I imagine the first two questions a reader might ask, upon coming across the basic ideas I'm going to be writing here, are, respectively, "Why would I want to read this?" and "Why are you bothering to write this?" So I will begin by answering those questions.

For the question of why someone would want to read this - well, personally, I enjoy reading other people's crackpot ideas, and trying to understand them. My hope is that I am not alone in this, and that other people enjoy the experience. If you don't want to read a crackpot's physics, then none of this is really for you, and that's fine.

For the question of why I am writing it, well, first, I enjoy other people's crackpot ideas, so I write it for the same reason anybody writes anything at all. But also, I really do, legitimately, think all of this is correct. I'm a self-aware crackpot, but I am really a crackpot. (And if I happen to be correct, I'm still a crackpot.)

The next question, I expect, is "Okay, so what's your crackpot physics idea?" And this question is a lot harder to answer, because, to a significant extent, I'm going to be spending a lot of time describing an idea that isn't actually the crackpot idea I have. I don't know how to explain the crackpot idea that I have. "The universe is a fractal" is an accurate description of the idea, but not actually -the- idea.

It's a boring idea, when you get right down to it, which makes it very frustrating how difficult the idea is to express. A lot of the difficulty comes down to the fact that the most natural representation for the ideas use different abstractions than the common ones in physics, so I have to justify those abstractions before I can even start on the ideas themselves.

So let's get started.

## Acceleration as Rotation

Start with two lengths of distance from a planet's surface, such that in a flat space-time, A and B are of equal length, where A is closer to the planet's surface than B. Suppose instead we are viewing these two lengths from a great distance away, such that the effect of the planet's gravity on us is negligible; from our observations, the two lengths are equal, by which I mean that light moves across A in the same time, from our perspective, that it takes for that light to move across B.

In General Relativity, A is, from a more local perspective, longer than B. We can think of this in a number of ways, but for now, just accept this notion as-is. Now, by necessity, an observer in the middle of A, timing the light crossing A, would measure a longer time than an observer in the middle of B who happened to be timing the light crossing B; if A is longer than B, then, in a sense, time is also "longer" in A; a clock at the middle of A ticks slower than an identical clock in the middle of B.

Now, usually, when considering questions of gravity in GR, we think in terms of curvature - but this is not, in fact, the only way of conceptualizing general relativity. We can also think in terms of rotation.

To illustrate this idea, we will begin by thinking in terms of a Newtonian force operating on an object - but we're going to keep in mind the modified distances. Note: This is an incorrect way of thinking about it, and is only used to demonstrate a way of thinking about General Relativity.

Think about the distance from the planet in terms of meters. And also, think about the distance from the planet in terms of seconds. For the distance from the planet in terms of meters, it should be obvious that the near (to the planet) side of the object experiences slightly greater gravity than the far side of the object. For our object, this is a tidal force; the only interesting thing to notice is that, for oblong objects, this can generate a very slight torque, causing the object to spin (but not very far).

Now, consider the distance in time - and observe that there is, in fact, a kind of torque there, as well. But what does it mean for an object to rotate in time?

Well, one potential answer might be found in Penrose-Terrell rotation - what is generally considered a purely visual phenomenon in which objects moving close to the speed of light appear to be rotated in particular ways. This is, I submit, not merely a visual phenomenon, but rather a fairly straightforward way of understanding velocity itself. Which is not to say it is the correct way of understanding things, but I will argue that it is -a- correct way of understanding things. We'll set this idea aside for now to investigate in more depth later - for now, let's just take a note that velocity kind of looks like rotation.

Now, the force, as described, isn't real. But suppose, for a moment, that the force, as described, doesn't need to be real. We can imagine the object, rotated in space-time by this imaginary Newtonian force. Can we extend our imaginations to imagining spacetime itself, rotated by this imaginary Newtonian force?

We don't really need to; that's curvature. Remember our two lengths? A is longer than B. Now, an observation: A is longer than B. A second in A is "longer" than a second in B. So far so good, right? But if we measure a length of distance in A, compared to B, we get more meters. If we measure a length of time in A, compared to B, we get -fewer- seconds. The idea of length is misleading in a particular way.

