Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Japan Association for Philosophy of Science

Causation and Intervention in Algebraic Quantum Field Theory

Yuichiro Kitajima

Published Jan 1, 2010• 0 citations
Publisher

Abstract

The basic idea of interventionist theories of causation is this: X causes Y iff there is a possible intervention on X for Y , and if the value of X were changed as a result of that intervention, then the value of Y would change.These theories are subdivided into reductive and non-reductive accounts.Reductive accounts, advanced by Menzies and Price (1993), reduce the notion of causation to a non-causal notion of intervention, while according to non-reductive accounts advanced by Woodward (2003), such a reduction is not possible.In the present paper, I investigate causation in algebraic quantum field theory from Woodward's point of view.I define the necessary condition for no causal relationship between the local algebras associated with two spacelike separated region, and show that this condition always holds under the usual axioms of algebraic quantum field theory.

DOI
10.4288/kisoron.38.1_9

Related papers

A survey of causality in algebraic relativistic quantum field theory

Francisco Calderón Ossa

The axiomatic formulation of an Algebraic Relativistic Quantum Field Theory leads naturally -via the Haag-Kastler axioms- to the fact that operators representing observables generate a von Neumann algebra localized in a space-time region in which said observations are made. I present and explain the axioms, as well as the mathematical preliminaries needed to understand them and apply them to the so-called causal diamond and Fermi's Two-Atom System. The latter shows the importance of formulating axioms concerning causality that try to make compatible the requirement from Special Relativity according to which no causal influence can travel faster than the speed of light and the quantum mechanical theory of measurement and preparability of states. For a relativistic field-theoretic setting, these concepts must be re-formulated, and this reasoning suggests that the operator algebra must be a type III von Neumann factor. I also introduce some philosophical problems concerning our usual notion of causality from Hume to contemporary theories of counterfactual causation and show how the algebraic structure of the theory is deeply related to the causal one and how this theory can be extended if we change the way we think about causality, measurements, and local preparability of states.

•Jan 1, 2019•0 citations

Using interventions to discover quantum causal structure

Sally Shrapnel

Identifying causal relations plays an indispensable role in science, economics, medicine and everyday life. Interventionist causation associates the discovery of such relations with the possibility of manipulation or intervention. A causes B, if manipulating A in the right way can bring about changes in B. The main technical tool, the causal model, can be seen as a device for telling us how and why certain actions are more effective than others. Such models have found application in almost every scientific discipline. However, despite several decades of sophisticated analysis and a wealth of technical results, interventionist causal methods are known to fail in the quantum case. The quantum domain, with its peculiar, counterintuitive features, is widely considered an inhospitable environment in which to apply our usual causal discovery tools. This causal skepticism presents us with a puzzle. Physicists are now able to manipulate and control quantum systems, and the design and construction of quantum technology relies on an ability to identify when one strategy will work and another will fail. From the perspective of interventionist causation, it seems that a formal account of quantum causal modelling ought to be possible. The main contribution of this thesis is to provide an extension of interventionist methodology to the quantum case. In Chapter 1, I introduce interventionist causation from the perspective of two giants of the field: Judea Pearl and James Woodward. The Causal Markov Condition (CMC) and Faithfulness assumptions are presented, and I draw particular attention to the discovery of casual structure. I touch on some of the well-known problems with interventionist causation per se. In Chapter 2, I put this methodology to work in a quantum mechanical context. Following tradition, we examine one of the Bell experiments in order to determine how the classical interventionist framework fails. Noting that the usual response is to demand that one drops either the CMC or Faithfulness, I suggest that neither approach is particularly satisfactory and argue for an alternative. I discuss some reasons why the interventionist is forced to pursue this different path. In Chapter 3, I motivate the possibility of an interventionist account of quantum causation. I first look at how physicists represent quantum technology in order to make interventionist and counterfactual inferences: via the use of quantum circuit diagrams. Using three examples I demonstrate the manner in which these diagrams can be used to facilitate causal inference. In Chapter 4, I examine some recent attempts at characterising quantum causal models due to work from the quantum foundations community. I present three such accounts and explain why I endorse a fourth, the focus of the next chapter. In Chapter 5, I present a new framework that allows for the discovery of interventionist quantum causal structure. I finish the thesis with a summary and some suggestions for further work.

