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Has anyone derived the Lorentz-transforms by using 'simple' geometrics? If so, could I get a link for the paper please. I tried to google for one but couldn't find.
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Can you be more specific as to what you mean by 'simple' geometrics? Who is the target audience? and what is their background?derz said:Has anyone derived the Lorentz-transforms by using 'simple' geometrics? If so, could I get a link for the paper please. I tried to google for one but couldn't find.
Target audience: everyone who wants to learn about SR or find a simpler way to derive itrobphy said:Can you be more specific as to what you mean by 'simple' geometrics? Who is the target audience? and what is their background?
Do you want a geometric construction? formulation via analytic geometry? or by trigonometry? vector methods? group methods? operational construction using light-rays?
Bondi's "Relativity and common sense" would be my recommendation, or some other book using an equivalent approach. This approach is sometimes known as k-calculus, but it actually involves only high school algebra.derz said:Target audience: everyone who wants to learn about SR or find a simpler way to derive it
I'd appreciate papers with geometric construction and papers that formulate SR with analytic geometry.
Sorry about not being specific in my first post, I'm not a native english speaker and wasn't sure what to look for
K calculus predated Bondi, Milne's "Kinematic Relativity" depended on it.pervect said:Bondi's "Relativity and common sense" would be my recommendation, or some other book using an equivalent approach. This approach is sometimes known as k-calculus, but it actually involves only high school algebra.
I may be biased, because Bondi's book was one of the first books I read.
Not sure whether it's exactly how you meant, but I found http://www.mathpages.com/rr/s1-07/1-07.htm" [Broken] very interesting..derz said:Has anyone derived the Lorentz-transforms by using 'simple' geometrics?
Such a premonition would have been an extraordinary triumph for pure mathematics [...] though it now can display only staircase wit
An excellent book that starts with the geometry (i.e. the metric) as a given, then works out the Lorentz transformations is Spacetime Physics (though my experience is only with the old red paperback edition).The present book explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasised throughout, and provides the basis of understanding of the special relativity effects of time dilation, length contraction, and the relativity of simultaneity. Bondi's K-calculus is introduced as a simple means of calculating the magnitudes of these effects, and leads to a derivation of the Lorentz transformation as a way of unifying these results. The invariant interval of flat space-time is generalised to that of curved space-times, and leads to an understanding of the basic properties of simple cosmological models and of the collapse of a star to form a black hole. The appendices enable the advanced student to master the application of four-tensors to the relativistic study of energy and momentum, and of electromagnetism. In addition, this new edition contains up-to-date information on black holes, gravitational collapse, and cosmology.