We could ask, where the meters came from, and where the seconds went to - but once we formulate this question, the answer becomes a bit obvious, particularly in the context of thinking about space-time itself being rotated. The seconds became meters; part of time "rotated in" to become part of space, and part of space "rotated out" to become part of time, and because the speed of light is the conversion factor and heavily favors space over time, we gained meters, and lost seconds.

This rotation is all relative; A doesn't think A is rotated, A thinks B is rotated. B doesn't think B is rotated, B thinks A is rotated. And some sufficiently distant observer thinks both of them are rotated (and they, obviously, think the distant observer is rotated).

This is all viewing these things from a static perspective; as soon as you let time start passing, objects in A and B start falling. Notice that, as they fall, they rotate. Notice, moreover, that if something stops them from falling - they still try to rotate.

We can actually describe falling entirely in terms of rotation, but that's somewhat more complex a topic. For now, instead, just notice that, if we take motion through time as a given - that is, if we start with an assumption that time passes - then the rotation of space-time gives rise to rotation of objects - noticing that the length of a second is greater on one side of an object than the other, there is torque expressed on the object itself, generated by the fact that one side of the object is trying to travel at a different speed than the other.

None of this is, to my mind, particularly interesting - it's just a different way of thinking about how General Relativity operates.

## Velocity as Rotation

How, exactly, does rotation in space-time cause motion? Also, what exactly do 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.)

Or, to consider that explanation from another perspective, objects don't agree on the precise vector of time, and each travels along a line which, from its own perspective, correctly represents time.

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. Let's take it as an assumption.

Motion, like rotation, is relative. Indeed, once we think of motion as rotation, it becomes very difficult to see it as anything but relative. And one problem we immediately run into is the fairly straightforward question - if this is rotation, why can't we just rotate 90 degrees, and hit light-speed?

One answer is that, when we consider motion as rotation, we need to consider it as hyperbolic; if this statement doesn't make any sense to you, go ahead and skip this paragraph. The idea that motion-as-rotation is hyperbolic is both right and wrong; it is right, in the sense that motion, considered from a particular perspective, must be a hyperbolic rotation; you can't, after all, ever actually reach C. Also, we can usefully model all this behavior mathematically, and it's clearly hyperbolic. It's also, in an important sense, wrong, because it's only true in a particular set of coordinate systems. I won't get into this much more than that, because this isn't an approach to thinking about the problem I find interesting.

Another answer is that, well, we can; this answer is also both right and wrong. Right, because that's kind of what happens when we fall into a black hole, after all. The reason it is difficult is entirely to do with our perspective, and the nature of time; accelerate hard enough, for long enough, and you'll pass that ninety degree mark, at least from the perspective of everyone else; from your own perspective, you can't rotate at all. What everyone else will see, of course, is a mass accelerating until it accumulates enough inertial energy to turn into a very fast-moving singularity. Wrong, because the event horizon of a black hole is not, in fact, ninety degrees away from flat space - I hesitate here, because I am not actually certain about the angle here, but I don't think it's too incorrect to describe the event horizon as a forty five degree rotation of space-time, relative to a sufficiently distant observer. The ninety degree rotation is an entirely different singularity, an entirely different horizon, a topic I'll try to cover later.

If you stop and think about it, this implies something very interesting about the curvature of fast-moving objects, which is both straightforwardly obvious, from the mass-energy tensor, and also strangely divorced from the way we usually actually think about fast-moving objects. If velocity is rotation, a fast-moving object is rotated; if the gravity well of a fast-moving object is rotated, it is increased. Gravity and velocity are, basically, the same phenomenon; rotation of space-time. The only real question is what is rotated, and how much, relative to what else.

Energy, both potential and realized, dissolve into rotation. That's not too interesting. The interesting thing is that, once you start conceptualizing gravity and velocity as rotation, you can conceptualize something else as rotation: Mass (and energy) itself.

## Mass as Rotation

There's a settled question in physics, which basically boils down to the question, "Do gravitational forces experience gravitation", to which the standard answer is "No".

