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Luke_A_Somers comments on Great Explanations - Less Wrong
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The math of special relativity helps not one whit in solving problems 1, 2 and 4. Problem 3 of course can be answered qualitatively without math, but to indicate with any specificity you will need math.
Moreover, you can be quite proficient with the math of SR and be floored by these. I knew an undergrad who could do acceleration problems yet couldn't work his way through problem 1, because the course had focused on gamma and neglected spacetime diagrams.
Spacetime diagrams are the math of special relativity. Doing algebra with gammas without insight on how it relates to the Minkowski spacetime is like the proverbial blind men grasping various parts of the elephant. (Why such godawful approaches are still foisted upon students is a mystery to me.)
I think someone without a detailed grasp of spacetime diagrams should be able to answer problem 1, as long as they know the following principles:
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