Dynamics as the Boundary of Identifiability

A radical epistemological reinterpretation of classical mechanics through the formal apparatus of dynamic system identification theory is proposed. Using rigorous definitions from Ljung (1999) --- data informativeness, persistent excitation, Fisher information matrix, and Hankel rank --- it is demonstrated that Newton's laws represent boundaries of information extraction from observations, not ontological statements about reality. The first law is reformulated as data uninformativeness under zero excitation ($\operatorname{rank}(\bar{F}) = 0$). The second law emerges from asymptotic variance of estimates: mass as the conditioning parameter ($\operatorname{Var}(\hat{m}) \propto m^4$). The third law is interpreted as self-consistency for closed systems with finite Hankel rank. It is shown that momentum is the conserved coefficient at $1/s$ in spectral decomposition, energy is the invariant quadratic norm preserved by norm-preserving evolution operators, and coordinates are indices of spectral modes, with center of mass as the unique minimal-rank parameterization. For rotational dynamics, it is demonstrated that phase loss under rotation transforms Fourier modes into Bessel functions, with Bessel zeros marking fundamental identifiability boundaries ($\mathcal{I} = 0$, Cram'er-Rao bound $= \infty$). The Dzhanibekov effect is reinterpreted as an informational event: temporary loss and stochastic restoration of orientation identifiability, yielding testable predictions about observer-dependence. A detailed case study of the lighthouse problem illustrates how identifiability boundaries emerge in practice: spatial observations alone yield a $b \cdot \omega$ degeneracy, resolvable only through extended sensor arrays providing three independent information channels (spectral frequencies, spatio-temporal delays, spatial distribution). It is proved that discrete source configurations are fundamentally limited to $K_{\max} \sim \log(\omega_{\max}/\omega_{\min})/\log M_{\max}$ distinguishable sources due to spectral crowding, while continuous configurations achieve infinite Hankel rank. The variational optimization problem of maximizing Fisher information under geometric constraints yields differential rotation on logarithmic spirals as the unique optimal solution, explaining the ubiquity of spiral structures in nature. A deep mathematical correspondence is established between the lighthouse problem and optical diffraction: rotational averaging in both cases produces Bessel functions, with Airy disks and identifiability boundaries arising from the same spectral topology defined by Bessel zeros. A parable illustrates how all mechanical concepts emerge from minimal observational capabilities: a physicist in total darkness with seeds, two ears, and a rotating chair reconstructs "space", "mass", and "time" purely from identification constraints.