Let me start off by saying that I am really a nobody in my field of research. Several months ago I reached out to a very well-known researcher, one of the big names, with a draft paper I was working on. I was very surprised to get an answer back from them. I originally wanted their input on a paper I was preparing for publication and thought having them add their two-cents into what I had written would really improve the paper. In exchange I offered them to be a co-author.
The researcher was hesitant to agree to my offer citing that they believed what I had was a really nice piece of work and they were concerned that by adding their name to the paper, people would end up attributing the work to them. Instead, given that my paper was theory heavy, they wanted to do a follow-up paper together that was focused on experimental verification of my theory and also bring in their PhD student to help. I can understand that they saw this as an opportunity for the PhD student to get in on a paper (who does not have any publications yet) and at the same time give me an opportunity to collaborate with them (the big name researcher). Everyone would benefit. Anyways, the researcher in question suggested the possibility of the PhD student taking the lead as first author and that we should rank authorship based on who contributed the most.
I am not sure if the PhD student was too busy, or just didn't understand the topic but for whatever reason they showed very little interest in actually doing the work to get the paper done. They did put their name as first author on the paper at the very beginning of the research effort but then did very little after that. I ended up writing at least 80% of the paper, and my collegue did all the data processing, with the PhD student capturing the data and writing an abstract and a paragraph in the introduction. I could see when they made edits to the paper and it was always last minute (the night before our meetings).
Now, I would not necessarily care too much about the author order here; however, because I don't think the PhD student understands the topic well at all, I don't want correspondence for the paper being sent to them. I wrote almost the entire paper and also all the details of the algorithm/theory used to produce the results. I know the material very well and am able to actually answer questions and discuss the work with those who may be interested.
This is an awkward situation for me. I don't know how to discuss/propose the authorship order change and also don't want to cause a fuss because I want to work with this researcher more in future projects. I saw this project as starting a relationship with this researcher and don't want to rock the boat too much. I have more ideas that I want to work with them on. Can anyone please help me navigate what to do?