•Nov 18, 2016•2 citations

Relativistic Causality in Algebraic Quantum Field Theory

John Earman, Giovanni Valente

This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory (AQFT). In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not (as has sometimes been claimed) by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events.

International Studies in the Philosophy of Science•Jan 2, 2014•52 citations

Causal closedness of quantum field theory

Gábor Hofer‐Szabó, Miklós Rédei, László E. Szabó

The Common Cause Principle in algebraic relativistic quantum field theory Algebraic quantum field theory (AQFT) predicts correlations between projections A, B lying in von Neumann algebras A ( V 1 ), A ( V 2 ) associated with spacelike separated spacetime regions V 1 , V 2 in Minkowski spacetime. These spacelike correlations predicted by AQFT lead naturally to the question of the status of Reichenbach's Common Cause Principle within AQFT. The aim of this chapter is to investigate the problem of status of Reichenbach's Common Cause Principle within AQFT. Since the correlated projections belong to algebras associated with spacelike separated regions, a direct causal influence between them is excluded by the Special Theory of Relativity. Consequently, compliance of AQFT with Reichenbach's Common Cause Principle would mean that for every correlation between projections A and B lying in von Neumann algebras A ( V 1 ) and A ( V 2 ), respectively, associated with spacelike separated spacetime regions V 1 , V 2 , there must exist a projection C possessing the probabilistic properties that qualify it to be a Reichenbachian common cause of the correlation between A and B . However, since observables and hence also the projections in AQFT must be localized, one also has to specify the spacetime region V with which the von Neumann algebra A(V) is associated that contains the common cause C . Intuitively, the region V should be disjoint from both V 1 and V 2 but should not be causally disjoint from them in order to leave room for a causal effect of C on the events A and B so that C can account for the correlation between A and B .

Cambridge University Press eBooks•May 16, 2013•0 citations

Causality and chance in relativistic quantum field theories

Richard Healey

Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.

arXiv:1405.3254•May 13, 2014•0 citations

Discovering Quantum Causal Models (final)

Sally Shrapnel

Costa and Shrapnel [2016] have recently proposed an interventionist theory of quantum causation. The formalism generalises the classical methods of Pearl [2000] and allows for the discovery of quantum causal structure via localised interventions. Classical causal structure is presented as a special case of this more general framework. I introduce the account and consider whether this formalism provides a causal explanation for the Bell correlations.

