"Spatial Width," "Coherence Length," and the Measurement Problem

[charters]

TL;DR Summary

A new paper makes a radical claim about interpretations of QM based on a simple optics thought experiment and a dubious purported distinction between the coherence length and spatial width of a light pulse.

A new (short 3 pg) paper, making quite a grandiose claim, caught my eye last night:

https://arxiv.org/abs/1908.07719
Abstract: We propose an experiment of two-path interference in which the optical path difference between the two interferometer arms is much larger than the spatial spread of single-photon pulses, thereby enabling the "which-path" information of an individual photon to be identified, without disturbing its passage at all, by measuring its time of flight. This apparently simple experiment poses a few conceptual puzzles, including the suggestion of inevitability of the von Neumann-Wigner interpretation of quantum mechanics.

Their idea is that one can set up a basic optics interference experiment where the lengths of the two arms are unequal such that (A) clocks on the exit port detectors could distinguish the short and long path but that (B) whenever the clocks are in fact not running, the paths will interfere measurably.

My understanding is this is simply wrong - if clocks can in principle distinguish the paths, the wavepackets will not overlap, which is a precondition for interference. So, the actual choice to activate the clocks or not is irrelevant.

The odd thing is the paper explicitly contemplates this objection and refutes it by claiming this objection relies on a "confusion" between the "spatial width" and "coherence length" of the light pulse. I don't understand what they mean by this or how this can matter, so I stand by my original position. However, the paper at least appears professional enough that I wanted to make sure I'm not the one who offbase here (ie consider this a sanity check). If they just ignored this problem with their idea it would be one thing, but the fact that they're explicitly aware of it and still have a response makes me second guess myself. So am I indeed wrong? Or is this a flawed paper?

PS: I will also say the refs they cite to support their refutation of my point are to the Franson experiments, which are entangled two-beam experiments, and so are not relevant/do not support their claim. These papers do say that the single photon interference visibility is based on the coherence length of the pulse relative to the path length difference. But they do not say that there is a situation where clocks could measure a path length difference while the *single photon* coherence length remains sufficiently large to admit *single photon* interference (which is the key for this new paper).

 

[Cthugha]

Well, the authors are correct that the coherence length of a light field consisting of single photons may be longer than the "spatial width", which I would roughly equate to the antibunching timescale. Phys. Rev. Lett. 108, 093602 (2012) by Matthiesen et al. shows this quite well.

However, the authors are completely wrong when it comes to their description of what the clocks do. The emission process basically consists of the emitter being in a superposition of being in the ground and the excited state and the light field containing zero or 1 photon. The longer this superposition stays intact, the longer the coherence time of the light field will be. Basically, you get entanglement between the light field and the emitter.

Now, there are just two ways to realize the "emission clock". Either you measure the photon - which would destroy it - or you measure the state of the emitter and deduce that photon emission took place, when you measure it twice and find it initially in the excited state and afterwards in the ground state. However, each of these measurement acts will destroy the entanglement between light field and emitter and destroy the superposition. This of course shortens the coherence time of the light field. If this coherence time is shorter than the path length difference, no interference will take place. This does not depend at all on whether a second clock is present that measures the arrival time, but solely on how frequently you measure the state of the emitter. Therefore, the authors' argument is invalid.

 

[charters]

However, each of these measurement acts will destroy the entanglement between light field and emitter and destroy the superposition. This of course shortens the coherence time of the light field. If this coherence time is shorter than the path length difference, no interference will take place

Thanks, this is helpful/the better way to make the argument.