The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of pr... more The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss its applications in these fields.
Recent no go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonst... more Recent no go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate that current modal interpretations are incompatible with relativity. In this paper we propose strategies for how to circumvent these theorems. We further show how these strategies can be developped into new modal interpretations in which the properties of systems are in general either holistic or relational. We explicitly write down an outline of dynamics for these properties which does not pick out a preferred foliation of spacetime.
Theoria-revista De Teoria Historia Y Fundamentos De La Ciencia, 2000
The correlations between distant systems in typical quantum situations, such as Einstein-Podolosk... more The correlations between distant systems in typical quantum situations, such as Einstein-Podolosky-Rosen experiments, strongly suggest that the quantum realm involves curious types of non-local influences. In this paper, I study in detail the nature of these non-local influences, as depicted by various quantum theories. I show how different quantum theories realise non-locality in different ways, which reflect different ontogical settings
The correlations between distant systems in typical quantum situations, such as Einstein-Podolosk... more The correlations between distant systems in typical quantum situations, such as Einstein-Podolosky-Rosen experiments, strongly suggest that the quantum realm involves curious types of non-local influences. In this paper, I study in detail the nature of these non-local influences, as depicted by various quantum theories. I show how different quantum theories realise non-locality in different ways, which reflect different ontological settings.
Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where ... more Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of probability and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that degrees of belief be coherent, and he argued that the whole of probability theory could be derived from these coherence conditions. De Finettiās interpretation of probability has been highly influential in science. This paper focuses on the application of this interpretation to quantum mechanics. We argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. Accordingly, the standard coherence conditions of degrees of belief that are familiar from the literature on subjective probability only apply to degrees of belief in events which could (in principle) be jointly verified; and the coherence conditions of degrees of belief in events that cannot be jointly verified are weaker. While the most obvious explanation of de Finettiās verificationism is the influence of positivism, we argue that it could be motivated by the radical subjectivist and instrumental nature of probability in his interpretation; for as it turns out, in this interpretation it is difficult to make sense of the idea of coherent degrees of belief in, and accordingly probabilities of unverifiable events. We then consider the application of this interpretation to quantum mechanics, concentrating on the Einstein-Podolsky-Rosen experiment and Bellās theorem.
Quantum mechanics portrays the universe as involving non-local influences that are difficult to r... more Quantum mechanics portrays the universe as involving non-local influences that are difficult to reconcile with relativity theory. By postulating backward causation, retro-causal interpretations of quantum mechanics could circumvent these influences and accordingly increase the prospects of reconciling quantum mechanics with relativity. The postulation of backward causation poses various challenges for the retro-causal interpretations of quantum mechanics and for the existing conceptual frameworks for analyzing counterfactual dependence, causation and causal explanation, which are important for studying these interpretations. In this chapter, we consider the nature of time, causation and explanation in a local, deterministic retro-causal interpretation of quantum mechanics that is inspired by Bohmian mechanics. This interpretation, the so-called 'causally symmetric Bohmian model', offers a deterministic, local 'hidden-variables' model of the Einstein-Podolsky-Rosen experiment that poses a new challenge for Reichenbach's principle of the common cause. In this model, the common cause ā the 'complete' state of particles at the emission from the source ā screens off the correlation between its effects ā the distant measurement outcomes ā but nevertheless fails to explain it. Plan of the chapter: 0 Introduction/abstract 1 The background 2 The main idea of retro-causal interpretations of quantum mechanics 3 Backward causation and causal loops: the complications 4 Arguments for the impossibility of backward causation and causal loops 5 The block universe, time, backward causation and causal loops 6 On prediction and explanation in indeterministic retro-causal interpretations of quantum mechanics 7 Bohmian Mechanics
A common view has it that there is a tension between quantum phenomena and the special theory of ... more A common view has it that there is a tension between quantum phenomena and the special theory of relativity. Yet, an ongoing debate concerning the prospects of relativistic quantum theories persists. In this paper, I consider two recent arguments for the impossibility of certain relativistic quantum theories, due to Arntzenius (1994) and Maudlin (1994). The main idea of both arguments
The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of pr... more The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss its applications in these fields.
