Velocity as Rotation

 Now, in the last post, I tried to reiterate one of the core ideas.  A part of the idea that was omitted is how, exactly, rotation in space-time causes motion.  Also, possibly, what exactly I mean by rotation in space-time.

So, what do I mean by rotation in space-time?  If we consider "motion" as rotation, then it would be rotation along the pair of axes formed by the vector of motion in three dimensions, and time.  This forms a two-dimensional plane; if we consider a set of structures in spacetime (be they particles, or just another geometry in space-time), a rotation of these structures along such a pair of axes, relative to an observer, creates motion.

How does it create motion?  By the passage of time itself.  The structure is moving along a dimension of time which is, from the observer's perspective, rotated into space; some of the time-motion of the structure is, from the observer's perspective, actually taking place in space itself.  That is, from the structure's perspective, it isn't moving in space at all; it is purely moving in time.  (And from its perspective, it is the rest of the universe that is rotated, and thus moving.)

Now, this is largely just moving the question from "What is motion" to "Why do objects move forward in time".  I have a number of suspicions and potential answers here, but ultimately the answer doesn't matter for our purposes; I haven't replaced one question with another, but instead simplified two questions into one.   Many more than two questions, actually.

Another omitted concept was how gravity-rotation can cause velocity-rotation; I gave the example of the fictional force and stopped there.  Now, we could use some of the common abstractions of relativity, like geodesics, but we don't actually need them here; all we need to do is observe the shape of space-time itself, and hold the passage of time as a given; the distance through time for the near and far ends (relative to a source of gravity) of a structure in space-time differ, as do the distances through space.  Thus, one side of the object is moving at a different speed than the other side, just considering passage through time.  Rotation.

We can conceptualize this different ways, actually - we can use space-time density instead of curvature or rotation, with similar results.  Or just consider the distances involved directly, and consider how the distances transform the geometries involved.  We can use any of these other ways of thinking about curvature to arrive at similar results, but rotation may be the easiest to conceptualize the next step of.