The simplest way to begin the explanation of the structure of physical reality in terms of expansion and contraction is to present a description of the space of the Universe in terms of it's contraction relative to a constant sized Universe. Using this, I will then describe the principle concepts of Einstein's special relativity theory in terms of variations in the size of the distance scales of reference frames, and this will ultimately lead to a more radical and complex description of the creation and structure of the Universe.
The basic premise of the big shrink interpretation of the creation and expansion of the Universe is that space-time can and should be described in terms of the rate at which the size of space within the Universe contracts relative to the overall size of the Universe. This changing relationship between the size of space and the overall size of the Universe provides a new basis for measuring time and space. In order to describe the contraction of space in mathematical terms, it is first necessary to describe a basic unit for measuring space, the speed of light, in terms of contraction.
An assumption that can be made is that the size of space can be measured in terms of the rate at which light passes through it. While the rate at which the amount of space within the Universe is increasing is presently unknown, the simplest case is that we consider the Universe to be wherever light is, with it seeming to expand in every direction at a rate of c. If we also assume, as is theorized in the big bang theory, that the initial size of the Universe was extremely small, then the radius of the Universe, defined as the measure to the furthest point possible within the Universe in any direction from a given point within the Universe, would then be equal to approximately 1x(c), at t=1, where t is the number of seconds that have passed since the beginning of time. (Approximate because I am assuming that the Universe has a finite size at t=0. The ratio,(x), between the radius of the Universe, R, and the velocity of light, c, at any time t, will be very close to t, since the initial size of the Universe is extremely small. For now I will describe the initial point in time in the Universe as ti, which is very close to zero, and use t and x interchangeably.) The equation c/R=1/t, where R is the radius of the Universe, would then approximately describe the velocity of light relative to the radius of the Universe at any point in time.
Though it not necessarily always the case, for now it can be assumed that the size of space within the Universe contracts relative to the overall size of the Universe at the same rate as does the speed of light. Thus, the equation C=1/t, where C=c/R, also describes the size of a unit of space measuring 1(c) relative to the radius of the Universe at time (t). The rate of contraction for a length of space (d) is approximately equal to -d/t per second. In cases where the radius of the Universe seems to expand at rates greater than c, appropriate rates of contraction for space can be used. This will be considered later.
With space contracting, each point in time can be described in terms of a size. The past is larger than the present, and the present is larger than the future. I will refer to a series of time frames where the size of each frame at each point in time is smaller than the size of the frame at a previous point in time as a "time continuum".
In describing space as contracting, it is best to consider space to be sectioned into basic units of a specific length, with each of these units contracting. The basic unit of space is not necessarily the smallest possible length of space. Planck's quantum length, approximately 1.61x(10 exp.-33)cm, can be considered to be the length of the basic unit of space. [When Tp equals 2x(10 exp. 17), which is equal to the age of the Universe in seconds divided by pi, Planck's quantum length equals approximately c/[Tp(sq.)xTp(sq.root)].]
According to the big bang theory, the initial size of the Universe was extremely small, on the order of (10exp. -16)cm. When the present age of the Universe, tu, equals approximately 18 billion years, this initial size is equal to approx.(Tp) x (Planck's Length). Here I am hypothesizing that the initial radius of the Universe, the velocity of light, the presently perceived age of the Universe, and Planck's length, are intrinsically related.
We can now describe a situation where, before the beginning of time within the Universe, the initial radius of the Universe, according to the Big Bang theory, was approximately 3x(10 exp. -16) cm. Dividing this by (Tp) gives us a length for an initial basic unit of space, equal to Planck's Length. Though no time had yet past within the Universe, we can define a non-zero initial point in time, tb, equal to R/c(Tp) seconds (where R equals the initial radius of the Universe), this equal to approximately 1/[Tp(sq.) x (Tp sq. root)] seconds, or Planck's time. Initial time, tb, can be seen as pre-Universal time, the time before the beginning of time within the Universal, or, if you like, the time involved in creating the initial conditions of this Universe. Thus at t=0, the beginning of time within the Universe, tb = 1/(Tp(sq.) x (Tp sq. root)) seconds. Initial time defines the initial relationship between the radius of the Universe and the velocity of light and the basic unit of space, and is intrinsically related to the maximum possible age for the Universe, (Tp)x(pi).
Sectioning space into smallest possible units gives a reference point which shows where new space is created, this varying according specific conditions. When we take the smallest unit of space as equal in length to Planck's length, at the beginning of time within the Universe, when t=0, there are approximately [(6x(10 exp. 17)/8] units of space of this length between the center of the Universe (the definition of center will be discussed later) and the edge of the Universe in any given direction. Thus at that point in time there are that many "space creation points" in that length of space, as space creation will occur in between these units. Also, if there is a smallest unit of space, groups of these units must contract together in order to create another unit of space of equal length, since the contraction of a single unit would not create space of sufficent length.
