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From Force to Geometry: A New View of Reality

A plain-language version of “From Force to Fractal”

4 min readNo jargon, no mathematicsPhysics

The short version

This paper proposes that the universe is not made of forces and particles, but of pure geometric structure. The author combines two ideas to argue that space itself has a fractal, "gappy" nature at the smallest scale, which would explain why quantum physics seems random and why current theories need awkward fixes.

Why old ideas fall short

For centuries, scientists used "force" as a handy label for how things push and pull. This worked well enough, but it described what things *do*, not what they *are*. Einstein made the first big break from this habit. He showed that gravity is not a force at all. It is simply the curvature of space itself. This was a huge step forward. But other parts of physics still cling to force-like ideas. The Standard Model of particle physics, for all its success, treats particles as tiny objects that carry forces between other objects. This creates an awkward split. Gravity is geometry, but the other forces are particle exchanges. The paper argues this split must end.

A philosophy of structure over stuff

The paper adopts a view called Ontic Structural Realism. This is the belief that relations between things matter more than the things themselves. In everyday life, we think objects come first and then interact. But modern physics suggests the opposite. The pattern of connections is the true reality. The "objects" are just where those connections meet. It also helps make sense of quantum particles, which lack fixed identities and seem defined only by their properties and connections. The paper uses this philosophy as a guiding principle, not just an afterthought.

The fractal turn

The next step is to question the smoothness of space itself. Einstein's geometry assumes space is continuous, like a sheet without gaps. But problems in quantum physics hint that this smoothness might be an illusion. Invariant Set Theory, developed by Tim Palmer, proposes instead that the universe evolves on a fractal attractor. This means the underlying structure is full of tiny gaps. It is not continuous at all. The paper calls this the "Fractal Turn." It moves from a smooth map to a textured territory. The fractal structure would be naturally resistant to the infinities that plague current theories.

How observers see smoothness

If space is gappy, why does it look smooth to us? The paper introduces "Metric Resolution" to explain this. Think of looking at a photo on a screen. If you stand far back, the picture looks smooth. Step closer, and you see pixels. Similarly, our human and technological limits keep us far from the tiny Planck-scale gaps. We perceive a blurred, continuous world. This blurring creates the useful but misleading concepts we call "force" and "quantum probability." They are not features of reality itself. They are artifacts of our limited view. The paper calls this boundary the "Information Horizon."

What the simulations showed

The author ran numerical simulations to test these ideas. The simulations used spectral dimensions and p-adic distance metrics. P-adic numbers are a way of measuring gaps in number theory, like counting how divisible a number is rather than how large it is. The simulations found that the effective dimension of space drops from four to about one and a half at the smallest scale. This matches known fractal patterns like the Sierpinski gasket. This "dimensional reduction" means quantum calculations would naturally stay finite. No awkward cut-offs would be needed. The gappy structure itself solves the renormalization problem.

What this does and does not mean

It suggests our current physical laws are high-resolution maps of a territory we cannot fully resolve. However, the paper openly states that direct observation at the Planck scale remains far beyond current technology. The "Crystalline Hypothesis" needs experimental proof. Future work might use gravitational wave detectors, high-energy colliders, or cosmic background radiation to find signs of fractal texture. The paper also notes that full mathematical development is incomplete. A complete "calculus on fractals" does not yet exist. The philosophical implications for human choice and ethics in a deterministic, timeless universe are left for future exploration.

Words used here

fractal
a shape that looks similarly complex no matter how much you zoom in, like a coastline that keeps showing new detail
invariant set
a special collection of points that a system keeps returning to, like water circling a drain in a stable pattern
ontic
having to do with what things really are, deep down, as opposed to what we merely know about them
p-adic
a way of measuring numbers based on their divisible structure rather than their size, useful for describing gap-filled spaces
renormalization
the awkward mathematical fixes currently needed to stop quantum calculations from blowing up to infinity
spectral dimension
a measure of how many directions something can effectively move in, which can change depending on the scale you look at

Learn more in plain language

This plain-language version was written by an AI model from the text of the paper and checked against plain-language rules: everyday words, no mathematics, no unexplained names. It leaves details out and can still be wrong; the paper is the source of record. To report a problem, open the paper, select the passage and choose Report.

