What concerns/worries a potential PhD supervisor might have when he/she sees an application from someone who already has a PhD and applying for the second one? The fields of study are distantly related (engineering - physics).
What questions should be addressed in the initial letter by the applicant?
The first PhD is not a complete failure but an applicant wants to pursue his ultimate interests. The applicant has a postdoc position secured but has serious doubts working in the field that is not of major interest for him. Postdoc applications in the field of main interest didn't result in getting a position.
The story about Raoul Bott is an outlier, stories about people stuck with something they don't like are not.
– InCheck May 14 '16 at 22:12