What is Time?

To begin: When we use the word "time", we are referring to multiple different things, which we treat as if they are the same thing.  There are two broad categories, however, which I think it is particularly useful to differentiate between: Time as timing, and time as history.

Here's the thing: There is absolutely no reason why these two things should be the same thing, and indeed, given what we know about the universe, maybe it should surprise us if they are, in fact, the same thing.  From an informational perspective, entropy is already, basically, kind of, a compression algorithm on the history of the universe; it increases because there's an ever-increasing amount of history to store.  Given that entropy is storing the history of the universe, albeit in an unrecoverable kind of way, why should we expect history to also be stored in some kind of multi-dimensional pattern covering the entirety of the universe, past and present?

Indeed, if you think about general relativity seriously, if history (which includes past, present, and future) is stored in some kind of dimensional pattern, the future (and past) should exert influence on the present.  There are some causal issues here.  And it'd be kind of weird for history to be represented twice, both in an entropy-compressed form, and in some kind of linear dimension form.

So maybe time-as-timing is entirely separate from time-as-history, which leads to the question, if time, in the sense of the fourth dimension required by general relativity, is purely a matter of timing, and not entirely a matter of a spacial dimension along which the past and future are stored, what shape would we expect time-as-timing to take?

A loop is the simplest answer there, but a spiral has certain qualities to recommend it, assuming certain properties can be managed; in particular, if you consider both chiralities of a spiral, there are points of intersection, but mostly divergence, which I think has some interesting ramifications.  But more generally, with loop-like structures, there is a characteristic behavior where going backwards in time is the same as going forwards in time, and you don't have coordinate mismatch problems.

What are coordinate mismatch problems?

Well, here's the thing: If time stores past and future, how can the time of two objects ever come out of alignment?  To meet, two objects have to be at the same points, in space and time. That is, time-as-storage-mechanism-of-history has some disagreement with relativity, in that you shouldn't be able to have two objects meet having different internal clocks; they should meet at the same time.

Electrical Charge

 I'm pretty sure electrical charge doesn't exist; it is a fictitious force.  I've played with a few models to account for it.

There is of course the Kaluza-Klein approach, which I've previously discussed.  That is one viable approach, although I think it isn't a fifth dimension at all, if it is the case, but rather time itself.

It could also be one of the two complex dimensions involved in the spiral which gives rise to the unified field; that is, a fictitious (in a sense) dimension.  This has other interesting implications if correct.  This would be an anti-symmetric tensor.

However, my preferred explanation is that we don't need an explanation at all.

I think I've written about what I call "electron pressure" here before.  The basic idea here is that there is only the unified field theory.  Protons repel one another in some range that I am reasonably certain can't go higher than 10^6 meters (this distance is elegant for a number of reasons which I might get into later).  They attract beyond that - gravity.

This predicts that magnetic fields should have a curious transition at some distance around 10^5, give or take an exponent, in which they briefly disappear, then reverse polarity.  I've found limited evidence that some asteroid magnetic fields do indeed have curious behavior around this distance, but this evidence is very weak, since nobody would report on asteroid magnetic fields behaving normally at this distance.

Electrons, meanwhile, being antimatter, behave in exactly the opposite manner.  They are attracted in the range of distance that protons are repelled; they also repel each other, but only because they're going backwards in time, and from their own perspective they attract one another.

(This implies that they are repelled at gravitational distances, which may or may not be falsifiable with data from nebulae and solar plasma jets; I haven't been able to determine the truth)

The important thing here is that electrons move, from our perspective, very very fast.  Certain energy transfers happen so quickly we cannot observe them at all.  In particular, they are transferring energy between themselves and protons.  And very particularly, they can distribute the momentum the protons would otherwise accumulate as they move away from each other, canceling the momentum out entirely.  It is a delicate balance that is relatively easy to disrupt by adding additional energy.

Being a particular kind of stable, finite singularity, which cannot obtain any more mass on their own, they are perfect energy transfer mediums; no energy is lost to internal tidal effects.

One thing to note: I describe this as distinct explanations, but in a sense, they're kind of the same explanation.  If the Kaluza-Klein theory can be extended to a closed time dimension, it might be extensible to a semi-closed time dimension.

And the spiral of rotation-of-rotation is, in a sense, a kind of pseudo-closed-dimension.  Distance, and thus time, is getting rotated; in a very particular sense, an object traveling in a straight line towards or away from a mass is traversing the same distance/time over and over again, just rotated in different directions.

The Next Step

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 mostly "No".

First, the standard answer is 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.  Negative mass binding.  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.

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 in 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 1+sin(x)/x^2; my approximation of the solution appeared to converge on a function with characteristics similar to sin(ln(x))/x.  This was an early attempt at attempting to rotate the geometry of rotation itself, but I was unable to solve the equation.