I am going to argue here that the standard answer is necessarily wrong. Gravity definitely gravitates. Negative mass binding is a thing. Take a balloon. A really big balloon, large enough to hold our solar system with extra room. Consider its volume when empty. Consider its volume when we put a solar system in it - remembering that the length of A is greater than the length of B. The volume is larger than the volume when empty. Consider that the mass-energy tensor is describing, effectively, the density of mass and energy in a volumetric space. Increase the space, decrease the density. Consider the gravitational effect of an object outside the solar system, outside the balloon. The density is lower than you might expect. Double the mass of an object, and you don't double the gravitational pull, because some of that gravity is lost to the extra volume involved.

Remembering furthermore that all you need, to create gravity, is the difference in distances - and it should be clear that gravity gravitates. We just have a particular idea of what it means for something to gravitate which doesn't apply to certain geometries; we think of gravitation as the particular effect of the gravitational geometry, on a particular other kind of geometry. But once we realize that the geometry involved effects all geometries, it should be clear that light gravitates - it's the same geometric transformation, applied to a different geometry. We can think of distances, or of rotation - rotate the light in space and time, and voila.

However, the interesting thing here is, if we consider mass and energy in terms of their distribution across a volume, and if we consider the curvature, the rotation, as proportional to the mass and energy thus distributed, it should be apparent that we don't actually need either mass or energy; acceleration is rotation, velocity is rotation. Potential energy is rotation, kinetic energy is rotation. What, now, is mass?

Well, insofar as we consider gravitic mass alone, we can clearly just call it "rotation". But consider for a second inertial mass. There's a question, whether inertial mass and gravitic mass are the same, or just happen to have the same value; well, once you start thinking of gravitic mass as rotation, I think it becomes clear that they are the same concept entirely. If mass is a rotated volume of space-time, and motion is a rotation of mass, then motion is a rotation-of-rotation, and the total rotation involved (the combined mass-energy value) is dependent upon both values equally.

Which is to say, if we quantize rotation, then the total rotation will be something like mass-rotation multiplied by velocity-rotation (with some important special relativity caveats - we'll return to that subject later). Double the mass, and you double the total rotation.

There is a problem here: What exactly is rotating? I suspect the answer "space-time itself" is going to be rather unsatisfactory, but that is the answer I must give. There are some geometries involved here which might offer some assistance to thinking about it, but they're not going to help much; I can accurately describe them as a type of geon, but the geometries I expect them to take do not seem to match what others expect.

# The Basic Crackpot Unified Field Theory

What happens if you rotate other geometries? Say, the geometry of rotation itself?

I have an idea for what the grand unified field theory will look like; I typically express this idea as sin(ln(x))/x. I have no particular attachment to this equation - I've found others that exhibit the behavior I'm looking for - except that it is the most parsimonious equation I've yet found with the behaviors I am looking for.

You can arrive at it in other fashions, say, by solving a recursive function of the integral of f(x)=1+sin(f(x))/f(x)^2; my approximation of the solution appeared to converge on a function with characteristics similar to sin(ln(x))/x, based on an assumption that any distances we measured would already take the equation itself into account, and only the rate of change of the equation itself would matter. This was an early attempt at attempting to rotate the geometry of rotation itself, but I was unable to solve the equation, and I seriously doubt the recursive function was the correct way to model the behavior I have in mind in the first place.

I don't know the correct way to derive the equation; however, it seems clear to me that, once you think about the act of rotating rotation, you should be on your way to the description of a force that looks like this, moving from the small to the large, with conventional physics explanations as appropriate:

At the gluon/quark level, we have Strong Gravity. I don't honestly know that much about this approach, and happened upon the fact of its existence by happy accident, but it fits.

Above that, we have a repulsive force keeping quarks apart. Then an attractive force holding collections of quarks together to form a proton. Then a repulsive force holding protons apart. Then an attractive force holding protons together in the nucleus. Then a repulsive force keeping nucleii apart. Then an attractive force - gravity. Then the cosmological constant, a repulsive force.

