Preprint: post-selected proper time mimics reversed decay only inside environmental memory

Elitzur's preprint, posted 7 November 2026 as arXiv:2611.12971 and not yet peer-reviewed, revives the 1990 quantum time-translation machine of Aharonov, Anandan, Popescu and Vaidman. A clock, or a sealed cell of excited atoms plus the field they radiate into, is prepared in a superposition of proper times, different gravitational potentials or inertial velocities, and a later measurement post-selects the control. The weak value of the time-dilation factor, alpha_w, can then exceed one, vanish, or go negative, so the post-selected sub-ensemble is described as having evolved for alpha_w t rather than t.

The witness is projective, not a weak measurement of a pointer. Atoms that had already begun to decay are, in the rare post-selected records, found more excited than when the cell was inserted. Elitzur says that result is exact and depends only on the atoms' survival amplitude. With two branches the effect lasts only while the decay is younger than the environment's memory time; after that the emission is Markovian. Post-selection then amplifies a minute difference set by the full energy spread of atoms plus field, not the linewidth, and the more excited witness fails.

What a headline about time running backwards misses is that nothing in a typical laboratory record is rewound. The effect lives only in a post-selected sub-ensemble, the same structure as weak values and superoscillations: a band-limited function can locally oscillate faster than its highest Fourier component, but only where the probability of that post-selection collapses. Elitzur's sharper claim is that the barrier is bandwidth, not entropy. Undoing decay past the memory time needs many branches, a strictly bounded environmental spectrum, and a success probability that falls exponentially with the oscillations to be undone.

Methods note: this is an analytic theory paper, not an experiment; no sample of runs, no measured post-selection rate, and the witness is a calculated projective outcome under branch superpositions. Four proposed ways to superpose a clock rate, from hollow massive shells to inertial velocities, remain designs on paper. What would strengthen the claim is a peer-reviewed calculation checked against a concrete cavity-QED or atom-interferometer model with a stated memory time, plus a predicted post-selection probability large enough to collect. Until then it constrains a thought experiment and does not show that laboratory time or causal order can be reversed.