Spacetime as a Causal Viscous Fluid: A Single Lagrangian for Gravity, Electromagnetism, and the Emergence of Schrödinger Dynamics

We present a deterministic field theory in which spacetime is modeled as a relativistic viscous fluid with density $\rho(x)$, phase $\theta(x)$, and four-velocity $u^\mu(x)$ on a dynamical Lorentzian manifold $(\mathcal M, g_{\mu\nu})$. Electromagnetism enters exclusively through the derivative (gauge-invariant) combination $B_\mu\equiv\partial_\mu\theta-qA_\mu$, structurally guaranteeing that the photon remains strictly massless.The viscous degrees of freedom ($\pi_{\mu\nu}$, $\Pi$) obey Israel--Stewart-type relaxation equations, rendering the system hyperbolic (causal).We prove in detail: (a)~the equations of motion from the action principle, (b)~$U(1)$ gauge invariance and the Ward identity ($m_\gamma=0$), (c)~recovery of free Maxwell equations in thelinear limit, (d)~hyperbolicity and energy stability. We show that the measurement independence assumption of Bell's theorem necessarily fails due to the Gauss constraint on initial data, offering a candidate mechanism for superdeterminism without ad~hoc assumptions (though the quantitative reproduction of the Tsirelson bound $|S|=2\sqrt{2}$ remains open).We further show that, via the Madelung transformation, the theory reproduces the Schrödinger equation in its non-relativistic limit: the phase equation becomes the continuity equation, thequantum potential emerges from the medium's gradient energy, and the medium configuration suggests a possible ontological reading as the physical pilot wave of de~Broglie--Bohm mechanics. We note that this required correcting the sign of the phase--density coupling, whichindependently removes a ghost in the phase sector. Preliminary numerical simulations of $1\!+\!1$D and $2\!+\!1$D toy models confirm Bell-bound saturation ($|S|=2.0\pm 0.04$); we discuss why single-particle Schrödinger dynamics emerges while multi-particle entanglement correlations do not, tracing this to theconfiguration-space problem.