Top Document: Invariant Galilean Transformations On All Laws Previous Document: 2. Table of Contents Next Document: 4. The Encyclopedia Brittanica Incompetency. See reader questions & answers on this topic!  Help others by sharing your knowledge If a law is different over there than it is here, it is not one law, but at least two, and leaves us in doubt about any third location. This is the Principle of Relativity: a natural law must be the same relative to any location at which a given event may be perceived or measured, and whether or not the observer is moving. The idea of location translates to a coordinate system, largely because any object in motion could be considered as having a coordinate system origin moving with it. If you perceive me moving relative to you  who have your own coordinate system  will your measurements of my position and velocity fit the same laws my own, different measurements fit? If a law has the same form in both cases it is called covariant. If it is identical in form, var ables, and output values, it is called invariant. What we're asking is that if the xcoordinate, x, on one coordinate axis works in an equation, does the coordinate, x', on some other, parallel axis work? Speaking in terms of the axis on which x is the coordinate, x' is the 'transformed' coordinate. The situation is complicated because we're talking about coordinates  locations  but in most mean ingful laws/equations, it is lengths/distances (and time intervals) the equations are about, and x coord inates that represent good, ratio scale measures of distances are only interval scale measures on the x' axis. [See Table of Contents for discussion of scales.] So, if we have an xcoordinate in one system, then we can call the x' value that corresponds to the same point/location the transform of x. In particular, the Principle of Relativity is embodied in the form of the Galilean transformation, which relates the original x, y, z, t to x', y', z', t' by the transform equations x'=xvt, y'=y, z'=z, t'=t in the simplified case where attention is focused only on transforming the xaxis, and not y and z. In the case of Special Relativity, the x' transform is the same except that x' is then divided by sqrt(1(v/c)^2), and t'=(txv/cc)/sqrt(1(v/c)^2). In either case, v is the relative velocity of the coordinate systems; if there is already a v in the equations being trans formed use u or some other variable name. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Invariant Galilean Transformations On All Laws Previous Document: 2. Table of Contents Next Document: 4. The Encyclopedia Brittanica Incompetency. Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: Thnktank@concentric.net (Eleaticus)
Last Update March 27 2014 @ 02:12 PM
