A little background:
I started my PhD in August 2019 at university X. I wanted to work on project A, but after I joined PhD, my adviser asked me to work on project B. He said that if I start working on project A, he won't be able to help me in any matter. He's a very nice guy, he said that I can work on whatever the project I want. I decided to start working on project B because I don't want to get lost and have nobody to help me out. (I had a horrible experience in my MS where I worked on a project about which my MS adviser didn't have any knowledge).
For the last 4 months, I have been working on project B. It's okay, but I don't feel happy about it. It doesn't motivate me. It doesn't give those internal joy-feelings.
My adviser is leaving this university and moving to university Y. He has offered me three options:
- Change research group and stay in university X
- I stay at university X and he will supervise me from university Y (he becomes an adjoint faculty, if department chair allows)
- Move out with him to university Y and start working on a new project (which is also not of my interests)
I don't want to choose option#2, for sure. Option#1 is also not quite suitable for me because no professor here is working on something that interests me (quantum machine learning). The salary that I am getting from university X is much more than the salary that I will receive from university Y. I might choose Option#3, because at least I know that this professor is a very open-minded, nice and genius guy. I have to make a decision before June 2020.
I want to apply for an other PhD position, the one which really interests me. Is it okay if I ask my current adviser to give me a recommendation letter and support my application? What reaction of him should I expect?