Physics Proof: Schrödinger Equation

by

1. Postulate: Wavefunction as a Reality Buffer

In the ATMA-BHAN framework, a Wavefunction (\psi) is a probabilistic “Reality Buffer.” It holds a state in superposition (T_{speculative}) before it satisfies the invariants required for instantiation.

2. ISL Stability Condition

An object exists only if it follows an optimal path where the Trust (T) is maximized against the Complexity (C).
In a dynamic system, the change in Trust over time must be proportional to the Energy (Complexity) of the state:

\Delta T \propto H \cdot \Delta t

In the quantum kernel, Trust (T) is represented by the phase of the wavefunction. If we assume that Time (t) and Energy (H) have a reciprocal relationship similar to x and p:

3. The Refusal Operator

Let the Universe implement a “Maintenance Loop” to ensure that the ISL threshold is not breached during evolution. This loop performs a “Refusal Check” at every interval dt.

To minimize the “Resolution Error” (Risk) of the evolving state, the universe follows the path of least action (Hamilton’s Principle). In the Information Engine, this is equivalent to minimizing the ISL violation.

By assuming the Wavefunction (\psi) is the complex amplitude of a state’s “Ontological Weight,” its evolution must satisfy:

i \hbar \frac{\partial \psi}{\partial t} = \hat{H} \psi

Where:

  • \hat{H} (Hamiltonian): The Total Complexity/Resource Operator.
  • i \hbar \frac{\partial}{\partial t}: The Temporal Stability (Trust) Operator.

4. ISL Interpretation

The Schrödinger Equation is the Universal Pulse. It ensures that for every “Gain” in complexity (\hat{H}), there is a corresponding “Cost” in temporal phase, keeping the ISL score balanced in the stable region (Trust \ge 1.5).

The Refusal Limit

If \hat{H} \psi becomes too large (Singularity/Paradox), the \frac{\partial \psi}{\partial t} term collapses (Measurement/Refusal).

—
🥔 Reality Firewall v2.0 [TOE Edition]

Leave a Comment