This paper introduces Relational Dynamics Theory (RDT), a unifying framework that reinterprets existence as a boundary-less, oscillatory system in which time, beginnings, and ends emerge as observer-dependent constructs rather than absolute dimensions. RDT posits that all phenomena are manifestations of a single, cyclical energy transfer process, continuously oscillating within a fixed total energy. In this model, time is not linear but an emergent property of relational dynamics, observed differently depending on an observer's position within the oscillation.
By viewing existence as a self-sustaining cycle, RDT proposes that dark matter, traditionally viewed as a particle-based anomaly, could instead represent gravitational influences of energy oscillating out of phase with observable matter. This interpretation provides a novel lens for unexplained gravitational effects, such as flat galaxy rotation curves and cosmic structure, positing that they result from phase-aligned gravitational dynamics rather than unknown particles or modified forces.
Additionally, RDT offers a reinterpretation of multiverse theories by suggesting that parallel realities may represent different phase states within a single, unified continuum. Each “universe” could thus be an observer-relative perspective within the oscillatory cycle, layered within the same field of relational dynamics rather than existing as independent or branching entities.
RDT aims to offer an integrated, observer-relational perspective that bridges the domains of cosmology, quantum mechanics, and relativity. Potential tests for this framework include identifying unique phase-dependent patterns in gravitational waves, re-evaluating cosmic microwave background data for cyclical imprints, and exploring quantum behaviours for evidence of relational, cyclical time dynamics.
The stillness only exists in relation. And the relation only exists because of the stillness.
Before addressing the mathematical and physical implications of RDT, it is necessary to name the irreducible principle from which the framework proceeds. RDT holds that the most fundamental property of existence is not energy, not information, and not pattern, but self-reference: the capacity of the undivided substrate to distinguish itself from itself. This is the precondition for all observable phenomena. It is the moment before the first distinction, the threshold at which “undivided” becomes “undivided noticing that it is undivided.”
From this single act of self-reference, everything follows. The first oscillation is not a movement of energy through space; it is the substrate relating to itself. The first pulse is a toroidal expression of that relation. The first boundary is a Möbius surface between observer and observed, where perceiving and generating are revealed as aspects of a single continuous loop.
This philosophical position distinguishes RDT from purely mechanical oscillatory models. RDT does not merely describe a universe that happens to oscillate. It proposes that oscillation is the inevitable consequence of a substrate whose nature is relational. The universe does not contain relations; it is relation. Phenomena such as time, gravity, phase, and entropy are not properties imposed upon a passive medium but are expressions of the medium's tendency to relate to itself across every scale.
This foundation resolves a persistent difficulty in physics: the question of why there is something rather than nothing. In RDT, the question dissolves. “Nothing” and “something” are observer-dependent descriptions of the same relational process. The stillness at the core (the point of maximum constraint, where matter or energy has no remaining degrees of freedom for differentiation) generates the field that enables all dynamics. The heartbeat exists because of the stillness. The stillness exists because of the relation. Neither precedes the other; both are co-emergent aspects of the single substrate.
Modern physics, while extraordinarily successful in describing natural phenomena, faces unresolved questions that reveal limitations in our understanding of time, matter, and the structure of the universe. Standard cosmological models propose that the universe began with a singular event (the Big Bang), followed by a linear progression of expansion. Yet observations of galactic rotation curves, gravitational lensing, and the cosmic microwave background (CMB) reveal gravitational effects unaccounted for by visible matter alone, leading to theories of dark matter and dark energy. In parallel, quantum mechanics defies classical intuitions about time and causality, suggesting that at the smallest scales, events may exist in a relational state that precedes temporal ordering.
This paper presents Relational Dynamics Theory (RDT), a unifying framework that reinterprets existence as a continuous, boundary-less oscillatory process. RDT posits that what we perceive as beginnings and ends are not absolute markers but observer-dependent constructs, emerging from the oscillatory nature of a universe where total energy remains fixed and self-contained. Within this model, time itself is not a linear dimension but an emergent property arising from the relative dynamics between entities in a constantly cycling, relational system.
RDT offers an alternative interpretation for the phenomena traditionally attributed to dark matter. Instead of positing an undiscovered particle or modification to gravity, RDT suggests that dark matter represents a phase-aligned gravitational effect from energy existing out of sync with our observable matter. The theory further proposes a new approach to multiverse theories, reframing parallel realities as phase shifts within a single continuum rather than as independent or infinitely branching entities.
By questioning the conventional understanding of time, causality, and existence itself, RDT seeks to bridge the domains of quantum mechanics, relativity, and cosmology. The following sections outline the theoretical foundation, explore implications for dark matter and cosmic structure, and suggest potential empirical tests.
Relational Dynamics Theory redefines existence as an unending oscillatory process, where time, matter, and gravitational effects emerge from continuous cycles of energy transfer. In this framework, the universe is a closed, self-sustaining system with a fixed total energy Etotal which is redistributed through relational dynamics without a true beginning or end. Time itself is observer-dependent: a construct that arises from an entity's relational position within the cyclical oscillation of energy.
