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Natural Science Forum / Physics / Relativity / September 2006Coordinates and variables
Hi, guys ! I am asking You and myself : Do the Lorentz transforms represent after all: 1. A change of variables; 2. A transformation of coordinates between different IRF ? State, please, your documented opinion referring to the case of uni-dimensional Lorentz transforms and the case of x^2 - c^2* t^2 <> 0 . (If you know of this subject as being discussed before, please let me know !) All the best ,LL > Hi, guys ! > I am asking You and myself : [quoted text clipped - 10 lines] > > All the best ,LL There is no difference between what Lorentz meant by "change of variables" and transformation of coordinates between IRFs. Phil | Hi, guys ! | I am asking You and myself : [quoted text clipped - 9 lines] | | All the best ,LL The cuckoo misforms were created by Einstein as an old joke, we've heard it before. http://www.androcles01.pwp.blueyonder.co.uk/Smart/Smart.htm Androcles > Hi, guys ! > I am asking You and myself : > Do the Lorentz transforms represent after all: > 1. A change of variables; Prima facie. > 2. A transformation of coordinates between different IRF ? Provided at least one coordinate system is known to be an inertial reference frame. > State, please, your documented opinion referring to the case of > uni-dimensional > Lorentz transforms and the case of x^2 - c^2* t^2 <> 0 . Lorentz transformations allow the spacetime interval to be an invariant, but they don't depend on a particular spacetime interval. > (If you know of this subject as being discussed before, > please let me know !) All subjects have been discussed ad infinitum, with the chaff dutifully filed away with the wheat, so that each may have the pleasure of winnowing. | > Hi, guys ! | > I am asking You and myself : [quoted text clipped - 21 lines] | filed away with the wheat, so that each may have the pleasure of | winnowing. And only chaff has been found. Winnower: http://www.androcles01.pwp.blueyonder.co.uk/Rocket/Rocket.htm Androcles .......... > Lorentz transformations allow the spacetime interval to be an > invariant, but they don't depend on a particular spacetime interval. ............. > All subjects have been discussed ad infinitum, with the chaff dutifully > filed away with the wheat, so that each may have the pleasure of > winnowing. I make, for myself, a clear distinction between a space-time interval with physical meaning , i.e. with possible connection to a length measurement, and the one defined formally as (x^2 - c^2 * t^2) for an arbitrary point. In this last case, the space-time interval, though invariant Lorentz transformation-wise, varies from place to place. >From there comes the different value of time from one place to another, in the same IRF( !!!!! ), which I think is a non sense. While this is of no importance when the space-time interval = 0, as it refers to a measurement using signals of speed c, in my present opinion, it has no clear and acceptable meaning if the interval<>0, other than a formal mathematical change of variables . I got no time for winnowing, yet I would appreciate You and other posters at this group directing me to appropriate sources or posts of which you know, as for example Sue just did. All the best, LL Hi No appetite for this subject? Too bad! One could think that there is no difference between a coordinate transformation involving 2 IRFs and the simple replacement of variables(coordinates) . This seems to be true, as we are talking of.... "what seem an observer see in the moving RF". But then, the coordinates *attributed* to the moving RF have no relevance for the moving IRF, so it is about a simple change of the variables, is it not? LL > Hi, guys ! > I am asking You and myself : [quoted text clipped - 10 lines] > > All the best ,LL The Lorenz transform represnts the spatial to temporal operation that converts a time independent Maxwell field to time dependent Maxwell field when considering the finite speed of light. "Retarded potential" http://farside.ph.utexas.edu/teaching/em/lectures/node50.html Uni-dimensional ? The transform applies to a volume of electric charge so any but a 3s + 1t representation is incomplete in some form or another. Several variations are discussed here: http://arxiv.org/abs/physics/0204034 Sue... |
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