Vorton Slip in Linear and Rotational Geometries

Vorton Slip in Linear and Rotational Geometries

A Formal AMS Description with Comparison to Classical Electromagnetism

Abstract

This article presents a formalized mathematical description of vorton slip within the Aetheric Magnetic Substrate (AMS) ontology. Motion is treated as coherent torsional phase migration constrained by geometry, rather than as force-driven particle transport. Linear and rotational boundary conditions are derived explicitly and shown to produce superconducting current flow and biological rotary motion respectively. An appendix contrasts this formulation with classical electromagnetic equations, clarifying points of agreement, divergence, and reinterpretation.

1. Ontological Assumptions

The AMS framework adopts the following foundational assumptions:

  1. Physical space is a continuous torsional substrate.
  2. Stable matter corresponds to topologically bound torsional configurations (“vortons”).
  3. Motion arises from coherent phase migration of torsion, not from net force acting on particles.
  4. Dissipation occurs only through loss of phase coherence or topological integrity.

These assumptions define the scope and limits of the formalism.

2. Fundamental Fields and Quantities

Let:

  • Φ(x, t): torsional phase field
  • τ(x, t): torsional tension density
  • ρₜ: coherent torsional density
  • κ: torsional mobility constant
  • χ ∈ {+1, −1}: chirality parameter
  • Γ: geometric constraint operator

The torsional phase gradient is defined as:

∇Φ = ( ∂Φ/∂xᵢ )

3. Vorton Slip Equation

Vorton slip is defined as coherent phase transport under sustained topology:

vₛ = κ ∇Φ

Key properties:

  • vₛ is not a particle velocity
  • No mass transport is implied
  • Slip exists only while Φ remains coherent

This equation is the AMS analogue of drift velocity, but without resistance terms.

4. Linear Geometry (Superconducting Current)

For linear or closed-loop translational geometries:

Γᴸ(Φ) = ∂Φ/∂x

The resulting current density is:

J = ρₜ vₛ = ρₜ κ (∂Φ/∂x)

This formulation implies:

  • Constant current for constant phase gradient
  • Persistence without applied voltage
  • No Joule dissipation while coherence is preserved

Resistance emerges only when:

⟨(δΦ)²⟩ ≠ 0

i.e. when phase coherence degrades.

5. Rotational Geometry (Biological Torque)

For closed rotational geometries parameterized by angle θ:

Γᴿ(Φ) = ∂Φ/∂θ

Angular vorton slip velocity:

ω = κ (∂Φ/∂θ)

The mechanical torque arises as constrained torsional release:

τ_mech = dLₜ/dt

where Lₜ is the torsional angular momentum of the bound configuration.

This formulation does not require an intermediate energy conversion step.

6. Direction Reversal via Chirality Inversion

Directional reversal occurs through chirality inversion:

χ → −χ ⇒ ω → −ω

No inertial braking or energetic reset is implied, consistent with observed instantaneous reversal in biological rotary systems.

7. Clutching and Topological Decoupling

Mechanical decoupling is expressed as a reduction in coupling constant:

κ → 0

The phase gradient remains:

∇Φ ≠ 0

But torsional expression into mechanical motion ceases. The field persists without dissipation.

8. Dissipation Criterion

Dissipation arises when phase coherence collapses:

∂Φ/∂t → stochastic

Resulting power loss:

P_loss ∝ ρₜ ⟨(δΦ)²⟩

This replaces resistive loss terms with coherence failure terms.

9. Unified Expression

All expressions reduce to:

Motion = Γ( κ ∇Φ )

Geometry determines the mode of motion; coherence determines efficiency.

Appendix A: Contrast with Classical Electromagnetism

A.1 Classical Current Model

Ohmic current is described by:

J = σ E

with dissipation:

P = J · E

Energy loss is unavoidable due to charge scattering.

A.2 AMS Reinterpretation

In AMS:

  • Electric field corresponds to imposed torsional phase gradient
  • Charge is a manifestation of torsional configuration
  • Current is phase migration, not particle drift

No intrinsic dissipation term exists unless coherence is broken.

A.3 Maxwell’s Equations (Contextual Mapping)

Maxwell Term AMS Interpretation
E Torsional phase gradient
B Static torsional equilibrium
Induction Phase reconfiguration
Radiation Propagating torsional disturbance

AMS does not invalidate Maxwell’s equations; it reframes them as emergent descriptions of torsional dynamics.

A.4 Superconductivity as a Boundary Case

Classical electromagnetism treats superconductivity as an exception requiring special quantum states.
AMS treats it as the natural limit of preserved torsional coherence under ideal boundary conditions.

Conclusion

By formalizing vorton slip in linear and rotational geometries, the AMS framework provides a unified, non-dissipative description of superconducting current and biological rotary motion. Classical electromagnetic equations remain effective macroscopic tools, but AMS offers a deeper structural interpretation in which efficiency arises from coherence rather than energy conversion.

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