The Fundamental Motion of Matter at the Speed of Light
Title: The Fundamental Motion of Matter at the Speed of Light: a Geometric-Frequency Transform (GFT) approach
Author: Orion Franklin, Syme Research Collective
Date: March, 2025
Abstract
This paper introduces the Geometric-Frequency Transform (GFT) as a novel framework to redefine motion, showing that all matter moves at the speed of light (c) in a distributed, frequency-dependent manner. Conventional physics treats velocity as a stepwise function of position over time, but GFT models motion as a continuous, geometric-frequency transformation, resolving long-standing questions about reference frames, relativistic effects, and possible hidden dimensions of motion. We propose that all objects are already traveling at c, but their velocity is partitioned across space, time, and frequency domains, leading to misinterpretations of motion as relative. This framework provides a new perspective on relativistic time dilation, dark matter, dark energy, and even potential mechanisms for faster-than-light (FTL) travel.
Introduction: Rethinking Motion in a Frequency-Based Universe
The Problem with Conventional Motion Models
Physics currently describes motion in terms of classical Newtonian mechanics or relativistic spacetime transformations. In both models, velocity is defined as:
v = dx/dt
However, this stepwise approach introduces cumulative errors in long-duration modeling and fails to address why objects appear stationary in one frame but move at cosmic scales. In contrast, GFT reformulates motion using continuous transforms, where velocity is not a direct function of space and time but a harmonic projection of a frequency-distributed motion.
Core Hypothesis: Motion at c Is Invariant
All objects, whether "stationary" or in motion, move at the speed of light (c) in totality.
What we perceive as velocity is just a projection of a deeper geometric-frequency flow.
Stepwise measurement errors arise because we only compute velocity in spacetime, ignoring higher-dimensional frequency components.
GFT Mathematical Framework
Total Motion Equation and the Pythagorean Triangle
To express this concept mathematically, we define a Geometric-Frequency Transform (GFT) equation:
C² = v_space² + v_time² + v_frequency²
Where:
v_space = Observable motion through 3D space
v_time = Motion through time (aging, relativistic effects)
v_frequency = Motion in a geometric-frequency domain (hidden motion components)
C = The total motion, always equal to c
This equation follows the Pythagorean theorem structure, where the total motion (c) acts as the hypotenuse of a right triangle in a multi-dimensional spacetime-frequency space. The implication is that motion can be conceptualized as a geometric relationship, where shifting velocity into one domain (e.g., space) necessarily reduces velocity in another (e.g., time).
Visual Representation
Consider a right triangle:
The base represents motion through space.
The height represents motion through time.
The hypotenuse represents the total motion at c.
If an object is moving through space at high velocity, its movement through time must shrink, causing relativistic time dilation. Conversely, an object "at rest" in space is actually moving through time at full speed (c).
Implications of GFT for Physics
Why We Perceive Some Objects as "Stationary"
If an object is "at rest" in space, then all of its motion is allocated to time and frequency domains.
The reason we experience time is that we are still moving at c, but mostly through the temporal and frequency dimensions.
Relativistic time dilation occurs when an object reallocates part of its motion into the space domain, reducing its velocity in the time domain.
Can GFT Explain Dark Matter & Dark Energy?
If objects move at c but part of their motion is outside our observable space-time, then:
Dark matter might be mass-energy that is moving in frequency-space, invisible to direct measurement.
Dark energy might be a shift in how motion is distributed across the frequency spectrum over cosmological time.
Can GFT Allow Faster-Than-Light (FTL) Travel?
If motion at c is constant but partitioned, then exceeding c may be a matter of reallocating motion into different domains rather than increasing total velocity.
GFT could provide a mathematical basis for frequency-based propulsion, where objects shift how they move rather than how fast.
Acceleration as Deceleration: The Paradox of Slowing to the Speed of Light
The Reversal of Acceleration and Deceleration
In conventional physics, acceleration is viewed as an increase in velocity. However, under the GFT framework, increasing velocity in 3D space is actually a deceleration in time, meaning that approaching the speed of light in space reduces an object's movement through time.
This implies that achieving the speed of light is not a function of pushing forward, but rather of slowing down one’s passage through time and frequency domains.
Why Deceleration is More Difficult Than Acceleration
Just as accelerating an object to near-light speeds requires enormous energy input, decelerating to a full stop in space (shifting all motion into time) is extremely difficult.
Matter is surrounded by other moving matter, all of which already moves at c. Any attempt to decelerate disrupts the local equilibrium, causing external forces to push an object back toward motion in space.
The Universe as a Self-Correcting Motion System
Because all matter moves at c in totality, the surrounding environment acts as a stabilizing system that prevents anything from fully stopping in space or time.
This could explain why perfect stillness never exists in the observable universe, and why even deep-space voids contain residual motion from cosmic structures.
Experimental and Theoretical Tests
To validate this, we propose:
Reanalyzing relativistic motion equations—replacing stepwise velocity with continuous geometric-frequency transformations.
Testing for missing frequency components in gravitational lensing data—if motion is partially in a frequency domain, it should create a small deviation from General Relativity predictions.
Simulating motion through a GFT-based transform—showing how objects at rest in 3D space still exhibit motion in a frequency domain.
Conclusion: A New Paradigm for Motion
Using Geometric-Frequency Transform (GFT), we redefine motion not as a simple function of space and time but as a continuous, frequency-distributed flow. This approach suggests that all objects are already moving at the speed of light (c)—our perception of motion is merely a projection of this deeper structure. This insight could lead to groundbreaking advancements in physics, including explanations for dark matter, dark energy, and the development of new propulsion methods for space travel.
Future Work
Extending GFT to quantum mechanics to explore its impact on wave-particle duality.
Investigating GFT’s applications in computational models for long-term physics simulations.
Exploring how controlled reallocation of motion across dimensions could allow practical faster-than-light travel.
Further examining how deceleration resistance affects spacecraft propulsion and potential applications in controlled motion redirection.
References
Einstein, A. (1905). "On the Electrodynamics of Moving Bodies." Annalen der Physik.
Wheeler, J. A. & Feynman, R. P. (1945). "Interaction with the Absorber as the Mechanism of Radiation." Reviews of Modern Physics.
Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). "Gravitation." W. H. Freeman.
Bohm, D. (1952). "A Suggested Interpretation of the Quantum Theory in Terms of 'Hidden' Variables." Physical Review.
Barbour, J. (2000). "The End of Time: The Next Revolution in Physics." Oxford University Press.
