J. Rogers, SE Ohio, 29 August 2025, 1715
Abstract
We propose that cosmological redshift observed in distant astronomical objects results from nested gravitational time dilation effects rather than cosmic expansion. This model suggests that observers embedded in hierarchical gravitational structures experience cumulative time rate differentials that manifest as redshift when observing sources at different depths in the cosmic gravitational hierarchy. We demonstrate that this temporal framework naturally explains the distance-redshift relationship without requiring expanding space, dark energy, or exotic physics, while providing a foundation for understanding gravity itself as emergent from overlapping temporal experiences.
1. Introduction
The standard cosmological model attributes observed redshift in distant galaxies to the expansion of space itself, requiring concepts such as dark energy to explain accelerating expansion. However, this interpretation rests on the assumption that gravitational effects cannot account for the observed redshift-distance relationship. We propose an alternative framework where cosmological redshift emerges naturally from the nested hierarchy of gravitational time dilation effects that permeate cosmic structure.
2. Theoretical Framework
2.1 Time as the Fundamental Substrate
Rather than treating mass as fundamental and time dilation as a consequence, we propose that temporal experiences are primary, with mass, energy, and gravitational effects emerging from the coupling of individual time experiences with universal temporal flow. In this framework:
- Each concentrated time experience manifests as what we observe as mass
- The interaction of time experiences creates what we measure as gravitational effects
- Physical laws represent projections of simple, dimensionless temporal relationships onto our arbitrary unit systems
2.2 Gravitational Time Dilation as Nested Hierarchy
Every observer exists within multiple nested gravitational wells simultaneously:
- Planetary gravitational field
- Stellar gravitational influence
- Galactic gravitational environment
- Galaxy cluster gravitational binding
- Supercluster-scale gravitational structures
- Embedded into a universal structure
Each layer contributes to the observer's local time rate relative to a hypothetical observer in intergalactic space. The cumulative effect creates a unique temporal signature for each location in the universe.
2.3 Dimensional Analysis and Natural Units
Physical laws emerge when dimensionless relationships at the Planck scale are scaled to human measurement units. For gravitational interactions:
- The fundamental relationship is the overlap of time experiences: (m₁/r) × (m₂/r)
- Scaling to Planck units: (l_P²/m_P²) × (m₁m₂/r²)
- Converting to SI force units: [(l_P²/m_P²) × F_P] × (m₁m₂/r²)
Where G = (l_P²/m_P²) × F_P serves as the conversion factor between natural units and arbitrary human units.
3. Observational Predictions
3.1 Redshift-Distance Relationship
In the temporal hierarchy model, redshift z observed from source to observer results from the time rate differential:
z = (t_observer/t_source) - 1
Where t_observer and t_source represent the local time rates in their respective gravitational environments. More distant sources are more likely to exist in significantly different gravitational environments, naturally producing a distance-redshift correlation.
3.2 Quantitative Example
Consider a photon emitted 1 billion years ago observed by two different observers:
Deep Space Observer (minimal gravitational embedding):
- Local time rate: 0.999997658415 (relative to absolute)
- Observed frequency: 1.078122475479
Earth-based Observer (nested in Solar/Galactic wells):
- Local time rate: 0.999991316027 (relative to absolute)
- Observed frequency: 1.078115637592
The Earth observer measures 0.00063424% lower frequency (more redshifted) due to deeper gravitational embedding. Over cosmological distances and through multiple gravitational structures, this effect compounds significantly.
4. Implications and Predictions
4.1 No Expanding Space Required
The temporal hierarchy model eliminates the need for:
- Cosmic expansion
- Dark energy
- Accelerating expansion
- Exotic physics beyond general relativity
4.2 Testable Predictions
- Directional Asymmetries: Redshift should show slight directional dependence based on our motion through the galactic gravitational field
- Local Group Effects: Objects within our local gravitational group should show systematically different redshift patterns
- Void vs. Cluster Sources: Sources in cosmic voids should appear less redshifted than those embedded in dense cluster environments at equivalent distances
4.3 Reinterpretation of Cosmological Data
- Hubble Constant: Becomes a measure of average gravitational time dilation gradient across cosmic distances
- Type Ia Supernovae: Apparent dimming reflects time rate differentials rather than acceleration
- Cosmic Microwave Background: Represents the time rate signature of the early universe's gravitational environment
5. Relationship to GPS and Practical Physics
This framework is grounded in observed physics. GPS satellites require constant correction for gravitational time dilation effects following exactly the m/r relationship proposed here. The system accounts for approximately 38 microseconds per day of time dilation, confirming that time rate differentials due to gravitational embedding are measurable, predictable, and technologically relevant.
6. Discussion
6.1 Advantages of the Temporal Model
- Empirical Grounding: Based on observed GPS time dilation effects
- Mathematical Simplicity: Reduces to dimensionless relationships at natural scales
- Eliminates Exotic Physics: No need for dark energy or cosmic expansion
- Unified Framework: Connects local gravitational physics with cosmological observations
6.2 Potential Challenges
- Surface Brightness Test: Must account for how temporal effects influence apparent brightness
- Nucleosynthesis: Requires reexamination of Big Bang nucleosynthesis calculations
- CMB Anisotropies: Need alternative explanation for observed temperature fluctuations
7. Conclusions
The temporal hierarchy model provides a compelling alternative to cosmic expansion for explaining cosmological redshift. By recognizing time experiences as fundamental and gravitational effects as emergent, we can understand redshift as a natural consequence of nested gravitational time dilation rather than expanding space.
This framework suggests that cosmological surveys are essentially mapping the temporal topology of the universe's gravitational structure. Rather than measuring recession velocities, we are observing the time rate signatures of different gravitational environments encoded in the light from distant sources.
Further investigation of this model could fundamentally reshape our understanding of cosmology, eliminating the need for dark energy while providing deeper insight into the temporal nature of physical reality.
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