Modern Physical Theories as Configurations within ODTOE

QUANTUM, STRINGS, AND EVERYTHING ELSE: MODERN THEORIES AS CONFIGURATIONS WITHIN ODTOE A Unified Map of Physics Through Observer-Dependent Theory of Everything Pankratov Anton Sergeevich Independent Researcher, Kazan, Russia E-mail: [email protected] · ORCID: 0009-0002-4870-2995 UDC 530.145 + 530.12 + 539.1 + 167.7

ABSTRACT Within the framework of ODTOE, it is demonstrated that all major theories of modern physics — quantum mechanics, general relativity, string theory, loop quantum gravity, QBism, integrated information theory, and others — are specific configurations of a unified field of potential states ℋ, each arising under certain values of coherence 𝑆 and observer dimensionality 𝑑. ODTOE is not an alternative to these theories, but a metatheory, within which each of them is a natural special case. A “periodic table of theories” is introduced, organized along two axes: coherence 𝑆 and scale 𝑑. It is shown that “grand unification” of physics is impossible without including the observer in the formalism — and this is precisely what ODTOE does. Keywords: quantum, string theory, GR, quantum gravity, ODTOE, metatheory, observer, coherence, configuration.

I. MAIN THESIS Each theory of physics is a description of one configuration 𝐶𝑖 ∈ 𝒞, constituted by observers with specific parameters (𝑆 , 𝑑, 𝐵). Theories do not contradict each other — they describe different regions of a unified configuration space.

𝑇𝑖 = 𝑂̂𝑖 (Ψ) given 𝑆𝑖 , 𝑑𝑖 , 𝐵𝑖

(I.1)

ODTOE is not yet another theory in a series. It is the space within which all theories exist as configurations. By P6: the number of simultaneous theories 𝑁𝑡ℎ𝑒𝑜𝑟𝑖𝑒𝑠 = 𝑁0 ⋅ (1 − 𝑆)𝑚 + 1. When 𝑆 → 1: one theory. When 𝑆 → 0: infinitely many. All current theories are a result of 𝑆 < 1.

II. WHAT IS A QUANTUM 2.1. Problem: The quantum is not explained, but postulated Quantum mechanics (QM) is the most precise theory in the history of science. But it does not explain its central object. What is a quantum? The standard answer: a minimal portion of energy (𝐸 = ℎ𝜈 ). But why is energy quantized? Why not continuous? QM says: “That’s how the world is structured.” ODTOE answers why. 2.2. Quantum through ODTOE

By axiom (A): 𝑅 = 𝑂(Ψ) . Observation is a discrete act: the operator 𝑂̂ is applied to the field Ψ and constitutes one configuration 𝑅. Not a continuous flow, but a separate act. Each act is one “click” of the transition ℋ → 𝒞. Quantum = minimal act of observation. Not a “portion of energy,” but a portion of constitution. Energy is quantized because observation is discrete. QM

Quantum = minimal portion of energy

Quantum = minimal act of observation 𝛿 𝑂̂ — minimal change in 𝛿𝑅 = 𝛿 𝑂(Ψ) configuration ℎ = “grain” of observation, minimal step of transition ℋ → 𝒞 Photon = 𝛿 𝑂̂ = minimal change of observation operator Ψ ∈ ℋ = field of potential states 𝑅 = 𝑂(Ψ) = act of constitution 𝑃 (𝐸‖𝐵) = 𝐵𝑘 (P4.1), when 𝑘 = 2: Born rule

𝐸 = ℎ𝜈 ℎ (Planck constant) Photon = quantum of field Wave function ‖𝜓⟩ Collapse ‖𝜓⟩ → ‖𝑛⟩ Probability 𝑃 = ‖⟨𝑛‖𝜓⟩‖2

2.3. Why ℏ = ℎ/2𝜋 By [2]: 𝜋 is a structural invariant of self-consistent observation. A complete cycle Φ = 𝜄∘ 𝑂̂ has “length” 2𝜋 (one rotation). The minimal act 𝛿 𝑂̂ is scaled through 2𝜋: ℏ = ℎ/(2𝜋). Planck’s constant is not an arbitrary constant, but the grain of observation, normalized to a complete cycle. 2.4. Wave function collapse — not a mystery The “measurement problem” is the central mystery of QM: what causes “collapse”? The Copenhagen interpretation: “observation.” But what observation is — is undefined.

ODTOE defines: observation = 𝑂(Ψ) = 𝑅. The operator 𝑂̂, depending on the observer (𝐵, 𝐴, 𝐻), is applied to the field Ψ and constitutes a specific configuration 𝑅. “Collapse” is not a physical process, but an act of constitution. Not “the wave function collapses” — but “the observer constitutes a configuration from potentiality.”

