Entanglement Limits

The Entanglement Horizon: Coherence Limits in a Charge-Admittance Universe

Abstract

Entanglement is often treated as non-local and unconstrained by spatial distance, yet in the Charge Admittance (CA) framework, this assumption requires reevaluation. We propose the existence of a maximum entanglement distance, or entanglement horizon, derived from the physical limits of coherent dipole separation in a resistive vacuum. This paper explores how entangled states rely on local field coherence, and how the underlying permittivity (ε0​) an permeability (μ0​) define the maximum spatial separation over which dipole-field coherence — and thus entanglement — can be maintained above vacuum noise. This sets a wavelength-dependent boundary for sustained quantum correlation.

Introduction

Quantum entanglement has been experimentally verified over hundreds of kilometers. However, in CA theory, physical media — not abstract spacetime — dictate interaction potential. If the universe has a definable field impedance structure, then coherence must be field-mediated. Just as there is a shortest wavelength (Planck scale) below which wave-particle duality breaks down due to excessive energy density, there may be a longest wavelength — or lowest frequency — below which coherent dipolar activity is indistinguishable from zero-point noise.

We define this maximum wavelength as:

    \[ \lambda_{\text{max}} = \frac{c}{f_{\text{min, coherent}}} \]

Conceptual Foundation

  • Planck Scale: At the high-frequency/short-wavelength end, energy becomes so concentrated that field collapse or arcing occurs — effectively annihilating coherent information.
  • Coherence Floor: At the low-frequency/long-wavelength end, dipolar separation and field tension become so diffuse that coherence is overcome by thermal or quantum noise.
  • Entanglement Requirement: Coherent phase relationships across space. Without sufficient signal-to-noise ratio, coherence cannot persist.

We propose that the entanglement horizon is defined as:

    \[ d_{\text{ent}} \leq \lambda_{\text{max, coherent dipole}} = \frac{c}{f_{\text{noise floor}}} \]

Impedance and Noise-Defined Boundary

In CA, space’s ability to support coherent transmission is dependent on:

  • The local μ0ε0 product (defines c)
  • The signal strength relative to local stochastic energy (ZPE)
  • Field density gradients and energy “drag”

We model the coherence requirement as a critical threshold:

    \[ \left| \vec{E}_{\text{signal}} \right| > \left| \vec{E}_{\text{vacuum noise}} \right| \]

Once the signal falls below this threshold, entangled systems cannot sustain phase correlation. The maximum wavelength sets the entanglement boundary — not through causal violation, but from field decoherence.

Observational Implications

  • Quantum decoherence becomes an emergent property of the lattice’s spatial extent and local impedance
  • Non-locality is constrained by medium properties, not fundamentally limitless.
  • LIGO and VLF systems already hint at this limitation — requiring extreme precision to detect long-wavelength signals, suggesting coherence difficulty at cosmological distances.

Proposed Experiments and Metrics

  • Define fmin, coherent​ by measuring the signal degradation of entangled systems across increasing distances.
  • Compare entangled photon decay rates with field-noise models in various media (e.g., fiber optics vs. vacuum).
  • Derive theoretical coherence lifetimes using local vacuum permittivity perturbations (modified ε0​ simulations)

Conclusions

In CA theory, entanglement is field-mediated and constrained by coherence boundaries. There exists a longest wavelength — and thus a maximum entanglement distance — dictated by the vacuum’s ability to support a stable dipolar configuration above the noise floor. The entanglement horizon emerges not as a metaphysical boundary, but as a measurable, impedance-defined property of structured space.