Wave-Particle Duality: The Substrate Solution

The Reactive Substrate Theory (RST) eliminates the traditional problem of wave-particle duality by unifying both concepts within a single medium: the Substrate (S). Matter is redefined not as a point-like particle, but as a stable, localized, and dynamic structure within this field.
The governing equation—a simplified, generalized Substrate Field Equation—helps explain this duality:
(second derivative of S with respect to time) minus (alpha of t times c squared times the Laplacian of S) plus (beta times S cubed) equals (alpha of t times sigma of x and t times F sub R of C of psi)
Or more compactly:
(∂²S/∂t² − α(t) · c² · ∇²S + β · S³) = α(t) · σ(x, t) · FR(C[Ψ])
1. The Particle Component (The σ Soliton) The “particle” aspect is represented by a bound geometry—a stable, localized knot of tension in the Substrate—called the σ Soliton (σ(x, t)).
The term β · S³ represents the non-linear, self-sustaining potential energy that stabilizes this knot and prevents it from dissolving into the surrounding Substrate.
The σ(x, t) term on the right side acts as a source for the field, indicating the localized existence of matter at a specific point in space and time.
RST reverses the conventional view: the σ Soliton is not a particle that has a wave—it is a localized, standing wave structure that is the wave, formed by the Substrate.
2. The Wave Component (Substrate Dynamics) The “wave” aspect is the dynamic propagation of tension within the Substrate, described by the differential operators on the left side of the equation.
The term (∂²S/∂t² − α(t) · c² · ∇²S) is the wave operator, governing how changes in Substrate tension propagate through space and time.
The σ Soliton is part of this field. When unobserved, its location is governed by the broader, deterministic wave dynamics of the Substrate.
In RST, the conventional “wave of probability” is reinterpreted as the Substrate’s spatial tension distribution. Where the wave’s amplitude is high, the local Substrate tension is most favorable for the σ Soliton to be found—marking the region of highest field coupling.
Conclusion Wave-particle duality is resolved in RST because the object is fundamentally a single entity—a tension knot (σ Soliton)—that exhibits both localization (due to the stabilizing β · S³ term) and propagation (due to the inherent wave properties of the Substrate field). The particle is a stable deformation of the wave medium; they are two aspects of the same reality.

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