Looks kind of like a sin wave. A rotation of our rotation. As for where the natural log comes from, that's a hard concept to explain; it's what I think the rotation looks like if you go from large to small, and pass through the event horizon of whatever geon you're examining. My original metaphor was a set of matryoshka dolls; an infinite recursion of an object as it turned inside out repeatedly on an ever-larger scale. Now I'm more likely to try to describe it in terms of time being a complex-dimensioned spiral and distance being the arclength of that spiral. I don't really have an explanation here which I think likely to actually convey the idea, only insist that, no, it actually makes perfect sense.

Note the conspicuous absence of electrical forces. I am pretty sure we just plain don't need them. But that's a topic of its own.

There are some other notes; for instance, I think it is notable that the nuclear forces actually do have the characteristic shape of sin(ln(x))/x, which I bring up in part to note that the behavior here works at least on one scale. Whether or not it works at all scales is another question entirely; here, I can only note that the distances, from the perspective of the particles involved, look fundamentally different from the distances we ourselves measure. A is longer than B; if all forces are rotation in this sense, if all forces are curvature, A becomes incredibly long in the case of nuclear forces, such that a hydrogen atom might be a meter across in diameter, if you were to measure from inside it.

## Conclusion

These are the basics of the ideas. Again, none of this should be taken too seriously; I'm a self-described crackpot, and while I legitimately think all of this is true, I'm also aware that that is exactly how I would feel about these ideas regardless of their veracity. I'll try to write up another short series describing some of the important things the relatively straightforward explanations here fail to consider; electrical fields being perhaps the most relevant and glaring item, but other topics include the nature of time, special relativity, and the nature of a subset of specific fundamental particles. Much of the problem here is just trying to convey the ideas.

Rotation is one abstraction, one way of representing these ideas; it is perhaps the easiest way to explain the ideas here, but that abstraction was not my first, nor do I think it possesses any exclusive explanatory power. It's just the most useful abstraction I've found, in terms of explaining the basic ideas here; the challenge of expressing these ideas has been quite surprising to me, and good ways of explaining everything still elude me in places. In particular, I mentioned at the start of this little essay that the idea here is a fractal model of reality, something which, by the end, probably seems irrelevant.

## Edits and Other Notes

### Equations

Let r be the axis of motion, and t be the axis of time. Supposing for a moment we express velocity, as observed from a sufficiently distant observer, as v(r)=c * sin(θ), and rate-of-time as v(t)=c * sin(ω) - such that, in terms of the Lorentz factor γ, v(t) = c*γ, or sin(ω) = γ. That is, supposing we express velocity as a rotation of the plane of the axes of time and the direction of travel relative to some observer, such that θ+ω=pi/2. θ (and thus ω) is defined as rotation relative to the observer's orientation.

Let M be the mass of the gravitational body, let G be the gravitational constant, let c be the speed of light.

Let rs=2*M*G/c^2 (Schwarzschild radius)

Let κ(r) = c / (2*r^2 * (1-rs/r)^1/2) <- I don't understand tensors well enough to use the Ricci curvature, so I invented my own curvature that I know represents the values I'm interested in, which is the derivative of Schwartzschild time dilation as t0/tf. Note this curvature is the GR curvature, not my crackpot curvature.

Let θ = asin(v(r) / c) <- We need to convert the velocity into a form we can work with. I am assuming all velocity is either directly towards the source of gravity; I don't know if, or how, the equation will change if this assumption is invalid.

Then the acceleration experienced by a particle in a gravitational field, as measured by an independent observer, should be:

acceleration (m/s^2) = c * k(r) * cos(θ) * rs

acceleration (dθ/dt) = (M * G) / (c * r^2 * (1-rs/r)^1/2) <- This is in terms of GR acceleration

Playing around with logarithmic spirals, there are two constants, a and b. a is a unit constant, and I think will need to be in meters; c^2/(M*G), or its inverse; both have things to recommend them (among other things, it "works" for part of the equation for curvature of a logarithmic spiral), but it seems a little bit odd to me to have mass there.

