3. DISTANCE-TIME THEORY page 4

3.18. Reference frame motion with speeds slower than c

Objects given a location in a traditional space are stagnant if no provision for the motion of these objects across space is defined. Therefore, the traditional view of a space requires a fourth dimension of time. In this view of space and time, or space-time, space moves across the fourth axis of time. Each distinct point of time is a distinct point of existence for space. At a given point of time, an object can exist at a different location in space compared to previous or later locations in space. This ability of relocation at different points of existence allows an object to move in space while space moves across the time axis. In distance-time theory, however, there is no fourth axis of time with a space extended out, separate from the time axis. Instead, in distance-time theory, motion is defined by eventon motion occurring at speed c relative to a reference frame at rest. A reference frame is a coordinate system that is a reference for a perspective. Any motion of another reference frame at velocity v, relative to the reference frame at rest, is a part of this motion of eventons at speed c. Therefore, relative to the reference frame at rest, a fraction of the distance-time (in the speed c) of these eventons goes into the velocity v of the other reference frame. This relationship of c to v is in contrast to traditional theories of space and time, which do not view all velocities v as only fractions of a whole number c. Since both reference frames share the same eventons, the same eventons define distance and time for both of these frames. As a result, the distance-time in v (the speed of the moving frame) is subtracted out of the distance-time of the moving frame relative to the reference frame at rest. However, the distance-time relative to the reference frame at rest does not have distance-time subtracted out. Using the S and S' reference frame, I illustrate in Figure 4 the relative motion of one reference frame to another.

In Figure 4, S' has a velocity v in the positive X axis direction. The X and X' axes, as well as the Y and Y' axes, lie parallel. The S clock is at the S origin, and the S' clock is at the S' origin. At the S and S' clock measurements of t = 0 and t' = 0, the S and S' origins coincide with eventon A. Relative to S, S' moves from (0, 0) at t = 0 to (x, 0) at t = t, and eventon A moves straight from (0, 0) at t = 0 to (x, y) at t = t. However, relative to the S' frame, this eventon A moves from (0',0') at t' = 0 to (0', y') at t' = t', which is straight along the Y' axis. Also, rod measurements within the S frame give

_______________________________________________________(11)

and

._______________________________________________________(12)

In Figure 4, the distance-time that eventon A crosses between (0, 0) and (x, y), in time period of (t − 0), is given by the distance-time Euclidean metric function, which is

.__________________________________________________________(13)

However, the amount of ct parallel to the X and Y axes are given by Eqs. (11) and (12), and they are dilated across ct. Thus, eventon A crosses D" distance in t time parallel to the X axis. Also, parallel to the Y axis, eventon A crosses D' distance in t time. The speed of eventon A parallel to the X axis is

.___________________________________________________________-(14)

The speed of eventon A parallel to the Y axis is

.___________________________________________________________-(15)

The ratio of distance to time in which an eventon crosses is always c. Thus, Eqs. (14) and (15) are not distance-time metric functions. Instead, relative to S, they are only rod measurements taken along the X and Y axes and divided by the S clock measurement, which gives partial velocities v and u of the total velocity c. Dividing Eq. (13) by t and combining the result with Eqs. (14) and (15) produces

.__________________________________________________________-(16)

the relationship between the total and partial speeds of eventon A. Combining Eqs. (11) and (14), I arrive at

._______________________________________________________(17)

Combining Eqs. (12), (15), and (16) yields

._____________________________________________________-(18)

Both Eqs. (17) and (18) give D" and D' as fractions of ct. Since D' and D" are crossed by eventon A while eventon A crosses ct, D' and D" are dilated, according to Eqs. (17) and (18), across ct.

Relative to the S frame, the S' frame moves with velocity v along the X axis. The distance-time crossed by this velocity v along the X axis is defined in Eq. (14) to be the distance-time D" = cT", which is the part of ct that occurs parallel to the X axis in Figure 4. This distance-time in v does not occur relative to S'. Only in the S frame does it occur as a fraction of ct distance-time. Relative to S, eventon A travels across D' = cT' parallel to the Y and Y' axes and inside S'. D" = cT" is the distance-time in the rest speed, u, of S' relative to S. Combining Eqs. (11), (12), and (13), I derive

._____________________________________________________-(19)

Similar to Eqs. (19) and (18), the distance-time in v, which is D" = cT", is subtracted out of the total distance-time ct, which eventon A crosses in S. This leaves D' = cT' distance-time within S' relative to S. Although other eventons have different paths from eventon A's event line, relative to S, all the paths of eventons within S' still have the distance-time in v subtracted out according to Eqs. (19) and (18), leaving the distance-time in rest speed u, which is D' = cT'. I used eventon A's event line in Figure 4 because with this event line the relationships are apparent between the distance-times in speeds c, v, and u. The distance-time in v is the difference between S and S' reference frames relative to S. Consequently, D" = cT" is the difference between the here-nows of the S and S' reference frames. The events in D" = cT", therefore, are located here-now relative to the S' reference frames. However, these events are still dilated across D = cT relative to the S reference frame. Since both u and v are dilated across cT, they both are slower than c. This is the reason that allows velocities of v that are slower than c in a distance-time manifold.

