3. DISTANCE-TIME THEORY page 1

 

3.1. Distance-time

Distance and time have traditionally been treated as being not equal. In this article, however, I combine distance with time to create distance-time. I start by defining a time line with a time coordinate, t. These points of t are defined as points of existence. In the case of t2 > t1, there is the period of time t2 – t1 = T. Next, I define distance as having a positive and negative direction in the same manner as time. Then, in the same direction as time, I superimpose distance on this time line so that for D, distance, divided by c, a constant, there is an equivalent T, a period of time. I call time lines with distance superimposed on them “distance-time lines”. This relationship, D/c = T, I call the “distance-time equation”. Distance-time is measured in either distance units or time units, and it possesses the characteristics of distance and time.

 

3.2. Eventons

In a three-dimensional coordinate system with X, Y, and Z axes, I place fictitious particles which I call eventons. I use these eventons to define distance and time in the coordinate system. An eventon's presence at any coordinate in the coordinate system defines a point of distance-time occurring at that coordinate. An eventon's presence at a coordinate is what I refer to as an “event”. Once an eventon leaves a coordinate, that coordinate is defined no longer at the event at which it was previously defined when the eventon was at that coordinate. While an eventon moves in the coordinate system, new events are defined by the eventon at each coordinate that the eventon contacts. These new events occur successively in only a positive direction and they define a distance-time line. A distance-time line defined by an eventon traveling in a coordinate system is an event line for that eventon. Since the event line for an eventon is a distance-time line, an eventon defines distance and time occurring along its path at a ratio of D/T = c. The eventon can only be at one event of its event line at a single point of time, relative to an observer in the coordinate system. Therefore, the only event an eventon defines at a single point of time is at the coordinate of the eventon's location. The rest of the event line is not defined relative to an observer at the same point of time. Consequently, any length is defined across a period of time and not at a single point in time. Therefore, relative to an observer, the X, Y, and Z axes would always be defined across a period of time and not at a single point of time. This contrasts with relativity theory in which, relative to an observer, the X, Y, and Z axes are defined at a single point of time. Also, I propose that eventons may pass through each other. I stress that an eventon is only a representation of distance-time's motion in a manifold. An eventon's event line is distance-time.

Eventons are like photons only in that they both have speed c. Eventons possess neither energy nor momentum, and they are not electromagnetic waves. Furthermore, they are not virtual and have no spin. Their only function is to represent distance-time, and they may not even exist. Nonetheless, they are important because they give one an easy visualization of distance-time.

The most basic definition of a particle is not that it has a spin, momentum, energy, or field. The most basic theoretical view of a particle is that it occupies a small region. This is only theoretical. In practice, one cannot detect the presence of a particle in a location unless it does more than occupy a small location. Using this most basic theoretical view, we see that eventons are fictitious point particles.

 

3.3. Distance-time manifold

I define a three-dimensional distance-time manifold as a three-dimensional coordinate system with X, Y, and Z axes, and there is neither distance nor time, except that which is defined by eventons. An indefinite number of eventons present at the same coordinate is a single event at that coordinate. These eventons move along every possible continuous path in both directions, linking coordinates. A photon possesses an eventon which moves along with the photon in the same direction and path. Regardless of an eventon's path or direction, the eventon defines positive amounts of distance-time within the coordinate system.

I imagine two eventons traveling a straight path between two locations, A and B. Both eventons move in opposite directions to each other, and they both begin their journeys at time t1 and end them at t2. Relative to an observer at A, B is located a negative distance into the past (t1 – t2) and a positive distance into the future (t2 – t1), even though both eventons move in a positive direction across distance-time relative to the observer. Thus, the observer could only measure a positive distance between points A and B regardless of their directions. This example shows that the event line of an eventon defined in the coordinate system is defined only by a distinct eventon. In order to measure this distance-time, it must be done via this eventon. Otherwise, it is not defined relative to an observer.

Within a distance-time manifold, the shortest amount of distance-time an eventon crosses, along a continuous path going from one coordinate, (x1 ,y1, z1) to another (x2, y2, z2), is given in distance units by the distance-time Euclidean metric function

. _______________________________(1)

Consequently, any particle in a distance-time manifold, moving straight from (x1, y1, z1) to (x2, y2, z2), must cross the distance-time defined by Eq. (1). This, also, includes particles with speeds slower than c, as I demonstrate in the subsequent section, 3.18. The distance-time premise is satisfied with Eq. (1). Since eventons cross a distance per period of time at a constant ratio c, relative to an observer in this manifold, they have a constant speed c.

