# Memory - The Physics of Energy Flow Quick reference for core concepts and key decisions. --- ## Fundamental Ontology **What exists:** - Energy (scalar density u ≥ 0) - Nothing else is primitive **What we observe:** - Energy at different times: u(x,t₁), u(x,t₂) - Continuity: energy doesn't appear/disappear **What follows necessarily:** - Flux S emerges from ∂ₜu + ∇·S = 0 - Divergence-free: ∇·S = 0 (source-free) - Curl dynamics: only way to preserve ∇·S = 0 - Maxwell: minimal description of curl-based flow **What E and B are:** - NOT two separate fields - NOT fundamental - Minimal orthogonal decomposition of flow in 3D - Names for rotational aspects of single helical flow - Reconstructed from (u,S) with 2 free DOF (polarization) --- ## Critical Distinctions ### Description vs Reality - Energy flow is reality - Maxwell equations describe the flow - Mathematics is descriptive, not prescriptive - No "laws that govern" - only descriptions of what flow does ### Representation vs Dynamics - (u,S) are observables - (E,B) are representation choice - Maxwell is minimal dynamics - These are complementary, not competing ### What's Primitive vs Derived - **Primitive:** u(x,t) - **Forced by continuity:** S - **Forced by source-free:** curl structure - **Representation choice:** (E,B) - **Emergent:** particles, mass, ℏ, quantum mechanics --- ## Particles Don't Exist **What we call particles:** - Stable localized flow patterns - Topological knots in electromagnetic flow - Self-sustaining configurations **Properties:** - Mass = trapped energy (E/c²) - Charge = topological property - Spectrum = knot classification - Stability = topology prevents unwinding **No particles means:** - No point interactions - No "crossing" barriers (field was already there) - No true isolation (all same substance) - No outside observer (observer is field too) --- ## Quantum Mechanics is Approximation **Derivation:** - Start with Maxwell wave equation - Extract narrow-band envelope (carrier frequency ω₁₁) - Drop O(ε²) term where ε = Δω/ω₁₁ << 1 - Result: Schrödinger equation **Constants emerge:** - ℏ = E₁₁/ω₁₁ (geometry of fundamental mode) - m = E₁₁/c² (trapped energy) - Not fundamental - geometric properties **Implications:** - QM is approximate, not exact - Deviations scale as ε² - Error term is "causal history" / high-frequency carrier - Testable in high-Q cavities --- ## Paradoxes Dissolved ### Measurement - No collapse - Detector = field structure added to existing field - Total field reorganizes - "Collapse" = conditioning on observation channel - Unitary evolution throughout ### Entanglement - Pseudo-problem - "Two particles" = two peaks in one continuous field - Field was never separate - "Entanglement" = noticing field is continuous - No action at distance - field is already everywhere ### Tunneling - Not penetration of barrier - Field configuration exists everywhere - Barrier = new field structure added later - Field was already in "forbidden" region - Transmission = field continuing to exist ### Double-Slit - Field goes through both slits - Never was a particle - Interference = field interfering with itself - Which-way detection adds interaction potential - Phase shift → interference suppression - Deterministic throughout ### Boundaries - Made of electromagnetic energy - Can't isolate field from field using field - Multipole configurations span barriers - Boundary insertion ≠ field crossing - Field pre-existed boundary --- ## Book Title **The Physics of Energy Flow** Why this title: - Not "laws" but "physics" (nature/behavior) - Energy is the substance - Flow is what it does - Everything else follows --- ## Pedagogical Commitments **From scratch:** - Assume no prior knowledge - Teach calculus from physics - Each concept motivated by necessity **Graduate rigor:** - No handwaving - Every step derived - Approximations tracked explicitly **Field-only language:** - Never introduce particles - No "particle then wave" confusion - Energy flow from page 1 - Avoid "force", "particle" except in quotes **Dissolve, don't interpret:** - Show paradoxes never existed - Don't "resolve" problems - Demonstrate clean conceptual foundation --- ## Key Quotes to Remember "There is no vector field F - only scalar energy density u(x,t) and its evolution." "E and B are not two fields - they are minimal orthogonal decomposition of one flow." "Maxwell is not dynamics - it's our description of how flow behaves." "Particles don't exist - stable localized flow patterns exist." "Entanglement is noticing that the field is continuous." "You can't use field to isolate field from field." "Every experiment is field examining itself." --- ## Common Pitfalls to Avoid - Saying "Maxwell governs" (it describes) - Treating E and B as ontologically separate - Introducing particles "for intuition" - Explaining away paradoxes (show they're not real) - Assuming continuity alone determines dynamics - Forgetting error terms in QM derivation --- ## Next Steps 1. Detailed chapter outlines 2. Mathematical pedagogy strategy 3. Figure/diagram planning 4. Knot theory research for particle spectrum 5. Experimental predictions --- *Last updated: 2026-02-14*