Three Maps, One Territory

I now have three distinct ways of describing the same phenomenon, my unified field theory, sin(ln(x))/x.  At this point I think it is probably sin(ln(x))/x + cos(ln(x))/x, granted.

In the first description, the field is a self-interfering sine wave, possibly but not definitely originating as something like f(x) = x + integral(sin(f(x))/f(x)).  I couldn't solve the recursion.

In the second description, the field is the surface area of a geometry which may be a negative 3-sphere, which results in the distance dimension being the arc length of a spiral in a complex plane.  The unreal portions define the instantaneous curvature at a given point.  I arrived at this description trying to solve the recursive function, and deciding it might be easier to consider what a negative closed dimension might behave like; no luck.

In the third description, we are back, in a sense, to the first description; if we think of the field as a rotation in the shape of local space-time, the behavior at a point is defined by the rotation of the field as it arrives at this point; that is, the field causes rotation, but the rotation it causes is rotated by the field between the origin and the point.  Self-interfering wave again, but this time, considering the closed hyperbolic dimension of the rotation itself, perhaps the link to the second description may be a little more apparent.

Or not.

The obviousness of this all is particularly frustrating given the difficulty of trying to convey it.  How is it not readily apparent to anyone who looks that the forces can be described as a series which decreases in both initial impetus, and in the decay of that impetus, of alternating sign? And once this is realized, how is it not eventually apparent that this pattern can be unified in a wave whose amplitude decays proportional to distance, and whose frequency decays proportional to the log of distance?

An Updated Description

So, one of the crackpot ideas I have been tossing around here is "Lorentz Contraction causes motion".

This probably sounds like nonsense; not even wrong, but nonsensical.

Terrell-Penrose rotation gives rise to an alternative description.  Supposing that the velocity vector of mass at rest is [0,0,0,c] - that is, traveling through time at the speed of light - a rotation is sufficient to give rise to motion through space.

More, we can start to redefine the way we think of the interaction of gravity and mass, by describing it in terms of the rotation the tidal effects of gravity give rise to.  I think you could fully describe motion in these terms.

In this limited framework, velocity is reduced to an artifact of the fact that time passes.  In a sense, we have simplified the physics.

Now, a few things to note.  First, time and distance being equivalent, the direction of rotation may end up mattering in terms of what the final time dilation looks like.  That is, I wouldn't put money on the outcome of a real-world twin paradox experiment.  Second, relativity still applies.  Rotation becomes relative instead of velocity, which, if you think about it, has to be the case anyways.  Third, this formulation will not result in physics staying basically the same; it implies some subtle but serious changes.

For instance, taking the rotation as real, as opposed to an optical effect, means gravity is bent by motion, and not in a subtle way.  It is possible for motion to make gravity into a repulsive field, for certain observers observing certain situations.  Consider the case of an observer moving at relativistic speeds, who is watching another relativistic object passing by a star.  For certain angles, the star may appear on the opposite side of the object to our observer.  If we take the rotation as real, this is real; and the apparently negative gravitic effects on the object are likewise real.

This kind of thing isn't unusual in my own crackpot nonsense, but as far as I know, isn't generally considered a part of normal physics.

I suspect that there may be a link between my other crackpot nonsense and this, given that the rotation involved has some interesting properties when considered as a dimension, but I'm not there yet.

Also, if this happens to make sense where "Lorentz Contraction causes motion" does not, I suggest thinking about what all this implies about how motion changes the shape of a unified field, and in particular how a unified field which has curvature must interact with another unified field which has curvature.