III. QUANTUM THEORY: ALL INTERPRETATIONS 3.1. Copenhagen interpretation (Bohr, 1927) Essence: observation causes collapse. Before observation — superposition. Observer is undefined. Through ODTOE: coincides with axiom (A), but ODTOE supplements it: observer is defined through (𝐵, 𝐴, 𝐻), collapse is defined through 𝑂̂, probability is defined through 𝑃 (𝐸|𝐵) = 𝐵𝑘 (generalization of the Born rule). The Copenhagen interpretation is a special case of ODTOE with unspecified 𝑂̂ [1, section 6.1]. 3.2. Many-worlds interpretation (Everett, 1957) Essence: there is no collapse. The wave function branches: all outcomes are realized in different “worlds.” Through ODTOE: P1 expands Everett’s branching: |𝑀𝑡𝑜𝑡𝑎𝑙 | = 𝐾 𝑁(𝑡) . But in Everett, branching is by quantum outcomes. In ODTOE — by observers and configurations. When 𝑆 → 1: one configuration (branches collapse). When 𝑆 → 𝑆𝑚𝑖𝑛 : infinite branching. Everett is a special case of ODTOE at 𝑆 = 𝑆𝑚𝑖𝑛 [1, section 6.2]. 3.3. QBism (Fuchs, Schack, 2002) Essence: a quantum state is not a property of the system, but an agent’s belief. Probabilities are subjective. Through ODTOE: coincides with D1.1 (B — contextual belief). But ODTOE adds: (i) internal structure of belief (𝐵 = 𝐹 ⋅𝐸 ⋅(1−𝜎)⋅Λ), (ii) collective effects (P5), (iii) extension beyond the quantum domain. QBism is a special case of ODTOE for one observer in the quantum domain [1, section 6.4]. 3.4. Relational QM (Rovelli, 1996) Essence: physical quantities are defined only relative to a specific observational system.

Through ODTOE: exact coincidence with axiom (A): 𝑅 = 𝑂(Ψ) — reality is relative to the operator. But ODTOE parameterizes the observer: (𝐵, 𝐴, 𝐻) allows one to compute the difference between observers, which Rovelli does not do [1, section 6.6]. 3.5. Quantum Darwinism (Zurek, 2003) Essence: classical properties emerge through “replication” of information in the environment. The environment is a “witness.” Through ODTOE: pointer states = configurations with high 𝐼(𝐶) (inertness). Decoherence = growth of 𝑆 in a cluster of observers. When 𝑆 → 1: one configuration = “classical” world [1, section 6.9]. 3.6. Summary table of quantum interpretations

Interpretation

Central idea

ODTOE-equivalent

What ODTOE adds

Copenhagen

Collapse upon observation

𝑅 = 𝑂(Ψ)

Parameterization of 𝑂̂ through

(𝐵, 𝐴, 𝐻) Everett QBism

Branching without ‖𝑀 ‖ = 𝐾 collapse State = agent’s belief 𝐵(𝑂, 𝐶)

𝑁(1−𝑆)

Continuous transition through 𝑆 Belief structure:

𝐹 , 𝐸, 𝜎, Λ Rovelli Zurek Hameroff-Penrose

Menskii

Relativity of description Environment as witness Consciousness through quantum coherence Consciousness chooses Everett branch

Axiom (A)

𝐼(𝐶), 𝑆 of cluster 𝐵= 𝐹 ⋅ 𝐸 ⋅ (1 − 𝜎) ⋅ Λ 𝑂̂ depends on (𝐵, 𝐴, 𝐻)

Computability of observer differences Quantitative model of decoherence Formula B as analogue of Φ in IIT Quantitative mechanism of “choice”

IV. GENERAL RELATIVITY 4.1. What is GR Einstein (1915): spacetime is not a background, but a dynamical entity. Mass curves spacetime, curved spacetime determines the motion of masses. Einstein equations: 𝐺𝜇𝜈 = 8𝜋𝐺 ⋅ 𝑇𝜇𝜈 . 4.2. GR through ODTOE Spacetime is a configuration 𝐶𝑆𝑇 ∈ 𝒞, sustained by “extremely high level of coherence 𝑆 of macroscopic observers” [1, section 6.3]. GR

Spacetime is a fundamental entity

Spacetime is a stable configuration at

𝑆→1 Metric 𝑔𝜇𝜈 Curvature (Riemann tensor) 𝑇 (𝐶𝑆𝑇 ) → cosmological scales Classical (deterministic)

Configuration parameters 𝐶𝑆𝑇 Gradient of potential ∇𝑈 (𝐶) 𝑇 (𝐶) = 𝑇0 /(1 − 𝑆)𝑛 when 𝑆 → 1 𝐷(𝜂) = 𝐷0 (1 − 𝑆) → 0 when 𝑆 → 1: stochasticity suppressed ODTOE: observer in formalism

Does not contain observer

Key conclusion: GR is the limiting case of ODTOE when 𝑆 → 1 and 𝑑 ≫ 1 (macroscopic observer). Under these conditions, the stochastic term is suppressed (𝐷(𝜂) → 0), the dynamics is quasi-deterministic, and the system is described by smooth geometry — Einstein equations.

