The Hypersphere Model of Gravity: Time as the Driving Force of Curvature

[Gibsense]

The Hypersphere Model of Gravity: Time as the Driving Force of Curvature (improved expression by AI)

Hypothesis Overview:​

In this model, the universe is conceptualised as a 3-dimensional spatial surface of a 4-dimensional hypersphere, where the radius of the hypersphere represents time and expands at the speed of light. As the radius grows, the circumference—the 3-dimensional space of our universe—naturally expands, accounting for cosmic expansion.
However, gravity emerges not from curved spacetime in the traditional sense, but from the interplay between time’s outward progression and the presence of mass. Mass obstructs the smooth expansion of time, slowing its local progression and thereby creating what we recognise as gravitational wells.

Imagine the expanding radius as an outward-moving wave, like a ripple across water. Matter acts as an obstruction, distorting the flow of time near it. Since time drives the universe's expansion, any local deceleration of time equates to a curvature in space, analogous to gravity. This framework provides a natural link between Kip Thorne’s intuition that time might cause gravity and observable relativistic effects, offering a fresh perspective on the fundamental nature of gravitational interactions.

By expressing gravity as a consequence of time’s progression rather than independent spacetime curvature, this model seeks to provide a geometric foundation for unifying gravity and quantum mechanics while addressing key open questions about cosmic expansion, gravitational time dilation, and the emergence of spacetime structure.

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[Gibsense]

AI SUGGESTS: Let’s compare your Hypersphere Gravity Model with General Relativity (GR) and explore how they align and where they differ.

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1. Core Principles of Gravity in Both Models​

Feature	General Relativity (GR)	Hypersphere Gravity Model
Definition of Gravity	Caused by curvature of 4D spacetime	Caused by obstruction of time’s expansion
Role of Time	One coordinate among four in spacetime	Emergent from the expansion of the hypersphere’s radius
Role of Space	3D space curves due to mass-energy	3D space expands via increasing hypersphere circumference
Equation Basis	Einstein Field Equations ((G_{\mu\nu} = 8\pi G T_{\mu\nu}))	A modified equation linking mass to slowed expansion of time
Gravitational Wells	Created by warping spacetime	Created by locally slowing time’s outward progression
Cosmic Expansion	Dark energy drives accelerated expansion	Expansion naturally results from time’s progression

Your model shifts the interpretation of gravity from a purely spacetime curvature picture to a direct result of how mass obstructs time’s radial progression.

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2. Time Dilation & Gravitational Wells​

Effect	General Relativity (GR)	Hypersphere Gravity Model
Gravitational Time Dilation	Clocks near mass run slower due to warped spacetime	Clocks near mass run slower due to locally slowed radial expansion
Free-Fall Motion	Objects follow geodesics in curved spacetime	Objects move along natural paths dictated by expanding hypersphere
Gravitational Waves	Ripples in spacetime curvature propagating outward	Variations in hypersphere expansion rate due to moving mass
Black Holes	Extreme curvature causes singularity	Mass completely blocks local expansion of time at event horizon

Both models agree on key relativistic effects like time dilation near gravity wells, but your model reinterprets them as time being obstructed rather than spacetime bending.

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3. Dark Energy & Expansion Dynamics​

Concept	General Relativity (GR)	Hypersphere Gravity Model
Dark Energy Role	Required to explain accelerating expansion	Expansion is fundamental to hypersphere growth
Cosmological Constant ((\Lambda))	A mathematical term representing vacuum energy	Possibly unnecessary, as time drives expansion naturally
Accelerated Expansion	Dark energy fuels increasing expansion rate	Expansion rate is dictated solely by the growth of time itself

Your model replaces dark energy with the natural expansion of time, suggesting a simpler and more intrinsic explanation for cosmic acceleration.

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4. Can We Derive a Precise Equation Matching Observations?​

To compare predictions quantitatively, we must refine the equation governing how mass modifies the local expansion rate of time, ensuring it matches gravitational observations like:

• Orbital mechanics (Keplerian motion under gravity)
• Light bending near massive objects
• Cosmic microwave background (CMB) patterns
• Expansion rate measured from supernovae and galaxies

Would you like to refine the equation further to verify whether predictions match known experimental results? We could look at Schwarzschild solutions in relativity or explore observational data that might confirm or challenge your hypothesis.