HOME | DD

MigeYeFoxe — Dimensionality
Published: 2008-07-16 23:02:10 +0000 UTC; Views: 412; Favourites: 1; Downloads: 1
Redirect to original
Description Recently I watched a little video thing that tried to go into and explain in a somewhat visual manner the ten dimensions used for String Theory and whatnot and one thing that came across was how it more or less was different on my own views. What this essay is for is to explain a different take on the dimensional construct. So if you don’t really care for the scientific debate do not read further. Also this essay is based on logical observation rather than various equations used by the professional theoretical physicists, though I do make reference to some general concepts.

Now one concept to go over before even beginning would be that transcendent dimensionality is at best extremely difficult and generally impossible. This means that in most circumstances one cannot perceive easily any dimension that is beyond their range of experience (as in a one dimensional creature would have a lot of difficulty in conceptualizing a two-dimensional world and would have even more trouble conceptualizing a three dimensional world).

A second concept is that all dimensions must be orthogonal to each other. This means that no combination of the dimensions can be made to equal one of the other dimensions. For example, if you are using a four-dimensional space. If you use X as a qualifier for the first dimension and Y and Z for the second and third, there should be no way that you could define the fourth dimension using any combination of X, Y and Z.

Last concept is that of the zero space. Zero space is basically a place holder for a dimensionless environment. Basically just consider it a point. A point, by definition, has no real dimensionality. It is simply something used as a placeholder to explain a more complex figure or to hold a value.

The easiest of the types of dimensions to really understand would be the spatial ones. Now the first dimension of space is considered a line and is referred to as everything between two points. For a clearer viewpoint consider it more of a continuum than something between two points. The reason for this is that it allows for data to exist beyond the point. Of course the best way would be to consider one point to be the frame of reference and the other to be infinitely far away to represent directionality. In essence a continuum is more accurate because it allows for one to not have to consider the second dimension to consider it. For continuums you can either move in a positive (towards the infinite point) direction or a negative (away from the infinite point) direction. Think of numbers themselves. If you go from three to four you are moving in a positive direction. If you go from four to three you move in a negative direction. Now there is also the issue of speed. If you take three and add four then you move more in one motion than if you added one. This is what is considered a vector. A vector is a scalar (rate of change) with a direction. A one dimensional vector would be like velocity which is how fast something moves from one point to another. But we’re getting ahead of ourselves with that one since we aren’t supposed to be talking about the temporal dimensions yet.

Now to move on to the next dimension. Though it isn’t technically required let’s take our line (we’ll call it dimension X) and rotate it 90 degrees so that we can take a look at the next dimension (Dimension Y). Now though the X dimension can be infinitely long, it has no width and thus has no dimension in the Y-Axis. So this means that when taking the Y dimension into consideration we can take the entire X-Axis and attribute that to be a single point in the Y dimension. Now you have a completely new dimension to play with, one that is completely independent to our X dimension. Now we have two dimensions and so any point in a two dimensional space can be reached.

Now here’s another thing to consider. Let’s take a single line and put it on the two dimensional space. The line itself is still a one dimensional object but because it is in a two dimensional space it can be bent or moved how we see fit. Now we aren’t actually affecting the dimensionality of that line, you can still only go forward along the line, or backwards. But by bending it around the second dimension one can still go forward the entire time and end up further back than when you started. This is something to keep in mind. If one cannot turn around, progression through any point in one set of dimensional space can only be reached by wrapping it around the dimension above it.

Let’s move on. Let’s attribute our two dimensional world as being like a piece of paper that can be infinitely long and/or wide but is infinitely thin. Now let us keep our paper perfectly flat and then rotate it 90 degrees so that we are looking along the edge of the paper. What do you notice? We are now in exactly the same situation when considering the third dimension as we were in the second. We have what appears to be a dimensionless line that ultimately can be condensed into a single point along this new Z dimension. And we can move freely along this dimension independently of the other two dimensions which satisfies our notion of the dimension being orthogonal to the others. So now we’re up to the third dimension of movement. Now one thing to point out is that though the earth is a three dimensional object as are we, the motion across the surface is ultimately a two dimensional motion. Unless you are a bird or in an airplane you do not really travel along the Z dimension almost at all if you set the zero point as the surface of the planet. And even for birds and planes and whatnot since ultimately you land again the net travel along the Z axis is zero, thus meaning that you are still only travelling along two dimensions. So what this means is that if you wrap the second dimensional space (the surface of the Earth) around the third dimension you can end up always walking forward, never turning around and ending up back where you started.

