Given this context, my question is, for special relativity, why do time dilation and length contraction happen?
Place two rulers right next to each other, and their length scales will agree. Now, place them at an angle, and have one ruler measure the other by orthogonal projection. Each of the observers represented by the rulers will conclude that the other one has 'contracted' by a factor given by the cosine of the angle.
Now, add a third ruler to complete the triangle. To go from one vertex to the opposite one, you can either follow along a single ruler, or via a bent path along two rulers. The symmetry has been broken, and the bent path will be objectively longer - that's the twin 'paradox'.
Things are more complicated than that because Minkowski space is non-Euclidean (for example, less time will pass for the travelling twin, ie the bent path will be the 'shorter' one), but if you want a simple analogy, I think that's a pretty decent one...
Place two rulers right next to each other, and their length scales will agree. Now, place them at an angle, and have one ruler measure the other by orthogonal projection. Each of the observers represented by the rulers will conclude that the other one has 'contracted' by a factor given by the cosine of the angle.
Now, add a third ruler to complete the triangle. To go from one vertex to the opposite one, you can either follow along a single ruler, or via a bent path along two rulers. The symmetry has been broken, and the bent path will be objectively longer - that's the twin 'paradox'.
Things are more complicated than that because Minkowski space is non-Euclidean (for example, less time will pass for the travelling twin, ie the bent path will be the 'shorter' one), but if you want a simple analogy, I think that's a pretty decent one...