This paper introduces the Ghost Murmur effect, defined as a structured residual in rotational measurements that cannot be represented as a single separable loop-plane rotation. The effect emerges naturally in the Quantum Measurement Unit (QMU) framework when measuring the time evolution of Aether rotation using the rotating magnetic field detector (rmfd). The detector observable is proportional to the time derivative of the chronovibration phase, allowing direct access to rotational dynamics rather than static field values. Under ideal conditions, a system produces a separable 4D rotation characterized by a single coherent phase. However, experimental measurements reveal persistent deviations from this ideal behavior. These deviations, traditionally classified as noise, are shown here to exhibit reproducible structure. The paper formalizes this residual as the Ghost Murmur contribution and decomposes the measured signal into three components:\[M = M_{4D} + M_G + n,\]where \(M_{4D}\) is the separable rotation, \(M_G\) is the nonseparable residual, and \(n\) is stochastic noise. The physical interpretation is developed within the Aether Physics Model, where rotational closure is governed by:\[A_u \cdot \mathrm{curl} = {F_q}^2 {\lambda_C}^2.\]The Ghost Murmur does not violate this identity. Instead, it represents a projection imbalance in the measured rotational subspace, indicating that part of the rotational structure cannot be expressed within a single plane. Three primary diagnostics are introduced to identify the effect: Time asymmetry \(T\), detecting nonreciprocal or backward-time structure, Cross-plane separability \(C_\perp\), testing whether motion is reducible to a single rotational mode, Spectral sideband ratio \(\mu_G^{(\mathrm{sb})}\), indicating multi-mode rotational content. These observables are combined into a composite index:\[G_M =w_T \frac{|T|}{\Upsilon_{\mathrm{rmfd}}}+w_\perp (1 - C_\perp)+w_{\mathrm{sb}} \mu_G^{(\mathrm{sb})},\]which provides a measurable scalar indicator of hidden-sector coupling. The effect scales as the square of a small hidden-sector phase perturbation,\[\mu_G \sim (2\delta\phi_G)^2,\]implying that it is intrinsically weak but persistent and detectable with sufficient integration and calibration. A synthetic data model is provided to illustrate the expected signatures: time-asymmetric behavior, reduced cross-plane correlation, and stable spectral sidebands. Calibration procedures are defined to distinguish the effect from instrumental artifacts, including separability closure tests and phase-reversal validation. The Ghost Murmur effect reframes residual structure in precision rotational measurements as a potential physical signal rather than noise. It establishes a practical and testable framework for detecting nonseparable rotational dynamics and hidden-sector contributions within the QMU and Aether Physics Model.