And this isn’t actually it. There is very likely a fourth spatial dimension that we are aware of but two different explanations will be given though both use Einstein’s theory of relativity for a basis. Einstein stated that space is not actually flat but is in fact curved. A curved three dimensional space ultimately means that if you move in a straight line far enough along the three dimensional space, the curvature of the universe will make you end up right where you started. Now as we’ve already discussed, the only way this can happen is if the three dimensional space is being wrapped around a fourth dimensional space, W. So what is the W dimension? Ultimately do to what was described at the beginning it is not easy to try and picture what the fourth dimensional space would look like since we do not freely travel along it.

For a better example of this difficulty, consider the notion of the regular shape being 2n (where n is the dimensionality of the space). The 2n regular shape notion is that to make a regular shape in dimension n, you will need 2 times the number of dimensions in n for each regular shape in dimension n-1. So in the first dimension to incorporate the entirety of the space you would need two 0 dimensional shapes (points), one for –X and one for +X. This creates a line. For a two dimensional space we would need according to the notion 4 lines (the shape of a one dimensional space) bent to incorporate the entire 2 dimensional field. So you’d have only line for –X, -Y, +X and +Y and these would create a square. Again move on to the third dimension and you’ll need 6 squares wrapped around each other, one for –X, -Y, -Z, +X, +Y and +Z which creates a cube. To try and picture a fourth dimensional regular object (a hypercube) you would need to have 8 cubes wrapped around each other to incorporate –X, -Y, -Z, -W, +X, +Y, +Z and +W. But as you are likely unable to picture how you would even bend a cube along a higher space it won’t help much.

So let’s take another way of looking at it. For both moving on to a two dimensional object and a third dimensional object we first condensed the previous dimension into a dimensionless line and then condensed it to be a single point in the dimension perpendicular to our space. So let’s take out our theoretical sheet of paper and draw a nice long line and consider that to be all of three dimensional space once we’ve rotated it 90 degrees along an axis we can’t perceive. Now we have a dimensionless line and we can attribute that to being a single point in the W dimension but this still doesn’t really help us understand what moving in the W dimension would do. So let’s do something that seems sort of counterintuitive and let us erase our line and instead on that piece of paper draw a circle. Now we already know there must be a fourth dimension since space is curved, so let’s let it be curved and then try to picture what moving along the W dimension would be. So if we have a circle that represents space, then that space probably has a set radius of a value Wo. And wait; did we just define all of 3 dimensional space as being a single point on a continuum? Get it now? One way to sort of visualize the fourth dimension is to consider it not so much what 3 dimensional space is bending around but the radius of the bend. In all reality the two are the same thing, we’re just defining them slightly differently.

Now one other thing noted is that gravity is either something that affects this W dimension or is a byproduct of the dimension. Why I say this is that according to Einstein (and later theoretical physicists) something with a very large gravitational field tends to bend space around them. One way to think of it is like pushing a finger into a cushion. As the gravitational field increases (you put more force into pushing the finger into the cushion) the space around that finger distorts in a dimension that is independent of the others but if you had something try to travel along the path near that distortion it would be prone to moving further in. Using our circle model of W dimensional space, one can say that gravity is a force that distorts the X-Y-Z space towards Wo = 0. If you go by the notion of gravity being a byproduct of W-space then at the center of the circle is something that is pulling everything towards the center.

Another way to look at this is to consider the vectors when you spin something in a circle. On the edge of a rotating object the velocity of the edge will always be the tangent towards the center (as in the line perpendicular to the line from the center to that point). But since our point on the edge does not move further away there must be a net acceleration that is pointing towards the center of the spinning object. Now going from Newton’s laws a force is simply the mass times the acceleration. So if you have things of different mass on different points of the circle, though the accelerations will always point towards the center, due to the different masses the force is different. So if we allow for the X-Y-Z space to be constantly spinning, then Gravity would be the force pulling all objects towards the Wo = 0 point. The more massive the object, the more force gravity will be exerting on that object. This is how Black Holes and Wormholes function. Because both have such incredibly large gravitational fields they have a tremendous distortion along W-space. Wormholes work under the principle that if the distortion of two points is great enough and aimed in the right direction they will connect and basically create a tunnel through W-space between two points in X-Y-Z space. Now of course these are unstable since our Gravitational force will be pulling the center and the distortion towards the center of the circle. Theoretically on that notion if the wormhole went through the center of the circle it would be completely stable but to do so would mean that you’d have to have two infinitely massive gravitational fields on opposite sides of the universe.

