Thanks! I don't believe these two concepts are related. You get back to the same point because the earth is _globally_ a sphere. However, time dilation and length contraction are _local_ concepts: they happen even for very small motions.
I guess a global object in spacetime analogous to a sphere in space is the hyperboloid t^2 - x^2 = r^2. Moving on this hyperboloid corresponds to changing boost velocity. But unlike a sphere, it is not closed, so moving in one direction does not get you back to the same point.
Apologies, I didn't mean to suggest that the two concepts are related.
For SR, I'm looking for an answer to "why?" that only has same satisfying flavor as the sphere question. I want the same "aha!" feeling.
For example, if I stand up from the sofa and walk across the room and come back and sit down next to my friend, I want a deep intuitive sense that of course it must be the case that less time has passed for me than the amount of time that my friend has experienced. Why does this happen?
An answer like "t'=t/sqrt(1-v^2/c^2) describes what happens", while correct, is not satisfying.
Similarly, if I wave my hand in front of my face, I want it to seem obvious to me that less time must have passed for my hand than for the rest of my body.
Given your experience writing the book, you must have developed an intuitive sense for the behavior of the effects of relativity and why they happen, so I am wondering how you would translate that into words for a general audience.
Imagine the context where a random person with a minimal math background at a party was to ask you why less time passes in the sofa scenario, using an actual sofa to demonstrate it.
They stand up and walk away from you and return and sit back down next to you and they want you to explain to them why less time has passed for them. They want you to explain why the room around them got shorter in the direction that they were walking.
These are effects that, while undetectably small, really happened.
I see. I don't know of a great answer, but it comes down to the constant speed of light. The simplest clock is two parallel mirrors with light bouncing back and forth. If someone is moving, then the light seems to take longer to bounce between them, so their clock appears slower. Wiki has a a good explanation:
I guess a global object in spacetime analogous to a sphere in space is the hyperboloid t^2 - x^2 = r^2. Moving on this hyperboloid corresponds to changing boost velocity. But unlike a sphere, it is not closed, so moving in one direction does not get you back to the same point.
May add to this answer later.