are investigated. A recent claim that the cause of inertial reaction forces can be attributed to an interaction of the electrical charge of elementary particles with the hypothetical quantum mechanical zero-point fluctuation electromagnetic field is shown to be untenable. It fails to correspond to reality because the coupling of electric charge to the electromagnetic field cannot be made to mimic plausibly the universal coupling of gravity and inertia to the stress-energy-momentum (i.e., matter) tensor. The gravitational explanation of the origin of inertial forces is then briefly laid out, and various important features of it explored in the last half-century are addressed.     

Where is the energy of slow light stored?

We analyze the energy storage process of light propagating with slow group velocity in a sample where electromagnetically induced transparency (EIT) is created by a strong coupling field. We compare the formation of slow light in EIT and in self-induced transparency (SIT). For SIT, soliton-like propagation of light with essentially reduced group velocity takes place because of the temporary storage of an appreciable part of the pulse energy in the atoms. For EIT, no energy of the probe is stored in the atoms. This energy is transformed to the coupling field and leaves the sample with phase velocity c without absorption. Slow light is formed by a low frequency coherence induced at the input by the probe and coupling fields in a two-quantum excitation process. This coherence propagates as a “spin wave” with small group velocity, and at a large distance from the input, the coherence rules the process of the energy transformation from the coupling field to the probe, reproducing exactly the temporal profile of the probe at the input.     

What is the problem in the locality problem?

In connection with my previous paper Locality, Reflection, and Wave-Particle Duality [Found. Phys. 17, 813 (1987)], in this paper I distinguish explicitly, in the locality problem, between assertions, deductively established results, interpretations, intuitions, and facts. This clarifies the structure of the problem.     

Is the evidence for dark energy secure?

Several kinds of astronomical observations, interpreted in the framework of the standard Friedmann–Robertson–Walker cosmology, have indicated that our universe is dominated by a Cosmological Constant. The dimming of distant Type Ia supernovae suggests that the expansion rate is accelerating, as if driven by vacuum energy, and this has been indirectly substantiated through studies of angular anisotropies in the cosmic microwave background (CMB) and of spatial correlations in the large-scale structure (LSS) of galaxies. However there is no compelling direct evidence yet for (the dynamical effects of) dark energy. The precision CMB data can be equally well fitted without dark energy if the spectrum of primordial density fluctuations is not quite scale-free and if the Hubble constant is lower globally than its locally measured value. The LSS data can also be satisfactorily fitted if there is a small component of hot dark matter, as would be provided by neutrinos of mass ∼0.5 eV. Although such an Einstein–de Sitter model cannot explain the SNe Ia Hubble diagram or the position of the “baryon acoustic oscillation” peak in the autocorrelation function of galaxies, it may be possible to do so, e.g. in an inhomogeneous Lemaitre–Tolman–Bondi cosmology where we are located in a void which is expanding faster than the average. Such alternatives may seem contrived but this must be weighed against our lack of any fundamental understanding of the inferred tiny energy scale of the dark energy. It may well be an artifact of an oversimplified cosmological model, rather than having physical reality.     

How particular is the physics of the free energy principle?

The free energy principle (FEP) states that any dynamical system can be interpreted as performing Bayesian inference upon its surrounding environment. Although, in theory, the FEP applies to a wide variety of systems, there has been almost no direct exploration or demonstration of the principle in concrete systems. In this work, we examine in depth the assumptions required to derive the FEP in the simplest possible set of systems – weakly-coupled non-equilibrium linear stochastic systems. Specifically, we explore (i) how general the requirements imposed on the statistical structure of a system are and (ii) how informative the FEP is about the behaviour of such systems. We discover that two requirements of the FEP – the Markov blanket condition (i.e. a statistical boundary precluding direct coupling between internal and external states) and stringent restrictions on its solenoidal flows (i.e. tendencies driving a system out of equilibrium) – are only valid for a very narrow space of parameters. Suitable systems require an absence of perception-action asymmetries that is highly unusual for living systems interacting with an environment. More importantly, we observe that a mathematically central step in the argument, connecting the behaviour of a system to variational inference, relies on an implicit equivalence between the dynamics of the average states of a system with the average of the dynamics of those states. This equivalence does not hold in general even for linear stochastic systems, since it requires an effective decoupling from the system's history of interactions. These observations are critical for evaluating the generality and applicability of the FEP and indicate the existence of significant problems of the theory in its current form. These issues make the FEP, as it stands, not straightforwardly applicable to the simple linear systems studied here and suggest that more development is needed before the theory could be applied to the kind of complex systems that describe living and cognitive processes.     

What precision in the Digital Terrain Model is required for noise mapping?

The Digital Terrain Model is the most basic and cumbersome element of any large-scale mapping projects. Accurate assessment of Digital Terrain Model data is an intricate but vital process. The impact of its accuracy on noise mapping has not been fully researched. The aim of this research on a specific case study is to analyse the differences in noise mapping results obtained from acoustic simulations carried out with different accuracies in Digital Terrain Model data. It seems that mapping with a 0.5 m degree of accuracy in elevation is sufficient for acoustic simulation, apart from the fact that it is easily achievable with current available techniques. In contrast, it can be concluded that mapping with 5 m accuracy in elevation is insufficient and may drastically change the evaluation of the percentage of people affected by noise.     

What is the ground-state structure of the thinnest Si nanowires?

Pristine silicon whiskers are compared through energy analysis by separating the surface, edge, and bulk contributions, and by energy computation for a variety of structures and diameters d. It is shown that for d<6 nm a polycrystalline wire of five-fold symmetry, rather than single-crystal types, represents the ground state. It remains stable in molecular dynamics tests up to approximately 1000 K. Its specific surface reconstruction also stands out in that it favors kinetics of whisker growth and thus appears potentially realizable.     

Principle of statistical energy analysis for non-conservatively coupled systems

Traditional Statistical Energy Analysis(SEA)theory can not dealwith dynamic problems concerned with non-conservativcly coupled systems.Inthis paper,based on the theory of power flow between them and energy distri-bution in non-conservatively coupled osillators,equations of power balanceand those for calculation of each concerned power flow and other power itemsare derived to develop SEA theory for non-conservatively coupled systems.Re-sults show that conservative coupling is only a special case of non-conservativecoupling situations,effect of coupling damping on power flow and energy dis-tribution in non-conservatively coupled systems are not negligible unless coup-ling damping is much smaller compared with internal one.As an application ofthe theory,energy problems of non-conservatively coupled plates are studiedtheoretically and experimentally.     

What is a photon?

Certain properties of photons viewed as quanta (particles of an electromagnetic field) are discussed. Specifically, the nature of localization (size) of photons along and across the direction of wave propagation is examined.