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When we wanted to break our solid object into “simpler” dimensions, we had to increase its motion to the speed of light. And yet, nothing can move faster than light. So our D2 entity, the photon (which we can represent mathematically as i2 or –1) is real, but mass-less, and has a velocity of c. When we step down a dimension, we reduce exponents by 1, and to reduce the exponent 2 of i2 to 1, to get i1, we can take the square root (in fact, that is the definition of i is that i equals the square root of negative one). It was the attaining the velocity of c that “split” D4 into D2 + D2; conversely, reducing motion below c would reunite D2 + D2 into D4. So if we wish to split D2 into D1 + D1, we certainly can’t lower its velocity (this doesn’t split, it joins), but we can’t increase it either, since c is the maximum velocity in the universe. Therefore, it stands to reason that the velocity of the point in motion, D1, or i1, is also c.
Ready to begin a discussion of D3? By using my ideas, we can make some sense of this very abstract notion, and link it to one of the real mysteries of astrophysics. I can think of three ways of getting to D3 from something we know. We can take D2, the photon and “kick it up a notch”, and do D2 + D1 = D3. In words, this means that we add a new 90° vector to our planar electromagnetic wave, producing an abstraction we can refer to as a “cubic wave”. I don’t know about you but I can’t visualize that (for a good reason, as you will see). We can also try D4 - D1 = D3. In words again, we are taking one dimension, say the depth, away from solid matter, to get a plane in motion (once again time as a spatial dimension), but what is a plane in motion? Maybe a tube of some sort. Maybe not. The third option involves negatives. To review: D4, i4 and +1 are all symbols we can use to represent solid matter as we know it. D2, i2 and -1 are symbols that correlate to electromagnetic waves or photons. The only difference between D4 and D2 is that D2 = D4 • c (remind you of something?
E = mc2, perhaps?). Substituting numerals, -1 = (+1) • c, and solving c = -1. In words, c has the effect of “negativizing” a phenomenon.
We have already referred to c’s “splitting” or destabilizing properties; how it is useful to concentrate on this anti-polarity feature.) So we can say that the photon is the “negative state” of matter. A little while ago, we stated that the point in D1or i1, has a velocity of c. What do you suppose would happen if we slowed this point to a sub-light velocity? If c really does produce an opposite, then i1or i , becomes its negative, i1or -i , which is the value of i3, which is, lo and behold, an alternate symbol for D3. D3 then (or – i,) is the realm of slower-than-light imaginary points.
Since it is sub-light it must have mass, but since it is imaginary, it has no substance. And this is exactly what our plane in motion is trying to describe, a surface with no thickness and therefore no substance, enclosing on itself trying to form a sphere (or a tube) with no volume. An imaginary figure with mass. Hey, astronomy buffs, what am I describing? This is dark matter! All that unaccounted-for mass that must exist in the universe but is undetectable. It’s undetectable because it’s not real. But because it’s slowed to sub-light, it has mass. And because these things are “negative singularities”, similar to the singularity responsible for the big bang and the subsequent universe except hollow inside (like bubbles or macaroni), they are super dense, far more dense even than black holes, so it makes sense, as physicists claim, that this dark matter should account for most of the mass in the universe, much more than visible matter. D3 = dark matter, matter which has been collapsed by one dimension.
At this point on our discussion four dimensions, the integral dimensions, have been explained. The seven fractional dimensions remain, and while each is still associated with naturally occurring phenomena in the universe, the job now becomes a lot tougher.
We are going to wade right into the thick of things, but first, a little stage setting. Let’s revisit that old trickster dimension, D1, time, which seems so elusive, yet has so many properties, and influences just about everything. To review, time is motion, specifically the motion of an imaginary point at velocity c. In theory, there was a period of dimensionality (duration is necessarily meaningless here) when a motionless singularity constituted a potential big-bang to begin the universe. In that instant, when the point acquired motion, the first dimension was born. But something else was created too, because when the point began to move, it needed a medium to move through, and this did not yet exist. So as consequences of D1, we also got something called space, and something else called distance; things respectively, for the creation to move through, and for it to displace as it went on its journey.
Up to now we have assumed that this distance was a straight line, since this is usually how distance is measured, and since there was nothing (apparently) to deflect a projectile from its course. Or was there?
In that moment in which the singularity burst from nonexistence into being, lots of things happened. One of those things was that the singularity’s ambiguous state as a mass-less/infinitely massive thing became unambiguous – the instant the new universe existed it was incredibly massive, so that all of a sudden there was this super-massive something sitting the center of a region of space, expanding outward into that region even as it was being created. Imagine that space as a huge net, stretched out evenly, nice and flat. Then into the net we drop a bowling ball. What happens? The weight of the ball causes the net to stretch, most noticeably where the ball sits, and less as you get further from it. But as far as the net extends there is a greater or lesser slope downward toward the center. If a marble had been sitting on the net before the bowling ball was dropped, it would have been perfectly stationary on the flat net. But with the bowling ball causing the net to have a different shape, the marble begins to roll towards the center. The greater the slope the faster the marble rolls. If you can’t see the net, it looks like the marble is actually being pulled toward the bowling ball by some mysterious attractive force. But we know about the net – understand that there is no force; the marble is simply rolling down a curved surface caused by the massive object at the center. And the distance the marble rolls is the length of a curved line, not a straight one.
