Rotation-Induced Microscopic Binding and the Emergence of a Contracting Rod A Finite-Stiffness Effective Theory with a Microscopic Mediator Model, Quantitative Thresholds, and Experimental Controls

Abstract

A rotating extended body is ordinarily expected to develop outward centrifugal strain. This expectation presumes that the microscopic equilibrium structure of the material is independent of the rotational state. The present paper studies a different conditional possibility: bulk rotation may couple to an internal phase or activity variable of the constituents, and the resulting change of internal state may strengthen their binding strongly enough to reduce their preferred separation. In that regime, the material can become shorter and stiffer as its angular velocity increases, despite the simultaneous outward centrifugal tendency. The analysis begins with the rod and spinning-top thought experiment. A rod transmits the inward force required for circular motion, but the rod itself is usually treated as primitive. Here the direction of explanation is reversed: the rod is derived as a coarse-grained network of microscopic bonds. A covariant finite-stiffness sector couples a scalar internal rate to the magnitude of material vorticity and contains the earlier strong-locking relation as a controlled limiting branch. To reduce the arbitrariness of the binding hypothesis, a microscopic mediator toy model is introduced: integrating out a stable scalar mediator produces an attractive amplitude that increases with the internal rate in an explicit parameter domain. A general repulsive-attractive pair potential is then analyzed using this induced amplitude. Two conditional theorems follow. First, the equilibrium bond separation decreases with the magnitude of bulk rotation. Second, the local bond stiffness and the coarse-grained elastic modulus increase with rotation. For a closed ring, the microscopic preferred circumference becomes rotation dependent. Combining this dependence with the local relativistic relation between laboratory circumference and summed comoving length yields the generalized exact branch r(Ω) = ρₛ(Ω) / √(1 + Ω² ρₛ²(Ω)/c²), where ρₛ(Ω) is the preferred proper radius generated by the microscopic binding sector. If ρₛ'(Ω) ≤ 0, the laboratory radius decreases monotonically. The tangential speed remains subluminal for every finite Ω and finite ρₛ. The paper also formulates an observer-scale independence lemma: changing the size or resolution of a passive observer changes the measurement map and available effective description, not the physical state of the observed system. This clarifies why a macroscopically continuous rod may consistently be repre

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