I was reading an old post, Can gravity be shielded, like electromagnetism?. One of the responsesresponses had this comment.
There are some experiments trying to measure whether antiprotons ( antimatter) is repelled by gravity.
There seem to be good reasons to doubt it - see the same comment or Anti-matter repelled by gravity - is it a serious hypothesis? [duplicate]Anti-matter repelled by gravity - is it a serious hypothesis? [duplicate]. But apparently not everyone is convinced.
My question is about these experiments.
I can see difficulties in trying to measure the weight of an anitproton or an antihydrogen atom. It sounds much easier to see if antineutrons are repelled or attracted by gravity. After all, it is easy to show that ultracold neutrons are attracted. For example, see this.
It should be an obvious step for somebody to try it with antineutrons. But a quick Google didn't turn up anything. So
Has it been tried?
Would it tell us anything about antiprotons or antihydrogen? My naive thinking is that $n \rightarrow p + e + \bar{\nu}_e + \gamma$, so that the effect of gravity on $n$ might be much like $p$ or $p + e$.