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The Quantum Framework for Our Mathematical Universe: Full Dissertation

The Quantum Framework for Our Mathematical Universe: Full Dissertation
Author: Andrew M. Kamal
Publisher: Andrew Magdy Kamal
Total Pages: 42
Release:
Genre: Science
ISBN:

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Utilizing multiple theorems derived from Z = {∀Θ∈Z→∃s ∈ S ʌ ∃t ∈ T: Θ= 〈 (s,t)}., and formulating the equation: X=O+Σ H +( n (log)Φ/P d x , as well as some mathematical constraints and numerous implications in Quantum Physics, Classical Mechanics, and Algorithmic Quantization, we come up with a framework for mathematically representing our universe. These series of individualized papers make up a huge part of a dissertation on the subject matter of Quantum Similarity. Everything including how we view time itself and the origin point for our universe is explained in theoretical details throughout these papers.


Our Mathematical Universe

Our Mathematical Universe
Author: Max Tegmark
Publisher: Vintage
Total Pages: 434
Release: 2015-02-03
Genre: Science
ISBN: 0307744256

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Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.


The Routledge Handbook of Idealism and Immaterialism

The Routledge Handbook of Idealism and Immaterialism
Author: Joshua Farris
Publisher: Routledge
Total Pages: 829
Release: 2021-09-12
Genre: Philosophy
ISBN: 100043334X

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The influence of materialist ontology largely dominates philosophical and scientific discussions. However, there is a resurgent interest in alternative ontologies from panpsychism (the view that at the base of reality exists potential minds, minds, or mind-lets) to idealism and dualism (the view that all of reality is material and mental). The Routledge Handbook of Idealism and Immaterialism is an outstanding reference source and the first major collection of its kind. Historically grounded and constructively motivated, it covers the key topics in philosophy, science, and theology, providing students and scholars with a comprehensive introduction to idealism and immaterialism. Also addressed are post-materialism developments, with explicit attention to variations of idealism and immaterialism (the view that reality depends on a mind or a set of minds). Comprising 44 chapters written by an international and interdisciplinary team of contributors, the Handbook is organised into five clear parts: Idealism and the history of philosophy Important figures in idealism Systematic assessment of idealism Idealism and science Idealism, physicalism, panpsychism, and substance dualism Essential reading for students and researchers in metaphysics, philosophy of science, philosophy of religion, and philosophy of mind, The Routledge Handbook of Idealism and Immaterialism will also be of interest to those in related discplines where idealist and immaterialist ontology impinge on history, science, and theology.


Feynman's Thesis

Feynman's Thesis
Author: Richard Phillips Feynman
Publisher: World Scientific
Total Pages: 142
Release: 2005
Genre: Science
ISBN: 9812563660

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Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space?time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article ?Space?Time Approach to Non-Relativistic Quantum Mechanics? [Reviews of Modern Physics 20 (1948), 367?387], Paul Dirac's seminal paper ?The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.


Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47)

Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47)
Author: William G. Faris
Publisher: Princeton University Press
Total Pages: 257
Release: 2014-09-08
Genre: Mathematics
ISBN: 1400865255

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Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.


Information—Consciousness—Reality

Information—Consciousness—Reality
Author: James B. Glattfelder
Publisher: Springer
Total Pages: 662
Release: 2019-04-10
Genre: Science
ISBN: 3030036332

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This open access book chronicles the rise of a new scientific paradigm offering novel insights into the age-old enigmas of existence. Over 300 years ago, the human mind discovered the machine code of reality: mathematics. By utilizing abstract thought systems, humans began to decode the workings of the cosmos. From this understanding, the current scientific paradigm emerged, ultimately discovering the gift of technology. Today, however, our island of knowledge is surrounded by ever longer shores of ignorance. Science appears to have hit a dead end when confronted with the nature of reality and consciousness. In this fascinating and accessible volume, James Glattfelder explores a radical paradigm shift uncovering the ontology of reality. It is found to be information-theoretic and participatory, yielding a computational and programmable universe.


Quantum Theory for Mathematicians

Quantum Theory for Mathematicians
Author: Brian C. Hall
Publisher: Springer Science & Business Media
Total Pages: 566
Release: 2013-06-19
Genre: Science
ISBN: 1461471168

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Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.


