CLASSICAL LAWS
| Principle | Plain Language Concept | Equation / Math Representation | Logic Notation |
|---|---|---|---|
| Definite States | States are definite and distinguishable. | Hamilton's equations: dq/dt = ∂H/∂p, dp/dt = -∂H/∂q | S1 != S2 |- ∃ O (O(S1) != O(S2)) |
| Local Causation | Every change has a local cause. Action at a distance is prohibited. | Local differential equations with finite propagation speed (Maxwell / wave eq): □φ = 0 (d'Alembertian operator) | ∀ y (Change(y) → ∃ x (Cause(x) ∧ Loc(x) ∧ Loc(y) ≠ ∅)) |
| Commutativity | Order of operations does not matter. | Classical observables commute under pointwise multiplication: f(q,p) * g(q,p) = g(q,p) * f(q,p) | ∀ A,B (A ∘ B = B ∘ A) |
| No Retrocausality | The future does not affect the past. | Initial-value problem for hyperbolic PDEs (unique forward evolution from Cauchy surface data) | ∀ A,B p(A | B_future) = p(A) |
| Info Conservation | Information is conserved in isolated systems. | Liouville's theorem (phase-space density conservation): dρ/dt + Σ_i ( (∂ρ/∂q_i)*(dq_i/dt) + (∂ρ/∂p_i)*(dp_i/dt) ) = 0 | I(t₀) = I(t₁) |
| Continuity | Change is continuous. Arbitrarily small changes are possible. | Continuity equation for any conserved density: ∂ρ/∂t + ∇·(ρ v) = 0 | ∀ x ∃ δ (|Δx| < δ) |
| No Minimum Scale | No fundamental indivisible unit of action. | Continuum limit (lattice spacing → 0, no fundamental cutoff): differential equations without discreteness | ¬∃ ε > 0 (Δ ≥ ε) |
QUANTUM RULES
| Principle | Plain Language Concept | Equation / Math Representation | Logic Notation |
|---|---|---|---|
| Operational Definition | Properties only become definite through measurement or interaction. | Born rule / measurement postulate: P(outcome) = ⟨ψ| P̂ |ψ⟩ | ∀ x (Prop(x) ↔ ∃ y Interact(x,y)) |
| Path Interference | Outcomes arise from interference of multiple paths with complex amplitudes. | Feynman path integral: Amplitude = Σ_{paths} exp(iS/ℏ) | Event(e) ⊢ Interference(Σ_{paths} amp) |
| Eigenvalue Measurement | Measurement yields eigenvalues via projection. | Spectral theorem / eigenvalue equation: Q̂ |ψ⟩ = q |ψ⟩ | ∀ Q Val(Q) ∈ Spec(Q̂) ∧ Projection |
| Non-Commutativity | Order of measurements matters. Conjugate observables do not commute. | Canonical commutation relation: [x̂, p̂] = iℏ | [A,B] ≠ 0 → (A ∘ B ≠ B ∘ A) |
| No Retrocausality | The future does not affect past measurement outcomes. | Unitary time evolution (forward only): U(t) = exp(-i Ĥ t / ℏ) (t > 0) | ∀ A,B p(A | B_future) = p(A) |
| Non-Local Correlations | Entanglement-type correlations permitted without FTL signaling. | Bell state correlation: |Ψ⁻⟩ = (1/√2)*(|01⟩ - |10⟩) ⟨σ₁·a σ₂·b⟩ = -a·b | ∃ A,B (Dist(A,B) > 0 ∧ p(A|B) ≠ p(A)) ∧ ¬Signaling |
| Minimum Action Scale | Planck's constant sets a fundamental lower bound on action. | Heisenberg uncertainty principle: Δx · Δp ≥ ℏ/2 | ∃ ε > 0 (Δ ≥ ℏ/2) |
METRIC TENSOR RECONSTRUCTION CRITERIA
| Scientific Principle | Plain Language Concept | Equation / Math Representation |
|---|---|---|
| Lorentzian Manifold Structure | Does the new object preserve or properly replace the fundamental primitives required for 4-dimensional Lorentzian geometry? | 4D Lorentzian manifold (M, g) with signature (-, +, +, +) |
| Non-Degenerate Metric | The fundamental geometric object must remain non-degenerate everywhere. Degeneracy is forbidden. | det(g_μν) ≠ 0 for all x ∈ M |
| Correspondence with GR / Newtonian Limit | The new object must naturally recover all tested predictions of General Relativity and Newtonian gravity in low-curvature regimes. | Weak-field limit recovers Einstein field equations and Poisson equation: ∇²Φ = 4πGρ |
| Causal Structure Preservation | The structure must maintain consistent causality with no permanent disconnection of regions allowed. | Global hyperbolic spacetime: existence of Cauchy surfaces and no closed causal curves |
| Dynamical Metric Reconstruction | The new object must fully account for the role of the classical metric without leaving structural gaps or requiring hidden mechanisms. | Full dynamical recovery of g_μν from the primitive object in tested regimes |
| Minimal Matter-Geometry Coupling | The new object must provide a natural way for matter and energy to couple to the geometry without introducing artificial fields or parameters. | Stress-energy tensor couples directly: G_μν + Λ g_μν = κ T_μν with κ = 8πG/c⁴ |
QUANTUM OPERATOR PRIMITIVE AXIOMS
| Scientific Principle | Plain Language Concept | Equation / Math Representation |
|---|---|---|
| Operator Representation of Observables | The fundamental object must be defined as an operator. | Self-adjoint operators on Hilbert space: † =  |
| Non-Commutativity of Observables | The primitive must have built-in non-commuting operators. | Canonical commutation relations: [x̂, p̂] = iℏ I |
| Primitive Unitarity | The object's evolution must be unitary by construction. | Unitary time evolution operator: U†(t) U(t) = I |
