arXiv:quant-ph/9903011

Topology measurement within the histories approach

Roman B. Breslav, G. N. Parfionov, Romàn R. Zapatrin

Published Mar 3, 1999• 3 citations

Abstract

An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of topology is suggested. The correspondence between these models and discretised spacetime models is established.

DOI: 10.48550/arxiv.quant-ph/9903011

Related papers

Empirical topology in the histories approach to quantum theory

G. N. Parfionov, Romàn R. Zapatrin

An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of topology is suggested. The correspondence between these models and discretized spacetime models is established.

arXiv:gr-qc/9703011Mar 5, 19971 citation

Spacetime topology from the tomographic histories approach I: `Classical' Case

I. Raptis, Petros Wallden, Romàn R. Zapatrin

The tomographic histories approach is presented. As an inverse problem, we recover in an operational way the effective topology of the extended configuration space of a system. This means that from a series of experiments we get a set of points corresponding to events. The difference between effective and actual topology is drawn. We deduce the topology of the extended configuration space of a ‘classical ’ (i.e. non-relativistic) system, using certain concepts from the consistent histories approach to Quantum Mechanics, such as the notion of a record. A few remarks about the case of a relativistic system, preparing the ground for a forthcoming paper sequel to this, are made in the end. 1 Introduction with Motivational Remarks In the standard formulation of relativity theory, the spacetime topology is a priori fixed by the theorist to that of a continuous manifold; hence, it is not an observable entity. Only the metric structure is traditionally supposed to be dynamically variable. With the exception of Wheeler’s celebrated, but largely heuristic, spacetime foam scenario

Jun 16, 20050 citations

Effective Topology from Spacetime Tomography

Petros Wallden

We recover the effective topology of spacetime using the notion of record from the decoherent histories approach to Quantum Theory. From a series of (gedanken) experiments, we obtain the set of possible events, grouped into sub-sets that corresponds to histories, but with no other information such as (causal) order or any notion of proximity. This corresponds to tomography of the "effective" spacetime, that is done in an operational way. Making certain assumptions about these records, and using the existence of upper bound in the speed of transfer of matter and information, we recover the full partial (causal) order up to certain ambiguities. The partially ordered set of events corresponds to an "effective" causal set which is a discretized version of spacetime with the causal relation as defining feature. We conclude with a derivation of the topology of this effective discretized spacetime.

Journal of Physics Conference SeriesMay 1, 20071 citation

Entangled histories

Jordan S. Cotler, Frank A. Wilczek

We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we demonstrate that our formalism allows us to analyze a quantum version of history in which we reconstruct the past by observations. In particular, we can pass from measurements to inferences about ‘what happened’ in a way that is sensible and free of paradox. Our framework allows for a richer understanding of the temporal structure of quantum theory, and we construct history states that embody peculiar, non-classical correlations in time.

arXiv:1502.02480Physica ScriptaMay 12, 201634 citations

Dynamical wavefunction collapse models in quantum measure theory

Fay Dowker B, Yousef Ghazi-Tabatabai

The structure of collapse models is investigated in the framework of quantum measure theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach which puts both systems on a spacetime footing. The nature of the coupling is exposed: the classical histories have no dynamics of their own but are simply tied, more or less closely, to the quantum histories.

arXiv:0712.2924Journal of Physics A Mathematical and TheoreticalMay 2, 200817 citations

Entangled History

Jordan S. Cotler, Frank A. Wilczek

We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we demonstrate that our formalism allows us to analyze a quantum version of history in which we reconstruct the past by observations. In particular, we can pass from measurements to inferences about what happened in a way that is sensible and free of paradox. Our framework allows for a richer understanding of the temporal structure of quantum theory, and we construct history states that embody peculiar, non-classical correlations in time.

Feb 9, 20150 citations