Fred Kronz - Academia.edu (original) (raw)

Papers by Fred Kronz

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2006

Various processes are often classified as both deterministic and random or chaotic. The main diff... more Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called 'ergodic hierarchy' (EH), which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion of 1 Forthcoming in Studies in History and Philosophy of Modern Physics 37(4). The final version of the paper differs from this draft. Please download the PDFfile of the final version from http://www.romanfrigg.org/writings.htm. 2 This work is fully collaborative; the authors are listed alphabetically.

The actual/virtual distinction is used to give an alternative account of quantum interference by ... more The actual/virtual distinction is used to give an alternative account of quantum interference by way of a new theory of probability. The new theory is obtained by changing one of the axioms of the canonical theory of probability while keeping the other axioms fixed. It is used to give an alternative account of constructive quantum interference in the two-slit experiment. The account crucially involves a distinction between actual and virtual probabilities. Although actual probabilities are operational and virtual probabilities are not, there is a substantial connection between them. Virtual probabilities may be obtained indirectly from actual probabilities. In showing this, interpretive considerations are brought to bear including some having to do with quantum non-locality. Directions for future research are discussed in closing.

Metascience, 2005

This book is a serious and ambitious effort to explain how complex systems can exhibit simple beh... more This book is a serious and ambitious effort to explain how complex systems can exhibit simple behaviour. A complex system is any system having a sizable number of independent parts that occasionally interact. The parts are dubbed enions, to signify that the motion of each is predominantly independent of that of the others. Some examples of complex systems and their enions are a gas and its molecules, an ecosystem and its organisms, an economic system and its players. By contrast, a self-organising system (e.g., an embryo) is not complex in this sense since its parts are highly coordinated; they cannot be regarded as enions. Nor is a solid an enion, since each of its atoms constantly interacts with its nearest neighbors. It is less clear whether colloids and viscous liquids are complex; intermolecular forces play a sizable role in their micro-constituents. Only in gases do such forces typically play a small role.

Studies in History and Philosophy of Modern Physics, 2008

In previous work, a non-standard theory of probability was formulated and used to systematize int... more In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a selfcontained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities. Published by Elsevier Ltd.

Journal of Philosophical Logic, 2007

A non-monotonic theory of probability is put forward and shown to have applicability in the quant... more A non-monotonic theory of probability is put forward and shown to have applicability in the quantum domain. It is obtained simply by replacing Kolmogorov’s positivity axiom, which places the lower bound for probabilities at zero, with an axiom that reduces that lower bound to minus one. Kolmogorov’s theory of probability is monotonic, meaning that the probability of A is less then or equal to that of B whenever A entails B. The new theory violates monotonicity, as its name suggests; yet, many standard theorems are also theorems of the new theory since Kolmogorov’s other axioms are retained. What is of particular interest is that the new theory can accommodate quantum phenomena (photon polarization experiments) while preserving Boolean operations, unlike Kolmogorov’s theory. Although non-standard notions of probability have been discussed extensively in the physics literature, they have received very little attention in the philosophical literature. One likely explanation for that difference is that their applicability is typically demonstrated in esoteric settings that involve technical complications. That barrier is effectively removed for non-monotonic probability theory by providing it with a homely setting in the quantum domain. Although the initial steps taken in this paper are quite substantial, there is much else to be done, such as demonstrating the applicability of non-monotonic probability theory to other quantum systems and elaborating the interpretive framework that is provisionally put forward here. Such matters will be developed in other works.

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2006

Various processes are often classified as both deterministic and random or chaotic. The main diff... more Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called 'ergodic hierarchy' (EH), which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion of 1 Forthcoming in Studies in History and Philosophy of Modern Physics 37(4). The final version of the paper differs from this draft. Please download the PDFfile of the final version from http://www.romanfrigg.org/writings.htm. 2 This work is fully collaborative; the authors are listed alphabetically.

The actual/virtual distinction is used to give an alternative account of quantum interference by ... more The actual/virtual distinction is used to give an alternative account of quantum interference by way of a new theory of probability. The new theory is obtained by changing one of the axioms of the canonical theory of probability while keeping the other axioms fixed. It is used to give an alternative account of constructive quantum interference in the two-slit experiment. The account crucially involves a distinction between actual and virtual probabilities. Although actual probabilities are operational and virtual probabilities are not, there is a substantial connection between them. Virtual probabilities may be obtained indirectly from actual probabilities. In showing this, interpretive considerations are brought to bear including some having to do with quantum non-locality. Directions for future research are discussed in closing.

Metascience, 2005

This book is a serious and ambitious effort to explain how complex systems can exhibit simple beh... more This book is a serious and ambitious effort to explain how complex systems can exhibit simple behaviour. A complex system is any system having a sizable number of independent parts that occasionally interact. The parts are dubbed enions, to signify that the motion of each is predominantly independent of that of the others. Some examples of complex systems and their enions are a gas and its molecules, an ecosystem and its organisms, an economic system and its players. By contrast, a self-organising system (e.g., an embryo) is not complex in this sense since its parts are highly coordinated; they cannot be regarded as enions. Nor is a solid an enion, since each of its atoms constantly interacts with its nearest neighbors. It is less clear whether colloids and viscous liquids are complex; intermolecular forces play a sizable role in their micro-constituents. Only in gases do such forces typically play a small role.

Studies in History and Philosophy of Modern Physics, 2008

In previous work, a non-standard theory of probability was formulated and used to systematize int... more In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a selfcontained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities. Published by Elsevier Ltd.

Journal of Philosophical Logic, 2007

A non-monotonic theory of probability is put forward and shown to have applicability in the quant... more A non-monotonic theory of probability is put forward and shown to have applicability in the quantum domain. It is obtained simply by replacing Kolmogorov’s positivity axiom, which places the lower bound for probabilities at zero, with an axiom that reduces that lower bound to minus one. Kolmogorov’s theory of probability is monotonic, meaning that the probability of A is less then or equal to that of B whenever A entails B. The new theory violates monotonicity, as its name suggests; yet, many standard theorems are also theorems of the new theory since Kolmogorov’s other axioms are retained. What is of particular interest is that the new theory can accommodate quantum phenomena (photon polarization experiments) while preserving Boolean operations, unlike Kolmogorov’s theory. Although non-standard notions of probability have been discussed extensively in the physics literature, they have received very little attention in the philosophical literature. One likely explanation for that difference is that their applicability is typically demonstrated in esoteric settings that involve technical complications. That barrier is effectively removed for non-monotonic probability theory by providing it with a homely setting in the quantum domain. Although the initial steps taken in this paper are quite substantial, there is much else to be done, such as demonstrating the applicability of non-monotonic probability theory to other quantum systems and elaborating the interpretive framework that is provisionally put forward here. Such matters will be developed in other works.