[Time, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe (...) within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless. (shrink)

It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.

In this paper, I develop Mauricio Suárez’s distinction between denotation, epistemic representation, and faithful epistemic representation. I then outline an interpretational account of epistemic representation, according to which a vehicle represents a target for a certain user if and only if the user adopts an interpretation of the vehicle in terms of the target, which would allow them to perform valid (but not necessarily sound) surrogative inferences from the model to the system. The main difference between the interpretational conception I (...) defend here and Suárez’s inferential conception is that the interpretational account is a substantial account—interpretation is not just a “symptom” of representation; it is what makes something an epistemic representation of a something else. (shrink)

This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still made in subtle ways, the article explores its occurrence in three examples: the Second Law, the concept of equilibrium and the definition of phase transitions.

It is widely supposed that every entity falls into one of twocategories: Some are concrete; the rest abstract. The distinction issupposed to be of fundamental significance for metaphysics andepistemology. This article surveys a number of recent attempts to sayhow it should be drawn.

This article examines ontological/dynamical aspects of emergence, specifically the micro-macro relation in cases of universal behavior. I discuss superconductivity as an emergent phenomenon, showing why microphysical features such as Cooper pairing are not necessary for deriving characteristic properties such as infinite conductivity. I claim that the difficulties surrounding the thermodynamic limit in explaining phase transitions can be countered by showing how renormalization group techniques facilitate an understanding of the physics behind the mathematics, enabling us to clarify epistemic and ontological aspects (...) of emergence. I close with a discussion of the impact of these issues for questions concerning natural kinds. (shrink)

Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to mistakes in Statistical Mechanics. I discuss (...) this argument and argue that the conclusion is misguided. In addition, I discuss an analogous example where a genuine physical discontinuity---the breaking of drops---requires the use of infinite idealizations. (shrink)

Phase transitions are an important instance of putatively emergent behavior. Unlike many things claimed emergent by philosophers, the alleged emergence of phase transitions stems from both philosophical and scientific arguments. Here we focus on the case for emergence built from physics, in particular, arguments based upon the infinite idealization invoked in the statistical mechanical treatment of phase transitions. After teasing apart several challenges, we defend the idea that phase transitions are best thought of as conceptually novel, but not ontologically or (...) explanatorily irreducible to finite physics; indeed, by looking at ongoing work on “smooth phase transitions” we even suggest that they’re not even conceptually novel. In the case of renormalization group theory, consideration of infinite systems and their singular behavior provides a central theoretical tool, but this is compatible with an explanatory reduction. Phase transitions may be “emergent” in some sense of this protean term, but not in a sense that is incompatible with the reductionist project broadly construed. (shrink)

This paper examines a fundamental problem in applied mathematics. How can one model the behavior of materials that display radically different, dominant behaviors at different length scales. Although we have good models for material behaviors at small and large scales, it is often hard to relate these scale-based models to one another. Macroscale models represent the integrated effects of very subtle factors that are practically invisible at the smallest, atomic, scales. For this reason it has been notoriously difficult to model (...) realistic materials with a simple bottom-up-from-the-atoms strategy. The widespread failure of that strategy forced physicists interested in overall macro-behavior of materials toward completely top-down modeling strategies familiar from traditional continuum mechanics. The problem of the ``tyranny of scales'' asks whether we can exploit our rather rich knowledge of intermediate micro- scale behaviors in a manner that would allow us to bridge between these two dominant methodologies. Macroscopic scale behaviors often fall into large common classes of behaviors such as the class of isotropic elastic solids, characterized by two phenomenological parameters---so-called elastic coefficients. Can we employ knowledge of lower scale behaviors to understand this universality---to determine the coefficients and to group the systems into classes exhibiting similar behavior? (shrink)

