Autor: A. Jaster | Datum: 2026/05/24 | DOI: 10.5281/zenodo.20368388
Building on the causal-Machian emergent time theory \citep{Jaster2026a} and its Planck-scale regularisation \citep{Jaster2026b}, we examine the implications for quantum field theory in an exploratory and phenomenological spirit. All field actions are evaluated on the physical clock metric $\hat{g}_{\mu\nu}$; the factor $\sqrt{\Theta}$ in the Lagrangian density follows from the identity $\sqrt{-\hat{g}}=\sqrt{-q}\cdot\sqrt{\Theta}$ and is geometrically derived. We work in signature $(-,+,+,+)$ with the convention $\mathcal{L}\supset-\frac{1}{2}\hat{g}^{\mu\nu}\partial_\mu\phi\, \partial_\nu\phi$. Throughout the paper $\Theta$ is treated as a fixed semiclassical background in the fixed-$\Theta$ approximation; the self-consistent variation generates non-local additional terms and is an open task. Two variants are analysed. In the \emph{base model} a single cosmological causal field $\Theta\approx1$ governs all current-epoch physics; all Standard Model predictions that depend only on the local metric are reproduced to the precision of $1-\Theta\approx e^{-10^{60}}$ (preferred-frame effects from $U_H^\mu$ are not included in this estimate). In the \emph{scale-separation model} $\Theta=\Tcosm\cdot\Tloc$, a local causal field $\Tloc$ at the scale $m_{\rm loc}^{-1}$ is introduced as an approximation valid to $\mathcal{O}(H_{\rm EW}/m_H)\sim10^{-17}$ and may provide candidate ingredients for a modified electroweak phase transition and for the Sakharov conditions; quantitative predictions require calculations not yet performed. The scale-separation model introduces no new dimensionful parameter, but a dimensionless coupling $\zeta$ (Section~\ref{sec:cpbary}) remains undetermined. The scalar $\Theta$ is a semiclassical constraint functional requiring no independent quantisation within the present framework.