LN1.1 — Matter-Energy Derivative

Chain Position: 6 of 188

Assumes

A1.1 (Existence) - Something exists
A1.2 (Distinction) - Distinguishability is prior to any property
A1.3 (Information Primacy) - Information is ontologically primitive
D1.1 (Information Definition) - Information reduces uncertainty about states
D1.2 (Bit Definition) - The bit is the minimal unit

Logical derivation: If information is primitive (A1.3), and matter/energy are defined entirely by their informational properties (mass, charge, spin, position = information), then matter/energy are derivative of information. This is modus ponens, not a new axiom.

Formal Statement

If information is primitive, matter/energy are derivative

Spine type: LogicalNecessity
Spine stage: 1

Cross-domain (Spine Master):

Statement: If information is primitive, matter/energy are derivative
Stage: 1
Bridge Count: 0

Enables

LN1.2 (It-From-Bit) - Wheeler’s formalization follows directly
A2.1 (Substrate Requirement) - If matter is derivative, we need the real substrate
The entire χ-field ontology - matter/energy become manifestations of χ
E=mc² reinterpretation - energy-mass equivalence as information-state transformation
Holographic principle - matter encodable as boundary information

Defeat Conditions

To falsify this logical necessity, one would need to:

Reject A1.3 - If information is NOT primitive, the derivation fails
Demonstrate a property of matter/energy that is non-informational - A property that cannot be reduced to a distinction, a measurement outcome, or a bit-string
Define “matter” without using informational terms - Describe what an electron is without mass, charge, spin, position, or momentum

Physical challenge:

Every particle property (mass, charge, spin, color, flavor) is a label — an informational tag
The Standard Model is a classification system for information patterns
Quantum field theory describes matter as excitations of fields — informational modes

No physicist has ever isolated “pure matter” apart from its informational description.

Standard Objections

Objection 1: “Matter is obviously fundamental”

“I can touch matter. Information is abstract.”

Response: You touch electromagnetic repulsion between electron clouds — an interaction described by quantum electrodynamics, itself an informational structure. The “solidity” you experience is the impossibility of two fermions sharing the same quantum numbers (Pauli exclusion) — an informational constraint. Your tactile experience is neural information processing. At no point do you contact “brute matter.”

Objection 2: “E=mc² proves energy is fundamental”

“Mass converts to energy. They’re the primitives.”

Response: E=mc² shows mass and energy are interconvertible — two forms of the same thing. But what is that thing? Both are fully described by informational properties. The equation is a transformation rule between information states, not a claim about ultimate primitiveness.

Objection 3: “The universe is made of particles”

“Particle physics studies fundamental particles, not information.”

Response: “Particles” in modern physics are excitations of quantum fields — localized information patterns. The Higgs field gives mass (information). Gauge bosons mediate forces (information transfer). Fermions have quantum numbers (information labels). The Standard Model is an information-theoretic classification system.

Defense Summary

This is a logical necessity, not an independent claim:

Premise: Information is primitive (A1.3)
Premise: Matter/energy are fully specified by informational properties
Conclusion: Matter/energy are derivative of information

The materialist’s “brute stuff” is a philosophical ghost — undefined, undetectable, and unnecessary. Modern physics already treats matter/energy as information-theoretic structures (quantum fields, gauge symmetries, conservation laws). LN1.1 simply makes explicit what physics already assumes.

Collapse Analysis

If LN1.1 fails:

A1.3 (Information Primacy) must also fail → chain collapses at axiom 3
OR we must accept matter/energy as co-primitive with information → dualism problems
χ-field loses physical grounding → becomes abstract mathematics only
Holographic principle becomes inexplicable → black hole physics fails
Wheeler’s “It from Bit” is false → modern physics interpretations collapse

Collapse radius: STRUCTURAL - Failure here forces rejection of A1.3, unraveling the foundation

Note: If someone rejects LN1.1, ask them: “Define matter without using any informational properties.” They cannot.