V. STRING THEORY 5.1. What is string theory String theory (1960s — present): fundamental objects are not point particles, but onedimensional “strings.” String oscillations produce various particles. Requires 10 or 11 dimensions (6–7 are “compactified”). Landscape ∼ 10500 possible vacua. 5.2. String theory through ODTOE String theory

String is a fundamental object

There is no fundamental object. There is 𝑂̂ and Ψ Different 𝑂̂𝑖 → different configurations 𝑅𝑖 Infinite dimensionality of ℋ. 10/11 is a specific configuration ‖𝑀 ‖ = 𝐾 𝑁(1−𝑆) — multiverse from P1 Observer with 𝑑 < 10 cannot actualize 10-dimensional configuration (D-Prot) ODTOE: observer in formalism

String oscillations → particles 10/11 dimensions

10500 vacua (landscape) No experimental confirmations Does not contain observer

Key conclusion: string theory is one of the configurations 𝐶string ∈ 𝒞. Its 10500 vacua are a subset of |𝑀 | from P1. We cannot verify it not because “there isn’t enough energy,” but because 𝑑(human) < 10: by D-Prot, an observer is unable to actualize configurations of dimensionality higher than its own. String theory sees the correct landscape of possibilities — but does not know who selects from the landscape. ODTOE answers: an observer with (𝐵, 𝐴, 𝐻).

VI. LOOP QUANTUM GRAVITY 6.1. What is LQG Loop quantum gravity (Rovelli, Smolin, 1990s): spacetime is quantized. The minimal unit of space is a “loop.” Spin networks describe quantum geometry. 6.2. LQG through ODTOE LQG

Space is quantized (discrete)

Space is a configuration, discreteness = discreteness of acts 𝑂̂ Minimal act of observation = 𝛿 𝑂̂, scale — ℏ Network of observers with coherence 𝑆

Minimal length (Planck) Spin networks

LQG

Loops

Φ = 𝜄 ∘ 𝑂̂ — loop of observation at Planck

No matter in formalism

scale ODTOE: matter = configuration sustained by observers

Key conclusion: LQG is ODTOE at the Planck scale (𝑑 = 0, 𝑆 → 𝑆𝑚𝑖𝑛 ). The “loops” of LQG are literally loops of observation Φ = 𝜄 ∘ 𝑂̂, wrapped into minimal elements of space.

VII. OTHER MODERN THEORIES 7.1. Quantum Field Theory (QFT) QFT

Field is a fundamental entity Particle = field excitation

Field = ℋ (potential states) Particle = 𝛿𝑅 = 𝛿 𝑂(Ψ) — minimal configuration Vacuum = configuration with 𝐼(𝐶) → 0,

Vacuum = ground state

𝑆 → 𝑆𝑚𝑖𝑛

Fleeting configurations with 𝑇 ≈ 𝑇0 Self-consistency through Ψ∗ = Φ(Ψ∗ )

Virtual particles Renormalization

7.2. Standard Model Standard Model

17 elementary particles 4 interactions

17 stable configurations at given 𝑆 and 𝑑 4 types of connections between coherence clusters ℋ at the macroscale: potentiality imparting “mass” (inertness 𝐼(𝐶)) GR = ODTOE at 𝑆 → 1. SM = ODTOE at 𝑆 < 1. Gap — in different 𝑆

Higgs field Does not include gravity

7.3. Integrated Information Theory (IIT, Tononi) IIT

Φ — measure of integrated information

𝐵 = 𝐹 𝑤1 ⋅ 𝐸 𝑤2 ⋅ (1 − 𝜎)𝑤3 ⋅ Λ𝑤4 —

Consciousness = Φ > 0 Neural substrate Does not extend beyond neurophysiology

measure of coherence Observer = 𝐵 > 0 ODTOE: any substrate (P1: any observer) ODTOE: from atom to Universe

7.4. Free Energy Principle (Friston) Friston

Brain minimizes prediction error Generative model of world Active inference

Observer minimizes ∇𝑈 (𝐶) by P2 𝑂(Ψ) = 𝑅 — configuration constitution Reconfiguration:

