If \{A(V)\} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V_1 and V_2 are spacelike separated spacetime regions, then the system (A(V_1),A(V_2),ϕ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A \in A(V_1), B \in A(V_2) correlated in the normal state ϕthere exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V_1 and V_2 and disjoint from both V_1 and V_2, a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system (A(V_1),A(V_2),ϕ) with a locally normal and locally faithful state ϕand open bounded V_1 and V_2 satisfies the Weak Reichenbach's Common Cause Principle.
The aim of this paper is to give a sharp definition of Bell's notion of local causality. To this end, first we unfold a framework, called local physical theory, integrating probabilistic and spatiotemporal concepts. Formulating local causality within this framework and classifying local physical theories by whether they obey local primitive causality --- a property rendering the dynamics of the theory causal, we then investigate what is needed for a local physical theory, with or without local primitive causality, to be locally causal. Finally, comparing Bell's local causality with the Common …
In classic cases, Reichenbach's principle implies that discriminating between common causes and causality is unprincipled since the discriminative results essentially depend on the selection of possible conditional variables. For some typical quantum cases, K.Reid $et$ $al$. \href{https://www.nature.com/articles/nphys3266}{[Nat. Phys. 11, 414 (2015)]} presented the statistic $C$ which can effectively discriminate quantum common causes and quantum causality over two quantum random variables (i.e., qubits) and which only uses measurement information about these two variables. In this paper, we f…
Repeated unbiased measurements cause a continual application of the weak causality principle, leading to an apparent arrow of time for continuously-monitored quantum systems.
In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that --leaving aside instrumentalism which restricts the physical meaning of QM to the algorithmic prediction of measurement outcomes-- the many interpretations which can be found in the literature can be distinguished through the way they model the measurement process, either in terms of the efficient cause or in terms of the final cause. We will discuss and analyze why both, 'final cause' and 'efficient cause' models, f…
It has long been recognized as a difficult problem to determine whether the observed statistical correlation between two classical variables arise from causality or from common causes. Recent research has shown that in quantum theoretical framework, the mechanisms of entanglement and quantum coherence provide an advantage in tackling this problem. In some particular cases, quantum common causes and quantum causality can be effectively distinguished using observations only. However, these solutions do not apply to all cases. There still exist enormous cases in which quantum common causes and qu…
We distinguish two sub-types of each of the two causality principles formulated in connection with the Common Cause Principle in [Hen05] and raise and investigate the problem of logical relations among the resulting four causality principles. Based in part on the analysis of the status of these four principles in algebraic quantum field theory we will argue that the four causal principles are non-equivalent.
The principle of common cause is discussed as a possible fundamental principle of physics. Some revisions of Reichenbach's formulation of the principle are given, which lead to a version given by Bell. Various similar forms are compared and some equivalence results proved. The further problems of causality in a quantal system, and indeterministic causal structure, are addressed, with a view to defining a causality principle applicable to quantum gravity.
It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras $\cA(V_1),\cA(V_2)$ associated with spacelike separated spacetime regions $V_1,V_2$ have a (Reichenbachian) common cause located in the union of the backward light cones of $V_1$ and $V_2$. Further comments on causality and independence in quantum field theory are made.
Explaining observations in terms of causes and effects is central to all of empirical science. Correlations between entangled quantum particles, however, seem to defy such an explanation. To recover a causal picture in this case, some of the fundamental assumptions of causal explanations have to give way. Here we consider a broad class of models where one of these assumptions, Bell's local causality, is relaxed by allowing a direct influence from one measurement outcome to the other. We use interventional and observational data from a photonic experiment to bound the strength of this causal in…
We investigate the Cherenkov radiation triggered by qubit acceleration simulated by superconducting circuit. By analyzing the radiation probability, we confirm the existence of Cherenkov speed threshold, implying that simulating superluminal qubit motion is possible for such a scenario. A question immediately arises: Is such motion compatible with the causality principle? To address the question, we perform a causality test on the simulating system based on the recently developed notion of temporal quantum correlations, pseudo-density matrix and temporal quantum steering. The results suggest t…
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality, which asserts that an effect never precedes its cause, in any reference frame. By analyzing a numerical example of Bell's experiment with entangled pairs of photons, we show how observers in two inertial reference frames can disagree about the causality relation between two events. One observer claims that event 1 is the cause of event 2, while the other clai…
Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a subjective lack of information regarding the physical reality of the system. In the present paper, I explore how the operator formalism accommodates the vast number of possible states and measurements by characterizing its essential function as a description of causality relations between initial conditions and subsequent observations. It is shown that any complete…
Bell's 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbach's Principle of Common Cause. Despite being a hallmark of scientific thought, dropping the principle has been widely regarded as a much less bitter medicine than the perceived alternative---dropping relativistic causality. Recently, however, some authors have proposed that modified forms of Reichenbach's principle could be maintained even with relativistic causality. Here we break down Reichenbach's principle into two independent assumptions---the Principle of Common Cau…
Quantum mechanics permits nonlocality---both nonlocal correlations and nonlocal equations of motion---while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality---``superquantum" correlations, and nonlocal ``jamming" of correlations---and derive new results for the jamming model. In one space dimension, jamming allows reversal of the sequence of cause and effect; in higher dimensions, however, effect never precedes cause.
In papers published in the 25 years following his famous 1964 proof John Bell refined and reformulated his views on locality and causality. Although his formulations of local causality were in terms of probability, he had little to say about that notion. But assumptions about probability are implicit in his arguments and conclusions. Probability does not conform to these assumptions when quantum mechanics is applied to account for the particular correlations Bell argues are locally inexplicable. This account involves no superluminal action and there is even a sense in which it is local, but it…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global evolution G is required to be shift-invariant (it acts the same everywhere) and causal (information cannot be transmitted faster than some fixed number of cells per time step). At least in the classical, reversible and quantum cases, these two top-down axiomatic conditions are sufficient to entail more bottom-up, operational descriptions of G. We investigate whethe…
Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quant…
Quantum causality violates classical intuitions of cause and effect and is a unique quantum feature different from other quantum phenomena such as entanglement and quantum nonlocality. In order to avoid the detection loophole in quantum causality, we initiate the study of the detection efficiency requirement for observing quantum causality. We first show that previous classical causal inequalities require detection efficiency at least 95.97% (89.44%) to show violation with quantum (nonsignaling) correlations. Next we derive a classical causal inequality I_{222} and show that it requires lower …
Intervention theories of causality define a relationship as causal if appropriately specified interventions to manipulate a putative cause tend to produce changes in the putative effect. Interventionist causal theories are commonly formalized by using directed graphs to represent causal relationships, local probability models to quantify the relationship between cause and effect, and a special kind of conditioning operator to represent the effects of interventions. Such a formal model represents a family of joint probability distributions, one for each allowable intervention policy. This paper…
In my commentary, I will argue that the conclusions drawn in the paper "Noncommutative causality in algebraic quantum field" theory by Gábor Hofer-Szabó (and similar publications) are incorrect. As proven by J.S. Bell, a local common causal explanation of correlations violating the Bell inequality is impossible.
