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Re-Evaluating theReciprocal System of theory

Questioning the Rotational Base

If one can have linear vibration, without anything to vibrate,

Then

Why cannot one have rotation, without anything to rotate?

The attempt to answer that question led to a 4-year research effort by KVK Nehru and Bruce Peret... and they discovered the answer. But the answer, itself, is not as important as the journey getting there...

Larson’s RS identifies 4 distinct “regions” of speed, with 3 boundary conditions:

Space/time

s/t

Time/space

t/s

Material Sector

Unit Speed

Cosmic Sector

Unit Space

Unit Time

Time

1/t

Space

1/s

Regions of MotionRegions

Space/time (Larson’s time-space) Conventional reference frame.

Time/space (Larson’s space-time) “Anti-matter” (cosmic) reference.

Time Atomic configuration space.

Space Anti-matter configuration space.

Boundaries

Unit Speed Crossover point between material and cosmic sectors

Unit Space Boundary between the conventional reference system and the region of material atomic configuration.

Unit Time Boundary between the cosmic “anti-matter” reference system and the region of cosmic atomic configuration.

Space/time Region Speeds

For now, only the material sector perspective will be considered, as that is the region of our common experience.

- Translational motion has a minimum quantity of 1, because the natural datum of motion in the RS is unit speed. But there is no upper limit to that speed. The units of translational motion are the natural units of linear speed.

- Rotation has no minimum quantity, so it can only exist as a modifier to other motions. It has a maximum quantity of 1 (π), because further increases move the angle back to its starting point of zero angle, where the rotation repeats.

- The minimum quantity of motion will always occur. Thus, linear motion in space/time will always occur, which we observe as the outward progression of the natural reference system—the “Hubble Expansion”.

- From the perspective of the space/time (Larson’s time-space) region,linear motion must precede rotational motion.

Time Region Speeds

The Unit Space boundary separates the Time Region from the space/time region, making everything within the inverse of the space/time region. Zero becomes Infinity; Infinity becomes Zero, and Unity stays Unity.

- Rotational motion has a minimum quantity of 1, because the natural datum of motion in the RS is unit speed. But there is no upper limit to that speed, so the angle of this rotation can be infinite. This type of rotation, where it doesn’t loop around back to zero, is called a “Turn”.

- Linear motion has no minimum quantity and becomes “optional”. When it does occur, upon reaching its maximum it turns back and heads towards zero, producing a vibration, measured as a “Shift” between “Turns”.

- The minimum quantity of motion will always occur. Thus, rotational motion in the time region will always occur, which we observe as a “rotational base”.

- From the perspective of the time region,rotational motion must precede linear motion.

Primary and Secondary Motions

Primary Motions

Given a natural datum of Unity, the minimum quantity of motion must always occur.

These are PRIMARY MOTIONS:

Secondary Motions

When there is no minimum quantity, the motion can act only as a modifier to a primary motion. These motions are always rhythmic in nature, because of the maximum quantity of 1 unit.

These are SECONDARY MOTIONS:

Geometries

When we compare the characteristics of the time and space/time regions, it becomes obvious that the space/time region is represented by rectangular (linear) relationships, expressed by real numbers and the time region is represented by rotational (polar) relationships, expressed using imaginary numbers (aka “rotational operators).

- Rectangular and Polar geometries are geometric inverses of each other, and thus abide by the reciprocal relationship that is the basis of the Reciprocal System of theory.

- Each region must therefore have an underlying geometry attached to it, to properly determine the rules of perspective transformation to account for the influences of the observer principle.

The key word here being: perspective. Even with this simple reciprocal analysis across the unit space boundary, it becomes obvious that the location of the observer must be considered when analyzing the systems of motion, for without it, contradictions abound.

With the advent of computer modeling, the techniques for creating perspective transformations have become well-defined and commonplace, known as the study ofProjective Geometry.

Learning from ContradictionsTwo seemingly contradictory claims have been made:

From the perspective of the space/time region, linear motion can occur without anything moving, but rotational motion must have an underlying linear motion to rotate.

From the perspective of the time region, rotational motion (turn) can occur without anything to rotate, but linear motion must have an underlying rotational motion to vibrate.

Space/time Region

Time Region

Primary Motion

Linear Translation

Primary Motion

Turn

Secondary Motion

Oscillation as Rotation

Secondary Motion

Shift

Geometry

Euclidean:Rectangular

Geometry

Euclidean:Polar

Number System

Real

Number System

Imaginary

Dimensions

3 Axial

Dimensions

3 Planar

Geometric PerspectivesNames of Motions

Primary

Secondary

Space

(Rectangular)

Translation

Rotation

Counterspace

(Polar)

Turn

Shift

Space and CounterspaceCounterspace is the inverse of “space”; the space of common understanding, and is nothing more than a name for a “polar time region”.

The cosmic equivalent to counterspace is “countertime”, the inverse of time, and is the “polar space region”.

Spatial (Euclidean) Geometry

Point

Origin

Plane

Plane

Infinity

Point

Unit Boundary

Parallel Lines

Counterspatial (Polar Euclidean) Geometry

Spatial & Counterspatial Geometry∞

1

0

Inward in Counterspace

ES

ES:

Equivalent Space

P0

Π∞

∞

1

0

Inward in Space

Time

Time:

Motion in Time Only

Π0

P∞

Directions of MotionOutward in Space

Outward in Counterspace

Summary of Regions

- Each Region has an associated geometry, with associated limits.
- Crossing a unit boundary causes an inversion of geometry and limits.
- The location of the observer plays an important role in interpreting motion.
- Projective Geometry, with its tools of space and counterspace, can be used to effectively transform motion from one region to another.

Summary of Motions

- Linear translation CAN exist without something to translate.
- Linear vibration CANNOT occur without something to vibrate.
- Turning CAN occur without something to turn.
- Rotation CANNOT occur without something to rotate.

Conclusions

- Unit linear motion in the space/time region is identified as the progression of the natural reference system.
- Unit turning motion in the time region is identified as the rotational base.
- Rotational bases exist at ALL locations in the natural reference system.

Epilog

- Can rotation exist without something to rotate? Yes… within the Time Region as the “Turn”.
- Do “direction reversals” occur as a primary motion? No… only as a modification of existing motion.
- Part 2 of the RS2 Presentation uses these conclusions to create non-unit motions: photons and particles.

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