Some Thoughts on Energy Conditions and Wormholes

This essay reviews some of the recent progress in the area of energy conditions and wormholes. Most of the discussion centers on the subject of ``quantum inequality'' restrictions on negative energy. These are bounds on the magnitude and duration of negative energy which put rather severe constraints on its possible macroscopic effects. Such effects might include the construction of wormholes and warp drives for faster-than-light travel, and violations of the second law of thermodynamics. Open problems and future directions are also discussed.Comment: 24 pages; to appear in the Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity and Gravitatio

Minkowski Vacuum Stress Tensor Fluctuations

We study the fluctuations of the stress tensor for a massless scalar field in two and four-dimensional Minkowski spacetime in the vacuum state. Covariant expressions for the stress tensor correlation function are obtained as sums of derivatives of a scalar function. These expressions allow one to express spacetime averages of the correlation function as finite integrals. We also study the correlation between measurements of the energy density along a worldline. We find that these measurements may be either positively correlated or anticorrelated. The anticorrelated measurements can be interpreted as telling us that if one measurement yields one sign for the averaged energy density, a successive measurement with a suitable time delay is likely to yield a result with the opposite sign.Comment: 24 pages, 5 figures; Some additional comments added in Sect. IIB and a more compact argument given in App.

Trust, Reciprocity and Rules

In the absence of enforceable contracts, many economic and personal interactions rely on trust and reciprocity. Research shows that although this reliance often works well, sometimes it breaks down. Simple rules mandating minimum standards on reciprocation prevent the most egregious trust violations, but may also undermine behavior that would have otherwise produced higher overall economic welfare. We test the efficacy of exogenously imposed minimum return rules using experimental trust games. We find that rules fail to increase trust and trustworthiness. Thus low minimum standards significantly decrease economic welfare. Although sufficiently restrictive rules restore welfare, trust and trustworthy behavior never returns.trust games, experiments, reputation, information, reciprocity

Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc

Transparency, Efficiency and the Distribution of Economic Welfare in Pass-Through Investment Trust Games

We design an experiment to examine welfare and behavior in a multi-level trust game representing a pass through investment in an intermediated market. In a repeated game, an Investor invests via an Intermediary who lends to a Borrower. A pre-experiment one-shot version of the game serves as a baseline and to type each subject. We alter the transparency of exchanges between non-adjacent parties. We find transparency of the exchanges between the investor and intermediary does not significantly affect welfare. However, transparency regarding exchanges between the intermediary and borrower promotes trust on the part of the investor, increasing welfare. Further, this has asymmetric effects: borrowers and intermediaries achieve greater welfare benefits than investors. We discuss implications for what specific aspects of financial market transparency may facilitate more efficiency.financial intermediation, financial market transparency, pass through securities, multi-level trust games, experiments

Probability distributions of smeared quantum stress tensors

We obtain in closed form the probability distribution for individual measurements of the stress-energy tensor of two-dimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a shifted Gamma distribution with the shift given by the previously known optimal quantum inequality bound. For small values of the central charge it is overwhelmingly likely that individual measurements of the sampled energy density in the vacuum give negative results. For the case of a single massless scalar field, the probability of finding a negative value is 84%. We also report on computations for four-dimensional massless scalar fields showing that the probability distribution of the smeared square field is also a shifted Gamma distribution, but that the distribution of the energy density is not.Comment: 9 pages, 1 figure. Minor edits implemente

An Electronic Ordering System for Table Service Restaurants

As the title of this paper suggests, we have designed an ordering system for table service restaurants. The ordering system is the process of communication from customer-to-waitress-to-cook. In this first chapter, some of the problems which occur in table service restaurants will be briefly discussed and described to give the reader an idea of what this ordering system will attempt to solve. The specific problems and the proposed solution will be pointed out. The reader is probably asking, Just what is a table service restaurant?\u27\u27 A service restaurant is a restaurant where there is some type of service provided--by waitresses, busboys, maitre\u27d, etc. There are several ways to classify restaurants. Here we have described the characteristics of table service restaurants as classified by the Small Business Reporter. Included in this classification are the “service restaurants which provide luxury service, and the coffee shops which have limited service and come under the category of fast food service. The luxury service restaurants are both those restaurants that provide elaborate decor, specific atmosphere, well prepared and pleasantly served food, and those restaurants that cater more toward the family groups with less elegant menus, cheaper items, and less service and atmosphere. The exact border between luxury service and fast food service” is not very clear. In many instances they overlap, or, the same establishment has both types. The basic difference between the luxury service restaurant and the fast food service restaurant is based on the value-price relationship of eating out. The customer whose value-price relationship is centered on food as entertainment seeks more decor, more room, more service, more ti.me to enjoy his meal. On the other hand, the customer whose value-price relationship is based on food as a necessity or convenience will settle for less decor, less service, less time, less space, and more convenience and pre-prepared foods. The labor in these “service restaurants makes this type of operation more expensive and, therefore, less attractive to those who are primarily interested in a refueling stop . The utilization of seating capacity is lower in a service restaurant than in a fast food restaurant, because the customer may spend 25 to 50 percent of his time, while seated seated at the table, waiting for service. Therefore, the use of equipment, men and materials must be optimized in order to make the service restaurant a success. To put it simply, a good cash and food control system which optimizes the profits of a restaurant is what every food service manager likes