When the velocity of light is described by the equation C=1/t, the rate at which C contracts diminishes with the passage of time. Consequently, the rate at which C contracts is dependent upon the amount of time that has passed since the initiation of contraction. However, relative rates of contraction for dilated time continuums can be ascertained.
In order to describe the rates of the contraction for space in dilated time continuums relative to the rate of the contraction of space in a non-dilated time continuum, it is first necessary to consider what dilated time means in terms of contraction. Since time dilation results in a slowing down in the rate at which time passes, in a dilated time continuum, at any given point in time, the number of seconds that have passed since the initiation of contraction is less relative to the number of seconds that have passed in a non-dilated time continuum, by a factor of 1/u, where u is the time dilation factor. When the equation C=1/t describes the relative velocity of light at different points in time, the velocity of light at the point in time, t/u, described by a time continuum which is dilated by a factor of u is expanded relative to a non-dilated time continuum's velocity of light, by a factor of u. Thus, in regards to past frames, when time is dilated by a factor of u, the distance that a photon travels during a given interval of time, this interval described as t' in a non-dilated time continuum and t'/u in a dilated time continuum, will be the same for all time continuums. This means that in contraction theory, when time is dilated, the size of space in terms of light moving through it must be contracted by a factor of 1/u relative to the size of space for the past frame that corresponds with that particular time dilation factor. This "contraction of the past" will be explored later.
Special relativity shows that there is a difference between the nature of a photon's motion through space and matter's motion through space. The most obvious difference is that the velocity of a photon is constant, while matter's is not. Moreover, matter's velocity causes a change in the rate at which time passes, as measured from a non-dilated frame. While photons propagated from a moving source are affected by time dilation, a photon's motion does not bring it about. Another important difference is that when a photon is propagated from a source in motion, since the velocity of the photon is constant and time is dilated, the photon moves a smaller distance away from the source after an interval of one non-dilated second than it would if it were propagated from a source in a non-dilated frame. This effectively shrinks the space of the dilated frame in terms of photons moving through space. This is exactly the opposite of what occurs for matter in a dilated frame. Matter in a dilated frame moves through space at faster rates than if the frame were not considered to be dilated, since it moves through the same amount of space as it would if it were not in a dilated frame, but in a shorter amount of time as measured for the dilated frame. This effectively expands space in terms of matter's motion through it. In contraction theory these differences are caused by the nature of the contraction of space.
Until now the contraction of space within the Universe has been considered in terms of a photon's motion through space. Matter's motion through space can also be described in terms of contraction. To do this, matter's motion should be viewed from a slightly different perspective than it usually is. It's been pointed out that, in contraction theory, a body of matter located at the furthest distance possible in the Universe from a given point, (a), will appear to move away from that point at a velocity approaching c, simply because our standard of measurement is contracting, unless that body of matter also has a velocity approaching -c toward point (a). Herein lays a basis for describing the motion of matter through space in terms of contraction. By describing the size of space in terms of matter moving away from photons, as opposed to the more conventional manner of describing the size of space in terms of photons moving away from matter, it is possible to describe matter's motion in terms of it contracting toward the center of a frame [Universe].
Describing the motion of matter in terms of matter contracting toward the center of a frame can be done even for matter that is already situated at the center of the frame, in this case point (a), in the following way. When photons are simultaneously propagated from point (a) in every direction, a sphere of light expands from (a) in every direction at the speed of light, thus keeping a constant position relative to the edges of the Universe in the respective directions of propagation. Consequently, matter situated at (a) can be considered to be moving away from each photon at a rate of c. If we assume that each point in space within the Universe expands outward at c, as do photons, then in order for a point in space to be in a non-dilated frame, or motionless in the conventional sense, that point must also contract back toward it's original position at c. Below I illustrate this.
Referring back to the section where a photon's motion is described in terms of the space between it and the edge of the universe in the direction of propagation contracting, it can be seen that this can also be used to describe position expansion and position contraction. Thus, matter's position in a non-dilated frame can now be considered to be moving toward the furthest reaches of the universe in every direction because the space between it and these furthest points is contracting, and contracting back towards the center of the universe (or frame). Below I illustrate this in one direction.
The concept of position expansion and contraction leads to an unusual possibility. Since the two phenomena occur in opposite directions, if they are equal in strength, they can exist at any strength without necessarily being perceived. Moreover, if, under certain circumstances, they both exist as described, but only one or the other is perceived, then it would appear that space exists when in fact, from the perspective of someone who perceives both, there is no space. Thus, it becomes possible to construct dimensions of space where none seem to be. The space of these dimensions can be quantitatively measured in terms of the rates of their opposite motions. Henceforth, I will refer to this type of spatial dimension as an ex-con dimension.