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:

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 like a sin wave.  A rotation of our rotation.  Note the conspicuous absence of electrical forces.  I am pretty sure we just plain don't need them; I believe it is sufficient that electrons are antimatter.  But that's a topic of its own.

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.

Acceleration and Velocity as Rotation

 Consider, for a moment, the following information.

Given two lengths of distance from a planet's surface, as depicted in the diagram below; in a flat space-time, A and B are of equal length.  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 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.  Now, this is an incorrect way of thinking about it, and is only used to demonstrate a way of thinking about it.

Now, 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.

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 this graph?

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.

Let's consider velocity as rotation again.

Now, 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 lightspeed?

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 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.  That's 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.

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 itself.  That's somewhat more complex, but it ties into the general Crackpot Physics grand unified theory going on here.  It's a boring, and probably somewhat disappointing, grand unified theory; everything is just rotation of space-time?  Yep.  Well, that or rotation of rotation, which is where the grand unification comes from.

The Circle and the Sphere

Consider, for a moment, half a sphere, as a contemplation of gravity; a bowl shape.

Consider the circle, whose radius r is the distance from the center of the gravity well.

How do you measure r?  Do you measure from the bottom of the bowl, following the curve of the walls of the bowl?  Or do you measure from what would be the center of the whole sphere?

How do you measure the surface area of the circle?  Do you measure the curved space of the bowl?  Or the space of an imaginary flat disc?

These questions are important, and as far as I can tell, don't get a lot of attention.  If you measure the radius from the bottom of the bowl, following the curve of the bowl - and if you measure the surface area as the curved space - then you get a fascinating and important result, in terms of understanding what gravity is, and what it does.

I have read arguments from physicists that gravity is not self-interfering.  But there is an important phenomenon, which in view of the circle, casts doubt on that statement: Negative mass binding.  The gravity exerted by a body, at a given distance, is less than twice the gravity that would be felt if you halved the mass of the body.

But it's easily explained if you think in terms of our circle.  First, the distance is greater - follow the curve of the sphere, rather than moving through imaginary space.  But using our increased distance, the surface area of the circle does not increase as pi*r^2 - or, considering a sphere in three dimensional space, the volume is not actually 4/3 pi 4^3, because in either case, the volume under consideration is not in fact Euclidean.  The greater the gravity - the greater the curvature - the less accurately these equations describe surface area, or volume, respectively.

At some distance, however, these equations start being more accurate.  They're more accurate still if you remove the excess surface area, or volume, respectively.  You can, in a sense, segregate out the excess volume, and consider only the flat-space amount of volume.

Now, if you consider curvature as mass-energy over unit volume - that is, if you think of gravity in terms of curvature, and curvature to be associated with a specific amount of mass-energy, this implies a neat little trick: If you can successfully calculate the amount of excess volume, and the amount of mass-energy associated with that volume, you can simply subtract out this amount from the mass-energy.

Which is what we do.  Gravitational binding energy; negative mass binding.

Now, what's interesting is that we have a much simpler way of calculating the same thing; we just figure out how much energy is necessary to take everything apart again.  Notice the implication here; compressing a volume of space releases energy.

Consider mass, whose very existence represents - through gravity - a compression of a volume of space.

There's an important contradiction there.  But let's set it aside for the moment.  Two questions, for those who are feeling iffy about all of this: When you measure distance from a large mass, do you measure the distance across curvature, or the distance across flat space?  Why should gravity traverse an imaginary flat space, rather than the curved space?

Now, thinking of these circles in terms of other things may also be illuminating.  Or confusing.  Consider the circumference of our circle; is an event horizon the point at which the circumference does not vary with distance-over-curved-space?  Does this imply infinite volume?  Does it imply infinite distance?  Can you have infinite distance but finite volume?  What about the case when circumference increases as distance decreases?

In order: Not necessarily, not necessarily, yes, and "This is a very important case to consider."

The point at which circumference no longer varies is the point at which time and distance are no longer distinct dimensions; they are the same dimension.  To a significant extent, at this point, it's no longer really meaningful to talk about volume; from one perspective, there's finite volume, and from another perspective, there's infinite volume.

An event horizon, once you consider it in terms of our circle, is just a cylinder whose length is at a tangent to our three dimensions.  The infinity arises from trying to measure the cylinder from the perspective of the dimensions is it tangential to.  From the perspective of the cylinder itself, it has a finite volume.

