Elements in the Philosophy of Physics – serie

This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of 'physical representation' (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of 'the Relativity Principle,' or 'Galileo's Ship.' This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the past century, namely understanding the physical significance of the notion of 'local' gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary representational media such as the covariant phase space formalism.

Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as ontology, possibility, explanation, induction, counterfactuals, time, determinism, and fundamentality. I suggest that laws are fundamental facts that govern the world by constraining its physical possibilities. I examine three hallmarks of laws-simplicity, exactness, and objectivity-and discuss whether and how they may be associated with laws of physics.

This Element is broadly about the geometrization of physics, but mostly it is about gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the Standard Model of particle physics. At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry. The over-arching question this Element aims to answer is: why is descriptive redundancy fruitful for physics? I will provide three inter-related answers to the question: ``Why gauge theory?'', that is: why introduce redundancies in our models of nature in the first place? The first is pragmatic, or methodological; the second is based on geometrical considerations, and the third is broadly relational.

Statistical mechanics is the third pillar of modern physics, next to quantum theory and relativity theory. It aims to account for the behaviour of macroscopic systems in terms of the dynamical laws that govern their microscopic constituents and probabilistic assumptions about them. In this Element, the authors investigate the philosophical and foundational issues that arise in SM. The authors introduce the two main theoretical approaches in SM, Boltzmannian SM and Gibbsian SM, and discuss how they conceptualise equilibrium and explain the approach to it. In doing so, the authors examine how probabilities are introduced into the theories, how they deal with irreversibility, how they understand the relation between the micro and the macro level, and how the two approaches relate to each other. Throughout, the authors also pinpoint open problems that can be subject of future research. This title is also available as Open Access on Cambridge Core.

This Element provides an entry point for philosophical engagement with quantization and the classical limit. It introduces the mathematical tools of C*-algebras as they are used to compare classical and quantum physics. It then employs those tools to investigate philosophical issues surrounding theory change in physics. It discusses examples in which quantization bears on the topics of reduction, structural continuity, analogical reasoning, and theory construction. In doing so, it demonstrates that the precise mathematical tools of algebraic quantum theory can aid philosophers of science and philosophers of physics.

This Element has three main aims. First, it aims to help the reader understand the concept of computation that Turing developed, his corresponding results, and what those results indicate about the limits of computational possibility. Second, it aims to bring the reader up to speed on analyses of computation in physical systems which provide the most general characterizations of what it takes for a physical system to be a computational system. Third, it aims to introduce the reader to some different kinds of quantum computers, describe quantum speedup, and present some explanation sketches of quantum speedup. If successful, this Element will equip the reader with a basic knowledge necessary for pursuing these topics in more detail.

This Element offers an introduction to selected philosophical issues that arise in contemporary particle physics, aimed at philosophers who have limited prior exposure to quantum field theory. One the one hand, it critically surveys philosophical work on the representation of particles in quantum field theory, the formal machinery and conceptual implications of renormalization and renormalization group methods, and ontological and methodological questions raised by the use of effective field theory techniques in particle physics. On the other, it identifies topics in particle physics that have not yet received philosophical attention and sketches avenues for philosophical analysis of those topics. The primary aim of the Element is to provide philosophers of physics with an entry point into the literature on the philosophy of particle physics and identify interesting directions for future research for students and researchers alike.

The Element reconstructs, analyses and compares different derivational routes to a grounding of the Arrow of Time in entropy. It also evaluates the link between entropy and visible disorder, and the related claim of an alignment of the Arrow of Time with a development from order to visible disorder. The Element identifies three different entropy-groundings for the Arrow of Time: (i) the Empirical Arrow of Time, (ii) the Universal Statistical Arrow of Time, and (iii) the Local Statistical Arrow of Time. The Element will also demonstrate that it is unlikely that high entropy states will always coincide with visible disorder. Therefore, it will dispute that there is a strong link between the Arrow of Time and visible disorder.

Cosmology and astrophysics provide a unique resource for philosophers of science: due to novel physics, the remoteness of their targets, and the range of relevant spatiotemporal scales, research in these areas pushes the methodology of empirical science to its limits. It should therefore not be surprising that philosophy of cosmology, and, to a lesser degree, philosophy of astrophysics, have seen an explosive growth over the past two decades. This Cambridge Element surveys the existing literature, identifies areas for future research, and highlights how philosophy of cosmology and astrophysics have implications for debates in general philosophy of science.

Dimensional quantities such as length, mass and charge, i.e., numbers combined with a conventional unit, are essential components of theories in the sciences, especially physics, chemistry and biology. Do they represent a world with absolute physical magnitudes, or are they merely magnitude ratios in disguise? Would we notice a difference if all the distances or charges in the world suddenly doubled? These central questions of this Element are illustrated by imagining how one would convey the meaning of a kilogram to aliens if one were only allowed to communicate via Morse code.

