Causality has often been confused with the notion of determinism. It is mandatory to separate the two notions in view of the debate about quantum foundations. Quantum theory provides an example of causal non-deterministic theory. Here we introduce a toy operational theory that is deterministic and non-causal, thus proving that the two notions of causality and determinism are totally independent.
Causality has often been confused with the notion of determinism. It is mandatory to separate the two notions in view of the debate about quantum foundations. Quantum theory provides an example of causal non-deterministic theory. Here we introduce a toy operational theory that is deterministic and non-causal, thus proving that the two notions of causality and determinism are totally independent.
Causality has never gained the status of a 'law' or 'principle' in physics. Some recent literature has even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of the reversibility of the laws of physics, based either on the determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such a notion of causality appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establishing a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The notion of causality is logically completely independent of the misidentified concept of 'determinism', and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude by arguing that causality naturally establishes an arrow of time. This implies that the scenario of the 'block Universe' and the connected 'past hypothesis' are incompatible with causality, and thus with quantum theory: they are both doomed to remain mere interpretations and, as such, are not falsifiable, similar to the hypothesis of 'super-determinism'.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
In this chapter we introduce the postulate of causality, and derive the mathematical structure of a causal OPT. We show how the present definition of causality is equivalent to the Einsteinian one, and argue that it is the only possible notion once it is stripped from its spurious deterministic connotation. In addition, the notion of causality used here is compliant with the historical philosophical concept since David Hume, and with the idea used in common reasoning, inference, and modeling in human sciences. In brief, the present notion of causality can be stated as the requirement of no signaling from the future . This is also the only requisite for an OPT in order to satisfy the principle of no signaling without interaction . In mathematical terms in an OPT the causality postulate is equivalent to the uniqueness of the deterministic effect, which in turn is equivalent to the ability to normalize states. The notion of causality is so naturally embedded in our understanding of reality that it often remains unconsciously implicit in foundational research, even in recent axiomatizations. Causality: From Cinderella to Principle Causality has been the object of a very extensive literature encompassing hundreds of books and technical articles in a wide spectrum of disciplines, ranging from pure philosophy to economics, law, natural sciences, and obviously, physics. Also due to its involvement in such heterogeneous blend of disciplines, causality has long been a vexed notion. Perhaps the most natural connection between concepts of causality in different branches of knowledge is the one at the borderline between physics and philosophy, since the early work of Aristotle, up to the cornerstone of Renée Descartes, who broke the ground for the modern view of David Hume and Immanuel Kant, through to contemporary works on physical causation. Causality has always remained in the realm of philosophy, staying only in the background of physics, without the status of a “law” or the rank of a “principle.” Most of the time causality creeps into physical theories in the form of ad hoc assumptions based on empirical evidences, as when we discard advanced potentials in electrodynamics or when we motivate the Kramers–Kronig relations. In other cases, causality is embodied in the “interpretation” of the theory, as for the Special Relativity of Einstein.
The purpose of this paper is to give a brief survey the implications of the theories of modern physics for the doctrine of determinism. The survey will reveal a curious feature of determinism: in some respects it is fragile, requiring a number of enabling assumptions to give it a fighting chance; but in other respects it is quite robust and very difficult to kill. The survey will also aim to show that, apart from its own intrinsic interest, determinism is an excellent device for probing the foundations of classical, relativistic, and quantum physics. The survey is conducted under three major presuppositions. First, I take a realistic attitude towards scientific theories in that I assume that to give an interpretation of a theory is, at a minimum, to specify what the world would have to be like in order for the theory to be true. But we will see that the demand for a deterministic interpretation of a theory can force us to abandon a naively realistic reading of the theory. Second, I reject the “no laws” view of science and assume that the field equations or laws of motion of the most fundamental theories of current physics represent science’s best guesses as to the form of the basic laws of nature. Third, I take determinism to be an ontological doctrine, a doctrine about the temporal evolution of the world. This ontological doctrine must not be confused with predictability, which is an epistemological doctrine, the failure of which need not entail a failure of determinism. From time to time I will comment on ways in which predictability can fail in a deterministic setting. Finally, my survey will concentrate on the Laplacian variety of determinism according to which the instantaneous state of the world at any time uniquely determines the state at any other time. The plan of the survey is as follows. Section 2 illustrates the fragility of determinism by means of a Zeno type example. Then sections 3 and 4 survey successively the fortunes of determinism in the Newtonian and the special relativistic settings..
It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this work leaves open whether causal concepts are fundamental to quantum theory, or only find application at an emergent level of classical devices and measurement outcomes. Here, we present a framework of quantum causal models, with causal relations defined in terms intrinsic to quantum theory, and the central object of study being the quantum process itself. Following Allen et al., Phys. Rev. X 7, 031021 (2017), the approach defines quantum causal relations in terms of unitary evolution, in a way analogous to an approach to classical causal models that assumes underlying determinism and situates causal relations in functional dependences between variables. We show that any unitary quantum circuit has a causal structure corresponding to a directed acyclic graph, and that when marginalising over local noise sources, the resulting quantum process satisfies a Markov condition with respect to the graph. We also prove a converse to this statement. We introduce an intrinsically quantum notion that plays a role analogous to the conditional independence of classical variables, and (generalizing a central theorem of the classical framework) show that d-separation is sound and complete for it in the quantum case. We present generalizations of the three rules of the classical do-calculus, in each case relating a property of the causal structure to a formal property of the quantum process, and to an operational statement concerning the outcomes of interventions. In addition, we introduce and derive similar results for classical split-node causal models, which are more closely analogous to quantum causal models than the classical causal models that are usually studied.
This paper examines how such fundamental notions as causality and determinism have undergone changes as a direct result of empirical discoveries. Although such notions are often regarded as metaphysical or a priori concepts, experimental discoveries at the beginning of this century—radioactive decay, blackbody radiation and spontaneous emission—led to a direct questioning of the notions of causality and determinism. Experimental evidence suggests that these two notions must be separated. Causality and indeterminism are compatible with the behavior of quantum-mechanical systems. The argument also sheds some light on the Duhem-Quine thesis, since experimental results at the periphery of the conceptual scheme directly affect conceptions at the very core.
In the wake of relativistic field theories in physics, all of our most fundamental physical theories shared three properties regarding the way that they described the world. First, properties of objects were always determined. Second, systems always evolved deterministically. Thirdly, no causal relationship between two separate regions in space was immediate or had superluminal effect. These properties of theories are called determinacy, determinism and local causality, respectively. These properties all correspond to classical metaphysical principles about the structure of the world. It will be shown that the theory of quantum mechanics has none of these properties and so therefore introduces a tension between the classical metaphysical description of the world and the descriptions given by our most fundamental physical theories. John Stewart Bell showed that no entirely correct theory of quantum mechanics has the property of local causality. I argue that this implies that local causality is metaphysically untenable.