Phase transitions are well-understood phenomena in thermodynamics (TD), but it turns out that they are mathematically impossible in finite SM systems. Hence, phase transitions are truly emergent properties. They appear again at the thermodynamic limit (TL), i.e., in infinite systems. However, most, if not all, systems in which they occur are finite, so whence comes the justification for taking TL? The problem is then traced back to the TD characterization of phase transitions, and it turns out that the characterization is (...) the result of serious idealizations which under suitable circumstances approximate actual conditions. (shrink)

According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well‐known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article takes singularities seriously and analyzes their role by (...) using the well‐known distinction between data and phenomena , in an attempt to better understand the origin of the puzzle. *Received April 2009; revised July 2009. †To contact the author, please write to: University of Cambridge, Department of History and Philosophy of Science, Free School Lane, Cambridge CB2 3RH, United Kingdom; e‐mail: [email protected]. (shrink)

It has been argued, most trenchantly by Nancy Cartwright, that the diversity of the concepts and regularities we actually use to describe nature and predict and explain its behavior leaves us with no reason to believe that our foundational physical theories actually "apply" outside of delicately contrived systems within the laboratory. This paper argues that, diversity of method notwithstanding, there is indeed good reason to think that the foundational laws of physics are universal in their scope.

Recent work by Robert Batterman and Alexander Rueger has brought attention to cases in physics in which governing laws at the base level “break down” and singular limit relations obtain between base- and upper-level theories. As a result, they claim, these are cases with emergent upper-level properties. This paper contends that this inference—from singular limits to explanatory failure, novelty or irreducibility, and then to emergence—is mistaken. The van der Pol nonlinear oscillator is used to show that there can be a (...) full explanation of upper-level properties entirely in base-level terms even when singular limits are present. Whether upper-level properties are emergent depends not on the presence of a singular limit but rather on details of the ampliative approximation methods used. The paper suggests that focusing on explanatory deficiency at the base level is key to understanding emergence in physics. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

This thesis gives a philosophical assessment of a contemporary movement, influential amongst physicists, about the status of microscopic and macroscopic properties. The fountainhead for the movement was a short 1972 paper `More is Different', written by the condensed-matter physicist, Philip Anderson. Each of the chapters is concerned with themes mentioned in that paper, or subsequently expounded by Anderson and his followers. In Chapter 1, I aim to locate Anderson's existence claims for `emergent properties' within the metaphysical, epistemological and methodological doctrines (...) that identify themselves as `emergentist'. I argue, against the commentators' consensus, that the New Emergentists make claims about the metaphysical status of physical properties, and should not be read as concerned only with matters of research methodology for physics. In Chapter 2, I look at the physical examples that the New Emergentists appeal to, and propose a way of formulating their main claims within modern analytic metaphysics. I argue that it is possible to view their thesis as an updated version of `British Emergentism' a movement popular in the early years of the twentieth century. I support this contention by comparing examples of emergent properties put forward by the British and the New Emergentists. Chapter 3 is a discussion of the significance of renormalisation techniques. I attack a set of claims by Robert Batterman, who presents renormalisation as an explanatory strategy unrecognised by the philosophy of science. I separate several different methods of renormalisation analysis, and argue that he has conflated them. In Chapter 4, I discuss the theoretical representation of phase transitions in condensed matter physics; in particular, their appeal to the limit of an infinite system. I examine and refute various claims to the effect that the ineliminability of this limit in modelling phase transitions is of great metaphysical significance. I suggest a definition of phase transitions for finite systems that dissolves this illusion, and gives us reason to trust the results of the theories that only apply in the infinite limit. %I then comment on the significance of these results for a suggestion of Laura Ruetsche, that quantum statistical mechanics should be used as a guide to the interpretation of quantum field theory. Chapter 5 revisits the doctrines of the New Emergentists in order to place their views within some wider philosophical debates. I look at how their doctrines bear on issues in the interpretation of quantum mechanics, in the philosophy of mind and the philosophy of science. I close by returning to the context within physics, in which the New Emergentists originally made their presence felt: the controversy over whether elementary particle physics should enjoy greater status than other areas. (shrink)