On the one hand, we should be multiplying by mass at the end; after all, we're taking an interaction between particles, and multiplying by the total number of particles.

On the other hand, self-interference is an important part of the concept here, and including mass in the logarithmic spiral might be exactly what is necessary to incorporate this kind of self-interference. General Relativity incorporates the self-interference as Negative Mass Binding, but I think this approach only works because of the scales involved; just subtracting part of mass shouldn't work the same way when the concern isn't limited to reducing the amount of mass-energy available to distribute over the rest of the curve, but is instead a change in rate of change of the rotation.

The constant b is the real issue.

In terms of the rotation of space-time itself - that is, the rotation called gravity - we should have a fairly simple equation:

t0/tf = sin(Φ)

So this rotation, defined in terms of GR (that is, this isn't the equation in my crackpot physics), would be:

sin(Φ) = sqrt(1-rs/r)

So returning to an earlier equation and expressing it in terms of this new rotation:

acceleration (dθ/dt) = (M * G) / (c * r^2 * sin(Φ))

This still isn't entirely satisfying, as the goal is to express acceleration strictly in terms of this rotation, so I'll return to this when I have a satisfactory replacement.

### Event Horizons and Spirals

Consider the event horizon of a black hole. There are three dimensions to consider; two closed dimensions forming a spherical shell, and one dimension with some unusual properties, distance-from-the-black-hole.

The distance from the black hole has some interesting characteristics, most importantly that the curvature (from a sufficiently distant outside observer's perspective) increases as you move from that observer towards the event horizon. If we were to map this dimension onto a Cartesian coordinate system so as to visualize the curvature involved, I think that, as you approach the event horizon, the dimension approaches a spiral shape. I think the spiral is hyperbolic from a distant observer's perspective, but locally, after correcting for the metric, may take on a different shape (and indeed I expect it to be logarithmic).

### The Potential for a Maximum Acceleration

What does the curvature look like locally?

Locally, I think the curvature asymptotically approaches some value. The local correction for curvature is going to need to be corrected for the Schwarzschild metric; the higher the acceleration exerted, the more the metric will reduce that acceleration; acceleration is m/s^2, and the Schwarzschild metric applies equally to both distance and time, so while velocity is invariant in the metric, force and acceleration are not.

Alternatively, curvature is offsetting to some degree the degree to which it curves space, from a local perspective, by the additional space "created" by that curvature. (Note: I don't believe space can be created or destroyed, this is just a misleading metaphor. The "created" space is just time. This becomes particularly obvious in the case of an event horizon, where space and time are rotated completely; the infinite future becomes infinite contained space, the finite spacial extent becomes a finite future, and thus anything falling into a black hole crosses infinite space in finite time. Note that the space "created" in the event horizon, originally the infinite future rotated in to replace space, is itself timelike from another perspective, so time gets rotated in to replace space, but then is still time, just from a rotated perspective; from our perspective it's just space.)

However, I struggle to rephrase the Schwarzschild metric in a fashion that would allow me to evaluate this claim.

### Possible Cosmology

Everything is in the event horizon of a singularity, everything is made of singularities, all singularities exist in the event horizon of another singularity, each singularity contains effectively infinite singularities, the universe is a network of surfaces of 3-sphere bubbles, time connects singularities to the singularity containing them and is a spacial dimension made timelike by gravity.

Time is created by gravity, as the curvature rotates singularities on an axis formed between an imaginary axis and time; this rotation gives rise to a spiral as time is expressed.

This spiral creates curvature in the time of the contained singularities, giving rise to gravity.

### Insane List of Problems I Think This Framework Solves

Included mostly to give some reference point for what I think all this has something to say about, and also as a kind of warning, because maybe nothing should be able to answer this many unresolved questions.

Hierarchy Problem

Kuiper Cliff

(Theory of Everything)

Arrow of Time

Color Confinement / Quantum Chromodynamics

Horizon Problem

Dark Energy / Cosmic Acceleration (No acceleration needed)

Dark Matter / MOND / Galaxy rotation curve problem (The inverse square law gives way to a linear law for certain scales)

Axis of Evil

Supersymmetry (Yes!)