Causation in Physics demonstrates the importance of causation in the physical world. It details why causal mastery of natural phenomena is an important part of the effective strategies of experimental physicists. It develops three novel arguments for the viewpoint that causation is indispensable to the ontology of some of our best physical theories. All three arguments make much of the successes of experimental physics. This title is also available as Open Access on Cambridge Core.

This Element presents the philosophy of special relativity, from the foundations of the theory in Newtonian mechanics, through its birth out of the ashes of nineteenth-century ether theory, through the various conceptual paradoxes which the theory presents, and finally arriving at some of its connections with Einstein's later theory of general relativity. It illustrates concepts such as inertial frames, force-free motion, dynamical versus geometrical understandings of physics, the standard hierarchy of classical spacetimes, and symmetries of a physical theory; it also discusses specific topics in the foundations of special relativity such as Einstein's 1905 derivation of the Lorentz transformations, the conventionality of simultaneity, the status of frame-dependent effects, and the twin paradox.

This Element explores the formal and conceptual foundations of phase space formulations of classical and quantum mechanics. It provides an overview of the core mathematical and physical content of Hamiltonian mechanics, stochastic phase space mechanics, contact Hamiltonian mechanics, and open and closed quantum mechanics on phase space. The formal material is unified via three interpretative themes relating to structured possibility spaces, Liouville's theorem and its failure, and the classical and quantum notions of open and closed systems. This Element book is intended for researchers and graduate students in the philosophy and foundations of physics with an interest in the conceptual foundations of physical theory.

Dimensional quantities such as length, mass and charge, i.e., numbers combined with a conventional unit, are essential components of theories in the sciences, especially physics, chemistry and biology. Do they represent a world with absolute physical magnitudes, or are they merely magnitude ratios in disguise? Would we notice a difference if all the distances or charges in the world suddenly doubled? These central questions of this Element are illustrated by imagining how one would convey the meaning of a kilogram to aliens if one were only allowed to communicate via Morse code.

Statistical mechanics is the third pillar of modern physics, next to quantum theory and relativity theory. It aims to account for the behaviour of macroscopic systems in terms of the dynamical laws that govern their microscopic constituents and probabilistic assumptions about them. In this Element, the authors investigate the philosophical and foundational issues that arise in SM. The authors introduce the two main theoretical approaches in SM, Boltzmannian SM and Gibbsian SM, and discuss how they conceptualise equilibrium and explain the approach to it. In doing so, the authors examine how probabilities are introduced into the theories, how they deal with irreversibility, how they understand the relation between the micro and the macro level, and how the two approaches relate to each other. Throughout, the authors also pinpoint open problems that can be subject of future research. This title is also available as Open Access on Cambridge Core.

Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as ontology, possibility, explanation, induction, counterfactuals, time, determinism, and fundamentality. I suggest that laws are fundamental facts that govern the world by constraining its physical possibilities. I examine three hallmarks of laws-simplicity, exactness, and objectivity-and discuss whether and how they may be associated with laws of physics.

The Element reconstructs, analyses and compares different derivational routes to a grounding of the Arrow of Time in entropy. It also evaluates the link between entropy and visible disorder, and the related claim of an alignment of the Arrow of Time with a development from order to visible disorder. The Element identifies three different entropy-groundings for the Arrow of Time: (i) the Empirical Arrow of Time, (ii) the Universal Statistical Arrow of Time, and (iii) the Local Statistical Arrow of Time. The Element will also demonstrate that it is unlikely that high entropy states will always coincide with visible disorder. Therefore, it will dispute that there is a strong link between the Arrow of Time and visible disorder.

This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of 'physical representation' (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of 'the Relativity Principle,' or 'Galileo's Ship.' This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the past century, namely understanding the physical significance of the notion of 'local' gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary representational media such as the covariant phase space formalism.

Causation in Physics demonstrates the importance of causation in the physical world. It details why causal mastery of natural phenomena is an important part of the effective strategies of experimental physicists. It develops three novel arguments for the viewpoint that causation is indispensable to the ontology of some of our best physical theories. All three arguments make much of the successes of experimental physics. This title is also available as Open Access on Cambridge Core.

This Element provides a somewhat comprehensive interpretation of general relativity, a description of what reality would be like if the theory were true. This concerns (i) what possibilities it represents, (ii) the internal structure of those possibilities and their interrelations, and, to some extent, (iii) how those possibilities differ from what's come before. By providing an interpretive foil that one can amplify or amend, it aspires to shape the research agenda in the foundations of general relativity for established philosophers of physics, graduate students searching for work in these topics, and other interested academics. This title is also available as Open Access on Cambridge Core.