Another application for ex-con motion is in describing the mass of matter. Mass can be described in terms of rates of expansion and contraction, with the greater rates describing greater mass. This concept will be developed further at a later time.
Expansion and contraction rates can also each be described in terms of a combination of various levels of expansion and contraction. Consequently, position expansion and contraction can be described in a slightly different manner than just presented, as the following example shows. The space between matter and photons is created because matter contracts back to it's original position, while a photon does not. Matter, however, can be considered to contracting back at a slightly slower rate, for example, -[c-(c/tp)], than it expanded, (c). There would also be, however, a shifting of the whole frame, this including the matter and the photon, back at a rate of -c/tp, returning matter to it's original position, and the photon to a position that reflects the reduction in the velocity of light. This is illustrated below.
We now have a situation where space within the universe contracts at a rate such that the radius of the universe will appear to expand at a rate of 2c in every direction. Under these circumstances, if the radius of the universe is to appear to expand at a rate of only c, then the overall radius of the universe must also contract, at a rate of c, in every direction. I'll call the contraction of space within the universe "spatial contraction" and the contraction of the universe itself "overall contraction".
Since it is the combination of spatial contraction and overall contraction that determines the rate at which the universe appears to expand, it is possible to choose any rate for the contraction of space in order to describe a particular rate of apparent expansion for the universe as long as the appropriate rate for overall contraction is chosen. However, there are reasons for choosing particular rates, as the following example shows. Let's assume that what we see from a given point in the universe as the radius of the universe is in fact only the part of the universe that is visible to us. I'll call this the "apparent universe". The radius of the apparent universe at any given point in time is equal to one half the radius of what I'll call the "actual universe". This would be true if we were to assume that on the other side of the furthest perceivable point in space within the universe in a given direction the universe actually extends further, the same distance as the maximum possible distance that can be perceived in a given direction from any point in the universe. This is a reasonable assumption since it simply means that a "whole universe" can be perceived from anywhere within the universe. Consequently this would mean that the radius of the actual universe at any given time would be equal to 2(ct), where (t) is the number of seconds that have past since the beginning of time. Thus, in the actual universe, space on each side of a given point within the universe would then seem to be created at a rate of 2c.
If spatial contraction is considered to simply occur at a rate such that the actual universe appears to expand at a rate of 2c, and, the universe itself is considered to contract at a rate such that the space of the universe appears to expand at a rate of only c, this defining the apparent universe, then what we measure as the actual universe at any given time will necessarily shrink with the passage of time. This is because the actual universe must always be equal to twice the size of the apparent universe, but with a rate of contraction for space such that the radius of the universe appears to expand at a rate of 2c, and with the past larger than the present, the size of the past actual universe will appear to grow relative to the present apparent universe at a faster rate than 2c. However, the relationship between the two different types of contraction, spatial and overall, can be described in a slightly altered manner, and, by doing so, it becomes possible to maintain a constant size for the actual universe.
While assuming that the radius of the actual universe appears to expand at a rate of 2c, it is still possible to define the apparent radius of the universe, which seems to expand at a rate of c, as a frame of reference for spatial contraction. The frame itself, however, should be considered to be moving toward the furthest point in the actual universe in the direction under consideration at a rate of c, while at the same time, a point located at the furthest point in the actual universe in that direction should be considered to be moving back toward the original position of the frame at a rate of c, bringing the frame with it. The net velocity of the frame would then be zero. I'll call the outward motion of the frame "universal expansion", and the inward motion "universal contraction". The combination of the two comprises overall contraction.
As presented, there are three reference frames relative to which contraction and motion are measured. Spatial contraction contracts space relative to frame (A), which is moving at a rate of c outward toward a point located at the furthest point in the actual universe in a given direction [this defining frame (B)], while frame (B) contracts relative to the actual universe [this defining frame (C)], causing motion at a rate of -c for frame (A) back to it's original position. I illustrate this below.
The thin line represents the motion of a photon. This structure can be described in three dimensions and for all points in space. Also, the motion of each of the different frames can be described in terms of contraction toward the furthest points in the universe (as explained earlier in describing the motion of photons), and contraction toward the center of the non-dilated reference frame.
