The case of Piezoelectricity
Research Assistant (to be confirmed)
In recent years, many philosophical discussions about emergence have shifted focus from the philosophy of mind to the philosophy of the physical sciences. It has been suggested that physics presents us with emergent phenomena (Batterman 2002, 2011), or that chemistry is the embodiment of emergence (Luisi 2002). Many of the discussed examples of emergent phenomena come from the study of materials. They include phase transitions (Batterman 2002), superconductivity (Anderson 1972, Morrison 2012), ferromagnetism and antiferromagnetism (Cox and Pines 2005), the quantum Hall states (Laughlin and Pines 2000). From a theoretical standpoint, emergent phenomena have been associated with symmetry breaking (Anderson and Stein 1988, Anderson 2004), mathematical singularities (Batterman 2002), multiple realizability (Cunningham 2001, Bedau 2008), computational irreducibility (Bedau 2008, Wolfram 1985).
Our project aims to explore the existence of emergent phenomena in materials. The fact that the physical and chemical properties of materials can be intersubjectively scrutinized, that they are amenable to measurement, to experiment and to a quantitative understanding to a greater extent than those in other special sciences, makes the study of materials an ideal domain for the investigation of emergence.
Our Proposed Research: The Case of Piezoelectricity
Our proposed research focuses on a striking phenomenon observed in some materials: piezoelectricity. A material is said to be piezoelectric if the application of an external mechanical stress gives rise to electric polarization (direct effect) and it experiences mechanical deformations when placed in an electric field (converse effect) (Yang, 2005). The piezoelectric effect is defined by the following equations:
where P is polarization, T is stress, S is strain, E is the intensity of the electric field, and d is the piezoelectric coefficient of the material.
Piezoelectricity is as philosophically interesting as it is technologically useful. The definition of piezoelectricity is functional (describes a behaviour under certain conditions) and phenomenological in the sense that it is agnostic about the mechanism (we had a correct phenomenological characterization of piezoelectricity long before we knew its underlying mechanisms – see Katzir 2003, 2006). Many types of materials are considered piezoelectric: crystals (quartz, Rochelle salt), manmade materials (ceramics like lead zirconate titanate, PZT, polymers like polyvinylidene fluoride, PVDF), cement, gels (agar), materials of biological origin (bone, collagen). From a philosophical standpoint, it is tempting to view piezoelectricity as a case of multiple realization. Also, piezoelectricity has been described as “one of the most useful of broken symmetry phenomena as it manifests itself in condensed matter systems” (Anderson 2004). Since multiple realizability and broken symmetry are two ways in which philosophers and physicists have thought about emergence, our project aims to investigate whether piezoelectricity is an emergent phenomenon. In particular, we are interested to see whether there is a sense in which piezoelectricity can be considered ontologically emergent (as opposed to just epistemically emergent).
To address this question, we need to distinguish between two different types of questions. Following Batterman (2002), who distinguished between questions about instances of a pattern and questions about the pattern itself, we distinguish between questions about the emergence of piezoelectricity in a given material, and questions about the emergence of piezoelectricity as a pattern of physical behaviour across materials. Thus, our two questions are:
i) For a given instance of piezoelectric behaviour (where the equations of piezoelectricity apply), does that behaviour qualify as emergent, and if so, in what sense?
ii) Is piezoelectricity as a pattern of physical behaviour (across materials) emergent, and if so, in what sense? Is there a sense in which the equations of piezoelectricity themselves can be viewed as emergent?