Consistent histories of systems and measurements in spacetime

Traditional interpretations of quantum theory in terms of wave function collapse are particularly unappealing when considering the universe as a whole, where there is no clean separation between classical observer and quantum system and where the description is inherently relativistic. As an alternative, the consistent histories approach provides an attractive "no collapse" interpretation of quantum physics. Consistent histories can also be linked to path-integral formulations that may be readily generalized to the relativistic case. A previous paper described how, in such a relativistic spacetime path formalism, the quantum history of the universe could be considered to be an eignestate of the measurements made within it. However, two important topics were not addressed in detail there: a model of measurement processes in the context of quantum histories in spacetime and a justification for why the probabilities for each possible cosmological eigenstate should follow Born's rule. The present paper addresses these topics by showing how Zurek's concepts of einselection and envariance can be applied in the context of relativistic spacetime and quantum histories. The result is a model of systems and subsystems within the universe and their interaction with each other and their environment.Comment: RevTeX 4; 37 pages; v2 is a revision in response to reviewer comments, connecting the discussion in the paper more closely to consistent history concepts; v3 has minor editorial corrections; accepted for publication in Foundations of Physics; v4 has a couple minor typographical correction

Foundations of a spacetime path formalism for relativistic quantum mechanics

Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincar\'e invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, "off-shell" theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to non-relativistic quantum mechanics.Comment: RevTex 4, 42 pages; V6 is as accepted for publication in the Journal of Mathematical Physics, updated in response to referee comments; V7 includes final editorial correction

Exploiting the Hierarchical Structure of Rule-Based Specifications for Decision Planning

Rule-based specifications have been very successful as a declarative approach in many domains, due to the handy yet solid foundations offered by rule-based machineries like term and graph rewriting. Realistic problems, however, call for suitable techniques to guarantee scalability. For instance, many domains exhibit a hierarchical structure that can be exploited conveniently. This is particularly evident for composition associations of models. We propose an explicit representation of such structured models and a methodology that exploits it for the description and analysis of model- and rule-based systems. The approach is presented in the framework of rewriting logic and its efficient implementation in the rewrite engine Maude and is illustrated with a case study.

Tool paper: Combining Alf and UML in modeling tools: An example with papyrus

Conference of 15th International Workshop on OCL and Textual Modeling, OCL 2015 ; Conference Date: 28 September 2015; Conference Code:118142International audienceThe Unified Modeling Language has been used largely in the software community to draw pictures for designing and documenting software written in other languages. The real executable semantics of a program are determined by the programming language, while the UML models themselves do not have a precise enough meaning to fully specify the executable functionality of the system being developed. Recently, however, there has been a great deal of work toward the standardization of precise, executable semantics for UML models - the "meaning" behind the pictures: Foundational UML (FUML) adopted by the Object Management Group in 2008, the Action Language for FUML (Alf) adopted in 2010, the recently completed Precise Semantics for UML Composite Structures (PSCS) and the Precise Semantics for UML State Machines (PSSM), now in progress. Together, these standards effectively provide a new combined graphical and textual language for precise, executable modeling. In particular, the Alf language goes beyond simply providing a textual "action language" for detailed behavioral code within graphical models, by including textual notation for FUML structural object-oriented modeling constructs (e.g., packages, classes, associations, etc.). This opens up the possibility of tooling allowing various parts of a UML model to be represented both graphically and textually (while preserving the same semantic level), with bidirectional synchronization between the two representations. This paper presents the achievement of an initial integration of UML and Alf in the context of the Papyrus tool for the specification of executable models

Executable Modeling with fUML and Alf in papyrus: Tooling and experiments

Conference of 1st International Workshop on Executable Modeling, EXE 2015 ; Conference Date: 27 September 2015; Conference Code:119946International audiencefUML and Alf are two OMG standards dealing with executable modeling in UML. fUML focuses on semantic aspects, while Alf focuses on syntax. Papyrus (the UML/SysML modeler of the Eclipse foundation) provides tool support for these two standards. The purpose of this article is to provide the community with feedback and lessons learned by the Papyrus team regarding their implementation and usage of these standards, with the perspective of domain-specific uses of the tool. The feedback related to fUML is intended to highlight how tool developers can leverage fUML semantics to develop user and/or domain-specific model execution environments. The feedback related to Alf focuses on key end-user functionality: the combined usage of Alf and UML, with or without profiles