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Einstein’s theories have become part of popular culture. The fact that time passes differently for different observers (“time dilation”) is a staple of science fiction, from Planet of the Apes (1968) to Interstellar (2014).
Much of this book has focused down to ever smaller scales, from atoms to nuclei to fundamental particles. At the other extreme is cosmology, the study of the overall structure and history of the universe. This chapter will introduce the Big Bang model of cosmology, what it does and doesn’t explain about the history of the universe, and some of the evidence for the model.
The one-particle-at-a-time double-slit and many other early twentieth-century experiments convince us that a photon or electron is associated with a “wavefunction.” This function follows the normal mathematics of waves (including constructive and destructive interference), and probabilistically guides the position and other properties of the particle.
We solve the radial differential equation to find the quantized energies and the radial wave functions of the bound states of the hydrogen atom. We present the energy spectrum of hydrogen and the electron probability densities of the energy eigenstates and of superposition states.
Chapter 3 presented a series of experiments that demanded serious changes to classical physics. These experiments pointed to particle-like behavior – quantization – of electromagnetic radiation.
A brief history of smallness. • Seventeenth and eighteenth centuries: Scientists understand that matter is made of particles too small to see, and they devise a host of ingenious experiments to determine the nature and properties of these particles. In hindsight, we would describe much of this work as groping toward a clear distinction between atoms and molecules.
According to the theory of relativity, Newton’s laws only work for objects traveling much slower than the speed of light. This does not mean that we need one set of laws for fast objects and a different set for slow objects; the equations of relativity work at all speeds. But Einstein’s equations and Newton’s laws make essentially the same predictions as each other for slow objects, and diverge significantly for fast ones. Early twentieth-century physicists were able to measure objects moving close to the speed of light, and such objects followed Einstein’s laws – not Newton’s.
Modern Physics intertwines active learning pedagogy with the material typically covered in an introductory survey, from the basics of relativity and quantum mechanics through recent developments in particle physics and cosmology. The flexible approach taken by the authors allows instructors to easily incorporate as much or as little active learning into their teaching as they choose. Chapters are enhanced by 'Discovery' and 'Active Reading' exercises to guide students through key ideas before or during class, while 'ConcepTests' help check student understanding and stimulate classroom discussions. Each chapter also includes extensive assessment material, with a range of basic comprehension questions, drill and practice calculations, computer-based problems, and explorations of advanced applications. A test bank and interactive animations as well as other support for instructors and students are available online. Students are engaged by an accessible and lively writing style, thorough explanations, 'Math Interludes' which account for varying levels of skill and experience, and advanced topics to further pique their interest in physics.
This book is designed for an undergraduate, one-semester course in experimental research, primarily targeting programs in sociology, political science, environmental studies, psychology, and communications. Aimed at those with limited technical background, this introduction to social science experiments takes a practical, hands-on approach. After explaining key features of experimental designs, Green takes students through exercises designed to build appreciation for the nuances of design, implementation, analysis, and interpretation. Using applications and statistical examples from many social science fields, the textbook illustrates the breadth of what may be learned through experimental inquiry. A chapter devoted to research ethics introduces broader ethical considerations, including research transparency. The culminating chapter prepares readers for their own social science experiments, offering examples of studies that can be conducted ethically, inexpensively, and quickly. Replication datasets and R code for all examples and exercises are available online.