Insights Introducing Relativity on Rotated Graph Paper: A Graphical Motivation

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The discussion centers on the concept of illustrating relativity through the use of rotated graph paper, emphasizing a non-algebraic motivating argument for understanding time dilation and length contraction. The author references a previous work that established the equality of light-clock diamond areas and provides algebraic proof in a related article. The motivation for the graphical approach is aimed at enhancing comprehension of special relativity concepts. The omitted non-algebraic argument from the earlier draft is now included in the new piece, enriching the educational framework. This approach seeks to make the principles of relativity more accessible to learners.
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(based on https://www.physicsforums.com/threads/teaching-sr-without-simultaneity.1011051/post-6588952 and https://physics.stackexchange.com/a/689291/148184 )

In my earlier Insight Spacetime Diagrams of Light Clocks,
I stated without proof that the areas of all light-clock diamonds are equal.
In my article, “Relativity on Rotated Graph Paper”, Am. J. Phys. 84, 344 (2016)
I provided algebraic proof.

In the penultimate draft, I had a non-algebraic motivating argument (which also motivates time dilation and length contraction)
that had to be left out because the article was already too long.
This argument now appears in Introducing relativity on rotated graph paper...

Continue reading...
 

Thread 'Is using r as a coordinate in Birkhoff's theorem a limitation?'

In Birkhoff’s theorem, doesn’t assuming we can use r (defined as circumference divided by ## 2 \pi ## for any given sphere) as a coordinate across the spacetime implicitly assume that the spheres must always be getting bigger in some specific direction? Is there a version of the proof that doesn’t have this limitation? I’m thinking about if we made a similar move on 2-dimensional manifolds that ought to exhibit infinite order rotational symmetry. A cylinder would clearly fit, but if we...
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