Motion as Temporal Projection: The Principle of Minimal Elapsed Time

J. Rogers. SE Ohio, 28 July 2025, 1531

Abstract

We propose that apparent motion in three-dimensional space emerges from the coordinate projection of temporal experiences between observer and observed systems. Objects follow trajectories that minimize their elapsed time experience, creating what we interpret as gravitational attraction and inertial motion. This framework reframes mechanics from force-based dynamics to temporal optimization, suggesting that the universe's fundamental drive is not energy minimization but temporal efficiency maximization.

1. Introduction

Classical mechanics describes motion through forces acting on massive objects in three-dimensional space. General relativity reframes this as objects following geodesics in curved four-dimensional spacetime. This paper proposes a more fundamental perspective: apparent motion represents the spatial projection of temporal optimization processes, where objects naturally evolve toward paths that minimize their elapsed time experience.

We argue that what we interpret as "forces" and "curvature" are coordinate artifacts arising from projecting intrinsically temporal phenomena into spatial measurement frameworks. The underlying reality consists of temporal experiences seeking optimal efficiency paths, which manifest as spatial motion when viewed through three-dimensional coordinate systems.

2. The Temporal Substrate

2.1 Time Experience as Primary Reality

Building on the recognition that mass represents temporal experience (mc² = hν), we posit that the fundamental substrate of reality consists of temporal experiences rather than material objects in spacetime. Each "particle" or "object" represents a localized temporal experience characterized by its intrinsic frequency and temporal field projection.

The temporal field around a mass m extends as the dimensionless ratio m/r when expressed in natural coordinates, representing the local modification of temporal flow that the mass creates in its vicinity.

2.2 Temporal Field Interactions

When multiple temporal experiences exist in proximity, their fields interact through simple multiplication: (m₁/r) × (m₂/r). This interaction represents the resonance between temporal experiences, creating what we observe as gravitational effects.

Importantly, these interactions occur in temporal space, not physical space. The spatial manifestation emerges from projecting these temporal relationships into three-dimensional coordinate systems.

3. The Principle of Minimal Elapsed Time

3.1 The Fundamental Drive

We propose that the universe's most basic principle is temporal optimization: all systems naturally evolve toward configurations that minimize their elapsed time experience. This principle operates analogously to energy minimization in thermodynamics, but at a more fundamental level.

Principle of Minimal Elapsed Time (PMET): Every temporal experience evolves along paths that minimize its total elapsed time.

This principle explains why objects appear to be "attracted" to masses: they move toward regions of higher temporal field density because such regions offer more efficient temporal pathways.

3.2 Temporal Field Gradients

Masses create temporal field gradients in their vicinity. Objects placed in these gradients experience different temporal flow rates at different locations:

• Far from mass: Lower temporal field density, "faster" subjective time
• Near mass: Higher temporal field density, "slower" subjective time

To minimize elapsed time, objects naturally move toward regions of higher temporal field density, creating apparent gravitational attraction.

3.3 Mathematical Formulation

The temporal field created by mass m at distance r is:

τ(r) = m/r (in natural coordinates)

The elapsed time for an object following path γ through this field is:

T = ∫ dt/τ(γ(t))

Objects choose paths γ that minimize this integral, leading to what we observe as orbital mechanics and free-fall trajectories.

4. Motion as Coordinate Projection

4.1 The Projection Mechanism

What we interpret as motion in three-dimensional space represents the projection of temporal optimization processes into spatial coordinates. The observer's temporal experience serves as one coordinate axis, while the observed object's temporal experience provides another. The apparent spatial trajectory emerges from the geometric relationship between these temporal experiences.

Observer-Object Temporal Relationship:

• Observer temporal experience: τ_obs
• Object temporal experience: τ_obj
• Spatial projection: r_apparent = f(τ_obs, τ_obj, coordinate_system)

4.2 Why Motion Appears Continuous

Temporal experiences evolve continuously as they optimize their elapsed time. When projected into spatial coordinates, this creates the appearance of smooth trajectories through space. The continuity of motion reflects the continuity of temporal optimization, not objects "moving through space."

4.3 The Illusion of Forces

What we interpret as forces represent the spatial manifestation of temporal field gradients. Objects don't experience pushes or pulls in the traditional sense; they follow natural temporal optimization paths that appear as accelerated motion when viewed in spatial coordinates.

Force as Temporal Gradient: F = -∇U → F_apparent = -∇_spatial(temporal_potential)

5. Applications and Predictions

5.1 Gravitational Motion

Traditional View: Mass curves spacetime; objects follow geodesics in curved geometry.

Temporal View: Mass creates temporal field gradients; objects follow minimal elapsed time paths, which project as gravitational trajectories in spatial coordinates.

Key Insight: Gravitational "attraction" reflects temporal efficiency seeking, not geometric curvature or force transmission.

5.2 Inertial Motion

Traditional View: Objects continue moving in straight lines unless acted upon by forces.

