Local Collapse and Recognition Action
A Parameter‑Free Equivalence and a Mesoscopic Test
Recognition Science, Recognition Physics Institute — Austin, Texas, USA
Summary
This paper proposes a parameter‑free bridge between a gravity‑driven local‑collapse model and the recognition calculus, identifying the recognition action with twice the residual rate‑action, \(C=2A\). The mapping yields Born weights, a shared weak‑measurement threshold, and a near‑term mesoscopic test without introducing tunable parameters.
Abstract
We connect a gravity‑driven local collapse in which deviations from Schrödinger evolution are quantified by a residual \(S=\int\!\|R\|\,dt\) and exponential rates \(r=e^{-2A}\), to the recognition calculus with the unique local cost \(J(x)=\tfrac12(x+1/x)-1\), path action \(C=\int J(r(t))\,dt\), weights \(w=e^{-C}\), and amplitude \(\mathcal A=e^{-C/2}e^{i\phi}\). Under the same locality and energy‑gauge assumptions, we identify \(C=2A\), reproducing: (i) geodesic two‑branch rotation with \(\|R\|=\dot\theta\) and \(S=\pi/2-\theta_s\); (ii) multi‑outcome weights \(P_I\propto e^{-2A_I}=e^{-C_I}\); and (iii) the weak‑measurement threshold \(A\sim 1 \Leftrightarrow C/2\sim 1\). We formulate a shared, near‑term test on nanogram‑scale mechanical superpositions and isolate falsifiable differences that would split the two approaches.
Key Points
- Constructive identification \(C=2A\) links recognition calculus and residual action.
- Born weights, weak‑measurement threshold, and sequential factorization follow with no knobs.
- Mesoscopic predictions for ng‑scale superpositions; crisp falsifiers (post‑orthogonality plateau, no dispersive DP kernel, gauge independence).