Generations of matter

Neutrino Mass

### Insane List of Problems I Think This Framework Makes Irrelevant

Interpretation of quantum mechanics

Locality

Cosmic Inflation

Horizon Problem

Vacuum Catastrophe

Cosmic Censorship Hypothesis

Notes to myself:

Let r be the axis of motion, and t be the axis of time. Supposing for a moment we express velocity, as observed from a sufficiently distant observer, as v(r)=c * sin(θ), and rate-of-time as v(t)=c * sin(ω) - such that, in terms of the Lorentz factor γ, v(t) = c*γ, or sin(ω) = γ. That is, supposing we express velocity as a rotation of the plane of the axes of time and the direction of travel relative to some observer, such that θ+ω=pi/2. θ (and thus ω) is defined as rotation relative to the observer's orientation.

Let the curvature at a given point in spacetime be expressed as κ. I think the equation for acceleration might take something like the form dθ/dr = κ(r) * cos(θ).

Struggling with the math for this. Curvature expresses the radius of a circle; what I'm looking for is something more like torque. Rotational acceleration.

Why is there rotational acceleration? Because the near side and far side of a particle are instantaneously moving at different velocities. Why is the rotation in time? Because the disparity in velocity exists with respect to the axes corresponding to time (future light-cone) and distance (to the gravitational body).

This is going to be proportional to the difference in velocity. κ(r) represents the instantaneous curvature. cos(θ) is expected because as θ approaches pi/2 (as spacial velocity approaches the speed of light), the acceleration approaches 0. We need to multiply by c here as well, since that is the rate of change; dθ/dr = c * κ(r) * cos(θ).

For acceleration in terms of m/s, I get the following equation:

Let M be the mass of the gravitational body, let G be the gravitational constant, let c be the speed of light.

Let rs=2*M*G/c^2 (Schwarzschild radius)

Let κ(r) = c / (2*r^2 * (1-rs/r)^1/2) <- I don't understand tensors well enough to use the Ricci curvature, so I invented my own curvature that I know represents the values I'm interested in, which is the derivative of Schwartzschild time dilation as t0/tf.

Let θ = asin(v(r) / c) <- We need to convert the velocity into a form we can work with. I am assuming all velocity is either directly towards the source of gravity; I don't know if, or how, the equation will change if this assumption is invalid.

Then the acceleration experienced by a particle in a gravitational field, as measured by an independent observer, should be:

acceleration (m/s^2) = c * k(r) * cos(θ) * rs

I've tested the equation; it appears to work, except for one problem: That last factor, the Schwarzschild radius, makes no sense to me here; the actual acceleration the particle experienced using my original equation was incorrect. I expected -a- value there, because otherwise the units wouldn't make sense. This may be a product of the way I reinvented curvature.

However, none of this is actually what I set out to do, since we're using m/s^2, instead of radians/s^2; that is, I was originally setting out to figure out either dθ/dt^2 or dθ/dr. What I ended up with doesn't actually look like what I wanted.

Usually people emphasise that boosts are separate from rotations. however mathematically boosts are rotations rather than disaplacements or such.

I couldn't read from the prose how the difference between lengths A and B get established.

I too have wondered about how solid the "no boosting to infinity" restrictions are. If one takes a unit de-sitter Space that should cover all the directions. From one point of intuition at first glance it would feel that all the directions should be "locally adjacent" ie one should be able to travel on all points of a sphere by sliding the angle the radius is off-set from the origin.

When drawn as a in a space-time diagram one gets an upwards opening parabola and a downwards opening parabola. But then it is puzzling on why they seem to be disconnected regions. I think I have something that speaks about the same are as your discussion 45 degree and 90 degree angles. The parabolas have asymptose at lightspeed ie 45 degree. However if one focuses on positive distance then the region from 45 to 135 doesn't have anything, the elsewhere region where 90 degrees would lie is never visited. If one wants to include minus distances then there are going to be sidewyas parabola like strctures but the stark magnitude flip from positive to negative doesn't seem like those would actually be in smooth contact. That is by having a constant radius and letting the angle be undetermined one gets the analog of the unit-sphere, the unit de-sitter space, and this does NOT include the "side-areas". But it could be interesting if there was a smooth way to slide from the upregion to the downregion. Whether this is a cheating or allowed move is a bit beyond me.

