The experiment proposes to introduce a time delay between two paths of a coherent signal by distorting them with a gravitational field (i.e. that of Jupiter). The experimenters would then check for interference between the two signal paths to verify quantum behavior on the "cosmic scale".

The "traditional" result would predict no interference, because the time delay means betrays "which-path" information.

But I don't see any way for this experiment to turn up anything but a mundane answer. If the two wavefunctions do not overlap because they are happening at different times, how can they possibly interfere?

(And where there is overlap, we lose our ability to distinguish "which-path", and we expect the interference to return).

I'm not sure what you mean by "the wave functions... happening at different times".

First of all, the two-slit experiment is interesting (in part) because it works if you use a continuous stream of particles and observe their pattern, or discrete particle packets and observe the pattern resulting from combining many packets together. The key result is that the same pattern is observed in both cases, except if we can tell which slit a specific particle went through. It's possible to design an experiment where you can detect which slit a particle goes through, but still let the particle through both slits. Detect the slit -> no interference; don't detect the slit -> interference. Using discrete packets makes it easier for the detection aspect.

Secondly (to clarify) the experiment would use one signal wave which, due to the distances involved , would spread wide enough to hit multiple moons at the same time. The returning signals would be combined to look for interference patterns.

In this experiment, the two (or more!) moons are the equivalent of the slits in the traditional experiment. If we cannot detect which moon bounced a particular packet we should see an interference pattern, as per previous experiments. If we can detect the moon, we shouldn't see a pattern.

The unique question this experiment asks which we haven't previously is: Can the effects of gravity be used to detect the outcome of a quantum event? where of course the quantum event is a photon packet bouncing off of moons.

Yes, the two moons are analogous to slits, in that they're point-like objects interacting with a large, coherent wavefront. The "slits" will be identified (according to the proposal) because the gravitationally distorted light path also introduces a time delay, such that it takes longer to pass by one moon than it does the other.

This means the signal will be split into two pulses, one arriving before the other. You detect a pulse from moon 1, then another pulse from moon 2. You know which moon any particular photon passed by because you can look at when it arrived.

The experimenter seems to be asking "can we observe interference between the two pulses even though we know which 'slit' the photon passed through because mumble mumble mumble gravity".

But there is no way for interference to happen, gravity or otherwise. Those pulses do not overlap (as far as I can tell) by the design of the experiment, because they are not happening at the same time. In other words, if pulse 1 has wavefunction psi_1(x,t) and pulse 2 has wavefunction psi_2(x,t), then <psi_1|psi_2> is nearly zero-- there is no overlap. There is no `t` where psi_1 and psi_2 have appreciable magnitude (and where they do, we would expect to see interference anyway, and we would no longer be able to tell the origin of the photon).

If there is no overlap, there is no interference, whether you are measuring planets or slits. So I don't see what we could possibly learn from this experiment, or where the experiment designer expects to see interference; it is all but guaranteed to deliver results that are exactly in line with a tabletop interference experiment.