Temporal Equivalence Principle: Localized Proper-Time Gradients and the Spatial Proximity of Discordant Pairs

The discordant quasar-galaxy pairs catalogued by Halton Arp — low-redshift galaxies apparently joined by luminous bridges, filaments, or foreground absorption to companions at redshifts one to two orders of magnitude larger — remain an unresolved anomaly of observational cosmology. Under the standard interpretation, redshift is identified with distance through the Hubble relation and every such pair is dismissed as a chance superposition of unrelated objects. This paper applies the Temporal Equivalence Principle (TEP) — the bi-metric scalar-tensor framework in which matter, clocks, and light propagate on the causal metric g~_μν = A²(φ)g_μν + B(φ)∇_μφ∇_νφ with universal coupling A(φ) = e^(-φ) — to a twelve-pair catalogue drawn from the published literature and verified against the NASA/IPAC Extragalactic Database. In TEP the observed redshift factorises into a background clock-rate factor set by the ambient temporal level hosting the source and an intrinsic conformal factor generated by the emitter's own proper-time field, 1 + z_obs = A_0 / (A_bg A_int). For two objects at a common distance the shared background term divides out exactly, yielding the distance-independent diagnostic A_int(Q) = (1 + z_G)/(1 + z_Q): a direct measurement of the companion's local clock-rate offset. Applied to the catalogue, the diagnostic returns intrinsic conformal factors spanning A_int = 0.33 (NGC 7319) to 0.98 (NGC 1232A) — a smooth distribution of local field depths rather than the discrete quantisation demanded by earlier intrinsic-redshift proposals (e.g., Karlsson 1971; Burbidge 2001) — while the standard reading is forced to place companions up to ~360 times farther away than the galaxies to which they appear connected. The physical-association evidence is evaluated independently of any redshift model: surface-brightness transects across the claimed bridges are tested against rotated control axes, the published Ca II and H I absorption systems fix the line-of-sight ordering, an empirical quasar-density test compares the Arp host fields against seeded random fields, and the Poisson chance-alignment probability is computed per pair and for the joint ensemble under selection-aware density and geometry conditioning. The resolved NGC 7603 filament is detected as real emitted light along its measured path (+3.9σ over the inter-object segment, +5.7σ peak, reproduced in three photometric bands). The Lyα path-length audit could be executed on exactly one catalogue sightline and falsified it, placing the companion of NGC 3067 at its cosmological distance. For the remaining eleven surviving systems, the joint probability evaluates to a catalogue severity statistic of P = 3.6 × 10^-13 under the conservative empirical quasar density, sharpened to 4.9 × 10^-19 under the axis-conditioned geometry of the morphology-claimed systems and 7.2 × 10^-22 under the measured X-ray-selection density (yielding a look-elsewhere crossover volume of ~310 parent fields). Independent geometric-coherence tests — minor-axis anisotropy, radial redshift ordering, and physical-scale clustering at redshift-independent distances — probe structure the catalogue was not selected on; they return significant structure where the hypothesis predicts it, while paired-redshift and symmetry tests return bounding nulls. The scalar-field transition is inferred on the NGC 7603 filament — the only Arp structure carrying measured interior redshifts (z = 0.243 and z = 0.391 between the endpoints) — where the non-monotonic four-point transect is fitted with a nested-wells field model — compact local proper-time depressions superposed on the shared pair field — whose well depths are estimated by Markov Chain Monte Carlo with full residual diagnostics, each well confined to a projected width below 1.2 kpc of its emitter. All tests are aggregated into a single falsification table opposing the TEP spatial-proximity hypothesis against chance superposition. The audit also identifies the observation that would settle the question for the flagship system: a single blue-arm echelle exposure on the z = 2.114 companion of NGC 7319 would deliver the decisive z > 2 forest sightline. The surviving discordant systems emerge not as anomalous background coincidences but as candidate naturally occurring differential-clock experiments, and their redshift differentials are the expected deterministic signature of localized proper-time gradients on a static spatial manifold. Website: https://mlsmawfield.com/tep/arp/ Repository: https://github.com/matthewsmawfield/TEP-ARP/ DOI: 10.5281/zenodo.22938154 Keywords: Temporal Equivalence Principle – Halton Arp – discordant redshifts – anomalous redshifts – quasar-galaxy associations – intrinsic redshift – proper-time gradient – proper-time field – scalar-tensor theory – modified gravity – two-metric cosmology – variable clock rates – non-expanding universe – temporal landscape – Markarian 205 – NGC 4319 – NGC 7603 – NGC 7603B – NGC 3067 – 3C 232 – NGC 1073 – NGC 7319 – Stephan's Quintet – NGC 1199 – NGC 3628 – NGC 4258 – NGC 2639 – NGC 1097 – NGC 1232 – Arp 41 – Atlas of Peculiar Galaxies Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All materials required for full reproducibility—including data downloads, analysis scripts, code, and manuscripts—are open-source. Feedback and contributions to further test these results are welcome.