I think I've corrected this; I failed to note that A is closer to the planet's surface than B, which was more obvious in the original version where I had a picture. Or do you mean I don't justify it in terms of the new abstraction I've established?

I'm not 100% certain what you mean by "no boosting to infinity" here, so it's hard to interpret the rest of the statement.

I think we're talking about the space "inside" a singularity; if I'm mistaken, let me know.

So the 45 and 90 degree explanation is built on an assumption of orthogonality between time and the three spacial dimensions that I'm not sure is entirely accurate. Consider a mass; now consider a point a meter away from that mass. I think the "natural" spacial dimensions here are: Distance (the line directly into/away from the mass), and then four cardinal directions relative to Distance. Is Distance actually meaningfully distinct from Time? If we take simultaneity seriously, a change in Distance is equivalent, in a specific sense, to a change in Time.

In your response to another post, you write "If you are thinking in euclidean terms it might seems that x,y,z,t can be relabeled into each other. However with relativity there is an "odd signature" going either (+---) or (-+++)."

So time is inverted, relative to the other dimensions. More, given that Time and Distance are in a specific sense equivalent, I'd suggest Time is not actually orthogonal to Distance, but parallel, and "pointed" in the opposite direction. So we have something like this:

<--------------------------------------->

+ Distance -

<--------------------------------------->

- Time +

So, if we are pointed in a positive direction in distance, we're pointed in a negative direction in time; that is, moving away from an object is moving towards its history (because time is emitted, not kept). Considering an arrow pointed into a singularity, we expect it to have the following vector: (-+) - moving closer to the object, and also towards its future. Rotate it 90 degrees, so its orientation in distance becomes its orientation in time, and we get (+-). (Which okay, looks more like a 360 degree rotation, but I will insist it's a 90 degree rotation for difficult-to-explain reasons.) That is, after the ninety degree motion, we're now pointed away from the singularity, and also into its history.

So I think the apparently unconnected parabolas of the upregion and downregion are actually the same region.

Yes, the added bit helps clarify what the difference is supposed to be.

However the scenarios don't exactly work like that and I am having trouble parsing out whether it is just an unconventional framing or is there a signficant deviance. Yes, if we are far away and the bars are horizontal then a laser pulse will cover them in the same time. However the lower bar is subject to a distortion in time. If we place an analog clock with hands next to the lower bar that clock will appear to tick less than 1 time unit by the time the pulse has moved to the tips of the bar (assuming that local observer would think that it was covered in exactly 1 time unit). I am not sure you are using light as ruler in a correct way.

The "boost to infinity" is just that energy requirements for high speeds seem to grow without bound. One way to measure change is one measure changing per change in another measure for example x per t. If a draw a curly line that has an U-turn in it I could get into trouble that at some point in the U turn the "next instantenous moment in coordinate time" could get a bit ambigious. Another concept could be the "next dot of the curve" and for curves that go relatively straight that next blob is likely to be in the "global forward" direction. So thinking in terms of max displacement per global forward tick vs maximum curl between adjacent blobs that the swiggle can have don't neccesarily meet.

Sorry, the signature is of the squares. The fuller equation is x^2+y^2+z^2-t^2=s^2. Increasing spatial separation gets you more of the measure, increasing time separation gets you less of the measure. If you take it in a certain way the underlaying number go complex but because people are allergic to the imaginary numbers people stay on the square level where it is just positive and negative reals.

The minus sign doesn't get you "anti-directionality", (which would be parallel but opposite). You took my prompt in a somewhat consistent direction but I was misleading in making you head that way. Riemanninan rotations are weird and I can't tell whether you are working with euclidean rotations, whether you have yet to incorporate the riemannian weirdness or you have another take on the weirdness. I don't example know whether it makes sense to use 360 degrees when talking about boosts. If you do 36 10 degree rotations and get back to where you started. But you can take a small/moderate boost and you can keep doing it for a very long time without it "wrapping around".

