Symmetry and Causation: A General Theory of Biological Individuality

I propose and defend a method of identifying individuals that is applicable across the biological sciences and yet sensitive to the details of particular theories. Specifically, I propose that an individual with respect to a given biological theory is an entity that instantiates the structure of a special class of transformations called the ‘dynamical symmetries’ of the theory. Here, a dynamical symmetry is understood roughly as a transformation of the state of a system that commutes with the increment of another system variable. This notion of individual is dependent upon the causal regularities in a particular domain of biology. However, the approach is completely general in that the same characterization of ‘individual’ in terms of symmetries applies across all biological domains. The metaphysical and methodological appeal of this approach to identifying individuals derives from the fact that the entities identified in this way share robust causal features and yet are causally independent of one another. To demonstrate the generality as well as the plausibility of the approach, I consider examples from evolutionary theory and ecology

How Symmetry Undid the Particle: A Demonstration of the Incompatibility of Particle Interpretations and Permutation Invariance

The idea that the world is made of particles — little discrete, interacting objects that compose the material bodies of everyday experience — is a durable one. Following the advent of quantum theory, the idea was revised but not abandoned. It remains manifest in the explanatory language of physics, chemistry, and molecular biology. Aside from its durability, there is good reason for the scientific realist to embrace the particle interpretation: such a view can account for the prominent epistemic fact that only limited knowledge of a portion of the material universe is needed in order to make reliable predictions about that portion. Thus, particle interpretations can support an abductive argument from the epistemic facts in favor of a realist reading of physical theory. However, any particle interpretation with this property is untenable. The empirical adequacy of modern particle theories requires adoption of a postulate known as permutation invariance (PI) — the claim that interchanging the role of two particles of the same kind in a dynamical state description results in a description of the identical state. It is the central claim of this essay that PI is incompatible with any particle interpretation strong enough to account for the epistemic facts. This incompatibility extends across all physical theories. To frame and motivate the inconsistency argument, I begin by fixing the relevant notion of particle. To single out those accounts of greatest appeal to the realist, I develop the logically weakest particle ontology that entails the epistemic fact that the world is piecewise predictable, an ontology I call ‘minimal atomism’ (MA). The entire series of scientific conceptions of the particle, from Newton’s mechanically interacting corpuscles to the ‘centers of force’ in classical field theories, all comport with MA. As long as PI is left out, even quantum mechanics can be viewed this way. To assess the impact of PI on this picture, I present a framework for rigorously connecting interpretations to physical theories. In particular, I represent MA as a set of formal conditions on the models of physical theories, the mathematical structures taken to represent states of the world. I also formulate PI — originally introduced as a postulate of non-relativistic quantum mechanics — in theory independent terms. With all of these pieces in hand, I am then able to present a proof of the inconsistency of PI and MA. In the second part of the essay, I survey responses to the inconsistency result open to the scientific realist. The two most plausible approaches involve abandoning particles in one way or another. The first alternative interpretation considered takes the property bearing objects of the world to be regions of space rather than particles. In this view, the properties once attributed to particles in quantum states are attributed instead to one or more regions of space. PI no longer obtains in this case, at least not as a statement about the permutation symmetry of property bearers. Rather, the new interpretation naturally imposes an analogous constraint on quantum states. The second major approach to evading the inconsistency result is to dispense with objects altogether. This is the recommendation of so-called ‘Ontic Structural Realism’ (OSR). The central OSR thesis is that structure rather than entities are the basic ontological components of the world. OSR is intended to embrace the ‘miracle’ argument in favor of scientific realism (it would be a miracle if a scientific theory were predictively successful unless it were also approximately true with regard to its description of reality) while avoiding the pessimistic meta-induction (most predictively successful theories along with their associated ontologies have been overturned, so we should expect the same of our current theories). I demonstrate that one principal motivation for OSR based on the under-determination of interpretations in QM is actually dissolved by the incompatibility result. At the same time, I suggest reasons to think that OSR fares no better with respect to the pessimistic meta-induction than traditional realism does. Thus, while PI and MA may be incompatible, object ontologies remain the best option for the realist

Symmetry and Causation: A General Theory of Biological Individuality

I propose and defend a method of identifying individuals that is applicable across the biological sciences and yet sensitive to the details of particular theories. Specifically, I propose that an individual with respect to a given biological theory is an entity that instantiates the structure of a special class of transformations called the ‘dynamical symmetries’ of the theory. Here, a dynamical symmetry is understood roughly as a transformation of the state of a system that commutes with the increment of another system variable. This notion of individual is dependent upon the causal regularities in a particular domain of biology. However, the approach is completely general in that the same characterization of ‘individual’ in terms of symmetries applies across all biological domains. The metaphysical and methodological appeal of this approach to identifying individuals derives from the fact that the entities identified in this way share robust causal features and yet are causally independent of one another. To demonstrate the generality as well as the plausibility of the approach, I consider examples from evolutionary theory and ecology

Soft-Collinear Factorization and Zero-Bin Subtractions

We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) Delta -regulator. To be well-defined, the effective theory requires zero-bin subtractions for the collinear sectors. The zero-bin subtractions depend on the gauge boson mass M and are not scaleless. They have both finite and 1/epsilon contributions, and are needed to give the correct anomalous dimension and low-scale matching contributions. We also demonstrate the necessity of zero-bin subtractions for soft-collinear factorization. We find that after zero-bin subtractions the form factor is the sum of the collinear contributions 'minus' a soft mass-mode contribution, in agreement with a previous result of Idilbi and Mehen in QCD. This appears to conflict with the method-of-regions approach, where one gets the sum of contributions from different regions.Comment: 9 pages, 5 figures. V2:ref adde

The quantum Casimir operators of \Uq and their eigenvalues

We show that the quantum Casimir operators of the quantum linear group constructed in early work of Bracken, Gould and Zhang together with one extra central element generate the entire center of \Uq. As a by product of the proof, we obtain intriguing new formulae for eigenvalues of these quantum Casimir operators, which are expressed in terms of the characters of a class of finite dimensional irreducible representations of the classical general linear algebra.Comment: 10 page

Kerr metric, static observers and Fermi coordinates

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.Comment: 15 page latex iopart class documen

The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange

The resummation of soft gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2 to n massless processes for the first time at two loops. Using color generator notation, we show that it is proportional to the one-loop matrix. This result reproduces all pole terms in dimensional regularization of the explicit calculations of massless 2 to 2 amplitudes in the literature, and it predicts all poles at next-to-next-to-leading order in any 2 to n process that has been computed at next-to-leading order. The proportionality of the one- and two-loop matrices makes possible the resummation in closed form of the next-to-next-to-leading logarithms and poles in dimensional regularization for the 2 to n processes.Comment: 5 pages, 1 figure, revte