Is it reasonable to do a second master's degree just for the letters of recommendation? I have a master's degree in theoretical physics. I want to do a PhD and start a career in research.
The problem is my letters of recommendation. I had a horrible relationship with my master's supervisor, who was also my undergraduate supervisor. I ended up graduating, but with no publications and no thesis. He will not provide a letter. I've already asked other professors: some said no; a few did agree, but they don't really know me. My field is very theoretical, so getting a job and asking my boss for a letter does not seem like it would be helpful.
The only thing I can think of is to do a second master's degree with the specific goal of forming relationships with professors who can write me letters of recommendation. Does this seem like a reasonable thing to do? I'm scared about getting too old or failing again at the thesis.
I can share my experience. I completed my graduate program online so I only had one recommendation from my masters program. I then had two recommendations from my work experiences. I was accepted at my 'goal' university and awarded a fellowship that covers tuition and provides a stipend for  living expenses. When I spoke to the chair of my department about how/why I was awarded the fellowship, he said that the most important admissions requirements were GRE score and GPA. He said that recommendation letters are often not even read. They become of interest if there is a debate about accepting a student. He also said that recommendation letters have lessened in importance because no one trusts them anymore (due to lawsuits and everyone's fear of writing something that could be questioned.) They DO read your writing. So any essays or proposals that you are asked to write are important.
I do not know if this is accurate for all universities. I did serve on an admissions committee at a private school for many years, and I would agree with his assessment. We dealt with such large numbers of admission candidates that we only read recommendation letters for a few cases.
You could always apply to both PhD and masters programs, but I definitely wouldn't let recommendation letters prevent you from applying immediately to PhD programs.