Dimensional hierarchy in attosecond photoemission as a symmetry projection effect

This preprint proposes a projection-based explanation for the striking “dimensional hierarchy” reported in spin-resolved attosecond photoemission—where measured vertical transition delays increase by roughly an order of magnitude from three-dimensional Cu(111) to quasi-one-dimensional CuTe. Rather than interpreting the hierarchy as a direct slowing of intrinsic quantum phase evolution under reduced symmetry, the work shows that much of the spread can be accounted for as a measurement-frame projection effect. The central claim is that the experimentally reported laboratory delay t is related to an internal dynamical time coordinate \tau by a computable symmetry projection factor \chi_{\mathrm{sym}} constructed from band velocities, i.e. t \approx \chi_{\mathrm{sym}}\,\tau. Under this mapping, phase progress in \tau is near-universal across the compared materials, while the apparent hierarchy in t emerges from geometry-dependent dilation between internal and laboratory frames. A single-parameter fit collapses the measured spread by a factor of 3.8 with \chi^2/\mathrm{dof}=1.28, using full uncertainty propagation from both experimental and band-structure contributions. Beyond fitting, the framework yields falsifiable predictions for when and how the hierarchy should strengthen, weaken, or invert under controlled changes in symmetry and band-velocity structure. Conceptually, the results motivate treating “slower transitions” not as a necessary change in intrinsic dynamics but as a consequence of how internal temporal evolution projects into measured time under symmetry constraints—an interpretation consistent with internal-time dynamics. Keywords: attosecond photoemission; Eisenbud–Wigner–Smith delay; internal time; symmetry projection; phase-space dimensionality; spin-resolved ARPES