The Non-Local Universe

The Non-Local Universe
Author: Robert Nadeau
Publisher: Oxford University Press
Total Pages: 257
Release: 2001-05-31
Genre: Science
ISBN: 019803041X

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Classical physics states that physical reality is local--a point in space cannot influence another point beyond a relatively short distance. However, In 1997, experiments were conducted in which light particles (photons) originated under certain conditions and traveled in opposite directions to detectors located about seven miles apart. The amazing results indicated that the photons "interacted" or "communicated" with one another instantly or "in no time." Since a distance of seven miles is quite vast in quantum physics, this led physicists to an extraordinary conclusion--even if experiments could somehow be conducted in which the distance between the detectors was half-way across the known universe, the results would indicate that interaction or communication between the photons would be instantaneous. What was revealed in these little-known experiments in 1997 is that physical reality is non-local--a discovery that Robert Nadeau and Menas Kafatos view as "the most momentous in the history of science." In The Non-Local Universe, Nadeau and Kafatos offer a revolutionary look at the breathtaking implications of non-locality. They argue that since every particle in the universe has been "entangled" with other particles like the two photons in the 1997 experiments, physical reality on the most basic level is an undivided wholeness. In addition to demonstrating that physical processes are vastly interdependent and interactive, they also show that more complex systems in both physics and biology display emergent properties and/or behaviors that cannot be explained in the terms of the sum of parts. One of the most startling implications of non-locality in human terms, claim the authors, is that there is no longer any basis for believing in the stark division between mind and world that has preoccupied much of western thought since the seventeenth century. And they also make a convincing case that human consciousness can now be viewed as emergent from and seamlessly connected with the entire cosmos. In pursuing this groundbreaking argument, the authors not only provide a fascinating history of developments that led to the discovery of non-locality and the sometimes heated debate between the great scientists responsible for these discoveries. They also argue that advances in scientific knowledge have further eroded the boundaries between physics and biology, and that recent studies on the evolution of the human brain suggest that the logical foundations of mathematics and ordinary language are much more similar than we previously imagined. What this new knowledge reveals, the authors conclude, is that the connection between mind and nature is far more intimate than we previously dared to imagine. What they offer is a revolutionary look at the implications of non-locality, implications that reach deep into that most intimate aspect of humanity--consciousness.


The Many-Worlds Interpretation of Quantum Mechanics

The Many-Worlds Interpretation of Quantum Mechanics
Author: Bryce Seligman Dewitt
Publisher: Princeton University Press
Total Pages: 264
Release: 2015-03-08
Genre: Science
ISBN: 140086805X

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A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. In his interpretation, Dr. Everett denies the existence of a separate classical realm and asserts the propriety of considering a state vector for the whole universe. Because this state vector never collapses, reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, is not the reality customarily perceived; rather, it is a reality composed of many worlds. By virtue of the temporal development of the dynamical variables, the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result, and in most of which the familiar statistical quantum laws hold. The volume contains Dr. Everett's short paper from 1957, "'Relative State' Formulation of Quantum Mechanics," and a far longer exposition of his interpretation, entitled "The Theory of the Universal Wave Function," never before published. In addition, other papers by Wheeler, DeWitt, Graham, and Cooper and Van Vechten provide further discussion of the same theme. Together, they constitute virtually the entire world output of scholarly commentary on the Everett interpretation. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.


The Foundation of Reality

The Foundation of Reality
Author: David Glick
Publisher: Oxford University Press
Total Pages: 286
Release: 2020-04-29
Genre: Philosophy
ISBN: 0192567225

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Are space and time fundamental features of our world or might they emerge from something else? The Foundation of Reality brings together metaphysicians and philosophers of physics working on space, time, and fundamentality to address this timely question. Recent developments in the interpretation of quantum mechanics and the understanding of certain approaches to quantum gravity have led philosophers of physics to propose that space and time might be emergent rather than fundamental. But such discussions are often conducted without engagement with those working on fundamentality and related issues in contemporary metaphysics. This book aims to correct this oversight. The diverse contributions to this volume address topics including the nature of fundamentality, the relation of space and time to quantum entanglement, and space and time in theories of quantum gravity. Only through consideration of a range of different approaches to the topic can we hope to get clear on the status of space and time in our contemporary understanding of physical reality.