I honestly believe I have actually communicated the idea I have in mind to absolutely nobody. I try again every now and then, so, let’s try another approach.
Suppose that dark energy is a repulsive force centered on each particle, in the same sense that gravity is an attractive force centered on each particle.
It should be plausible that every force fits into the general relativity framework - that is, every force represents curvature; positive curvature for repulsive, negative curvature for attractive. It is plausible that Kaluza-Klein offers a “geometric” explanation for electricity. (That is, it is a particular -shape- of curvature, over spacetime.)
Suppose there exists a function that can describe every force simultaneously.
I don’t have that function. What I do have is a possible hint: sin(ln(x))/x, for a Newtonian version analogous to the inverse square law of 1/x^2 - it gets close to describing reality, by which I mean it predicts the basic geometry of the observed forces, but doesn’t quite manage to line up with the distances; it’s scaled incorrectly, somehow. Now, there are geometric reasons to expect the inverse square law, by which I mean it can be derived from the first principles of something like the three dimensional Cartesian coordinate system - but I think there are -also- geometric reasons to expect something -like- the equation sin(ln(x))/x; they’re hard to explain, but they don’t depend on the number of spacial dimensions being 3.
Whether or not my geometric reasoning makes sense is basically an assumption. The reasoning is difficult to explain, and there’s a particular step which I cannot explain at all; it makes sense to me, but I have no idea what sequence of words to emit to make it make sense to anybody else. I don’t imagine it makes sense to anybody else. I consider the primary issue of my crackpot nonsense to be the problem of communicating the ideas.
So, I’m trying again. Consider curvature as a rotation of an imaginary object moving outward, its rotation causing spacetime itself to rotate; in particular, if we imagine an arrow that is pointed away from the object in space, and towards the object in time, the rotation is on the axis of the direction the arrow is pointing and the time direction; spacetime is rotated such that some of “time” is rotated into “space”, and vice versa.
This imaginary object is -not- rotating in spacetime; it is rotating in some number of imaginary dimensions; I do not think the number is significant, because I think on some level all imaginary dimensions are equivalent to one another, in particular with respect to a non-complex dimension. These dimensions connect to “real” space as, rather than a line, two endpoints; at the surface area of an infinitely small point, and the origin of that infinitely small point. The rotation is a curved connection from infinity to 0; a spiral. As the object rotates, and moves away from the origin, it “unspools” from both ends; time (and distance) is the straightline distance from infinity, and the rotation of spacetime is the straight-line distance to the origin; the infinity, however, is canceled out, as the curvature created by the object as it moves requires it to traverse the same infinity before it can reach finite spacetime. (Since it is exactly the same infinity, I think it is reasonable to say it cancels itself out, as opposed to the usual issues with working with infinities.)
The object is imaginary, to be clear. I don’t really know how to describe the shape of the actual idea, where all of this happens without an intermediary force; it’s a negative-dimensional geometry that exists all around us. We exist in negative dimensions - but, because time is a negative dimension too, and that is the dimension we experience existence along, our perception is that the other dimensions are positive; the curve cancels itself out, from our perspective. Mostly! Because it leaves a mark in the orientation of spacetime; curvature. Differences in perspective about the orientation of spacetime (from a particle’s point of view). Time is the negative dimension we experience existence along, and runs from infinity to zero, as opposed to zero to infinity; every particle is “spiraling inwards”. Distance is thus “the other object’s history”; that is, the distance from particle A to particle B is equivalent to the “difference” in time the two objects have.
Time and distance are the same thing, but they’re also not the same thing. It is useful, if not entirely accurate, to imagine them as parallel dimensions; one of these dimensions can be described as having the infinities at the origin and 0 at the horizon (time - the future points “inward”), and one of these dimensions can be describes as having 0 at the origin and the infinities at the horizon (distance - which points “outward”). I think they’re the same dimension overlapping itself; if we go from the horizon to the particle, moving inward, I think that -at- the particle, the dimension rotates in a complicated way, and ends up pointing outward again. So in a sense, each particle occupies two different points on this dimension; with respect to itself, each particle is situated both at the infinities and at the origin. And with respect to another particle, each particle is situated at two different finite non-zero points on this dimension.
In a certain respect this means there is a duality between deSitter space and anti-deSitter space, these two spaces both exist simultaneously, and each particle occupies a position in both. Or, alternatively - time is a negative dimension, and distance is the interpretation of extent of time with respect to time.
If any of this makes any sense to anybody.
I’ve tried a number of attempts to derive a “correct” equation based on those reasons, but my mathematical skills, simply, aren’t up to the job. I’m not sure I have the right spiral, either - I expect a spiral, but I don’t know which one. The logarithmic spiral is promising because of the natural log in the equation that isn’t quite right, and I’ve found ways to get something like sin(ln(x))/x + cos(ln(x))/x as a potential equation - but still can’t quite get it to work.
There is something I think is promising here, however.
Starting a new comment chain for clarity.
Are you studying algebraic cycles?
I think there is something promising here as well.
Below is the link to a chat transcript between GPT-4 and I about your article and its concepts. I am not smart enough to really discuss them with you or fully evaluate the machine’s claims, but what I have been able to validate I have. Plus you did mark this as crackpot. You get what you get in that case.
If you look through the transcript you’ll see that the most promising concept this Centaur Session developed from your article (to my mind, anyway) was the idea of entropy as a negative geometric force on spacetime, with a definition of entropy that includes quantum and observer effects.
Do you think I came anywhere close to the mark? And if I either did or you appreciate the level of effort, do you mind if ask you something? In the film Johnny Mnemonic would you want to be (or think you would be) a:
1) LoTek
2) HiTek
3) Courier
https://chat.openai.com/share/ceb327db-a556-42c4-8086-d49bf8fdcbb7