On The Emergence Theme Of Physics

The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.

This book is a state-of-the-art review on the Physics of Emergence. The challenge of complexity is to focus on the description levels of the observer in context-dependent situations. Emergence is not only an heuristic approach to complexity, but it also urges us to face a much deeper question ? what do we think is fundamental in the physical world?This volume provides significant and pioneering contributions based on rigorous physical and mathematical approaches ? with particular reference to the syntax of Quantum Physics and Quantum Field Theory ? dealing with the bridge-laws and their limitations between Physics and Biology, without failing to discuss the involved epistemological features.Physics of Emergence and Organization is an interdisciplinary source of reference for students and experts whose interests cross over to complexity issues.

A standard view of elementary particles and forces is that they determine everything else in the rest of physics, the whole of chemistry, biology, geology, physiology and perhaps even human behavior. This reductive view of physics is popular among some physicists. Yet, there are other physicists who argue this is an oversimplified and that the relationship of elementary particle physics to these other domains is one of emergence. Several objections have been raised from physics against proposals for emergence (e.g., that genuinely emergent phenomena would violate the standard model of elementary particle physics, or that genuine emergence would disrupt the lawlike order physics has revealed). Many of these objections rightly call into question typical conceptions of emergence found in the philosophy literature. This book explores whether physics points to a reductive or an emergent structure of the world and proposes a physics-motivated conception of emergence that leaves behind many of the problematic intuitions shaping the philosophical conceptions. Examining several detailed case studies reveal that the structure of physics and the practice of physics research are both more interesting than is captured in this reduction/emergence debate. The results point to stability conditions playing a crucial though underappreciated role in the physics of emergence. This contextual emergence has thought-provoking consequences for physics and beyond, and will be of interest to physics students, researchers, as well as those interested in physics.

The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical. Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field. Contents: Hamiltonian MechanicsHamilton–Jacobi TheoryMatter Waves, Schrödinger's Equation, and Bohm's Theory The MetatronUncertainties and Quantum BlobsQuantum States and the Density MatrixVarying Planck's ConstantAppendices: The Symplectic GroupThe Metaplectic RepresentationBorn–Jordan QuantizationTwisted Product and Convolution Readership: Undergraduate and graduate students of mathematics and physics, interested in analysis and differential equations, probability and statistics, geometry and topology and mathematical physics. Keywords: Classical Mechanics;Hamiltonian Mechanics;Quantum Mechanics;Planck's Constant;Mathematical Physics;Algebraic GeometryReview:0

The main purpose of this book is to introduce a broader audience to emergence by illustrating how discoveries in the physical sciences have informed the ways we think about it. In a nutshell, emergence asserts that non-reductive behavior arises at higher levels of organization and complexity. As physicist Philip Anderson put it, “more is different.” Along the text's conversational tour through the terrain of quantum physics, phase transitions, nonlinear and statistical physics, networks and complexity, the author highlights the various philosophical nuances that arise in encounters with emergence. The final part of the book zooms out to reflect on some larger lessons that emergence affords us. One of those larger lessons is the realization that the great diversity of theories and models, and the great variety of independent explanatory frameworks, will always be with us in the sciences and beyond. There is no “Theory of Everything” just around the corner waiting to be discovered. One of the main benefits of this book is that it will make a number of exciting scientific concepts that are not normally covered at this level accessible to a broader audience. The overall presentation, including the use of examples, analogies, metaphors, and biographical interludes, is geared for the educated non-specialist.

In this age of superstring theories and Big Bang cosmology, we're used to thinking of the unknown as impossibly distant from our everyday lives. But in A Different Universe, Nobel Laureate Robert Laughlin argues that the scientific frontier is right under our fingers. Instead of looking for ultimate theories, Laughlin considers the world of emergent properties-meaning the properties, such as the hardness and shape of a crystal, that result from the organization of large numbers of atoms. Laughlin shows us how the most fundamental laws of physics are in fact emergent. A Different Universe is a truly mind-bending book that shows us why everything we think about fundamental physical laws needs to change.

This book surveys the science at a semipopular, Scientific American-level. It is even-handed with regard to competing directions of research and philosophical positions. It is hard to get even two people to agree on anything, yet a million billion water molecules can suddenly and abruptly coordinate to lock themselves into an ice crystal or liberate one another to billow outwards as steam. The marvelous self-organizing capacity of matter is one of the central and deepest puzzles of physics, with implications for all the natural sciences. Physicists in the past century have found a remarkable diversity of phases of matter—and equally remarkable commonalities within that diversity. The pace of discovery has, if anything, only quickened in recent years with the appreciation of quantum phases of matter and so-called topological order. The study of seemingly humdrum materials has made contact with the more exotic realm of quantum gravity, as theorists realize that the spacetime continuum may itself be a phase of some deeper and still unknown constituents. These developments flesh out the sometimes vague concept of the emergence—how exactly it is that complexity begets simplicity.