Papers by Gábor Hofer-Szabó
The Reichenbachian definition of the common cause is formally generalized for the quantum case in... more The Reichenbachian definition of the common cause is formally generalized for the quantum case in two different ways according to two possible definitions of the conditional probability on a Hilbert lattice, and it is shown that, unlike in the classical case, neither of the two definitions is consistent.
arXiv: Quantum Physics, May 22, 1998
It is shown that, given any finite set of pairs of random events in a Boolean algebra which are c... more It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.
This Chapter provides a brief overview of the interconnections between the various causality and ... more This Chapter provides a brief overview of the interconnections between the various causality and locality concepts in algebraic quantum field theory such as causal dynamics, primitive causality, local primitive causality, no-signaling, selective and nonselective measurements, local determinism, stochastic Einstein locality.
International Journal of Theoretical Physics, 2004
A partition {C i } i∈I of a Boolean algebra S in a probability measure space (S, p) is called a R... more A partition {C i } i∈I of a Boolean algebra S in a probability measure space (S, p) is called a Reichenbachian common cause system for the correlated pair A, B of events in S if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set I is called the size of the common cause system. It is shown that given any correlation in (S, p), and given any finite size n > 2, the probability space (S, p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions of S contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated.
The common cause principle says that every correlation is either due to a direct causal effect li... more The common cause principle says that every correlation is either due to a direct causal effect linking the correlated entities or is brought about by a third factor, a so-called common cause. The principle is of central importance in the philosophy of science, especially in causal explanation, causal modeling and in the foundations of quantum physics. Written for philosophers of science, physicists and statisticians, this book contributes to the debate over the validity of the common cause principle, by proving results that bring to the surface the nature of explanation by common causes. It provides a technical and mathematically rigorous examination of the notion of common cause, providing an analysis not only in terms of classical probability measure spaces, which is typical in the available literature, but in quantum probability theory as well. The authors provide numerous open problems to further the debate and encourage future research in this field.
In this chapter we turn to Reichenbach’s Common Cause Principle. The principle is generalized to ... more In this chapter we turn to Reichenbach’s Common Cause Principle. The principle is generalized to the LPT framework and the status of the various Common Cause Principles in algebraic quantum field theory is investigated. Then we motivate the noncommutative generalization of the principle and compare the Common Cause Principle with Bell’s local causality.
This paper is a further consideration of Hemmo and Shenker’s (2012) ideas about the proper concep... more This paper is a further consideration of Hemmo and Shenker’s (2012) ideas about the proper conceptual characterization of macrostates in statistical mechanics. We provide two formulations of how macrostates come about as elements of certain partitions of the system’s phase space imposed on by the interaction between the system and an observer, and we show that these two formulations are mathematically equivalent. We also reflect on conceptual issues regarding the relationship of macrostates to distinguishability, thermodynamic regularity, observer dependence, and the general phenomenon of measurement.
European Journal for Philosophy of Science
Philosophy of Science
I will argue that Kochen-Specker arguments do not provide an algebraic proof for quantum contextu... more I will argue that Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality since, for the argument to be effective, (1) operators must be uniquely associated with measurements and (2) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either 1 or 2 is not met. Arguments meeting 1 contain commuting operators that do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting 2 associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality.
States in algebraic quantum field theory "typically" establish correlation between spac... more States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set C, non-C screens off the correlation between A and B.
Quantum Theory and Local Causality
Quantum Theory and Local Causality
In this Chapter we explicitly construct a locally causal LQT for the EPR scenario. The model is t... more In this Chapter we explicitly construct a locally causal LQT for the EPR scenario. The model is the 1+1 dimensional local quantum Ising model (Muller and Vecsernyes). We show that the model is not only locally causal in Bell’s sense but also able to implement four pairs of events correlating in the singlet state.
In this Chapter we introduce the mathematical formalism of a local physical theory (LPT). Briefly... more In this Chapter we introduce the mathematical formalism of a local physical theory (LPT). Briefly, a LPT is an association of local operator algebras to spacetime regions subjected to the requirements of isotony, microcausality and covariance, all borrowed from algebraic quantum field theory. Depending on whether the local algebras are commutative or noncommutative, we call a LPT a local classical theory (LCT) or a local quantum theory (LQT). At the end of the chapter we motivate the application of von Neumann algebras in the LPT framework.
Uploads
Papers by Gábor Hofer-Szabó