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derz
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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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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.
robphy 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?
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.
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
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.
The geometric derivation of SR is a method for understanding the principles of special relativity using geometric concepts instead of mathematical equations. It involves visualizing spacetime as a 4-dimensional space and examining the effects of motion and gravity on this space.
The geometric derivation of SR provides a more intuitive understanding of the theory and allows for a deeper insight into concepts such as time dilation and length contraction. It also allows for a more elegant and concise representation of the theory.
In the traditional derivation, SR is derived from mathematical equations, specifically the Lorentz transformations. In the geometric derivation, the theory is derived using the principles of geometry and the concept of spacetime as a 4-dimensional manifold.
Some key concepts in the geometric derivation of SR include the concept of spacetime as a 4-dimensional manifold, the invariance of the speed of light, and the effects of motion and gravity on the geometry of spacetime.
The geometric derivation of SR is a precursor to Einstein's theory of general relativity, which extends the principles of special relativity to include the effects of gravity. The geometric approach to SR serves as a foundation for understanding the more complex concepts in general relativity.