Chirality and Helicity from Double Spin Field Geometry

Introduction: Chirality and helicity are central to understanding the behavior of fermions in quantum field theory. Traditionally treated as abstract mathematical features, these properties can take on deeper significance when reconsidered from a geometric and field-dynamic perspective. This article introduces a novel approach in which the electron is modeled as a composite structure exhibiting two distinct types of rotational motion—an internal rotation embedded in vacuum field space and an external spin observable in three-dimensional spacetime.

We propose that the internal spin, or 'vacuum twist,' is responsible for chirality, while the external rotation determines the particle’s helicity through its alignment with momentum. This double spin framework not only clarifies the physical distinction between chirality and helicity, but also provides a natural mechanism for mass generation through vacuum synchronization. The model aligns with emerging ideas in field-based theories and offers new avenues for unifying quantum behavior with gravitational dynamics.

1. Defining Double Spin

We assume the electron possesses two rotational components:

• Inner Spin: Represents a rotation in vacuum field space, associated with vacuum phase synchronization. This defines chirality.
• Outer Spin: A rotation in real 3D space, generating the observable magnetic moment. Its projection onto the direction of motion defines helicity.

Diagram A: Double Spin Field Structure

2. Chirality and Helicity Definitions

Chirality is defined as the handedness of the internal vacuum rotation:

\[ \chi = \begin{cases} +1 & \text{if internal spin is right-handed} \\ -1 & \text{if internal spin is left-handed} \end{cases} \]

Helicity is defined as the projection of the outer spin vector onto the momentum direction:

\[ h = \frac{\vec{S}_{\text{ext}} \cdot \vec{p}}{|\vec{S}_{\text{ext}}||\vec{p}|} \]

Diagram B: Helicity Frame Dependence

3. Mass from Vacuum Synchronization

In this model, mass arises from the synchronization of left- and right-chiral field states across a vacuum phase delay. This replaces the traditional Higgs mechanism with a geometric field interaction:

\[ \mathcal{L}_{\text{mass}} = g \bar{\psi}_L \Phi \psi_R + \text{h.c.} \]

Here, \( \Phi \) is not a scalar Higgs field, but a synchronization field derived from the vacuum’s phase memory.

Diagram C: Chirality Synchronization

4. Interpretation and Consequences

• Chirality becomes a geometric feature of the internal field twist.
• Helicity reflects the kinematic state of the electron in space.
• Mass results from stable coupling between opposite chirality states via vacuum synchronization.
• Weak interaction couples only to left-chiral fields due to asymmetry in internal vacuum field configuration.

5. Summary

Concept	Standard Meaning	Double Spin Interpretation
Chirality	Abstract handedness of spinor	Inner vacuum field rotation
Helicity	Spin \(\cdot\) momentum	Outer spin projection on motion
Mass	Higgs coupling \( \psi_L \leftrightarrow \psi_R \)	Vacuum synchronization delay
Weak force	Left-chiral interaction only	Allowed by internal field geometry

6. The Moon Analogy: Understanding Chirality and Helicity Through Orbital Rotation

To better visualize the distinction between chirality and helicity, we can draw a useful analogy from celestial mechanics—specifically, the complex rotation of the Moon.

The Moon experiences three kinds of motion:

• Self-Rotation: The Moon rotates once on its axis every 27.3 days, which defines a stable, intrinsic spin. This is analogous to chirality in the electron, representing internal rotational structure.
• Orbit Around Earth: Also every 27.3 days, this orbit keeps the same side of the Moon facing Earth due to tidal locking. This synchrony resembles the mass-generating coupling between left- and right-chiral states in fermions.
• Orbit Around the Sun: The Moon follows Earth in its annual orbit, analogous to the momentum vector of the electron, which sets the direction used to define helicity.

When we sum all three rotational components as angular velocity vectors in space, we get a net spin axis. This is directly analogous to an electron’s helicity: the projection of its spin along its momentum vector.

Just as the Moon’s self-rotation (chirality) remains fixed while its total orientation (helicity) may appear different in varying frames of reference, an electron’s helicity can flip under a Lorentz boost, but its chirality remains invariant. The analogy reinforces the idea that chirality is an internal, geometric field property, while helicity is frame-dependent and observable in motion.

This planetary model offers an intuitive picture of how nested rotational dynamics can yield the same kinds of symmetry relationships that define quantum spin behavior—especially in field-based theories that go beyond point-particle models.