Physics Layer

Standard Model as Information Classification

Particles = information labels: Every particle in the Standard Model is defined entirely by its quantum numbers:

Particle	Mass (MeV)	Charge	Spin	Color	Weak Isospin
electron	0.511	-1	1/2	-	-1/2
up quark	2.2	+2/3	1/2	r,g,b	+1/2
photon	0	0	1	-	-
Higgs	125,000	0	0	-	-

Each row is an information packet. The “particle” is nothing but these numbers plus their dynamics (governed by Lagrangian = more information).

Quantum Field Theory

Fields, not particles, are fundamental: $L = \overset{ˉ}{ψ} (i γ^{μ} D_{μ} - m) ψ - \frac{1}{4} F_{μν} F^{μν}$

The Lagrangian density ℒ is a mathematical object—information about how fields interact. “Matter” is excitations of these fields (informational modes).

Feynman diagrams: Encode scattering processes as graphs. Vertices = interaction rules (information). Propagators = field dynamics (information). Cross-sections = probabilities (information).

Mass-Energy Equivalence Reinterpreted

E = mc² as information transformation:

Mass m encodes rest-frame energy information
Energy E encodes total information content
The equation states these are EQUIVALENT information measures
Pair production (γγ → e⁺e⁻): photon information → electron information
Annihilation (e⁺e⁻ → γγ): electron information → photon information

No “stuff” is created or destroyed—information transforms.

Holographic Principle

Black hole entropy (Bekenstein-Hawking): $S_{B H} = \frac{k _{B} c ^{3} A}{4 G ℏ} = \frac{A}{4 ℓ _{P}^{2}} k_{B}$

The entropy (information content) of a black hole scales with AREA, not volume. This implies:

Matter inside the horizon is fully encoded on the boundary
3D “stuff” is an illusion of 2D information
The information IS the black hole

AdS/CFT: Gravity in the bulk ↔ quantum field theory on boundary. “Emergent spacetime” from entanglement patterns.

Conservation Laws as Information Conservation

Noether’s theorem: Every symmetry → conserved quantity

Time translation → energy conservation
Space translation → momentum conservation
Rotation → angular momentum conservation
Gauge → charge conservation

These are INFORMATION conservation laws. The symmetry is an informational pattern; the conserved quantity tracks that pattern through time.

Connection to χ-Field

If matter/energy are derivative:

χ is the substrate from which they emerge
Physical constants (c, ħ, G) are χ-field parameters
Mass/charge/spin are χ-field configuration labels
The Standard Model Lagrangian encodes χ’s self-interaction rules

Mathematical Layer

Category-Theoretic Reduction

Functor F: Phys → Info: Define a category Phys with:

Objects: physical systems
Morphisms: physical processes

Define a category Info with:

Objects: information states
Morphisms: information channels

Claim (LN1.1): There exists a faithful functor F: Phys → Info such that:

F is injective on objects (distinct physical systems → distinct info states)
F preserves composition (physical processes = information processing)

If F exists and is faithful, physics REDUCES to information theory.

Structure-Preserving Maps

Physics isomorphic to information structures:

Hilbert space H ≅ complex vector space (information container)
Unitary evolution U ≅ invertible information transformation
Observables A ≅ Hermitian operators (information extractors)
States ρ ≅ density matrices (information encoders)

The mathematics of QM IS the mathematics of quantum information.

Supervenience

Formal definition: Matter/energy M supervenes on information I iff: $\forall x, y : (I (x) = I (y)) \Rightarrow (M (x) = M (y))$

No difference in M without difference in I. Two systems with identical informational descriptions are physically identical.

Corollary: Physical identity = informational identity. “Matter” has no independent reality.

Wheeler-DeWitt Equation

Quantum gravity suggests timeless information: $\hat{H} ∣Ψ ⟩ = 0$

The Wheeler-DeWitt equation has no time parameter. “Time” emerges from correlations within Ψ. The universe is a timeless informational structure; temporal evolution is internal.

Information-Theoretic Reconstruction of QM

Chiribella, D’Ariano, Perinotti (2011): Quantum mechanics can be derived from purely informational axioms:

Causality (no signaling from future)
Perfect distinguishability
Ideal compression
Local distinguishability
Pure conditioning

QM = unique theory satisfying information-theoretic constraints. This is direct evidence that physics is information theory.

