DFT-6: The Reciprocal Relation, Multi-Dimensional Time, and the Foundations of Projection

MWells · Post by **MWells** » Tue Dec 02, 2025 11:48 pm

In the previous post, we reached a turning point in Larson’s development. We now understand linear vibration, scalar rotation, gravitation, and the emergence of vectorial motion in a gravitationally bound system. These stages alone already challenge many common assumptions about the nature of space, time, motion, and force. But Larson does not stop there. Chapters 6–8 of Nothing But Motion introduce something even more fundamental—something without which neither compound rotation nor the later RS2 particle results can be understood.

This is the point at which Larson reveals the deeper structure behind the universe of motion:
space and time are strictly reciprocal, and time is three-dimensional in the same sense that space is.

This post will unfold that structure carefully. No DFT reinterpretation will be added yet; everything here is pure RS. After this foundation is fully established, we will be ready to explore how DFT extends it in a natural way.

1. The Reciprocal Relation Is Literal, Not Figurative

Larson begins Chapter 6 with what may be the most important single statement in the entire Reciprocal System:

“Throughout the universe space and time are reciprocally related.”

This is not a metaphor.
It is a structural identity.

If motion is defined as the ratio of space to time,

$v = \frac{s}{t},$

then any increase in space has the same effect on the magnitude of the motion as any decrease in time, and vice versa.
This means:

Space and time do not exist as independent containers.
They do not define a background in which motion occurs.
They only exist as aspects of motion itself.

Thus we do not “place motion in space and time”; we extract spatial and temporal aspects from motion.

From this follows a principle that is easy to state but profound in consequence:

Space and time have the same physical properties, except for being reciprocal.

Wherever physical space exhibits a behavior, time must exhibit the same behavior in its own aspect.
Wherever time displays a characteristic (such as uniform progression), space must display the reciprocal characteristic (such as outward expansion).

Larson writes that our perception obscures this symmetry: we experience “static spatial extension” because gravitation locally suppresses outward progression; we experience time as purely “one-dimensional progression” because we do not directly observe time as structure.

But this asymmetry in perception does not imply an asymmetry in nature.
In the underlying physical reality:

Time is as real as space.
Space is as real as time.
Both are three-dimensional.
Both participate in motion in the same sense.

This reciprocal relation is the foundation for everything that follows.

2. Why Time Must Be Three-Dimensional

Larson’s argument for three-dimensional time is subtle but rigorous.

We observe time as a uniform progression—what Larson calls clock time, the simple tick-tick succession that carries every process forward. But there is no reason to assume that this progression exhausts the content of time. In RS terms, the progression is merely the temporal analog of the outward progression of space.

If space possesses:
• 3 coordinate dimensions, and
• a uniform outward progression

then time must possess:
• 3 coordinate dimensions, and
• a uniform outward progression in its own aspect.

Time is not “1D because it feels that way.” Clock time is 1D; coordinate time is 3D.
It is only the progression of time that shows one dimension.
The coordinate structure of time—its three independent temporal axes—does not manifest directly in ordinary experience, because we are not aware of temporal displacements.

Larson is explicit:

“The three dimensions of time have the same physical significance as the three dimensions of space.”

Once this insight is accepted, the consequences unfold automatically:

Time can host displacement.
Time can host rotation.
Time can host location.
Time can host independent motion of the same order as motion in space.

This is one of the thresholds where readers of RS often hesitate—but the mathematics and the logic strictly require it. The reciprocal relation would be logically inconsistent if one aspect (space) supported three dimensions of displacement while the other (time) did not.

Thus the early RS universe is not “space + time.”
It is:

a six-dimensional scalar manifold (3 space, 3 time) whose dimensions appear only when motion is projected.

This will later become a natural place for the DFT S- and T-frames to emerge, but we will not introduce that yet.

3. Speeds Below Unity and Speeds Above Unity

Once time is recognized as three-dimensional, Larson introduces a seemingly simple distinction that unlocks major parts of RS physics:

Speeds less than unity (i.e., $v < 1$ ) are motions in space.
Speeds greater than unity (i.e., $v > 1$ ) are motions in time.