Similarly, since the distance along each coordinate axis is defined across a period of time, the coordinate axes cannot be imagined at a single point of time but only across a period of time relative to an observer. The only location that can be imagined in the now is where the observer is located, and this is relative only to the observer. Hence, a distance-time manifold cannot be imagined to exist at a single point of time, but an observer can imagine a distance-time manifold across the period of time that the eventons travel. This description is actually how an observer experiences distance in nature across a period of time.

 

3.4. Scalar coordinate

The time coordinate t is defined as a scalar coordinate within the three dimensions represented by the X, Y, and Z axes, and the difference between distinct points of t is still measured in time units. Henceforth, I call the (x, y, z) coordinates "vector coordinates" "to distinguish between them and the scalar coordinate t. The increasing of t represents eventons moving in a positive direction across distance-time. Therefore, if t2 > t1,

._____________________________________________(2)

In the special case of when an eventon moves along a continuous path across the shortest amount of distance-time between two distinct vector coordinates, I use the Euclidean distance-time metric function of

._______________________________________(3)

 

3.5. Rest speed

I contend that an eventon, A, crosses a constant amount of distance-time before it returns to a vector coordinate P. Since an eventon's event line defines distance-time within a distance-time manifold, A, being located at point t, defines P to be at point t when A is at P. I further contend that the distance-time is infinitesimal between the contacts that A makes with P; therefore, P moves across continuous scalar points of t, while A moves across scalar points of t. The point of time occurring at P is the present moment for any observer at P. Because the distance-time occurring at P is defined with an eventon, the speed of distance-time occurring at P is speed c relative to the coordinate system. This speed across distance-time at point P is called the rest speed at point P. All particles of matter in a distance-time manifold are defined as possessing eventons that move in every possible path. As a result, there is an eventon moving in a similar path to that of A at every particle of matter. Within a distance-time manifold, therefore, all matter flows through points of t and possesses a rest speed c across distance-time. Since a coordinate system only exists relative to an observer's definition, the vector coordinate system is defined relative to an observer's point in time, too. Consequently, a coordinate system flows through points of t with an observer. This does not mean, however, that the coordinate system is at the same point of time as the observer; it only means that it flows through time with the observer. At every single point of present time relative to the observer, the coordinate axes would still be extended out across different points of time as measured by the observer via particles. To summarize, these axes flow through time with the observer, even though they are extended out across different points of time from the observer's point of time.

 

3.6. Distinct sets of events for every point t

At t1, I define a distinct set of eventons at a vector coordinate P, defining an event at P. A number of these eventons follow paths that contact point P, only once making the event at t1 and P unique. Since P can be any vector coordinate in a distance-time manifold at t1, a unique set of events occurs throughout the distance-time manifold. While a distance-time manifold flows through points of t, it therefore flows through distinct sets of events.

 

3.7. Motion

The concept of motion (change) is an independent concept from the concepts of time and space. Motion is defined in the traditional classical and relativity theories of time and space by defining points of time to happen at a finite rate in space. In these traditional theories, the finite speed of time is not quantified in and relative to a reference frame. Another perspective on the speed of time in these traditional theories is to perceive space moving to different points on the time axis at a finite speed and in a positive direction along the time axis. However, if time is not given a finite speed, space is stuck at a single point of time, and the motion of bodies in space is impossible. Hence, the concept of motion is added to the concept of time so that points of time occur at a finite rate in space. Although motion is a concept independent from the concepts of space and time, time and space quantify motion. When an object moves across a quantity of distance in a period of time, the motion of the object is quantified, and, as a result, the object has a specific speed.

To delineate motion into the distance-time manifold, I give the eventon movement across a distance-time line. The ratio of distance to time crossed by the eventon quantifies the motion of the eventon but does not cause motion of the eventon. In the relationship between the eventon and a distance-time line, the motion of the eventon must be defined as a separate concept because motion is an independent concept from the concept of distance-time. If the eventon were not defined as changing location on the distance-time line, the eventon would be stagnant at a single point on the distance-time line. However, I define the eventon as moving in a positive direction along its event line. Since the ratio of distance to time crossed by an eventon crossing its event line is a constant D/T = c, the speed of the eventon is quantified to be a constant speed c relative to the coordinate system within the distance-time manifold. Thus, the speed c is intrinsic to the distance-time manifold, and all other speeds smaller than c are fractions of it.