The Leibniz‐Clarke Correspondence

Extended Theories of Gravity

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

What Price Spacetime Substantivalism? The Hole Story

Photonic band gap materials are holograms with extremely high refractive index contrasts. The refractive index function can be approximated by a small number of plane waves, as a consequence of the photonic crystal periodicity. Photonic crystals can hence be constructed with a simple holographic recording of a very small number of optical plane waves, and appear in this regard as the simplest holograms. Various photonic band gap structures are theoretically analysed and those concepts are illustrated experimentally with the fabrication of a two-dimensional triangular lattice in GaAs. The extension of the method to the three-dimensional diamond structure is discussed.

Photonic band gaps and holography

Leibniz’s principles made for an elegant and coherent philosophy. In part metaphysical, in part methodological, they addressed fundamental questions - in the treatment of symmetry, in the relationship of physics to mathematics, in logic that are if anything even more pressing today than they were in Leibniz’s time. As I shall read them, they also expressed a distinctive and uncompromising form of realism, a commitment to the adequacy of purely descriptive concepts. This doctrine has been called ‘semantic universalism’by van Fraassen (1991), and the ‘generalist picture’by O’Leary-Hawthorne and Cover (1996): it will become clearer in due course just what it entails. The principles that I shall consider are the Principle of Su¢ cient Reason (PSR) and the Principle of Identity of Indiscernibles (PII). In the …rst instance I shall take them both to be methodological principles. The former I shall read as requiring that the concepts of physics be entirely transparent. Analysis and explanation are to proceed without any limits. The perspective is impersonal: any epistemological limitation, to do with our human situation or perceptual apparatus, is to be viewed as a purely practical matter, re‡ecting no fundamental constraint. This puts in place a part of the generalist picture. The PSR clearly promotes the use of mathematical concepts in physics. The PII, in contrast, depends on a sharp distinction between purely mathematical concepts, and physical ones. Leibniz too made use of this distinction (between ‘real’and ‘notional’or ‘ideal’concepts), but in his hands the principle depended heavily, though often tacitly, on his metaphysical theory of substance (and, with quali…cations, on his philosophical logic). He was led to a restrictive formulation of it in consequence: There are never in nature two beings which are perfectly alike and �);

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Physics and Leibniz's Principles

Cold atoms in dissipative optical lattices exhibit an unusual transport behaviour that cannot be described within Boltzmann–Gibbs statistical mechanics. New theoretical tools and concepts need thus be developed to account for their observable macroscopic properties. Here we review recent progress achieved in the study of these processes. We emphasize the generality of the findings for a broad class of physical, chemical and biological systems, and discuss open questions and perspectives for future work. Cold atoms trapped in dissipative optical lattices can behave in ways that cannot be described within the framework of Boltzmann–Gibbs statistical mechanics. Recent theoretical and experimental developments may lead to a better understanding of these processes.

The Leibniz‐Clarke Correspondence

Citations

Extended Theories of Gravity

What Price Spacetime Substantivalism? The Hole Story

Photonic band gaps and holography

Physics and Leibniz's Principles

Beyond Boltzmann–Gibbs statistical mechanics in optical lattices

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