If you are working from an euclidean standpoint then it will surprise you that taking all the events that are equidistant from a central event do not form a sphere. Your current language suggests that you use terminology with that kind of assumtion. We can talk about delta-Vs ie changes in velocity but that doesn't lend to rotation language. To the extent that we use a rotation understanding numbers don't make sense.

There is a thing where black holes make time and spcae reverse roles. I don't know whether you diverge from that or have a unconvetional grab of it. For my part I was talking flat space and the implication of big curvature would require more explanation anyway (but I don't want to hear about until rotation amounts are clear)

That's what I mean by the observers measuring different times for light crossing the different points; the major thing is that A is longer than B, because I'm trying (possibly failing) to suggest that the difference in distance arises from the fact that an observer in A is measuring some distance that an observer in B would call time, instead.

I think I see, yes. I think it's correct to say that energy requirements grow without bound - but I also think that that is a Newtonian framing of the question, in which "velocity" is a property of matter, which has an inexplicable maximum value.

...but I'm failing utterly to come up with an explanation that I think conveys that velocity isn't just a scalar property of matter. I think it's all going to sound like nonsense. I'll think about this and return to it.

If it helps - it probably won't - I think time is distance projected onto (desuspending into?) an imaginary plane. Specifically I think time is probably a spiral, in which distance is the arc length, and my unified field theory is one of the two complex dimensions.

So this is where the "We need to consider rotation as hyperbolic" approach comes in. A ten degree rotation from one frame of reference is not a ten degree rotation from another frame of reference; frames of reference won't agree on how far a given rotation is. From the perspective of an object inside space-time, I think you have to think of rotation as hyperbolic. When I think about these things, however, I'm usually thinking about them from a perspective I can only describe as outside all frames of reference.

That said, the space-time relationship I am attempting to describe is definitely not Euclidean.

I mention Matryoshka dolls; my view of time is something like nesting Matryoshka dolls. Consider the event horizon of a black hole, notice that it is the surface of a 3-sphere (two dimension making the obvious surface of a sphere, plus a distance dimension); now "unroll" the event horizon's distance dimension along the dimension that is directional with the distance dimension of the event horizon. The other two dimensions remain closed - you have three dimensions, made up of one "linear" dimension and two closed dimensions. However, we didn't actually unroll that third dimension, we more ... mapped it onto a linear dimension, so it still has curvature (also it wasn't precisely a closed dimension like the other two in the first place, it was more like the desuspension of a closed dimension). As we move away from the black hole, our mapping moves in a loop. Relative to our linear direction we have mapped onto, curvature is positive for part of the loop, and negative for part of the loop; this curvature is "impressed" upon space-time itself. So the "structure" of the black hole is, through this mapping, infinitely superimposing itself on spacetime as we move away. (But I think that maybe thinking of the black hole as the "real" structure, which is duplicated/imprinted outward from itself, is wrong; the black hole is this repeated structure in its entirety).

Time, then, is sometimes anti-directional, and sometimes directional, with respect to distance, as a function of distance. When it's anti-directional, time is bent towards the object; with it's directional, time is bent away from the object.

Or we could express all that as rotation-of-rotation; the rotation of space-time itself is rotating, as we move away from the black hole.

If any of that makes sense, which I kind of doubt.

...huh. No, I don't mean a Euclidean sphere. Or, above, a Euclidean 3-sphere, although maybe the surface of a 3-sphere remains at least approximately correct, I'd have to think about that.

True, I think. Well, they can make sense, but it'd probably require the hyperbolic version of rotation in order to make sensible use of numbers.

Maybe unconventional? Strictly speaking it doesn't matter if you start with two space dimensions and one time dimension, or three space dimensions, but I think singularities bend time into space, or space into time, "creating" the fourth dimension, which is why it doesn't act like a properly independent fourth dimension in some respects; it's just a superimposition. (Also all particles in this are expected to be singularities, or possibly quasi-singularities in the case of neutrinos)