Recent no go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonst... more Recent no go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate that current modal interpretations are incompatible with relativity. In this paper we propose strategies for how to circumvent these theorems. We further show how these strategies can be developped into new modal interpretations in which the properties of systems are in general either holistic or relational. We explicitly write down an outline of dynamics for these properties which does not pick out a preferred foliation of spacetime.
Theoria-revista De Teoria Historia Y Fundamentos De La Ciencia, 2000
The correlations between distant systems in typical quantum situations, such as Einstein-Podolosk... more The correlations between distant systems in typical quantum situations, such as Einstein-Podolosky-Rosen experiments, strongly suggest that the quantum realm involves curious types of non-local influences. In this paper, I study in detail the nature of these non-local influences, as depicted by various quantum theories. I show how different quantum theories realise non-locality in different ways, which reflect different ontogical settings
The correlations between distant systems in typical quantum situations, such as Einstein-Podolosk... more The correlations between distant systems in typical quantum situations, such as Einstein-Podolosky-Rosen experiments, strongly suggest that the quantum realm involves curious types of non-local influences. In this paper, I study in detail the nature of these non-local influences, as depicted by various quantum theories. I show how different quantum theories realise non-locality in different ways, which reflect different ontological settings.
Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where ... more Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of probability and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that degrees of belief be coherent, and he argued that the whole of probability theory could be derived from these coherence conditions. De Finettiās interpretation of probability has been highly influential in science. This paper focuses on the application of this interpretation to quantum mechanics. We argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. Accordingly, the standard coherence conditions of degrees of belief that are familiar from the literature on subjective probability only apply to degrees of belief in events which could (in principle) be jointly verified; and the coherence conditions of degrees of belief in events that cannot be jointly verified are weaker. While the most obvious explanation of de Finettiās verificationism is the influence of positivism, we argue that it could be motivated by the radical subjectivist and instrumental nature of probability in his interpretation; for as it turns out, in this interpretation it is difficult to make sense of the idea of coherent degrees of belief in, and accordingly probabilities of unverifiable events. We then consider the application of this interpretation to quantum mechanics, concentrating on the Einstein-Podolsky-Rosen experiment and Bellās theorem.
Quantum mechanics portrays the universe as involving non-local influences that are difficult to r... more Quantum mechanics portrays the universe as involving non-local influences that are difficult to reconcile with relativity theory. By postulating backward causation, retro-causal interpretations of quantum mechanics could circumvent these influences and accordingly increase the prospects of reconciling quantum mechanics with relativity. The postulation of backward causation poses various challenges for the retro-causal interpretations of quantum mechanics and for the existing conceptual frameworks for analyzing counterfactual dependence, causation and causal explanation, which are important for studying these interpretations. In this chapter, we consider the nature of time, causation and explanation in a local, deterministic retro-causal interpretation of quantum mechanics that is inspired by Bohmian mechanics. This interpretation, the so-called 'causally symmetric Bohmian model', offers a deterministic, local 'hidden-variables' model of the Einstein-Podolsky-Rosen experiment that poses a new challenge for Reichenbach's principle of the common cause. In this model, the common cause ā the 'complete' state of particles at the emission from the source ā screens off the correlation between its effects ā the distant measurement outcomes ā but nevertheless fails to explain it. Plan of the chapter: 0 Introduction/abstract 1 The background 2 The main idea of retro-causal interpretations of quantum mechanics 3 Backward causation and causal loops: the complications 4 Arguments for the impossibility of backward causation and causal loops 5 The block universe, time, backward causation and causal loops 6 On prediction and explanation in indeterministic retro-causal interpretations of quantum mechanics 7 Bohmian Mechanics
A common view has it that there is a tension between quantum phenomena and the special theory of ... more A common view has it that there is a tension between quantum phenomena and the special theory of relativity. Yet, an ongoing debate concerning the prospects of relativistic quantum theories persists. In this paper, I consider two recent arguments for the impossibility of certain relativistic quantum theories, due to Arntzenius (1994) and Maudlin (1994). The main idea of both arguments
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