By "main" research advisor I mean: with him, I got my most valuable research experience, greatest results and of course I invested most of my research time. Our field is Physics and I am making some achievements, but when I asked him for a recommendation letter for my PhD application, he refused and said I would not want his letter if he really writes one. I'll give his reason at the end, but I want to state my own question here first.
Will it be weird that I state my research experience with him very clearly (I think it will make a strong part) in my SoP but without his recommendation? Will the admission committee wonder where this advisor's recommendation is? If this is not a problem, does it even help that I merely mention this experience in SoP without the support of a letter? I have another piece of research experience from a very prestigious place and I have the LoR from my supervisor there, but that one doesn't have strong results as this main piece of experience and I am counting on this experience to make my application strong.
Here is his reason why he doesn't want to recommend me which might be trivial to my question but I guess you would want to know.
First, my undergrad major is an engineering field that has almost nothing to do with Physics. My advisor said if he is recruiting graduate students, he would only consider Physics Bachelors to be graduate students because it will be very hard and even impossible for students trained in other majors to shape their thinking to be suitable to do research in Physics. I am no exception, although I am doing part-time research with him and have taught myself most Physics core coursework (Damn, another equally prestigious Physics Professor in the neighbouring office just holds the opposite view). For me, his suggestion is that I should treat Physics as a hobby but forget about going to graduate school. (We encountered a nasty math problem which was important for logical completeness of our work some time ago, and he got around it with a trick which to me was "ridiculous" by then. I proposed my own alternative method, but in his view my method is rigid, and he then used my failure of understanding his trick to tell me that my thinking is already not suitable for Physics.)
Second, he is really really an "idealist" in doing research. Since I am applying for grad school, I want to speed up a little bit to revise our work to have a presentable draft (I had already derived the results by then, we were polishing the writing and dealing the above-mentioned math problem). He said I was appearing to be like a "pragmatist" because I was not acting or thinking slowly and calmly like an idealist. He even got a bit unhappy with me when I was arguing with him, wanting him to explain his trick (mentioned in the first reason) more clearly, when I was so desperate to understand it.
As a result, he said I would not want his letter since his opinion is just he won't recommend me to a graduate program although I did research with him.