A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the (...) perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented. (shrink)

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization (...) H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles. (shrink)

Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory (QT) is indeed a functional tensor theory, i.e., it can be described by functional tensor (...) equations. The main equations of QT are shown to be compatible with the principle of functional relativity. By accepting the principle as a hypothesis, we then explain the origin of physical dimensions, provide a geometric interpretation of Planck’s constant, and find a simple model of the two-slit experiment and the process of measurement. (shrink)

In this book, S. A. Lloyd offers a radically new interpretation of Hobbes's laws of nature, revealing them to be not egoistic precepts of personal prudence but rather moral instructions for obtaining the common good.

The elephant in the room -- Crabs and octopuses -- The central intelligence of a frog -- The cerebral cortex and consciousness -- Social consciousness -- Yoda and Darth: how can we find -- Consciousness in the brain? -- The hard problem and other perspectives on consciousness -- Conscious machines -- Uploading minds -- How to build visual consciousness.

REVIEWS: This is a very helpful volume and a good addition to contemporary scholarship on the valuable and little-known Jaina contribution to philosophy. Prof.Nagin Shah has edited the book well, including clear introduction and a very complete index.

Concept of Avidyā in the Vedānta philosophy of Śaṅkarācārya; a study.

Short stories from the lives of Prophet Muḥammad and Shiite Imams as a model of Islamic ethics.

Islamic philosophy; Ibn al-Muṭahhar al-Ḥillī, al-Ḥasan ibn Yūsuf, 1250-1325; Muslim scholars; 13th century; history.

This book explores the relation of John Henry Newman's idea of conscience to what he called conscience "in the ordinary sense of the word," examining such neglected difficulties in this area as the relation between individual conscience and the authority of the church, and rights of conscience.

Dictionary of terminology of Yoga philosophy.

On fundamentals of Nyaya philosophy with Nūtanāloka autocommentary and Ālokaprakāśa commentary by disciples.