In contraction theory, time begins within the Universe with the start of the contractiopn of space within the Universe relative to an expanded intiail size for the Universe. This initial size and condition must come into existence, and this would have occurred during what I've referred to as pre-Universal time, a period equal to Planck's time. I will address the creation of this initial condition later. For now I will focus on the description of spatial contraction relative to the overall size of the Universe.
From the initial condition, this meaning the primortal substance of the Universe in expanded form, (as opposed to the singularity of Big Bang. How this initial condition is formed will be addressed later), the contraction of the speed of light and of the spatial units begins, and, after one second, the radius of the Universe equals approximately 1x(c). As contraction continues, the size of the spatial units and of the speed of light become smaller and smaller relative to the radius of the Universe, and, thus, the radius of the Universe appears to expand in every direction at c. This is illustrated below.
The expanded nature of the past can be taken into account by describing this aspect of space in terms of an integral. When the velocity of light is described by the equation C=1/t, where C equals the velocity of light (c) at any time (t) proportional to the radius of the Universe, (t) is the number of seconds that have past since the beginning of time in the Universe, and when it is assumed that at t=1 the radius of the Universe equals approximately c(1), then of each basic units of space has it's own past aspect. For a single dimension, length for example, this past aspect is described by the integral (I, from ti to t[)[ l/t(^t)], (I represents integral and ^ represents change), where ti equals 1/Tp. Since the number of basic units of space between the center and the edge of the Universe at any given time equals ct/(c/Tp x Tp sq. root), the total amount of integral space represented by a length of space equal to the radius of the Universe is equal to tTp x Tp sq. root times the integral (I,ti to t)[1/t(^t)]. (This also holds true when space is considered in terms of Planck' s length, since, even though the length is smaller than the basic unit, there are more units at this length.) Summing in three dimensions will give the total integral space within the Universe.
With this view, the past aspects of each unit of space overlap, and future aspects will separate from each other. However, if it is true that the perceived age of the Universe is related to the size of the fundamental unit (also the initial size of the Universe), then the total amount of integral space in the Universe is always constant, and the age of the Universe simply determines how space is distributed at any given time. Consequently, while the expanded space of the past has fewer units of space, it is "denser" than the contracted space of the present, which itself has fewer units and is denser than space in the future. The passage of time in the Universe separates and "exposes" more space. Below I illustrate this.
Due to the situation described above, in order to define a reference frame that is motionless relative to a point, (a), in space, it is necessary that all other points in space be considered to be moving toward that motionless point, (a), and at a rate that is determined by the distance between each point and point (a). For a point in space separated by the maximum distance possible within the Universe from point (a), it is necessary that this point move toward (a) at a velocity approaching c in order to be regarded as motionless, in the conventional sense, relative to point (a).
Another related consequences of contractions results from the fact that not only does space contract, but all entities within the Universe contract with the passage of time. As with space, the amount that an entity contracts per second is determined by both the rate of contraction at the point in time considered and the size of the entity. As contraction occurs, two entities, even if there is no space between them, will recede from each other because of their loss in size. Consequently, they must move toward each other if they are to maintain a constant relative position.
With this new view of the Universe, the propagation of light can be directly tied to the contraction of space within the Universe. This relationship can be described in the following manner. The distance, (d), between any body of matter that is considered to be motionless and the furthest point in the Universe in any given direction can be considered to be constant. Our standard of measure for distance, the velocity of light, though, is contracting in such a way that the distance (d) appears to increase at a rate of c. A photon released from the motionless body will move toward the furthest point in the Universe in a given direction at a rate of c. According to conventional wisdom, the distance, (f), between the photon and the furthest point in the Universe in the direction of propagation, as measured from the photon, remains constant, since, according to conventional wisdom, the Universe is expanding in that direction at the rate of c. According to contraction theory, though, the distance, (f), is contracting, and at a rate of -c. Consequently, it can be hypothesized that a photon's motion toward the furthest point in the Universe in the direction of propagation is caused by the contracting of the space between the photon and the furthest point in the Universe in that direction.
One point that should be made clear here is that the measure to the furthest point in the Universe in a given direction is the same when taken from anywhere in the Universe. This would be true for either of two reasons. One reason would be that, even though I've described the Universe as having an initial size, it's actual size may be larger, even infinite. In this case, what I've described as initial size would simply be the initial size of the perceivable Universe as measured from a given point within the Universe. The second possibility is that the Universe is curved, like the surface of a sphere. Measuring the distance to the edge of the Universe would be similar to measuring the distance from a point on the surface of a perfect sphere to the horizon. It is the same everywhere. Consequently, for either reason, as a photon moves toward the furthest point in the Universe in a given direction, it is not getting closer to it. However, the photon is getting closer to the furthest perceivable point in the Universe as measured from it's previous positions. For example, if it is assumed that the Universe is approximately 18 billion years old, a photon released from a source approximately 9 billion years ago will now be located half way to the furthest point in the Universe as measured from the point where it was originally released. In this way it is possible to differentiate between different positions within the Universe.