One of the reasons that space should be considered to be expanding and contracting as just presented is the relative nature of motion. As stated earlier, in determining the actual positions of photons released from sources in motion relative to each other, one must consider the reference frame relative to which the motion is measured. As perceived from different reference frames, the photons will be considered to be in different positions. If one assumes that the dilated states of an entity which is considered to be in a non-dilated reference frame exist simultaneously with the non-dilated state of that entity, it is possible to describe the entity and it's non-dilated reference frame's position relative to it's own dilated states. The following example shows this. Let's again take a circle with a radius of c(1) and with (a) as it's center to represent the positions of photons emitted from a body located at (a) after one second, this representing a motionless non-dilated reference frame [reference frame (n)]. That same body, along with the circle representing the positions of photons released from it after one second as perceived from that body, perceived from different reference frames, which, from the perspective of (n), are considered to be in motion and to be dilated reference frames, would be shifted relative to the positions for the photons after one second as perceived from (n), the amount of shift being dependent upon the degree of dilation of each frame. Consequently, when one considers the dilated states of a single body, the different positions of the circles relative to the body represent the different positions for the photons relative to the body after one non-dilated second when the body is considered to be in different dilated reference frames. The non-dilated states of the shifted circles, in which a matter entity would be located at the center of these circles, are the parallel non-dilated states that I've mentioned. The center of these circles would also represent the positions of matter in motion relative to the original motionless non-dilated frame (n). In figure (2) I illustrate this.
What becomes clear here is that when matter is in motion, photons propagated from that matter are also affected by that motion, though the effect is not perceived from the non-dilated frame. This leads to another concept that is unique to contraction theory. Dilated states for entities exist simultaneously with the non-dilated state of the entity. These dilated states also correspond to parallel non-dilated states; that is, while an entity may be considered to be in a dilated state from one perspective, there simultaneously exists another perspective from which the entity is considered to be in a non-dilated state. Thus, parallel non-dilated states co-exist with each other, with each manifesting itself to the others as a dilated state. The complete structure of any entity must include both it's non-dilated and dilated states.\
When the dilated frames are included in the description of space, space must be considered to expanding in every direction at a rate of at least 2c. This supports the assumption that due to the contraction of space within the Universe the radius of the actual Universe will appear to increase at a rate of 2c. It is the extended space of the actual universe that accommodates dilated reference frames.\
Let's now consider some of the implications of there being an actual and an apparent universe, where the actual is twice the size of the apparent, on the creation of space within the Universe. Assume that the visible Universe has an initial radius, Ri, and space within the Universe contracts in such a way that it appears that the Universe is expanding at a rate of c. This means that any two points within the Universe will appear to separate from each other at a velocity that is determined by the amount of separation, with points situated at the furthest reaches of the Universe appearing to move away from the center at a velocity of c. The resulting velocity because of the space between positions is described by the equation v=(L/R)c, where v is rate that two points in space are separated from each other, L is the distance between the points, and R is the radius of the Universe. Now consider that another universe with the same size radius as the first exists right next to the first. If the space within this universe contracts in the same way as does the first, then the centers of these universes will appear to move apart with a velocity of 2c. Also consider a third universe with it's center at the same point as the first, but with a radius that is twice as large. The center and the edge of this universe will appear to move apart at 2c. We can consider space within this universe to be contracting at a rate determined by the equation c2=(R2)/t, where c2 is the velocity of light in this universe and R2 is the radius of the universe, both of which are twice that of the smaller ones. Below I illustrate this.
In regards to integral space, for each of the smaller universes, along a line from the center to the edge, the integral space created due to spatial contraction is equal to tTp(Tp sq. root)(intergral I, ti to t)(1/t)^t. Added together this equals 2tTp(Tp sq. root)(intergral I, ti to t)(1/t)^t. Integral space created due to spatial contraction for the larger universe, where space is created according to the equation c=R2/t, equals ttp(tp,sq.root)(integral I, ti to t)(2/t)^t. This equals the sum of the integral space created due to the spatial contraction of the two smaller universes.
With integral space in the larger universe described the integral 2tTp(Tp sq. root)(integral I, t to iIt)(2/t)^t, another correlation arises. This also equals the integral space created in one of the smaller universes if it's space contracts according to the equation c=1/t2. I'll now refer to this type of universe as a squared universe. This reveals an equivalency in integral space creation for various rates and types of contraction. With this it becomes possible to integrate the squared universe into the apparent and actual universe. As space is created in the actual, it's center can be considered to be expanding outward at a rate of c, as is the case in the apparent universe. However, instead of reducing the rate of integral space creation for the actual, the space of the actual contracts at a greater rate, maintaining it's integral space. Below I illustrate this.
The dilated states of non-dilated frames can now be described in terms of variations in rates of expansion and contraction. Referring again to diagram (2), the circles represent the positions of photons released from a source after one second, and each circle represents a different dilated reference frame. As the degree of dilation increases, the position of the source relative to the circle is further and further off center. Eventually, at the greatest degree of dilation, the source will almost be at the circumference of the circle. This It should be noted here that these velocities also apply to the parallel non-dilated states of dilated frames.]
