Does time follow information? Indications from the zeptosecond birth-time data of H₂

Ram Kirpitch

Published Oct 14, 2026• 0 citations

Abstract

We re-analyse the published molecular-frame data of the zeptosecond birth-delay experiment in one-photon double ionization of H₂ at 800 eV [Grundmann et al., Science 370, 339 (2020)]. Four estimators of the zeroth-order fringe phase that are insensitive to the emission envelope give a delay slope of 391 ± 39 (stat) ± 52 (method) ± 50 (zero point) zs, (1.59 ± 0.33) R/c, linear in cos β; the fringe maximum gives (2.06 ± 0.28) R/c. The fast-electron fringe visibility is V = 0.543 ± 0.013. A coherence-scaled transit law, τ_eff = τ_ref/α with α the measured visibility of the analysed wave and τ_ref = R/c, predicts these values without a free parameter. Against the light-phase model and the ab initio time-dependent Schrödinger predictions, the fast-electron data give χ² = 8.2 for 2 degrees of freedom (p = 0.017) for the standard description and χ² = 0.9 (p = 0.63) for the coherence law, a likelihood ratio of 38. The product of visibility and delay, the invariant of the law, is 1.03 ± 0.15 and 0.86 ± 0.18 in units of R/c for the two fast-electron observables, against 1 predicted; correlated ab initio dynamics gives 0.63. The data favour an addition to standard quantum dynamics at the level of 2.4–3.3 standard deviations, confined to the zeptosecond birth window. Two checks that use no fringe-position fit support the result: the smearing of the β-integrated fringe gives a total pattern shift of 511 ± 35 zs, and the visibility differs between forward and backward light directions (0.579 against 0.508, 4.2 standard deviations) while the product of visibility and delay is the same in both halves. The law follows from one principle: the birth completes at the energy spread of the minimal-energy split of the electron's state, which by a theorem of Tóth and Petz is its quantum Fisher information, αΔE, rather than at its variance; the split is realised by the record the event writes into the ion and the second electron, and the effect is confined to the birth window in which that record is written. The birth is an entanglement event: the delay obeys τ_eff √(1 − C²) = τ_ref with C the concurrence of the electron with its record, C = 0.84 for the fast electron. The thesis that accompanies the measurement shows the coherence lost by the fast electron conserved in the electron pair, the balance on which the law rests. We explain why energy measurements of the photoelectric effect could not see the effect, identify three tests in data already recorded (the delay slope across bond length and energy sharing, and Auger-gated K-shell ionization of N₂ at six photon energies), and specify a repetition of the experiment that decides at the five-standard-deviation level.

DOI: 10.5281/zenodo.23370670

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A Proposed Coherence-Time Invariant from Information Conservation and Its Experimental Tests

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