Source Material

01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx (sheets explained in dump)
01_Axioms/AXIOM_AGGREGATION_DUMP.md

Prosecutorial Analysis

Common Sense Truth: The way things look and feel (matter and energy) is just how fundamental patterns (information) show up to us. Accepted by common sense: Requires explanation/analogy, but accepted.

Common Sense Variable: MatterEnergy = Function(Information) (Matter/Energy are manifestations of Information)

Formal Statement: If information is primitive, matter/energy are derivative.

The Prosecutor’s Defense

The Charge: The defendant, representing any worldview that still clings to matter or energy as the ultimate, irreducible ground of reality, is charged with intellectual inconsistency. Having been compelled to accept that reality is fundamentally information (A1.3), we now present the logical conclusion: if information is the blueprint, then matter and energy are merely its manifestations. To deny this is to claim that the house is more fundamental than the blueprint from which it was constructed.

The Cross-Examination:

To the Materialist, who still insists “Matter is primary”: Your definition of “matter” requires properties: mass, charge, spin, position, momentum. Each of these is a distinction (A1.2), and each distinction is a bit of information (A1.3, D1.2). Therefore, “matter” is nothing more than a complex, coherent organization of information. It is not underneath information; it is information, structured. To claim matter is primitive and information is primitive is a contradiction. The more fundamental primitive subsumes the other.
To the Physicist, who posits “Energy is the fundamental currency”: Energy, in every quantifiable form, requires an informational definition. A photon has frequency and wavelength. A field has state and amplitude. These are patterns, distinctions, bits. Consider the equivalence E=mc². This equation does not suggest energy is magically creating matter from nothing. It suggests a convertibility, an interrelationship between two forms of the same underlying reality. If ‘m’ and ‘E’ are both expressions of information (as we have established their constituent properties are), then their interconversion is simply a transformation of informational states.
To the Proponent of an Independent Physical Reality: You seek a “brute fact” beyond information. But what would such a fact be? An existent thing (A1.1) that is indistinguishable from anything else (violates A1.2)? An existent that has no defining properties (violates A1.3)? An existent that cannot be described (violates D1.1)? The moment you define your “independent physical reality,” you define it by its information. You are describing information and calling it something else.

The Verdict:

This is not a mere philosophical assertion; it is a logical necessity. If information is truly ontologically primitive—the deepest layer of reality—then everything we perceive as “matter” or “energy” must logically derive from it. Matter and energy are the output of the informational processing of the universe. They are the content, the display, the manifestation of the underlying code.

The prosecution confirms that matter and energ information y are derivative. Any claim otherwise creates an illogical inversion of causality, akin to claiming the film projection is more fundamental than the digital data on the disc.

The Common Sense Layer (Detailed Explanation)

Imagine the world of a video game. What’s “real” in that game? The characters, the buildings, the explosions. That’s the matter and energy of the game world.

But what’s really driving it all? It’s the code, the 1s and 0s, the information that tells the computer exactly what to draw, how fast to move, how bright to shine. The characters and buildings don’t exist separate from that code. They are that code, brought to life on the screen.

Our universe is the same. When scientists talk about particles, they describe their properties: how much they weigh, their spin, their charge. Those aren’t just features of the particle; those are the particle, as defined by information.

So, matter and energy aren’t some “stuff” that’s just hanging out by itself. They are the ways information organizes itself and expresses itself. They are the dance, and information is the music.

Asset Links

Logos Paper Placeholder:

Title Suggestion: The World as Code: How Information Shapes Matter and Energy.
Central Thesis: This paper will illustrate how the concepts of matter and energy, far from being fundamental, are the necessary and inevitable manifestations of an underlying informational reality, demonstrating the elegance and coherence of the Logos as the universe’s ultimate source code.
Case File Assignment: CF03_Prosecution_of_Materialism

Category: Existence_Ontology/|Existence Ontology

Depends On:

[Existence Ontology](./001_A1.1_Existence]]
002_A1.2_Distinction
003_A1.3_Information-Primacy
004_D1.1_Information-Definition
005_D1.2_Bit-Definition

Enables:

Related Categories:

[Existence_Ontology/.md)

[_WORKING_PAPERS/_MASTER_INDEX|← Back to Master Index

The 188 Axioms of Theophysics

Explorer

006_LN1.1_Matter-Energy-Derivative