How does relativistic proper time dilation ($\Delta\tau = 0$ for lightlike paths) affect spontaneous wavefunction collapse rates?

In standard quantum mechanics, the time parameter $t$ in the Schrödinger equation is treated as an absolute, global background parameter. However, in General Relativity, proper time $\tau$ is relational and depends on the local spacetime geometry and relative velocity $d\tau = \sqrt{1 - \frac{2GM}{rc^2} - \frac{v^2}{c^2}} \, dt.$ Spontaneous collapse models (such as Continuous Spontaneous Localization (CSL) or Penrose’s gravity-induced collapse) propose that quantum superpositions have a finite physical lifetime before collapsing into classical eigenstates. Consider a particle or photon moving along a lightlike path where the elapsed proper time is zero ( $\Delta \tau = 0$ ): Parameterization: Should a dynamical spontaneous collapse mechanism be parameterized by the global laboratory coordinate time $t$ or the particle's local proper time $\tau$ ? Time-Dilation Effect: If collapse lifetime depends on the local relativistic proper time flow ( $\text{Time}_{\text{flow}} \to 0$ ), does relativistic time dilation freeze or prolong the superposition state ( $T_{\text{superposition}} \to \infty$ )? The Photon Paradox: Does this imply that massless particles (or highly time-dilated systems) never undergo intrinsic spontaneous collapse until forced by interaction with a massive, non-zero proper-time reference frame? How do current relativistic extensions of spontaneous collapse models reconcile this fundamental mismatch between relativistic kinematics and quantum state reduction?