Markov blanket

𝑑𝐶/𝑑𝑡 = −𝛼/(𝐼 + 𝜀) ⋅ ∇𝑈 + 𝜂 𝑆𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 : boundary of coherence cluster

7.5. Computational Physics (Wolfram) Wolfram ODTOE Universe = computation Universe = self-observation: Ψ∗ = Φ(Ψ∗ ) Cellular automata Φ𝑛 — iteration of observation loop Rule = foundation Axiom (A) = foundation. Rules are configurations No observer ODTOE: observer is central element

7.6. Holographic Principle (t’Hooft, Susskind) Holographic principle

Information about 3D volume is encoded on 2D boundary AdS/CFT

Configuration of high dimensionality 𝑑 is observable from dimensionality 𝑑 − 1 Connection between configurations of different dimensionalities through D-Prot 𝑆𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 — boundary of cluster, on which information is “projected”

Boundary = “screen”

VIII. PERIODIC TABLE OF THEORIES All theories are organized along two axes: coherence 𝑆 (horizontal) and scale/dimensionality 𝑑 (vertical): S → S_min (desynchronized) d → ∞ (cosmos)

Multiverse (Everett, P1)

d = 3-4 (macro)

Quantum field theory

d = 1-2

S ~ 0.5 (partial) Cosmology Hawking-Hertog

Standard Model

Quantum

Chemistry

S → 1 (full) GR (Einstein) Classical mechanics Classical physics Thermodynamics

(meso)

mechanics

d = 0 (Planck)

Loop QG Strings

d = -1

Sub-Planck (?)

Region 𝑆 Lower left 𝑆𝑚𝑖𝑛 Lower right Upper left 𝑆𝑚𝑖𝑛 Upper right Center 0.5

∞ ∞ 2-3

Biology Atomic physics [3] Quarks Gluons

Nuclear physics Confinement

𝑑 Theory ODTOE-status

LQG, Strings Nuclear physics Multiverse GR, classical Standard Model, chemistry, biology

Maximum quantumness, minimal scale Full coherence at atomic level Maximum branching Single deterministic reality Intermediate regime

IX. WHY UNIFICATION FAILS 9.1. Problem Physics has been trying for 100 years to unite GR (gravity, 𝑆 → 1, macro) and QM (quanta, 𝑆 < 1, micro). It doesn’t work. Why? 9.2. ODTOE’s answer Because GR and QM are different modes of one system, not “different theories of one world.” They differ in the value of 𝑆 : • QM: 𝑆 < 1 → stochastic term 𝜂(𝑡) dominates → probabilities, superposition, uncertainty • GR: 𝑆 → 1 → 𝐷(𝜂) → 0 → determinism, smooth geometry, curvature To unite them = find a formula that contains both limits. In ODTOE it already exists:

𝑑𝐶 𝛼 =− ∇𝑈 (𝐶) + 𝜂(𝑡), 𝑑𝑡 𝐼(𝐶) + 𝜀

𝐷(𝜂) = 𝐷0 (1 − 𝑆)

When 𝑆 → 1: 𝐷(𝜂) → 0, stochasticity vanishes → GR. When 𝑆 → 𝑆𝑚𝑖𝑛 : 𝐷(𝜂) → 𝐷0 , stochasticity is maximal → QM. One equation. Two limits. One parameter 𝑆 . This is why “unification” fails within frameworks that do not include the observer: without 𝑆 there is no continuous transition between quantum and classical.

X. CONCLUSION 10.1. Quantum — not a mystery Quantum = minimal act of observation 𝛿 𝑂̂. Discreteness is a property of observation, not “the world itself.” ℎ is the “grain” of observation. Collapse is not a mystery, but a definition: 𝑅 = 𝑂(Ψ) . 10.2. All theories are configurations Each theory of physics is a configuration 𝐶𝑖 , constituted under specific 𝑆 and 𝑑. They do not contradict each other — they describe different regions of a unified ℋ. 10.3. Observer — the missing element For 100 years physics has tried to unite theories without the observer. This is like assembling a puzzle without the central piece. ODTOE inserts this piece: 𝑂̂ with parameters (𝐵, 𝐴, 𝐻) and coherence 𝑆 . 10.4. Formula

𝑅 = 𝑂(Ψ). QM = 𝑆 < 1. GR = 𝑆 → 1. Everything else is between them. 𝑆 is the key.

ACKNOWLEDGMENTS AND TOOLS In the development of ODTOE theory and all articles based on it, the following artificial intelligence tools were used: Claude Sonnet / Opus 4.6 Extended (Chat & Code) (Anthropic), ChatGPT 5.3 (OpenAI), Google Gemini (Google DeepMind). All substantive decisions belong to the author.

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