It is now appropriate to examine a second event line in Figure 4 defined by an eventon B. I place eventon B in Figure 4 traveling in a positive direction along the X and X' axes. At t = 0 and t' = 0, B coincides with the origins of S and S'. According to the metric function, within the S frame, B crosses

_______________________________________________________________-(20)

quantity of distance-time, and within the S' frame, B crosses

______________________________________________________________-(21)

quantity of distance-time. Using Eq. (20) for substitution into Eq. (17), I arrive at

._____________________________________________________________(22)

Dividing Eq. (22) by c, I change Eq. (22) into time units, getting

._____________________________________________________________-(23)

In Eqs. (22) and (23), D" = cT" (which is distance-time in the velocity v) is dilated along the X axis relative to the S frame. Since D" = cT" is the difference between distance-time occurring within S and S' relative to S, Eqs. (22) and (23) give this difference of D" = cT" along the X axis in terms of x. In order to put Eqs. (22) and (23) in terms of x', I substitute x' for x and −v for v, since S is moving in a –X' axis direction relative to S'. These substitutions give

____________________________________________________________(24)

and

.___________________________________________________________(25)

Both Eqs. (24) and (25) give the difference of D" = cT" in velocity −v between S and S' along the X' axis in terms of x'. I use Eqs. (22) through (25) at a later point in the article.

Since D" = cT" is the difference in distance-time between the S and S' frames, it is also the difference between the various sets of events occurring here-now in the S and S' frames. Consequently, for every distinct reference frame, there is a distinct set of events occurring here-now in that frame. Any of the Eqs. (22) through (25) can be used to describe the difference between the here-nows of the S and S' frames. I give a clearer description of this after I have derived a few more equations. I next substitute the distance-time of x in Eq. (20) into ct of Eq. (18), deriving

.__________________________________________________________(26)

In Eq. (26), D' = cT' is the distance along the X' axis in the S' frame which is contracted relative to S.

3.19. Speed limit

Distance-time theory offers two explanations not found in relativity theory regarding how speeds faster than speed c cannot be attained by particles crossing distance and time. The first reason is that space travels at speed c. Therefore, at speeds faster than c, space has not happened yet; thus, there is no space to travel across. The second explanation proposes that c is the only speed intrinsic to the structure of distance and time in the universe. All other speeds possess only a part of the speed c according to Eq. (16). Consequently, the maximum speed that v can be is c according to Eq. (16).

3.20. A perspective of a three-dimensional distance-time manifold

A three-dimensional distance-time manifold has an indefinite number of eventons moving along all possible paths and directions at every vector coordinate. Relative to any observer, a reference frame within this manifold possesses distance and time according to how distance and time is traversed by eventons. Whatever periods of time the eventons move across, relative to the observer, the reference frame are defined across those periods of time, too. The distance that the eventons cross along their paths relative to an observer is the distance occurring along that path in that reference. The motion of the eventons is intrinsic to the distance-time manifold, and the speeds of matter that are slower than c are part of the motion of these eventons. Hence, these speeds of matter, which are smaller than c in and relative to a reference frame, are fractions of the speed that the eventons experience in and relative to that reference frame. In essence, all experiences of time, distance, and motion in and relative to an observer's reference frame are given by the eventons. Therefore, a reference frame is essentially all the time and space that eventons traverse relative to an observer. This perception of a reference frame is a proper perception of a distance-time manifold. In summation, the distance-time manifold is a three-dimensional space, and this space has a finite speed because time is integrated into it. The way that time is integrated into it is by using the distance-time equation. Time is never on a fourth axis that is in some way curled up. The manifold is strictly three-dimensional. Essentially, it is the most classic and basic understanding of a manifold. Euclid would be proud. The only differences are the distance-time metric function and how it is interpreted. Of course, this gives strange consequences. Nonetheless, these consequences are directly related to the distance-time metric function's meaning.

How do I describe a point in this kind of dynamic manifold? The eventons are entering and exiting every point of a three-dimensional manifold. This entering and exiting of eventons moving in all directions I call an “event” or an “event point”.

