I understand the principles of relativity. I understand why we need relativity if we are to have the laws of physics be the same in all inertial frames. But physically speaking, how does relativity actually work? In particular, I was thinking about length contradiction, and I don't understand how moving objects shrink. I understand why they need to, just not how. Is the fabric of spacetime bending in some weird way around a speeding object in order to shrink the object? (Presumably, this might make sense, since massive objects warp spacetime, and fast moving objects have a large relativistic mass). Is this explainable using general relativity?
Edit: To elaborate, my question is more about the mechanics of what is happening to make the object appear shorter. For example, consider a straw in a glass of water, and a straw not in a glass of water. In both cases, the straw is the same. However, it looks weirdly disjointed when in the glass of water; from a new perspective, it looks different. However, there is a good explanation for why this is; the light refracts when changing mediums, and this thus changes your perception. I'm looking for a similar explanation as to "how" the perception that something has changed length actually comes about in S.R. –