A consequence of this interpretation of the motion of a photon is that for any photon located at any distance from a point in space, (a), which is considered to be motionless, it's perceived motion away from point (a) is at least partly due to the fact that, since the standard of measure for space is contracting, the distance that already exists between the photon and point (a) will simply appear to increase. The percentage of a photon's motion due to this contraction is determined by the photon's distance from point (a). This is equal to the negative of the velocity ascribed to this point in space (where the photon is located) in order to define a motionless reference frame relative to point (a). For a photon located at the furthest point possible in the Universe in a given direction from point (a), it's motion is completely due to this apparent motion resulting from contraction. Thus, a photon's motion can be considered to be a combination of apparent motion due to the contraction of the standard of measure for space, and actual motion because of the contraction of the space between it and the furthest point in the Universe in the direction of propagation.
The description of the contraction of space thus presented suffices when the rate of the passage of time is constant and universal. However, with his theory of special relativity, Albert Einstein showed that rates for the passage of time are relative and variable, depending upon the velocity of one system relative to another. The problem that relativity theory addresses is the fact that all measurements of the velocity of light show it to be constant in a vacuum, even when the source of the light is in motion. With special relativity theory, Einstein assumed that the velocity of light is constant. When this is the case, the rate at which time passes for a body in motion relative to another body must slow, or dilate, the amount dependent upon the velocity of the body. This time dilation enables one to consider light emitted from the body in motion to propagate at a velocity of c. The following diagram shows this.
Referring to the diagram , if there is a body of matter, (b), in motion relative to another body of matter, (a), and body (b) emits a photon of light in a direction perpendicular to the path of motion at the moment it passes body (a), then after one second that photon will be located at point (p), which is further from body (a) than from body (b). If the velocity of light is to be considered to be constant in all reference frames, then the only explanation for this is that, from the perspective of someone at (a), time is dilated for body (b). When time is considered to be dilated for the body in motion, the velocity is still c, since fewer seconds, by a factor of 1/u, where u is the factor by which time is dilated, will have passed for that body. The Lorentz-Einstein transformations describe the relationship between time dilation and velocity.
When one considers the velocity of light from a body in motion in the direction of, or in the opposite direction of motion, another concept, length contraction, must be introduced. The necessity for length contraction can be seen when one considers a system in motion comprising of a light source and a mirror set up a distance (L) in front the light source. With the system in motion in a direction such that the mirror is ahead of the source, from the perspective of a motionless observer a photon released from the source and directed toward the mirror appears to move at a rate of (c-v) from the source toward the mirror, and then, once it reflects off the mirror, returns to the source at a rate of (c+v). This compares to a velocity of c in both directions for a photon when the system is not in motion. Consequently, if this were simply the case, the photon would take a greater amount of time in reaching the mirror and returning to it's source in the system in motion as compared to a system not in motion, by a factor of u sq.. This would contradict the assumption of a constant velocity for light. Einstein's solution to this is to consider length measured in directions parallel to the direction of motion as contracted by a factor of 1/u for the system in motion. Thus, the essential effect of length contraction is to reduce the distance that the photon must transverse in leaving and returning to it's source, by a factor of 1/u. This, along with the time dilation factor of u, preserves a constant velocity for light.\par \pard\tab The relative nature of motion is fundamental to relativity theory. When two bodies are in motion relative to each other, either one can be considered to be at rest, thus either one can also be considered to be in a dilated time frame. This means that, after a given amount of time, determination of the actual positions of light photons emitted from each body relative to the bodys' positions is influenced by the choice of which body is considered to be in motion. In figure (1), below, body (a) can be considered to be at rest while body (b) is in motion relative to (a).
Beams of light are emitted from both (a) and (b) in all directions just as (b) passes (a). After one second, the positions of the emitted photons are such that they describe a circle (thicker line) with (a) as it's center and with a radius of c(1). As in the previous example, from the perspective of a person on body (a), considered not to be in motion, a photon emitted in a direction perpendicular to that of motion from body (b) at exactly the point in time when (b) passes (a) ends up further from (a) than (b) after one second. In fact, photons emitted in all but a few directions move different distances from (b) than from (a). However, from the point of view of an observer on (b), (b) is at rest and (a) is in motion. This would mean that the circle (thinner line) formed by the emitted photons would have as it's center (b). Consequently, where the photons actually are is determined by which body is considered to be in motion.\par \tab An important point that should be made clear here is that whether one chooses either (a) or (b) as the non-dilated motionless frame, with the other body perceived as being in a moving dilated frame, the non-dilated state of that moving body is not perceived from the perspective of the non-dilated motionless frame. However, it is possible to assume that the non-dilated state of that moving body does exist. It would then be a parallel non-dilated reference frame. A person, from the perspective of their own motionless non-dilated reference frame, would not perceive the non-dilated aspect of the frame in motion. That person sees only a dilated aspect of the frame in motion, even if the non-dilated aspect of that frame exists. In contraction theory, an extension of this concept is that for each position in the Universe there is a unique non-dilated reference frame associated with that position, since each position has an apparent motion relative to other positions.
