This is what I sometimes lament about astrophysics, N=1 is sufficient for proof. It's one observation of one event. You can't make any claims about that unless it's a direct violation of some which will occur 100% by theory. In this case there is no such guarantee.
Proof is a word that shouldn't be used lightly. I don't think anyone would see this as proof that quantum foam doesn't exist. The laws of physics allow for quantum foam to happen, which may lead us to start looking very differently at the structure of the universe. However, we now have some strong evidence from measurements over a reasonably large distance that quantum foam is not an immediately noticeable factor in the universe.
I kind of liked quantum foam as a possible way of explaining gravity observation that are not explained by the amount of visible matter and thus attributed to 'dark matter', because 'matter' is the only thing we know that would cause gravity. This tells me I shouldn't get too excited about that possibility.
Further, they cite two other bunches of photons that "Two other short duration photon bunches bolster the statistical significance of this limit"
Every result, except for those whose environment is completely fabricated (such as in pure mathematics), is a statistical or probabilistic one. The question here is if their data is significant or not, and if they have made any mistakes analysing it - not that they only had N=1.
Yes ( and I can assure you that anybody working on astrophysics is aware of the problem). In addition perfectly ordinary astrophysics can sometimes mimic the effects of such observations. On the other hand, given the current funding situation, there is simply no way to build a laboratory were you can use a 7 billion light year baseline in a controlled and repeatable way.