THEORY REQUIREMENTS
| Principle | Plain Language Concept |
|---|---|
| Testable Predictions | Makes new, falsifiable, practically testable predictions consistent with observation. |
| Internal Consistency | No internal contradictions. Renormalizable or UV-complete. |
| No-Go Theorems | Respects Coleman-Mandula and Weinberg-Witten constraints. |
| Noether's Theorem | Every continuous symmetry corresponds to a conserved quantity. |
| Unitarity | Time evolution preserves inner product structure. |
| Probability Preservation | Total probability remains normalized at all times. |
| Recover Known Physics | Reproduces established physics in appropriate limits. |
| Smooth Transitions | Transitions between regimes are continuous. |
| Minimal Parameters | Uses minimal free parameters. Constants derived or strongly justified. |
| Prefer Simpler | Simpler theory preferred when explanatory power is equal. |
| No Causality Violation | No CTCs, no FTL signaling, no fundamental information loss. |
| Entropy Bounds | Respects Bekenstein or covariant entropy bounds. |
| Computable Algorithm | Clear procedure exists to compute predictions from axioms. |
| Well-Defined Evolution | Clear, computable rule for time evolution given any initial state. |
| General Covariance | The laws of physics must take the same form in all coordinate systems (in the context of Gravity/Spacetime). |
| Locality / Cluster Decomp. | The requirement that experiments performed far apart should not influence one another's results (crucial for QFT). |
| Gauge Invariance | If your theory uses fields to describe forces, it almost certainly requires gauge symmetry to be mathematically consistent. |
| Background Independence | The theory should not assume a fixed "stage" of spacetime but should define it (mainly for Quantum Gravity). |
ASSUMPTIONS IN PHYSICS
| Assumption | Plain Language Concept |
|---|---|
| Assumption 1 | Gravity exists at quantum scales. Status: Unverified. Extrapolated from classical observation. No direct experimental evidence at quantum scales. |
| Assumption 2 | Gravity has a quantum carrier (graviton). Status: Unverified. Inferred by analogy with other forces. Graviton has never been detected. |
| Assumption 3 | Quantizing the metric is the correct method. Status: Confirmed to fail mathematically. Produces non-renormalizable infinities at two loops. |
| Assumption 4 | Spacetime is continuous at all scales. Status: Untested below 10⁻¹⁸ meters. Planck scale sits at 10⁻³⁵ meters. No experimental data in that range. |
| Assumption 5 | Laws of physics are the same at all scales. Status: Unverified at Planck scale. Already known to change between classical and quantum domains. |
| Assumption 6 | Time is a background parameter. Status: Directly contradicted by general relativity. GR requires time to be dynamic, not a fixed stage. Both frameworks cannot be simultaneously correct on this point. |
| Assumption 7 | Unitarity must be preserved across quantum-gravity boundary. Status: Unverified as universal requirement. Black hole information paradox is a direct consequence of this assumption conflicting with known physics. |
| Assumption 8 | Vacuum energy is manageable at Planck scale. Status: Contradicted by calculation. Quantum vacuum energy prediction exceeds observed value by 10¹²⁰. Worst quantitative prediction in physics. |
| Assumption 9 | Energy is the correct fundamental quantity to quantize. Status: Problematic. Energy is not globally conserved in curved spacetime. Quantizing a quantity that is not well-defined in the target domain is a structural problem. |
| Assumption 10 | Superposition applies to spacetime geometry. Status: Never observed. All confirmed quantum superposition involves matter and energy fields. No experimental evidence that geometry itself superposes. |
| Assumption 11 | Spacetime is flat for quantum field theory calculations. Status: Known to be technically wrong. Used anyway as approximation. Carried forward unchanged into quantum gravity attempts without re-examination. |
AREAS OF DEBATE
| Topic | Plain Language Concept |
|---|---|
| Cosmological Constant | Observed value matches data. Quantum Field Theory predicts 10¹²⁰ times larger value. Mismatch remains unresolved. |
| Dark Energy | Expansion is accelerating. Recent data suggest the acceleration is not constant and may be weakening. Debate continues on whether acceleration is real or an artifact of data analysis. |
| Dark Matter vs Modified Gravity | Flat galaxy rotation curves are well-established. Two competing explanations: invisible dark matter (mainstream) OR gravity behaves differently at very low accelerations (MOND/critics). |
| Core Impasse | Strong gravity regime (solar system): Theories work well. Weak gravity regime (galaxy outskirts): Clear discrepancy. Quantum regime: Gravity has never been observed; quantizing it leads to contradictions. |