Primitive Causality Research Articles

The causal axioms of algebraic quantum field theory: A diagnostic

Algebraic quantum field theory (AQFT) puts forward three “causal axioms” that aim to characterize the theory as one that implements relativistic causation: the spectrum condition, microcausality, and primitive causality. In this paper, I aim to show, in a minimally technical way, that none of them fully explains the notion of causation appropriate for AQFT because they only capture some of the desiderata for relativistic causation I state or because it is often unclear how each axiom implements its respective desideratum. After this diagnostic, I will show that a fourth condition, local primitive causality (LPC), fully characterizes relativistic causation in the sense of fulfilling all the relevant desiderata. However, it only encompasses the virtues of the other axioms because it is implied by them, as I will show from a construction by Haag and Schroer (1962). Since the conjunction of the three causal axioms implies LPC and other important results in QFT that LPC does not imply, and since LPC helps clarify some of the shortcomings of the three axioms, I advocate for a holistic interpretation of how the axioms characterize the causal structure of AQFT against the strategy in the literature to rivalize the axioms and privilege one among them.

On causality of wave motion in nonlocal theories of elasticity: a Kramers–Kronig relations study

In this paper, the subject of the principle of causality and the physical realizability in the wave motion characteristics within a linear nonlocal elastic medium is examined. The principle of primitive causality is examined via Kramers–Kronig (K–K) relations and the principle of relativistic causality or the Einstein causality is examined via wave motion responses. Gradient as well as integral type nonlocality has been considered. Methodology here involves a Fourier frequency domain based spectral analysis and the wave motion characteristics include: wave modes, group speeds and frequency response function. In general, due to existence of atleast one of the non-physical features in the characteristics, violation of the causality is observed. The non-physical features include: existence of infinitesimally small or zero speeds; existence of very large or infinite speeds; existence of negative speeds; and absence of attenuation of waves. Violation to the primitive causality takes place as a disagreement to the K–K relations, either due to existence of negative and/or zero group speeds or due to absence of wave attenuation in the possible wave modes. Violation to Einstein causality is observed due to existence of infinitely large group speeds. Agreement to the primitive causality is achieved due to the presence of both wave dispersion and wave attenuation in the wave modes. Although existence of infinitely large group speeds violates Einstein causality, however, violation of the primitive causality is not observed. Upon considering only the physically realizable wavemodes, it is observed that, a local Neumann type boundary condition may be sufficient to conduct a wave motion study in a class of nonlocal boundary value problems. As an application of the primitive causality to the Fourier domain analysis, the wavenumbers from the K–K relations are utilized to demonstrate a mitigation effect of certain non-physical features in the wave motion responses.

Generalized Veselago-Pendry lenses via complex transformation optics.

Field solutions for a conventional Veselago-Pendry (VP) flat lens with ϵ=-ϵ 0 and μ=-μ 0 can be derived based on transformation optics (TO) principles. The TO viewpoint makes it clear that perfect imaging by a VP lens is a consequence of multivalued nature of the particular coordinate transformation involved. This transformation is equivalent to a "space folding" whereby one point in the transformed domain (source point) is mapped to three different points in the physical domain (the original source point plus two focal points). In theory, a VP lens would enable the recovery of the entire range of spectral components, i.e. both propagating and evanescent fields, thus characterizing a "perfect lens". Such lens, if lossess, is indeed "perfect" for monochromatic waves; however, for any realistic wave packet the space folding interpretation provided by TO makes it clear that a VP lens violates primitive causality constraints, which precludes any practical realization. Here, we utilize complex transformation optics (CTO) to derive generalized Veselago-Pendry (GVP) lenses without requiring a multivalued transformation. Unlike the conventional VP lens, the proposed lenses can fully recover the evanescent spectra under more general conditions that include the presence of (anisotropic) material loss/gain.

On the concept of Bell’s local causality in local classical and quantum theory

The aim of this paper is to implement Bell’s notion of local causality into a framework, called local physical theory. This framework, based on the axioms of algebraic field theory, is broad enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will arise as the classical case of our definition. 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 to be locally causal. Finally, comparing local causality with the common cause principles and relating both to the Bell inequalities we find a nice parallelism: Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.

Does the Reeh–Schlieder theorem violate relativistic causality?

The Reeh–Schlieder theorem is a purely relativistic result in local quantum field theory, which is often regarded as raising a conflict with relativistic causality, namely the requirement that causal processes cannot propagate faster than light. Allegedly, under an operational interpretation, the theorem would entail non-local effects, in that by performing an operation within a region of Minkowski spacetime one could instantaneously change the state of the field over another spacelike separated region. Here, we argue that such a conflict is only apparent. Indeed, a suitable understanding of the notion of local operations helps one dissolve the puzzle. Accordingly, even if one does not exclude superluminal signalling, the latter cannot be controlled, and thus it may not be used to give rise to causal paradoxes. On the other hand, we maintain that relativistic causality is expressed by the axiom of local primitive causality, assuring no superluminal propagation of a field. The Reeh–Schlieder theorem can be shown to be fully consistent with such a condition, and hence it does not imply that matter and energy carried by a quantum field can travel faster than light. Therefore, there is no violation of relativistic causality at all.

