Axiom · Chain Position 101 of 346

GEOMETRY FROM INFORMATION

John 1:3 "Through him all things were made"

** Unification occurs through Logos Field as common substrate.

Scripture Bridge
John 1:3 "Through him all things were made": The theological grounding for this concept.

Connections

Objections & Responses
Objection: "Spacetime is obviously fundamental - we experience it directly"
"I can see space, I can feel time passing. How can these be 'emergent'?"
Response

Direct experience is unreliable for fundamental ontology. We also "directly experience" solid matter, yet matter is mostly empty space with quantum fields. We experience a flat, stationary Earth, yet it is round and moving. The phenomenology of spacetime (our experience of it) does not imply that spacetime is ontologically primitive. What we experience as "space" and "time" may be the cognitive interface through which we access underlying information structure, just as what we experience as "color" is our interface to electromagnetic frequencies. The Theophysics claim is that spacetime is real (not illusory) but derivative (emergent from information), just as temperature is real but derivative from molecular motion.

Objection: "Wheeler's 'It from Bit' was speculative philosophy, not physics"
"There's no rigorous physics behind information-first approaches."
Response

This objection is simply outdated. Since Wheeler proposed "It from Bit" in 1990, the idea has received massive theoretical support:

  • Bekenstein (1981): Entropy bounds show information is fundamental
  • Jacobson (1995): Einstein's equations derived from thermodynamics
  • Maldacena (1997): AdS/CFT shows gravity emerges from quantum information
  • Ryu-Takayanagi (2006): Entanglement entropy = geometric area
  • Verlinde (2011): Gravity as entropic force
  • Swingle (2012): Tensor networks build holographic geometry
  • Maldacena-Susskind (2013): ER=EPR unifies entanglement and geometry

"It from Bit" is now a mainstream research program with thousands of papers and a Nobel Prize (for black hole information physics). The objection that it's "just philosophy" reflects unfamiliarity with modern theoretical physics.

Objection: "Information needs a physical substrate - you can't have information without matter"
"Information is patterns in physical systems. No physics, no information."
Response

This objection inverts the causal order. Yes, in our everyday experience, information appears to require physical storage. But the holographic principle shows that physics is information: the maximum information in a region is determined by the boundary area, not the physical volume. This means information is more fundamental than the spatial volume it seems to occupy. The chi-field is the substrate, but it's an informational substrate from which physical spacetime emerges, not a physical substrate that pre-exists information. The objection assumes the conclusion (physics is primary) to argue against the premise (information is primary).

Objection: "AdS/CFT only works in anti-de Sitter space, not our universe"
"Our universe has positive cosmological constant (de Sitter), not negative (anti-de Sitter). Holography might not apply."
Response

This is the most technically sophisticated objection and deserves a careful response:

1. AdS/CFT is proof of concept - It demonstrates that geometry CAN emerge from information. The specific spacetime is secondary.

2. dS/CFT proposals exist - While less developed than AdS/CFT, there are proposals for holography in de Sitter space.

3. Flat space holography - BMS symmetry and celestial holography extend holographic ideas to asymptotically flat spacetimes.

4. Local holography - The Rindler horizon argument (Jacobson) works in any spacetime, not just AdS.

5. Tensor networks don't require AdS - MERA and related constructions can produce various geometries.

The chi-field framework doesn't require AdS specifically; it requires information primacy, which is supported by multiple approaches beyond AdS/CFT.

Objection: "This is unfalsifiable metaphysics masquerading as physics"
"You can't test whether 'geometry comes from information.' It's not science."
Response

The claim is falsifiable through its predictions:

1. Holographic bounds - If information exceeds area/4G, the theory fails

2. Ryu-Takayanagi - If entanglement entropy doesn't match area, the theory fails

3. Emergent gravity effects - Verlinde's theory makes testable predictions about galaxy dynamics

4. Tensor network structure - Specific entanglement patterns should match geometric properties

Moreover, the alternative ("geometry is fundamental") makes no predictions at all - it simply asserts that spacetime exists. Which is more scientific: a framework that makes testable predictions, or a brute assertion of fundamentality?

Physics Layer

Wheeler's "It from Bit" - Complete Statement

Wheeler's formulation (1990):

"Every it—every particle, every field of force, even the spacetime continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits."

Three implications:

1. Participatory universe - Observers don't just record reality; they participate in creating it

2. Information primacy - Bits are more fundamental than its

3. Geometry is emergent - Spacetime itself is derived from information

Theophysics interpretation:

  • The chi-field is the source of all bits
  • Observers are chi-field configurations that elicit bits
  • Spacetime emerges from chi-field information structure
Mathematical Layer

Information Geometry Fundamentals

Statistical manifold:

Let M = {p(x|theta) : theta in Theta} be a family of probability distributions.

Fisher information matrix:

g_{ij}(\theta) = \int p(x|\theta) \frac{\partial \log p}{\partial \theta^i} \frac{\partial \log p}{\partial \theta^j} dx

g_{ij}(\theta) = -\mathbb{E}\left[\frac{\partial^2 \log p}{\partial \theta^i \partial \theta^j}\right]

Riemannian metric:

The Fisher metric defines a Riemannian geometry on the parameter space:

ds^2 = g_{ij}(\theta) d\theta^i d\theta^j

Properties:

1. Positive definite (for regular families)

2. Unique up to scaling (Chentsov's theorem)

3. Invariant under sufficient statistics

Evidence
Empirical Grounding
This isn't philosophy. This is measured.
  • Bekenstein Bound
Defeat Conditions

To Falsify This

  1. **Demonstrate that spacetime geometry is fundamental, not emergent** - Show that the metric tensor g_mu_nu is a primitive entity that cannot be derived from more fundamental information-theoretic structures. This would require disproving the Jacobson derivation of Einstein's equations from thermodynamics, refuting the Ryu-Takayanagi formula, and explaining why holographic bounds exist without information playing a fundamental role.
  2. **Refute the Ryu-Takayanagi formula and its generalizations** - Show that entanglement entropy does NOT equal area/4G_N in AdS/CFT. This would require finding violations of the formula in well-tested holographic systems, contradicting extensive numerical and analytical evidence from thousands of papers in the holographic literature.
  3. **Disprove emergent gravity theories** - Demonstrate that Verlinde's entropic gravity, Jacobson's thermodynamic derivation, and tensor network models of spacetime are all fundamentally flawed. This would require an alternative explanation for why gravity looks thermodynamic and why holographic bounds exist.
  4. **Show that information geometry does not connect to spacetime geometry** - Prove that the Fisher metric on probability distributions has no relationship to physical spacetime metrics. This would contradict the entire information-geometric approach to physics and require explaining the success of these methods as mere coincidence.
Cross-Domain Mappings
Domain Mapping
Physics Emergent spacetime / It from Bit / holographic geometry
Theology Logos as cosmic architect / divine order
Consciousness Mind shapes reality / observer-dependent geometry
Quantum Entanglement builds space / ER=EPR
Scripture John 1:3 "Through him all things were made"
Evidence AdS/CFT / Ryu-Takayanagi / tensor networks
Information Fisher geometry / information manifolds

Bridge Count: 7