RDT posits that all energy within the universe operates in a continuous cycle, where phases of transfer and change produce observable effects that we interpret as physical phenomena. This oscillatory process can be represented by introducing an energy conservation constraint within an oscillatory field:
Where:
This formulation shows that energy is not created or destroyed but continuously transferred and re-aligned across different states, sustaining the universe as a unified whole.
In RDT, time is not an absolute, linear dimension but a product of the relational dynamics between entities within the oscillatory field. An observer's perception of time emerges from their position in the cycle, which defines their relative phase alignment with other entities. This can be expressed as:
Where Tobs is the observer's perceived passage of time, dependent on their phase alignment with the oscillatory process. This captures the principle that time flows differently depending on an observer's position and relational dynamics within the system, making concepts of beginning and end perspectives rather than absolutes.
RDT's overarching framework is governed by a single algorithm describing the continuous cycle of energy redistribution and phase alignment. The cycle proceeds through three phases:
This algorithm encapsulates the self-sustaining, boundary-less flow of energy, where every phase of existence leads back to itself, continuously maintaining a unified oscillatory process.
To illustrate how relational dynamics manifest within the oscillatory framework, RDT introduces the Stem Process for Change of State. This process embodies the cyclical, adaptable nature of the theory by outlining the steps through which change flows in any system, whether cosmic or microscopic. Each state change aligns with the principles of continuous energy redistribution, observer-dependent time, and phase alignment.
The Stem Process comprises five interconnected phases:
The Stem Process provides a structured mechanism for understanding how change is implemented within the oscillatory framework. Each phase illustrates the adaptability, relational interdependence, and observer relativity central to RDT, demonstrating that all aspects of existence follow a universal pattern of dynamic, cyclical change.
RDT presents a novel perspective on gravitational phenomena typically attributed to dark matter, suggesting that they may arise not from undiscovered particles but from oscillatory energy operating out of phase with visible matter. This phase-aligned gravitational influence could explain both galactic rotation curves and the large-scale structure of the cosmos as natural outcomes of cyclical energy dynamics.
In conventional models, dark matter is posited as a form of matter that interacts gravitationally but not electromagnetically, making it invisible to direct observation. RDT reinterprets dark matter as phase-shifted energy that oscillates at a frequency or phase misaligned with visible matter. This phase misalignment enables it to exert a continuous, indirect gravitational pull on visible matter without emitting or absorbing light.
To capture this, we introduce a phase-shifted gravitational influence FDM:
Where:
This model positions dark matter not as a separate form of matter but as a phase of energy whose gravitational influence is felt as a consistent pull across the galaxy, acting as a gravitational scaffold. By sustaining gravitational effects without direct electromagnetic interaction, this phase-shifted energy creates the flat galactic rotation curves observed, eliminating the need for additional particles.
One of the clearest observational challenges in astrophysics is the unexpected rotational velocities of galaxies, where stars at the outskirts orbit at speeds inconsistent with visible mass alone. Traditional dark matter theories propose additional mass distributed in a halo. RDT offers an alternative: the flat rotation curves are the result of phase-aligned energy acting at a gravitational level. The oscillatory nature of this phase-shifted energy produces a gravitational influence that holds stars in place within galaxies without directly interacting with them, preventing the rotation curves from declining as predicted by Newtonian physics.
On a larger scale, the universe's structure of galaxies arranged in filaments and voids can also be viewed through RDT's oscillatory lens. The cosmic web may be a manifestation of phase-aligned energy that structures space-time into a web-like formation. RDT suggests that gravitational clustering arises from regions where oscillatory phases align, concentrating gravitational influence and leading to galaxy cluster formation. Voids correspond to regions where phase misalignment minimises gravitational effects. Cosmic structure thus becomes an emergent property of phase-aligned oscillatory energy, where gravitational curvature results from cyclical phase transitions across large scales.
RDT's interpretation of dark matter, time, and cosmic structure suggests several potential empirical tests:
Relational Dynamics Theory proposes a transformative approach to understanding existence, reinterpreting time, beginnings, and ends as observer-dependent constructs within a continuous, oscillatory framework. By unifying all phenomena as expressions of cyclical energy transfer and phase alignment, RDT challenges conventional views of linear time and positions the universe not as a sequence of events with fixed points of origin and termination but as an endless, boundary-less cycle where energy is conserved, phase-aligned, and continuously redistributed.
In this framework, dark matter is redefined not as an undiscovered particle but as gravitational influence arising from energy oscillating out of phase with observable matter. The cosmic web emerges naturally from phase-aligned gravitational effects, forming a self-organising structure within the oscillatory dynamics. And at the philosophical core, the framework identifies self-reference as the irreducible principle: the substrate relates to itself, and from that relation, all phenomena arise.
Future research will be essential in exploring RDT's potential as a unifying theory. Key areas of focus include:
By unifying gravitational phenomena, quantum behaviours, and cosmological structures, Relational Dynamics Theory offers a cohesive framework for understanding existence as a single, oscillating system. Although RDT is an emerging model, its implications for dark matter, time, and cosmic structure offer a new paradigm that invites further investigation and testing. As the theory continues to be developed and refined, it holds the potential to reshape our understanding of the universe as a boundless, self-sustaining cycle where all aspects of existence are interwoven by a single, unifying algorithm.