Home  Commentary  Surveys  Research  Background  Store  Previously  Site Info 
The basic layout of the site is as survey paths, which can be found under the Surveys link at the top of this and most other pages on this site. Each survey begins with a basic overview of the subject. Part of this overview include simulators of astrophysical phenomena that allow the reader to experiment with the phenomena. The later pages in a survey present the subject in greater and more mathematical depth. A path ends with research pages that describe current research projects and results in astrophysics. The links at the top of each page are Home, which is the current home page of this site, Commentary, which is an index of short essays on topics loosely related to astrophysics, Surveys, which is the index of survey paths, Research, which is the index of research pages and the page leading to recent news items, Background, which is the index page for all background information on astrophysics, including survey pages, simulator pages, tables, bibliographic references, and lists of web resources, Previously, which is an index of previous home pages, and Site Info, which describes the site and its author, and gives contact information. On the home page is found an addition link. This is the Store link, which leads to reviews of worthwhile books on astronomy and other relates subjects. Links on these pages enable the reader to buy these books from Amazon.com, which helps to financially sustain this web site. Each Wednesday, a new issue of The Astrophysics Spectator is published that comprises a new home page, a new commentary, whatever news the author notices, and background, research, and simulator pages added to the survey paths. The home page acts as an index to the newly added pages. This site also has an RSS channel, whose link is given at the bottom of the righthand column of this page. May 4, 2005This week is a light week. I add a page to the “Special Relativity” path that discusses length contraction, time dilation, and the skewing of simultaneity. This leads to a discussion of the twins problem of if a man travels to a star and back, and his twin remains on Earth, which twin is older at the end of the trip? The concepts of length contraction, time dilation, and the skewing of simultaneity are very abstract. They appear when one measures objects in motion within a coordinate system that is calibrated by passing light signals between clocks. For instance, I can set up a coordinate system on Earth by placing several clock at various points and calibrating the distance between pairs of clocks and the absolute time on each clock by measuring the light travel time between each pair of clocks. Within such a coordinate system, the measured length of an object in motion is shorter than it is when the object is at rest. The passage of time is measured to be shorter for a clock in motion than for a clock at rest. Events that occur simultaneously at rest occur in a sequence for an observer in motion. This may all appear paradoxical, because in physics there is no absolute rest frame: while I consider a traveler to be in motion, with myself at rest, that traveler can consider me to be in motion, with himself at rest. This implies that I will measure shorter lengths and a slower passage of time than will the traveler for the objects moving with the traveler, while the traveler will measure shorter lengths and a slower passage of time than will I for objects at rest with me. This points to an important distinction between what one measures within a coordinate system and what one sees. While different observers may measure different times and positions for objects, every observer must see the same events occur, so if light from different sources reach the same point at a given instance for one observer, it all reaches this point at a given instance for all observers, regardless of their motion. This leads naturally to the twin problem: if a man travels to a distant star and back, and his twin stays on Earth, which twin is older at the end of the journey? The puzzle revolves around time dilation. If each twin sees time slow for the other, how can more time pass for one twin than the other? The resolution of this faux paradox underlines the abstractness of measurement within a coordinate system. Jim Brainerd BackgroundMeasurement in Special Relativity. This page develops the concept of an inertial coordinate frame. This is the abstract approach to special relativity, leading to the concepts of time dilation, length contraction, and the skewing of simultaneity. This abstract world of measurement is very different from the world that we see. In illustrating the point, the twins problem and its shadow, the twins paradox, are discussed. (continue) 
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