Relativistic Causality in Algebraic Quantum Field Theory

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.

Causality and mathematical models in vibration and acoustics: A realistic perspective.

Acoustic and vibrations applications require stricter causality conceptions than primitive causality (effect never precedes cause). Relativistic causality (nothing travels faster than light) is irrelevant; there is no practical reason that a satisfactory continuum‐mechanical model, holding for low to moderate frequencies, be relativistically invariant. Modifying the requirement so that the speed of light is replaced by some acoustic speed is not satisfactory, as the insertion of dissipative mechanisms into any continuum‐mechanical model invariably results in small precursors which may precede sonic‐velocity wavefronts. These are small, but they are formally nonzero at arbitrarily large distances in advance of the front. The present paper follows Ginzberg (1955) and advocates acoustic causality: the requirements that (i) the precursors die out rapidly with distance, (ii) up to some frequency of interest acoustic disturbances genuinely propagate, with the attenuation per wavelength being substantially less than unity, and (iii) vibrations and propagation are governed by coupled partial differential equations. With these principles as a guide, approximate relations involving extrapolations into the complex plane are derived, and it is shown how error bounds can be placed on applications of various members of a derived family of Kramers–Kronig relations. Very low‐frequency relaxation processes account for proportional damping in vibrations.

Local primitive causality and the common cause principle in quantum field theory

If $$\mathcal{A}$$ (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 ( $$\mathcal{A}$$ (V 1 ), $$\mathcal{A}$$ (V 2 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈ $$\mathcal{A}$$ (V 1 ), B∈ $$\mathcal{A}$$ (V 2 ) correlated in the normal state φ there 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 ( $$\mathcal{A}$$ (V 1 ), $$\mathcal{A}$$ (V 2 ), φ) with a locally normal and locally faithful state φ and suitable bounded V 1 and V 2 satisfies the Weak Reichenbach's Common Cause Principle.

Perceived contingency of skill and chance events: A developmental analysis.

Outcomes in skill-controlled activities are contingent on people's attributes and behavior. Outcomes of chance activities are inherently noncontingent. In this study, we explored age differences in recognition of this distinction between skill and chance. Kindergarteners, fourth graders, eighth graders, and college students took part in one game of chance and one game of skill. After each game, subjects predicted winnings of other players who differed in certain attributes (e.g., intelligence) and behavior (e.g., effort) that would influence only skill outcomes. Two developmental trends emerged: (a) On both chance and skill tasks, older subjects expected variations in attributes and behavior to have less impact on task outcomes than did younger subjects; and (b) older subjects were more adept at making predictions that reflected contingency of skill and noncontingency of chance. Kindergarteners showed no ability to make skillchance distinction. Fourth graders were aware of distinction at a gross qualitative level, but their predictions showed that they were unaware of some of most important logical implications of that distinction. Eighth graders and college students were aware of skill-chance distinction and most of its logical implications; yet their predictions revealed a lingering belief that chance outcomes could be influenced slightly by variations in people's attributes and behavior. This last finding is interpreted in light of Rosch's (Rosch & Mervis, 1975) model of category formation. To make accurate judgments about what we can and cannot control, we must accurately judge contingency of outcomes. If an outcome (e.g., rain, a roll of dice) is not contingent on people's behavior, then we will be unable to control it. (For more details on determinants of control, see Weisz & Stipek, 1982.) There is mounting evidence that such noncontingency is very difficult for young children to detect. Piaget (1930) reported that children younger than 6 or 7 years show primitive psychological causality, that is, the belief that any desire whatsoever can influence objects, belief in obedience of external things (p. 303). The young child, as described by Piaget, has illusion that diverse physical events in

Primitive causality and optically active molecules

The primitive causality condition-namely that an effect cannot precede its cause-yields analytic properties and dispersion relations for the polarizability when the cause is an external electric field acting at the centre of an isolated molecule and the effect is the induced electric dipole moment. For a chiral molecule the lowest approximation that allows for the optical activity involves also the spatial derivatives of the electric field at the molecular centre, and a more stringent condition must be imposed in order to show the analyticity of the optical rotatory parameter as well as that of the polarizability. This condition is illustrated by the classical model of an optically active molecule consisting of two dissymmetrically coupled damped linear oscillators. The various approaches that can be used to derive dispersion relations for optically active isotropic media are briefly reviewed.

The construction of solution of nonlinear relativistic wave equation in λ:Φ44: theory

The nonlinear equation (⧠+m2) Φ (x) =λ:Φ3: for the quantum scalar field with special form of ordering of the interaction term is considered. The unique soultion Φ (x) of this equation is constructed. It satisfies the relativistic covariance, asymptotic, irredicibility and the relativistic primitive causality conditions in the sense of sesquilinear form. The spectral condition is also satisfied.

Postulates of Quantum Field Theory

We give a survey of the postulates which provide the framework of quantum field theory. Particular attention is given to the lesser known ones, namely, completeness requirements and ``primitive causality.'' Three field theoretical models are analyzed. These examples show that ``primitive causality'' is not a consequence of the commonly used postulates (which include the ``causal commutation relations''). ``Asymptotic completeness'' is not assured by any of the other postulates listed. In the formulation and analysis the concept of operator rings associated with space-time regions is used extensively.