That said, the locally-measured distance and time it takes for a particle to traverse the cylinder can still be infinite, even though the cylinder has a finite extent and volume.  That, however, is a contentious statement, and most physicists are going to disagree with it.  We'll move on for lack of a useful metaphor I can use to describe the notion of time here; I can only gesture at tan(x), which describes an infinity where another perspective sees a finite space, and say "Look here, and realize that time and distance have a similar relationship."

Returning to the contradiction, the problem arises in that mass is a contraction of space, and yet contracting space reduces, rather than increases, the amount of mass involved, from a certain perspective.  More mass = less mass.  Mass is its own opposite.

"Hang on," you start to say, "that isn't what that means at all.  Even accepting the idea that negative energy binding can be described as a variation in distance, mass isn't it's own opposite; rather, some mass is converted to energy.  Gravity is caused by mass and energy, and you're ignoring the energy that escaped the system - the binding energy - when the masses coalesced."

Which is all well and good, except that the change in mass, once you view it in the distance framework, is all imaginary; all the mass is still there.  The lost mass had to have been energy - and the energy that was released, was the potential energy of the system.  Potential relative to what - mass relative to what.  Well, if we consider an object formed from two objects that fell into one another, the potential relative to one another.

From an outside perspective, treating the two falling objects as a black box, energy is released, so the mass goes down.  Simple, right?

Well, from the distance-perspective, what is the potential energy?  What is the energy that is released?

Hopefully you can start to see the shape of where this is going: Energy can be expressed purely in terms of changes in distances between things.  Energy doesn't "add" to the curvature of space-time through a secondary process; energy -is- curvature in space-time.  A wave is just a moving change in distance.

And, realizing that energy and mass are the same thing, this leads to another conclusion: Mass doesn't curve space-time.  Mass is space-time curvature.  Mass doesn't cause gravity, mass is gravity.  And in that perspective, the curvature in question isn't missing - it's someplace else.  Yes, the energy left, but, if we count only cubic meters, every cubic meter is still accounted for; what has changed is where each cubic meter is.

Well, kind of.

The Question

 Is any of what I'm writing useful?

I have no idea.

Mostly I think I have a useful framework to consider things from, and, thus far, an utter inability to actually successfully communicate that framework.  I can try to communicate the fundamental concept in math, but the math isn't, in fact, the fundamental concept; from the perspective of the concept, both of these equations are fine:

sin(ln(x))/x

(e^x*cos(sqrt(e^x)))/(sqrt(e^x))

Even this equation is kind of okay:

sin(1/x)/x^2

The point isn't the specific equation, it's the idea the equation represents.  But I've handed these equations to a number of people who don't quite get the idea.  So, well, I keep trying to figure out how to communicate the idea, which is not in fact about any specific equation, but a way of thinking.

The Newtonian equation for acceleration in a gravity well is a=M*G/r^2.  The units of G are m^3/(kg*s^2).  Einstein noticed you could pull c^2 out of it (also 8pi, but that's dimensional rather than unit analysis) to get m/kg; multiply this by mass, and you get meters.  Let's call this distance o, and we get (ignoring the constants) o/r^2.  We can form a triangle out of o, and if r is the hypotenuse, we get sin(theta)/r.

Okay, you may say, what was the point of that?

Well, there really isn't a point; it doesn't really serve any particular purpose; all I can really say is that it demonstrates that sin(f(x))/x can be equivalent to 1/x^2; that is, it can demonstrate that sin(ln(x))/x isn't immediately and obviously incapable of modeling Newtonian gravity over certain distances.  It definitely is not proof that sin(ln(x))/x can do so, it just rules out the immediate intuitive-no I've gotten.

It also happens to be the answer to another intuitive-no I've gotten, on whether or not acceleration can be modeled as rotation in time.

That's been a lot of the work I've put into this; answering the intuitive-nos with a "Maybe".

Thing is?  I'm already pretty certain I have a firm intuitive grasp on the shape of the universe.  It's kind of mundane and boring; sin(ln(x))/x, even if it isn't the correct equation, has, I believe, the correct shape.  So does sin(1/x)/x^2, for values less than 1.  So does (e^x*cos(sqrt(e^x)))/(sqrt(e^x)).

Physics is full of this shape.  Strong Gravity, as a contender for an explanation of color confinement.  The energy potential of the Higgs mechanism.  The nuclear forces.  Gravity.  The cosmological constant.  Hell, the hierarchy problem itself; Schwartzschild Coordinates, when you really start looking at them, dissolve the hierarchy problem entirely; if hydrogen atoms are a meter across, the hierarchy problem is really just a problem of perspective.

The idea isn't magical.  It isn't spectacular.  It is kind of anti-spectacular; you haven't truly grokked it until you realize how disappointing it really is.  General relativity has ripples, alright, great.

Still, maybe somebody else can find more use for it than I can.  If I can ever communicate it.