The Observer Notebook · 2026-09-30

Time as a which-path detector

If gravity makes a clock tick differently on two paths, does the clock become a detector?

Known, reproduced

Send an atom down two paths at once and recombine them: you get interference fringes, unless something keeps a note of which path it took. An atom carries its own clock, and a clock held higher ticks faster (gravity's time dilation). So the clock's reading becomes the note, and the fringes fade with nothing touching the atom. An echo (flipping the clock mid-flight) can hide the note, but only at a cost, and the note moves into correlations rather than vanishing.

3×10⁻⁴error on V² + D² = 1EXACT SIM
4–11×less leak, bond-free echo vs time crystalEXACT SIM
2.5–5×crystal hides clock energy better, frame checkEXACT SIM
0.0774κ in 1 − V ≈ κ(ΔT)²/n̄, n̄ = 16 to 1024EXACT SIM
01

Two clocks drift apart, live

Each path carries a clock with one hand. The upper hand runs slightly fast. The fringe contrast is the overlap of the two clock states: V = |cos(gap/2)| for one hand, and the product of those over every hand for a clock with many. The which-path readability is D = |sin(gap/2)| for one hand.

Live · one atom, two heights, its own clock DEMO SCALE · GAP HUGELY SPED UP · A REAL STRONTIUM CLOCK NEEDS ~11 m·s

…

left · dials ride the two arms; the screen shows fringes 1 + V·cos(x) · right · V (ember) and D (moss) over this run; faint line = one hand with no echo, |cos(gap/2)| · hands: 8 gives a warm object (hands at mixed rates): it never realigns · echo flips both clocks every 1.5 s (a perfect π pulse mirrors each hand), so the gap closes again.

02

In plain words

Nobody measured anything. The shape of spacetime wrote the note in the atom's own clock, and V² + D² = 1 holds the whole way: what the fringes lose, the clock's record gains. The sim hit that bound to 3×10⁻⁴. For a real strontium optical clock you need about 11 metre-seconds of height gap times time apart before the fringes vanish.

An echo hides the note by flipping the clock, but then the clock stops telling proper time: the record is the reading. A time crystal is not a gravity shield. In the rotating-frame model its own bonds are the leak, and a bond-free echo leaks 4 to 11 times less. A later frame check, putting the clock's real energy back in, reversed the ranking: the crystal hides that energy 2.5 to 5 times better. With a quantum pulse of n̄ photons the leftover record shrinks like 1/n̄ (1 − V ≈ 0.0774(ΔT)²/n̄) and sits mostly in the correlations between clock and light.

Prior artZych et al. 2011 and Pikovski et al. 2015 (fetched, see KNOWLEDGE_BASE.md).

Next clickNone. The time thread is parked.

Not a lab result: a gravitational which-path measurement of this kind has not been done. The model idealises everything: perfect beam splitters, a perfect two-level clock, arms held at fixed heights (free-fall geometries largely cancel the effect, Roura 2020). The crystal results are 8-spin chains averaged over 16 draws; the quantum-echo results are one spin and one field mode. The time-dilation decoherence framing (Pikovski 2015) is contested. The panel speeds the gap up by many orders of magnitude, and its many-hand clock is 8 two-level hands, not a real warm body.

Nearby on the bench