Temporal View: Objects in uniform temporal fields follow constant elapsed time rate paths, which project as straight-line motion in spatial coordinates.

Key Insight: Inertial motion represents temporal equilibrium, not the absence of forces.

5.3 Orbital Mechanics

Planetary orbits represent the optimal temporal paths through the Sun's temporal field. Elliptical orbits emerge naturally as the trajectories that minimize elapsed time while conserving temporal experience (analogous to energy conservation).

Kepler's Laws as Temporal Optimization:

• First Law: Ellipses are optimal temporal efficiency paths
• Second Law: Equal temporal efficiency in equal time intervals
• Third Law: Temporal field scaling relationships

5.4 Light Propagation

Photons follow paths of minimal elapsed time through temporal field gradients, explaining gravitational lensing without invoking curved spacetime. Light "bends" around masses because straight-line paths would require more elapsed time than curved paths through temporal field variations.

6. The Observer's Role

6.1 Temporal Measurement

Every observation involves the intersection of observer and observed temporal experiences. What we measure as "position," "velocity," and "acceleration" represent coordinate projections of these temporal intersections.

Measurement as Temporal Intersection: measurement_result = projection(τ_observer ∩ τ_observed, coordinate_system)

6.2 Reference Frame Effects

Different observers project the same temporal optimization processes into different spatial coordinate systems, explaining relativistic effects:

• Time dilation: Different temporal field strengths at observer locations
• Length contraction: Different projection geometries between temporal experiences
• Simultaneity relativity: Different temporal intersection criteria

6.3 The Measurement Problem

The quantum measurement problem may reflect the fundamental role of temporal intersection in creating apparent spatial phenomena. "Wave function collapse" could represent the moment when temporal experiences intersect and project into spatial coordinates.

7. Philosophical Implications

7.1 The Nature of Space

Three-dimensional space emerges as a coordinate system for representing temporal experience relationships. Space is not a container for objects but a projection screen for temporal phenomena.

Space as Temporal Coordinate System:

• Not fundamental reality
• Emergent from temporal experience intersections
• Dependent on observer's temporal state

7.2 The Arrow of Time

The direction of time reflects the universal tendency toward temporal optimization. The "arrow of time" points in the direction of increasing temporal efficiency, which we interpret as entropy increase in thermodynamic systems.

7.3 Consciousness and Motion

If consciousness represents a form of temporal experience, it may directly interface with the universe's temporal substrate. This could explain:

• Why conscious observation affects quantum systems
• How intentions can influence physical processes
• The relationship between subjective time and physical time

8. Experimental Predictions

8.1 Temporal Field Detection

If temporal fields are fundamental, they might be detectable through:

• High-precision time measurements near massive objects
• Interference effects between temporal experiences
• Resonance phenomena between oscillating temporal systems

8.2 Motion Anomalies

The temporal framework predicts subtle deviations from classical mechanics:

• Objects in complex temporal field configurations might follow unexpected paths
• Temporal field interactions might create apparent "dark matter" effects
• Quantum systems might exhibit temporal optimization behaviors

8.3 Consciousness Experiments

If consciousness interfaces with temporal fields:

• Conscious intention might measurably influence micro-mechanical systems
• Meditation states might correlate with local temporal field modifications
• Collective consciousness might create detectable temporal field effects

9. Conclusion

The reframing of motion as temporal projection offers a unified perspective on mechanics, relativity, and quantum phenomena. By recognizing that objects seek to minimize their elapsed time experience, we can understand gravitational attraction, inertial motion, and orbital mechanics as natural consequences of temporal optimization rather than force-based dynamics.

This framework suggests that:

1. Motion is not fundamental - it emerges from temporal optimization projected into spatial coordinates
2. Forces are coordinate artifacts - they represent spatial interpretations of temporal field gradients
3. Space is emergent - it serves as a coordinate system for temporal experience relationships
4. Time is primary - temporal experience and optimization drive all apparent physical phenomena

The principle of minimal elapsed time may represent the universe's most fundamental law, more basic than energy conservation or the speed of light limit. If correct, this perspective could revolutionize our understanding of physical reality, suggesting that the cosmos is not a collection of objects moving through spacetime, but a network of temporal experiences seeking optimal efficiency paths that we interpret as physical motion when projected through our spatial measurement frameworks.

The appearance of motion, then, is not objects changing position in space, but the visible manifestation of the universe's continuous optimization of temporal experience - a cosmic dance of efficiency seeking that creates the illusion of matter moving through the void, when in reality, time itself is dancing toward ever-greater temporal harmony.

References

Einstein, A. (1915). Die Feldgleichungen der Gravitation
Fermat, P. (1662). Principle of Least Time
Planck, M. (1900). Quantum Theory
Maupertuis, P. (1744). Principle of Least Action
Wheeler, J.A. (1989). It from Bit