26,386 research outputs found
Discrete Quantum Gravity
We discuss the causal set approach to discrete quantum gravity. We begin by
describing a classical sequential growth process in which the universe grows
one element at a time in discrete steps. At each step the process has the form
of a causal set and the "completed" universe is given by a path through a
discretely growing chain of causal sets. We then introduce a method for
quantizing this classical formalism to obtain a quantum sequential growth
process which may lead to a viable model for a discrete quantum gravity. We
also give a method for quantizing random variables in the classical process to
obtain observables in the corresponding quantum process. The paper closes by
showing that a discrete isometric process can be employed to construct a
quantum sequential growth process.Comment: 19 pages which includes 3 figures created in LaTe
Examples of quantum integrals
We first consider a method of centering and a change of variable formula for
a quantum integral. We then present three types of quantum integrals. The first
considers the expectation of the number of heads in flips of a "quantum
coin". The next computes quantum integrals for destructive pairs examples. The
last computes quantum integrals for a (Lebesgue)^2 quantum measure. For this
last type we prove some quantum counterparts of the fundamental theorem of
calculus.Comment: I would like to submit this article for posting on Archiv
Markov random fields and Markov chains on trees
We consider probability measures on a space S(^A) (where S and A are countable and the σ-field is the natural one) which are Markov random fields with respect to a given neighbour relation ~ on A. In particular, we study the set G(II) of Markov random fields corresponding to a given Markov specification II, i.e. to a consistent family of "Markov" conditional probability distributions associated with the finite subsets of A. First, we review the relation between II and G(II). We consider also the representation of II by a family of interaction functions associated with the simplices of the graph (A,~) , together with some related problems. The rest of the thesis is concerned with the case where (A,~) is a tree. We define Markov chains on and consider their relation to the wider class of Markov random fields. We then derive analytical methods for the study of the set M(II) of Markov chains in G(II). These results are applied to homogeneous Markov specifications on regular infinite trees. Finally, we consider Markov specifications which are either attractive or repulsive with respect to a total ordering on S. For these we obtain quite strong results, including an exact condition for G(II) to contain precisely one element. We thereby generalise results obtained by Preston and Spitzer for binary S
From metaphysical principles to dynamical laws
My thesis in this paper is: the modern concept of laws of motion—qua dynamical laws—emerges in 18th-century mechanics. The driving factor for it was the need to extend mechanics beyond the centroid theories of the late-1600s. The enabling result behind it was the rise of differential equations.
In consequence, by the mid-1700s we see a deep shift in the form and status of laws of motion. The shift is among the critical inflection points where early modern mechanics turns into classical mechanics as we know it. Previously, laws of motion had been channels for truth and reference into mechanics. By 1750, the laws lose these features. Instead, now they just assert equalities between functions; and serve just to entail (differential) equations of motion for particular mechanical setups. This creates two philosophical problems. First, it’s unclear what counts as evidence for the laws of motion in the Enlightenment. Second, it’s a mystery whether these laws retain any notion of causality. That subverts the early-modern dictum that physics is a science of causes
Capping the Tax Exclusion of Employer-Sponsored Health Insurance: Is Equity Feasible?
Explores the feasibility of capping tax exemptions on premiums paid for employer-sponsored insurance without creating inequities by firm size, employees' age, and type of coverage -- by taxing benefits based on actuarial value or adjusting premiums
The Universe as a Quantum Computer
This article presents a sequential growth model for the universe that acts
like a quantum computer. The basic constituents of the model are a special type
of causal set (causet) called a -causet. A -causet is defined to be a
causet that is independent of its labeling. We characterize -causets as
those causets that form a multipartite graph or equivalently those causets
whose elements are comparable whenever their heights are different. We show
that a -causet has precisely two -causet offspring. It follows that there
are -causets of cardinality . This enables us to classify
-causets of cardinality in terms of -bits. We then quantize the
model by introducing a quantum sequential growth process. This is accomplished
by replacing the -bits by -qubits and defining transition amplitudes for
the growth transitions. We mainly consider two types of processes called
stationary and completely stationary. We show that for stationary processes,
the probability operators are tensor products of positive rank-1 qubit
operators. Moreover, the converse of this result holds. Simplifications occur
for completely stationary processes. We close with examples of precluded
events.Comment: 23 pages, 1 figur
Implementing National Health Reform: A Five-Part Strategy for Reaching the Eligible Uninsured
Recommends outreach strategies for Medicaid and subsidies, including identifying the eligible through tax forms, partnering with states to give hands-on assistance, designing consumer-friendly enrollment systems, and maximizing interagency coordination
How Effectively Does the American Recovery and Reinvestment Act Help Laid-Off Workers and States Cope With Health Care Costs?
Assesses the impact of the legislation to subsidize 65 percent of insurance premiums for eligible laid-off workers and to provide relief to state Medicaid programs. Analyzes House and Senate versions of each measure and their strengths and weaknesses
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