The classification does not mean the motion “occurs solely” in space or time; it means that one aspect dominates the scalar ratio.

This follows directly from the definition:

$v = \frac{s}{t}.$

If the numerator is smaller than the denominator, the motion is dominated by space.
If the denominator is smaller than the numerator, the motion is dominated by time.

This single rule explains:

why no physical entity ever exceeds the speed of light in space
why “superluminal” velocities appear in quasars and cosmological observations (they are temporal, not spatial motions)
why gravitational equilibrium inside unit distance yields solids and liquids
why atoms require rotation above unity in the temporal aspect
why “cosmic matter” appears as the inverse of material matter

The division between space motion and time motion emerges naturally from the definition of motion—not from relativity, topology, or any speculative interpretation.

This is a place where RS diverges sharply from conventional physics, but does so in pursuit of deeper symmetry, not by introducing metaphysical assumptions.

4. Gravitation Revisited in Light of Reciprocal Structure

With the reciprocal relation fully established, the true significance of scalar rotation becomes visible.

Rotation of the photon is a scalar phenomenon. It does not possess a vectorial axis; its apparent direction arises only when the scalar rotation is projected into a specific spatial coordinate system.

Rotations slower than unity:

exhibit inward displacement in space
and appear as inward gravitational motion

Rotations faster than unity:

exhibit inward displacement in time
and appear as “inverse gravitation,” a phenomenon that is not directly visible in spatial observation but is required for cosmic matter and the large-scale structure of the universe

The relation is symmetric.

Thus gravitation is not caused by masses acting on each other, nor by fields radiating through space.
It is the inevitable consequence of a rotational component of scalar motion whose inward aspect appears in the spatial frame.
This is precisely Larson’s “scalar rotation projected into the spatial reference system” formulation.

When rotation is viewed from the stationary spatial reference system, the inward scalar component manifests as the inverse-square acceleration toward all other units.

This analysis did not require:

forces
fields
geometric curvature
wave propagation

It required only the reciprocal space–time relation and the existence of scalar rotation.

5. Coordinate Time as a Real Component of Motion (Nehru’s Clarification)

Before we reach the DFT motion budget, we must lay the final RS foundation: the role of coordinate time.

Larson distinguished:

clock time: the uniform progression

coordinate time: temporal displacement that is the exact temporal homologue of spatial displacement

Nehru’s paper Precession of the Planetary Perihelia Due to the Coordinate Time clarified this distinction mathematically. He showed that gravitational motion of speed $v$ produces an additional temporal component of motion:

$\frac{dt_c}{dt} = 3\,\frac{v^2}{c^2}.$

This is not relativity theory.
It is not time dilation.
It is not space-time curvature.

It is simply:

gravitation is a three-dimensional scalar motion
each scalar dimension contributes $v^2/c^2$ units of coordinate time
the total is $3 v^2/c^2$

This accumulation of coordinate time explains:

Mercury’s perihelion shift
light deflection
gravitational redshift

all within the RS framework, without invoking relativity. None of these require space-time curvature; they arise from scalar motion accumulating coordinate structure.

The essential insight for DFT (which we will use later) is:

gravitational rotation adds structure in the temporal aspect of motion.

Nehru did not phrase it in those broad terms, but his calculation forces the idea:
motion has components, and those components accumulate structure in both space and time.

6. The Foundations of Projection: Where DFT Will Later Connect

Everything in this post so far has been pure Reciprocal System.
But the logical implications of these chapters set the stage for a broader interpretation:

Space and time have identical dimensional structure.
Both participate in motion.
Both host rotational, vibrational, and translational components.
Scalar rotation can appear as inward motion in either space or time depending on speed.
Independent motions accumulate coordinate structure.
Observed physical effects depend on which aspect of motion is being projected.
Motion in one aspect (space) limits the way motion can manifest in the other (time).

Larson repeatedly shows cases where:

the same underlying scalar motion
when viewed through different aspects (space or time)
yields very different observable consequences.

This is where DFT will later introduce:

a formal description of projection,
the S-frame and T-frame distinction,
and the motion budget as a general principle.

But we will hold off on those until DFT-7.