For specialists: the technical digest, quoted from the paper

In the paper's words

The transition from force-based epistemic placeholders to a purely geometric ontic bedrock represents the defining trajectory of modern theoretical physics. By synthesizing Ontic Structural Realism with contemporary developments in Invariant Set Theory, we propose a unified framework where reality is modeled as a hyperdimensional fractal manifold. We utilize numerical simulations of spectral dimensions and p-adic distance metrics to demonstrate the “gappy” nature of the ontic bedrock at the Planck scale.

The abstract, verbatim; every line below is quoted from the text.

What it claims

It asserts that the state space has a fundamental periodicity,

Numbers it reports

  1. In this proxy, a walker attempts to move in a random direction, but the move is rejected with a certain probability if it lands on a “gap.” This “Fractal Constraint Factor” (set to 20% rejection in our base model) statistically mimics the lacunar structure of a deterministic fractal like the Sierpinski gasket.

    from 4.6 Numerical Simulation

  2. This drop represents a 21% reduction in the available degrees of freedom for information propagation.

    from 5.1 Spectral Dimensions

  3. This means that the “gaps” between the valid states constitute 100% of the volume of the state space.

    from 2.3 Invariant

  4. It implies that the “gaps” between valid states occupy 100% of the volume of the state space.

    from 4.3 The

  5. In a standard continuous plenum, the integration measure $d^4x$ is non-zero everywhere, allowing for the accumulation of infinite energy densities at a point.

    from 5.2 The Vanishing Measure of

  6. If we knew the full p-adic expansion of the state, we could predict the outcome with 100% certainty.

    from 5.5 Bell-Test

How it is done

  1. This approach allows for a rigorous formalization of the “Flatlander” constraint, characterizing quantum indeterminacy not as a fundamental blurriness, but as a geometric boundary of the observer.

    from A

  2. and Its Discontents The Standard Model of particle physics represents a pinnacle of predictive success while simultaneously relying on a vast array of epistemic placeholders.

    from 1.3 The Standard Model

  3. This “smearing” of the bedrock creates the functional summaries we use to navigate the world, such as the “force” of gravity or the “probability” of a quantum event.

    from 1.6 Metric

  4. It sets the stage for extending this structuralist approach to the quantum domain, where the geometry may become far more complex.

    from 2.1 Ontic Structural

What would falsify it

  1. If the bedrock of reality is a fractal set, then the structural relations must be defined using non-Archimedean geometry.

    from 2.1 Ontic Structural

  2. If the bedrock is non-computable, then no finite algorithm can compress it further.

    from 2.2 The Epistemic/Ontic

  3. If the structure were not preserved—if the laws of physics changed completely at the Planck scale—then we would have no guide for building a theory of quantum gravity.

    from 3.4 Scale-Relative

Where the claim stops

  1. Our findings demonstrate that the spectral dimension of spacetime reduces from four to approximately 1.58 at the Planck scale, a result consistent with fractal-constrained manifolds such as the Sierpinski gasket.

    from A

  2. However, the Riemannian framework demonstrated that the “mediator” was in fact the metric properties of the manifold itself.

    from 1.2 The Riemannian Precedent

  3. While Riemannian geometry successfully eliminated the “force” of gravity, it maintained the assumption of a continuous, infinitely divisible spacetime plenum.

    from 1.5 The Fractal Turn

Where to read

  1. A274 words · 1 min
  2. 1.0 Introduction: The Ontic1,032 words · 4 min
  3. 2.05,269 words · 23 min
  4. 3.04,641 words · 20 min
  5. 4.04,795 words · 21 min
  6. 5.04,395 words · 19 min
  7. 6.04,773 words · 21 min
  8. 7.0 Conclusion:3,915 words · 17 min
  9. Appendices1,041 words · 5 min

Read from the paper itself: 68 sections, 30,343 words. Nothing in this digest is written by a model; a line that is not a sentence of the paper is not shown. Have a specific question? Ask this paper.

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