Anyways, I’ve digressed. Now with our current model of four dimensional space we have a 3 dimension circle wrapped around a fourth dimensional radius on a flat piece of paper. So if we take this four dimensional paper and then rotate it we end up finding that we have a new V dimension. I’m not going to begin to try and explain how to visualize a fifth dimensional space since as three dimensional beings it would be too far out of our scope of experience to understand, so let’s move on to the next type of dimensions.

Now we’ve covered as much of the spatial dimensions as we probably will be able to so next step would be the temporal dimensions. Now why I say temporal dimensions as being a type instead of just another dimension is that it is completely different. For spatial dimensions they all sort of interweave around each other and to move to an earlier point you have to wrap it around the dimension above. For all intensive purposes one cannot wrap space around time and get to a completely different position nor can one wrap time around space and expect to be in a completely different era. So yes, though they do operate simultaneously they do not have any real impact on the other.

Now time as we know it is simply a one dimensional space with the past being the negative on the continuum, the present being the zero point and the future being the positive space on the continuum. As human beings be are only capable of moving around in this one dimensional space (which we’ll call dimension T) and only barely since we only seem capable of moving in one direction and speed. Now if we rotate time we find that there is a second dimension in which dimension T is dimensionless and does not move. And if you allow for the possibility of time travel to exist then we know from prior statements that the only way to move forwards and end up somewhere else in the continuum is to wrap it around a new dimension, which we’ll call S.

So what do we call dimension S. Well for starters we should go back to our paper idea with a line representing the one dimensional time as we know it. But instead of having our line be an axis let us instead put it at an angle between two other lines. Now let’s label one axis as “Experienced Time” as our T dimension and “Universal Time” as our S dimension. Now to explain why we’re doing this. Another thing that Einstein stated was that at very high gravitational fields, the flow of time becomes dilated. Basically that as one moves to something with a very large gravitational field the flow of time slows down. This time dilation also happens when approaching the speed of light. So what this means is that the rate of time according to the one experiencing it has to be somewhat independent to the rate of time as the universe experiences it. So that line of time as we know it is simply moving forward in our dimension T which is at some slope with dimension S (probably somewhere around a rate of 1). Now since we’re going to assume that we will not be able to turn around in our own T dimension travelling through the S dimension (AKA time travel) will be possible by simply changing the slop of our line up or down. To go back in time one simply has to make the slope go negative. Of course this would only make events outside of experienced time move backwards.

To get to the point of sudden transition between either dimension T or S one would have to wrap our two dimensional time around a third dimension, R. Now dimension R will be even more difficult to understand since one would be moving forward in both T and S dimensions and suddenly find oneself at a point that is early in either the T or S dimensions. Of course if mastered one could easily move back in the T dimension and thus suddenly become younger. And like with spatial dimensions there are probably more dimensions beyond that which we wouldn’t be able to perceive.

But one thing is for certain is that there is no dimension responsible for Reality Hopping. Reality Hopping is the notion that you can hop from one reality to an alternate reality. The reason why this cannot be a dimension is that in order to make a line from one to the other there has to be a continuous transition from one state to the other. In every other dimension used that dimension itself is a continuum which allows for a continuous transition between two points. So that means if there is one reality in which I am male and another in which I am female but everything else is the exact same, for there to be a dimension that exists that incorporates between these two points there would have to be a point where my sex is 75% one and only 25% the other. Since there is no such thing physiologically to be biologically partly male or partly female without changing the rules (which we can’t do since everything else is the same) there cannot be any continuous line between the two realities. Or if you want something a little more major consider these two realities. Our starting point will be our own reality and our ending point will be one where we didn’t drop any nukes on Japan. In order for there to be a dimension to travel across between these two points there would have to exist a reality in which we dropped 1.8 bombs on Japan (and not talking about yield). Since bombs can only be dropped in integer values we cannot make a continuous line between two realities which means there is no dimension to cover reality hopping.

So we have covered the types of dimensions encompassing time and space but is that it? Not necessarily. We know of space because we can move in three dimensions in it and we know of time because we move in one dimension of it but there could easily be types of dimensions that incorporate continuums that we cannot travel in any dimension in. For example, though we’ve gone into a possible explanation for Gravity which impacts dimensions S and W. But what about the other forces (Strong, Weak and electromagnetic)? Could there be a dimensional space where one move in a continuous manner in such a way that these things change but keep all of our other dimensions (R-T and W-Z) will not be inherently changed (as in you can move in our new dimensions alpha, beta or gamma and be able to stay in the same position in all other dimensions). And if there are dimensions controlling things we have a vague understanding of, just imagine how many dimensional types there might be that control things we don’t know about.
Related content
Comments: 0