I've been searching for suitable PhD programs for me since last year, and I came across a fully-funded PhD program at University A with ties to the industry. Unfortunately, I had missed the PhD application deadline so I won't be able to apply until the next cycle, but the potential PhD supervisor has generously offered me a short-term research position (which I accepted) in the meantime as I prepare for my PhD application.
On the other hand, I was recently contacted by a potential PhD supervisor from another University B who is also doing similar research. I am drawn to this particular university since they are very well-known for their research in my very specific field of interest. Since I haven't committed to a graduate school yet, is it ethical for me to apply to both PhD programs at the same time?
PhD is a major commitment in terms of time, money, and energy. I want to work and study at the place that is best fit for me. Will I be burning bridges if I end up applying to multiple PhDs positions while doing a pre-PhD research fellowship at another institute?