Quantum Reality and Measurement: A Quantum Logical Approach

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context.Comment: 16 pages, Latex. Presented at the Conference "Quantum Theory: Reconsideration of Foundations, 5 (QTRF5)," Vaxjo, Sweden, 15 June 2009. To appear in Foundations of Physics

Digraph Complexity Measures and Applications in Formal Language Theory

We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this connection, and obtain several new algorithmic insights regarding both cycle rank and star height. Among other results, we show that computing the cycle rank is NP-complete, even for sparse digraphs of maximum outdegree 2. Notwithstanding, we provide both a polynomial-time approximation algorithm and an exponential-time exact algorithm for this problem. The former algorithm yields an O((log n)^(3/2))- approximation in polynomial time, whereas the latter yields the optimum solution, and runs in time and space O*(1.9129^n) on digraphs of maximum outdegree at most two. Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem. Namely, the star height problem for bideterministic languages is NP-complete, and this holds already for binary alphabets. Then we translate the algorithmic results concerning cycle rank to the bideterministic star height problem, thus giving a polynomial-time approximation as well as a reasonably fast exact exponential algorithm for bideterministic star height.Comment: 19 pages, 1 figur

Public Spending on Income-Tested Social Welfare Programs for Investment and Consumption Purposes

The Clinton administration contends that public spending for investment should be increased, but public spending for consumption should be decreased. This article reports findings from a study that investigated the trend in public spending from 1975 to 1992 for social welfare programs that are targeted to low-income families and individuals. The study found that public spending for social welfare programs for investment purposes declined generally during that period and public spending for consumption purposes increased primarily because of the increase in medical benefits

Lessons from Private Health Insurance

All across the country there is a sense of urgency, and even of crisis over what is happening in the health industry. Of special concern are the rapid rate of increase in the cost of health care services and the increasing national expenditures for health care. For fiscal year 1976, the total U.S. spending for health care reached $149.8 billion, or a per capita expenditure of$638. Expressed as a percentage of the gross national product (GNP), the national spending for health care reached a record-breaking 8.6 percent.1 From the early 1960s--except during the period from August 1971 through April 1974, when the prices of medical care services were controlled--these prices have risen about two times faster than those of non-health-care services. Thus the differential between the prices of these two types of services has increased markedly during the period. Especially disturbing is that the cost of hospital care services, expenditures for which comprise the largest proportion (40 percent) of total national health care expenditures, are increasing faster than any other type of medical care services

Reconstructing Bohr's Reply to EPR in Algebraic Quantum Theory

Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.Comment: 13 pages, Late

Schrdinger Equations with nonlinearity of integral type

We consider the Cauchy problem for the nonlinear Schrodinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. Concerning the problem with finite initial time, we prove the global well-posedness in the largest space L2(!R2 ). Concerning the problem with infinite initial time, we prove the existence of modified wave operators on a dense set of small and sufficiently regular asymptotic states