Cosmology and astrophysics provide a unique resource for philosophers of science: due to novel physics, the remoteness of their targets, and the range of relevant spatiotemporal scales, research in these areas pushes the methodology of empirical science to its limits. It should therefore not be surprising that philosophy of cosmology, and, to a lesser degree, philosophy of astrophysics, have seen an explosive growth over the past two decades. This Cambridge Element surveys the existing literature, identifies areas for future research, and highlights how philosophy of cosmology and astrophysics have implications for debates in general philosophy of science.

The search for a new scientific theory is typically prompted by an encounter with something in the world that cannot be explained by current theories. This is not the case for the search for a theory of quantum gravity, which has been primarily motivated by theoretical and philosophical concerns. This Element introduces some of the motivations for seeking a theory of quantum gravity, with the aim of instigating a more critical perspective on how they are used in defining and constraining the theory sought. These motivations include unification, incompatibilities between general relativity and quantum field theory, consistency, singularity resolution, and results from black hole thermodynamics.

This Element is broadly about the geometrization of physics, but mostly it is about gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the Standard Model of particle physics. At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry. The over-arching question this Element aims to answer is: why is descriptive redundancy fruitful for physics? I will provide three inter-related answers to the question: ``Why gauge theory?'', that is: why introduce redundancies in our models of nature in the first place? The first is pragmatic, or methodological; the second is based on geometrical considerations, and the third is broadly relational.

This Element explores the formal and conceptual foundations of phase space formulations of classical and quantum mechanics. It provides an overview of the core mathematical and physical content of Hamiltonian mechanics, stochastic phase space mechanics, contact Hamiltonian mechanics, and open and closed quantum mechanics on phase space. The formal material is unified via three interpretative themes relating to structured possibility spaces, Liouville's theorem and its failure, and the classical and quantum notions of open and closed systems. This Element book is intended for researchers and graduate students in the philosophy and foundations of physics with an interest in the conceptual foundations of physical theory.

This Element explores the conceptual complexity of time reversal in the philosophy of physics. It aims to show that time reversal, as a symmetry transformation, should not be regarded as a mere mathematical artifice applied to physical equations. It is rather a conceptually rich and multifaceted notion, one whose meaning and implementation are shaped by a combination of metaphysical commitments and heuristic-methodological strategies. Far from being a neutral tool, the way we define and apply time reversal encodes assumptions about the nature of time itself, its relation to motion, about the role of symmetries in physical theories, and about the relation between mathematical symmetries and the world they purport to describe. Such conceptual complexity also has implication for related debates, such as that of the direction of time.

This Element explores the conceptual complexity of time reversal in the philosophy of physics. It aims to show that time reversal, as a symmetry transformation, should not be regarded as a mere mathematical artifice applied to physical equations. It is rather a conceptually rich and multifaceted notion, one whose meaning and implementation are shaped by a combination of metaphysical commitments and heuristic-methodological strategies. Far from being a neutral tool, the way we define and apply time reversal encodes assumptions about the nature of time itself, its relation to motion, about the role of symmetries in physical theories, and about the relation between mathematical symmetries and the world they purport to describe. Such conceptual complexity also has implication for related debates, such as that of the direction of time.

A sound philosophy of mathematical physics balances a philosophy of mathematics with a philosophy of physics, sharpening the general applicability problem of mathematics by also taking care of: (i) the early modern `mathematization of the world picture'; (ii) the theory-laden character of the targets of mathematical models of modern physics; and (iii): Wigner's `unreasonable effectiveness of mathematics in the natural sciences'. Guided by a historical survey, I propose that theories of mathematical physics are meaning-constitutive a priori constructions, conventional but far from arbitrary and best described as hypothetical. Their models subsequently mediate between theory and nature, that is, between the a priori and the a posteriori. Models mediate by playing the role of Wittgensteinian yardsticks or objects of comparison to be held against nature as represented by data models, where the comparison is made via surrogative inference. This balancing act compromises realism.

A sound philosophy of mathematical physics balances a philosophy of mathematics with a philosophy of physics, sharpening the general applicability problem of mathematics by also taking care of: (i) the early modern `mathematization of the world picture'; (ii) the theory-laden character of the targets of mathematical models of modern physics; and (iii): Wigner's `unreasonable effectiveness of mathematics in the natural sciences'. Guided by a historical survey, I propose that theories of mathematical physics are meaning-constitutive a priori constructions, conventional but far from arbitrary and best described as hypothetical. Their models subsequently mediate between theory and nature, that is, between the a priori and the a posteriori. Models mediate by playing the role of Wittgensteinian yardsticks or objects of comparison to be held against nature as represented by data models, where the comparison is made via surrogative inference. This balancing act compromises realism.

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.