Abstract: Second International Conference on the Ontology of Space-time

Space-time: The Minkowski Space-time Diagram Extended (with an Alternative
Explanation of Gravity) Authors: Bob Gellert and Don Limuti 1/23/06

Another way to look at the fundamentals of nature (objects in time and space) is presented. The results are similar to present models but the source of gravity does not need to be considered the result of curved space-time, there is another choice. Gravity can be considered the direct result of wavelike matter in motion. The first law of motion “a body in motion tends to stay in motion” is the source of the force of gravity.

The authors’ goals for this paper:

First Goal: To develop a space-time diagram that shows how both matter (mass) and light (electromagnetic energy) fit into the playground of space-time. See the “rules of the game” at the end of this listing of goals. This space-time diagram will enable the visualization of curved space-time as a superposition of inertial constant velocity spaces (see Figure 1). To the observer the universe looks like transparent quilts (different velocity spaces) placed on top of each other. The conventional view of space-time weaves these individual space times into one monolithic lumpy quilt when masses are present, a very difficult process. The superposition scheme of the new diagram gives all the benefits of a single sheet of space-time without the topological mathematics.

Second Goal: To explain how light moves on the space-time diagram, and how this movement can be conceived of as being a quantum mechanical hop, an acceleration followed closely by a deceleration. With this notion we can understand how light can go from “0” velocity in a flashlight to the speed “c” in a classical fashion. In addition, we explain how light can change its direction in space without having to alter its average speed of propagation.

Third Goal: To fit matter onto the space-time diagram (see Figure 2). It is postulated that matter has a minimum velocity V0 as well as a maximum velocity c. This velocity manifests as a vibration. In a quantum mechanical fashion matter “hops” to maintain its velocity V0 with a variety of wavelengths the smallest being the deBroglie wavelength λ0 = h/(mV0) and the longest being the dimension of the mass. With these considerations, matter when placed on the space-time diagram can be considered as one object with a variety of wavelengths (multiples of the deBroglie wavelength) with a frequency of V0/λ0.

Fourth Goal: Provide an alternative to the “curvature of space-time” as the cause of gravity. Space-time still has a dynamic aspect that looks curved but this is not the cause of gravity. The force of gravity can be considered the result of matter having an intrinsic minimum velocity V0. This velocity is moving back and forth in space-time and does not propagate in space. The gravitational force operates over one period of this time cycle for the total mass. The time it takes for this force to develop is equal to h/m and is independent of distances. The value for V0 will be developed as a function of the gravitational constant G.

THE RULES OF SPACE-TIME:

General Rules

1.  Space-time is defined as the coordinate system in which light and matter exist as wave phenomena.

2.  Space-time consists of a series of inertial spaces each having a different velocity.

3.  Each inertial space is mapped out in rectilinear Cartesian coordinate form using standard clocks and rods.

4.  Special relativity is taken into account in that each inertial space is “shrunk” by the gamma factor determined by its velocity. Each inertial velocity space retains its rectilinear form.

5.  All players (all types of matter and energy) on the space-time playground must act as waves. They are quantum mechanical in nature and move by making “jumps”. This means that both light forms and matter forms on every move must have both a space value and a time value. If a player moves without both a space component and a time component, they will be disqualified for not being waves.

6.  The maximum space to time ratio available on the space-time grid is c:1

7.  The minimum space to time ratio available on the space-time grid is V0:1

8.  A table is shown of the space time ratios and how they relate to the two extreme velocities allowed on the grid:

Space Number / Time
Number / Speed
m/sec
Max Ratio / c / 1 / c
Min Ratio / V0 / 1 / V0

THE RULES OF SPACE-TIME: (continued)

Special Rules for Light (electromagnetic radiation)

1.  All light will be required to move at the max space to light ratio c, and is thus confined to the c velocity plane

(see Figure 1).

2.  Light will be considered as photons with a space component called wavelength λ and a time component called 1/f. The velocity of light is λf and is equal to c with the unit’s m/sec.

3.  Different wavelengths of light have the same velocity (slope) but move on their own λ and 1/f matrix.

4.  Light can be forced to change its wavelength. This constitutes a change position without a change in velocity.

Special Rules for Matter (mass)

1.  Matter is confined to the speeds v where: 0 ≤ v < c.

2.  All matter has at minimum a V0 vibrating component of velocity. It may have other energy components added to this intrinsic V0. Matter with just the intrinsic velocity is considered to have the mass M0.

3.  If velocity is added to a mass that is at rest M0, m will change with velocity according to the equation:

m = M0

4.  Like light matter will have a wavelength and frequency and will move on the space-time grid with its wavelength λ and its 1/f time component. The force between any two discrete masses is calculated by considering the distance between them as the matter wavelength. The total mass of the system is the sum of both masses and is located at the center of gravity of the masses.

End