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出版者:Cambridge University Press

作者:Alfred North Whitehead

出品人:

页数:620

译者:

出版时间:2009-7-20

价格:USD 48.00

装帧:Paperback

isbn号码:9781108001687

丛书系列:Cambridge Library Collection - Mathematics

图书标签:

• Universal Algebra
• Abstract Algebra
• Mathematics
• Logic
• Algebraic Structures
• Boolean Algebra
• Lattice Theory
• Mathematical Foundations
• History of Mathematics
• Set Theory

The Unfolding Tapestry of Modern Physics: Foundations and Frontiers A Comprehensive Exploration of Contemporary Theoretical Frameworks and Experimental Realities This extensive volume ventures far beyond the realm of abstract algebraic structures, immersing the reader in the vibrant, ever-evolving landscape of modern physics. It serves as a meticulous, in-depth guide, tracing the foundational principles upon which our current understanding of the universe rests, while simultaneously charting the most exciting and challenging frontiers of contemporary theoretical and experimental research. The narrative weaves together historical context, rigorous mathematical formalism (where necessary for clarity, though distinctly separate from the algebraic focus of the namesake), and profound philosophical implications, offering a holistic perspective on how we perceive and model physical reality. The initial sections anchor the reader firmly in the successes and inherent limitations of the Newtonian paradigm. We begin with a thorough re-examination of classical mechanics, moving systematically from Kepler’s laws and Galileo’s insights to the Lagrangian and Hamiltonian formulations. This is not merely a historical recap; rather, it establishes the conceptual bedrock against which revolutionary 20th-century physics had to rebel. Detailed chapters analyze the elegant, predictive power of classical field theory, particularly in electromagnetism, culminating in Maxwell’s equations—presented here in their continuum formulation, emphasizing the unification of electricity and magnetism as intertwined aspects of a single electromagnetic field. The discussion critically assesses where classical physics inevitably fractured: the black-body radiation paradox, the photoelectric effect, and the steadfast failure to detect luminiferous aether. The transition into the quantum realm is handled with deliberate care. The central chapters are dedicated to the formal development of non-relativistic quantum mechanics. Schrödinger’s equation, both time-dependent and time-independent, is dissected, focusing intently on its interpretation through the lens of wave functions, probability amplitudes, and the physical meaning of expectation values. The treatment heavily emphasizes canonical quantization procedures, Dirac notation, and the profound implications of the uncertainty principle as a fundamental limit on simultaneous knowledge, rather than a mere technological constraint. Spin—the intrinsic angular momentum of particles—is introduced not as an ad-hoc addition, but as a necessary component arising from the structure of the underlying symmetry groups governing spacetime interactions. Moving into relativistic mechanics, the text rigorously explores Special Relativity. The Lorentz transformations are derived from the fundamental postulates concerning the constancy of the speed of light and the principle of relativity. Subsequent sections delve into the unification of space and time into Minkowski spacetime, the relativistic dynamics of massive and massless particles (including the famous mass-energy equivalence), and the necessity of four-vectors in formulating physical laws covariantly. The relationship between momentum, energy, and the structure of causal propagation is illuminated through detailed geometric interpretations of spacetime diagrams. The subsequent, crucial section tackles General Relativity—Einstein's geometric description of gravitation. Unlike purely abstract mathematical treatises, this exposition grounds the tensor calculus firmly within physical intuition. We analyze the equivalence principle, the geodesic equation describing free fall, and the introduction of the metric tensor as the physical manifestation of spacetime curvature induced by mass and energy. Detailed case studies—such as the precession of Mercury's perihelion, the bending of light near massive objects, and the foundational concepts behind gravitational redshift—are analyzed using the field equations, emphasizing how the geometry is the physics. The chapter concludes by exploring the Newtonian limit, ensuring the continuity between Einstein’s formulation and classical gravitational theory. The latter half of the volume pivots toward the grand challenges of modern research. Particle physics forms a substantial core. This exploration begins with the Standard Model of particle interactions. Quantum Electrodynamics (QED) is introduced as the prototype for successful quantum field theories, detailing concepts like Feynman diagrams, renormalization procedures (explained conceptually as managing infinities that arise from virtual particle loops), and the verified predictions regarding anomalous magnetic moments. The focus then broadens to encompass the weak and strong nuclear forces. The discussion of the weak force centers on parity violation and the mechanism of neutrino oscillation, while the strong force is examined through the principles of Quantum Chromodynamics (QCD), highlighting asymptotic freedom and color confinement. The role of gauge bosons—photons, W/Z bosons, and gluons—in mediating these forces is thoroughly detailed. A significant portion of the book is dedicated to cosmology and the physics of the extreme universe. We move from the observational evidence supporting the Big Bang model (Hubble's Law, the Cosmic Microwave Background, and light element abundances) to the complex dynamics of the early universe. Inflationary theory is presented as the leading mechanism resolving the horizon and flatness problems, analyzed not as a proven fact, but as a compelling theoretical necessity under current models. The most speculative, yet empirically driven, frontiers are then examined: Dark Matter and Dark Energy. The evidence for each—from galaxy rotation curves and gravitational lensing to the accelerated expansion of the universe—is presented clearly, followed by an overview of leading candidate theories (e.g., WIMPs, axions, and quintessence models), maintaining a rigorous distinction between established observation and ongoing theoretical hypothesis. Finally, the volume culminates in a dedicated exploration of theoretical efforts attempting to bridge the chasm between General Relativity and Quantum Mechanics—the quest for a theory of Quantum Gravity. Various approaches, including String Theory (analyzing its landscape of possibilities and dimensional requirements) and Loop Quantum Gravity (focusing on the discrete nature of spacetime geometry at the Planck scale), are reviewed. The intent is not to present a unified theory, but to map the current terrain of investigation, highlighting the deep conceptual hurdles—such as the measurement problem in gravity and the definition of time in a quantum gravitational context—that define the cutting edge of physics research today. The concluding remarks summarize the immense success of established frameworks while emphasizing that the greatest, most fundamental questions regarding reality remain wide open.

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