3.21. Relative motion's effect on rod and clock measurements

Since I define events as existing at every vector coordinate independent of light or matter, eventons make up an ocean. In this ocean of eventons reside all particles of matter, light, and their respective reference frames of motion. The movement of the eventons gives a rest speed to all particles (except light, which does not have a rest speed) and allows for the speed of one particle relative to another. Of course, eventons only represent distance-time. As an actual particle, they may not exist. There are two types of measurements of distance-time: the clock measurement which measures the magnitude of distance-time, and the ruler measurement, which is a vector measurement. The latter is a vectorial measurement because eventons travel along the ruler in opposite directions. As a result, depending upon which direction one measures with the ruler, an eventon is moving in that direction.

A person experiences a rest speed across distance-time relative to an observer. If this person has a constant speed relative to an observer, the observer observes that this person gets his or her relative motion via the same eventons that gave him or her an individual rest speed. Therefore, some of the distance-time that is in this person's rest speed has now gone into his or her relative motion. There are two points I need to make. First, the rest speed comes from the magnitude of the distance-time that eventons traverse. Second, this rest speed gives clocks their measurements. Also, the magnitude of the vectorial distance travelled by the same eventons gives ruler measurements. Therefore, when some distance-time is removed from the eventons giving the rest speed for a person with a relative motion, this person's distance-time should be effected relative to an observer. Hence, the person’s clock and ruler measurements will be effected in the same manner.

In sum, all matter exists within an ocean of eventons, and they give us and all other objects all experiences of time and distance. This includes clock and ruler measurements as well as objects’ relative motions. Relative motion, as well as clock and ruler measurements, relies on the same eventons for distance-time. As a result, there is distance-time in the motion of an object, and this distance-time should be subtracted from the clock and ruler measurements of this moving object relative to an observer at rest.

3.22. Perceiving the distance-time idea

In special relativity, E = mc². This equation means that energy is equal to mass. Sometimes it is referred to as mass-energy. This does not mean that mass is multiplied by energy. (In chapter 4, I derive the mass-energy equation from the distance-time equation. In other words, E = mc², because D = cT, which I later show in chapter 4.) Similar to the mass-energy idea, in distance-time theory, distance is equal to time. This does not mean that distance is multiplied by time as well. In distance-time theory, I rely on the distance-time equation. D means a length. T means a period of time. Also, c is the speed of light in a vacuum. Only c and D can be a vector. T is always a scalar. This means it is only the magnitude of distance that is equal to the period-of-time. It is this scalar relationship that must always be satisfied. When I use a ruler to measure a distance, I use D/c = T to derive the time in the ruler measurement. According to this equation, if I divide the distance by the c, I get the time in the distance-time measured by the ruler. Wouldn't I get the inverse time, and shouldn't I use D/T = c? Time is often used inversely in physics. If I were to talk about the time it took for me to go from point A to point B, I would refer to the time in conversation, not to the distance, too. However, in reality, the actual time is in the denominator of the equation that gave the speed. I would use D = cT to derive the scalar distance in a clock measurement. If I am not calculating time from distance or distance from time, I primarily use equation D/T = c. This equation helps me appreciate the distance-time idea. Distance-time is a speed from which I can derive distance and time measurements. The best way to imagine distance-time in a three-dimensional manifold is to imagine something with speed c like an eventon. After all, distance-time does possess a real speed relative to matter.

3.23. Time is never a vector

The equivalency of distance to time is a scalar and constant relationship because time is never a vector. Distance and velocity can be vectors—not time. This means there is no vector energy either. Also, there are no three dimensions of time, and time cannot be used to create analogous geometric ideas like area or volume.

3.24. The classical fourth dimension

All that is needed to know about time and distance in this theory is given by eventons in the manifold. The distance-time manifold is kinetic—not static. Events continuously happen within this manifold. Why insist on four dimensions? The fourth dimension has never been proven to exist. Time as a fourth dimension comes from the classical idea of time on an axis separated from the three dimensions of space. Who invented that classical idea, and why should I accept it as a fundamental truth about the universe? Was it Descartes who invented the classical structure of space and time? All that the relativists did was adapt this classical structure to satisfy relativistic results such as the following: the speed of light in a vacuum is constant. In so doing, relativists created a four-dimensional space-time continuum. The only reason people accept the fourth dimension is because they have developed that model into their theories, and of course there are some very good theories that are four-dimensional. Just because ideas work in a four-dimensional space-time continuum does not mean that there are necessarily four dimensions. Nevertheless, space-time is very classical in its approach, and I do not trust it