The situation is analogous to the way massive entities shape the space around them, that is, give space a geometry that is not flat, but curved here, stretched there, endlessly twisted and varied. This geometry of space caused by mass is how Einstein described gravity. Why at this stage there are physicists still maintaining that gravity is one of the four forces of nature when it is fully explainable as a geometry of space is a bit confusing. One would think that the failure either to unify it theoretically with the other forces, or to find its associated particle, the graviton, would convince them otherwise, but so far it has not done so. They continue to try to crack the nut of the gravitational force, where no force exists. It is the geometry of space we are observing, and like other geometries in the universe, it has a dimension associated with it. But which one?
How do we decide which of the seven fractional dimensions is responsible for gravity, or rather, for the geometry of space? Let’s try an approach that looks for patterns or trends in the qualities we attribute to the various dimensions.
Dimension Summary – III
D1 is responsible for time, motion of imaginary points and the distance they travel along gravity influenced lines.
D2 is responsible for wave phenomena, specifically the electromagnetic force.
D3 is responsible for the “dark matter” which is undetectable but comprises most of the mass in the universe.
D4 is responsible for what we call ordinary matter, both massive and detectable.
What do you notice as you move from Dzero, total nonexistence, up through the dimensions to D4? I notice that there is a progression from the least substantive, most abstract manifestation; to the opposite of that – the manifestation that is wholly concrete and not an abstraction at all. Maybe by assessing the balance between the abstract and the concrete nature of a phenomenon, it is possible to order it, that is, place it in its proper position in the progression of dimensions, almost as if we were creating a size order. And if we are lucky, it may additionally be possible to identify elements being utilized by the operator D by deciding which two of the four basic dimensions are interacting to produce the appropriate fraction. In choosing, we must bear in mind that the seven available fractions all have a value less than 2, and five of them are less than 1.
This means that they all represent significant abstractions. It is a certainty that none of these dimensions contain massive entities, though it is possible, as with gravity, that their effects are far-reaching enough for us to be aware, or at least suspicious, of their existence.
The geometry of space then. I dare say this is a very foreign, abstract concept for most of us. The natural tendency is to view space as nothingness. To learn that it is both a vacuum, and has a definite geometry is a little hard to grasp. Yet most of get a pretty good mental picture of D1, even though the point in motion is completely imaginary. Is space then a greater abstraction than time? I imagine that it is, and that we’re looking for a fraction less than 1. Next, consider gravity’s far-reaching effects. Not only matter but also even something mass-less like light, is induced to follow the shape of space. So it would be illogical to choose 2 as our denominator, since that excludes the 4 that contain matter.
There are only two fractions whose denominator is 4, which would account for the matter, and everything contained in all lower dimensions. What is it then that reacts with either light or matter, to form space? What thing plays a role in the effect of gravity; appears in all the gravitational principles and equations? Distance! It is the distance from the distortion causing mass that determines the degree of the curvature of space, or in traditional terms, the strength of the gravitational “attraction”. Distance is created by the first dimension, motion. Therefore the only logical fraction for the dimension of gravity, or the geometry of space in one that points to the interplay of distance (D1) with each of the dimensions effected by that gravity (D4).
The conclusion: gravity = D¼.
The concern of the next topic will surprise no one, it is that familiar demon come back to haunt us, as it has done time and time again: the speed of light. My conclusions about how the speed of light relates to dimensionality are nearly ready, but thoughts about how to set down the logical progression and justification of my argument needs more work. So all I can give you at this point is a preview. In it, the salient highlights are as follows:
1. The speed of light is a misleading term, for while it is the speed of electromagnetic waves; it is also the speed of other cosmic phenomena, including things that have dimensionality less than 2.
2. The speed of light, or c, is indeed constant, but not in the way everyone believes. Constancy in the eyes of humans, and constancy in the eyes of the universe, is not the same thing. (I have already hinted at this).
3. The speed of light is a kind of threshold for a change of state of various cosmic manifestations, just as 32° F. is a threshold for the change of state of water. (Matter can be considered to be “frozen” energy.) Things at light-speed are mass-less; sub-light things acquire a mass. Dimensionally speaking, D2 corresponds to this dividing line.
4. The dimension of c is ½. I cannot at present provide the coherent explanation that I would like. Also, a big problem is that a dimension requires a geometry. That is something I have insisted on. I do not yet have a clear picture of a geometric model for c, nor do I immediately see how to derive one. This, of course, is the challenge. I am working on it.
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