•Jun 4, 2017•0 citations
The basic idea of interventionist theories of causation is this: X causes Y iff there is a possible intervention on X for Y , and if the value of X were changed as a result of that intervention, then the value of Y would change.These theories are subdivided into reductive and non-reductive accounts.Reductive accounts, advanced by Menzies and Price (1993), reduce the notion of causation to a non-causal notion of intervention, while according to non-reductive accounts advanced by Woodward (2003), such a reduction is not possible.In the present paper, I investigate causation in algebraic quantum field theory from Woodward's point of view.I define the necessary condition for no causal relationship between the local algebras associated with two spacelike separated region, and show that this condition always holds under the usual axioms of algebraic quantum field theory.
The axiomatic formulation of an Algebraic Relativistic Quantum Field Theory leads naturally -via the Haag-Kastler axioms- to the fact that operators representing observables generate a von Neumann algebra localized in a space-time region in which said observations are made. I present and explain the axioms, as well as the mathematical preliminaries needed to understand them and apply them to the so-called causal diamond and Fermi's Two-Atom System. The latter shows the importance of formulating axioms concerning causality that try to make compatible the requirement from Special Relativity according to which no causal influence can travel faster than the speed of light and the quantum mechanical theory of measurement and preparability of states. For a relativistic field-theoretic setting, these concepts must be re-formulated, and this reasoning suggests that the operator algebra must be a type III von Neumann factor. I also introduce some philosophical problems concerning our usual notion of causality from Hume to contemporary theories of counterfactual causation and show how the algebraic structure of the theory is deeply related to the causal one and how this theory can be extended if we change the way we think about causality, measurements, and local preparability of states.
Identifying causal relations plays an indispensable role in science, economics, medicine and everyday life. Interventionist causation associates the discovery of such relations with the possibility of manipulation or intervention. A causes B, if manipulating A in the right way can bring about changes in B. The main technical tool, the causal model, can be seen as a device for telling us how and why certain actions are more effective than others. Such models have found application in almost every scientific discipline. However, despite several decades of sophisticated analysis and a wealth of technical results, interventionist causal methods are known to fail in the quantum case. The quantum domain, with its peculiar, counterintuitive features, is widely considered an inhospitable environment in which to apply our usual causal discovery tools. This causal skepticism presents us with a puzzle. Physicists are now able to manipulate and control quantum systems, and the design and construction of quantum technology relies on an ability to identify when one strategy will work and another will fail. From the perspective of interventionist causation, it seems that a formal account of quantum causal modelling ought to be possible. The main contribution of this thesis is to provide an extension of interventionist methodology to the quantum case. In Chapter 1, I introduce interventionist causation from the perspective of two giants of the field: Judea Pearl and James Woodward. The Causal Markov Condition (CMC) and Faithfulness assumptions are presented, and I draw particular attention to the discovery of casual structure. I touch on some of the well-known problems with interventionist causation per se. In Chapter 2, I put this methodology to work in a quantum mechanical context. Following tradition, we examine one of the Bell experiments in order to determine how the classical interventionist framework fails. Noting that the usual response is to demand that one drops either the CMC or Faithfulness, I suggest that neither approach is particularly satisfactory and argue for an alternative. I discuss some reasons why the interventionist is forced to pursue this different path. In Chapter 3, I motivate the possibility of an interventionist account of quantum causation. I first look at how physicists represent quantum technology in order to make interventionist and counterfactual inferences: via the use of quantum circuit diagrams. Using three examples I demonstrate the manner in which these diagrams can be used to facilitate causal inference. In Chapter 4, I examine some recent attempts at characterising quantum causal models due to work from the quantum foundations community. I present three such accounts and explain why I endorse a fourth, the focus of the next chapter. In Chapter 5, I present a new framework that allows for the discovery of interventionist quantum causal structure. I finish the thesis with a summary and some suggestions for further work.
This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory (AQFT). In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not (as has sometimes been claimed) by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events.
The Common Cause Principle in algebraic relativistic quantum field theory Algebraic quantum field theory (AQFT) predicts correlations between projections A, B lying in von Neumann algebras A ( V 1 ), A ( V 2 ) associated with spacelike separated spacetime regions V 1 , V 2 in Minkowski spacetime. These spacelike correlations predicted by AQFT lead naturally to the question of the status of Reichenbach's Common Cause Principle within AQFT. The aim of this chapter is to investigate the problem of status of Reichenbach's Common Cause Principle within AQFT. Since the correlated projections belong to algebras associated with spacelike separated regions, a direct causal influence between them is excluded by the Special Theory of Relativity. Consequently, compliance of AQFT with Reichenbach's Common Cause Principle would mean that for every correlation between projections A and B lying in von Neumann algebras A ( V 1 ) and A ( V 2 ), respectively, associated with spacelike separated spacetime regions V 1 , V 2 , there must exist a projection C possessing the probabilistic properties that qualify it to be a Reichenbachian common cause of the correlation between A and B . However, since observables and hence also the projections in AQFT must be localized, one also has to specify the spacetime region V with which the von Neumann algebra A(V) is associated that contains the common cause C . Intuitively, the region V should be disjoint from both V 1 and V 2 but should not be causally disjoint from them in order to leave room for a causal effect of C on the events A and B so that C can account for the correlation between A and B .
Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.