Is independent research on physics posible? Some people may answer this question with a yes! Here are some examples of independent physicists:
A few examples of notorious physicists who held no Phd degree, but made imensely contributions to science are Freeman Dyson, C V Raman, J C Bose and M N Saha. They had some degree of formal education though. Some respectable physicists also may think so it is possible to be self educated, and to contribute to science, without enroling in a institute, or attend a formal graduate program course. Examples are Sabine Hossenfelder (most corageous postdoc prize, talk to a scientist, What I learn as a hired consultant for autodidact physicists), and the Nobel Prize Winer in Physics Gerard’t Hooft (How to become a good theoretical physicist)
Look for the Foundation Questions Institute. The Foundational Questions Institute, styled FQXi, is an organization that provides grants to “catalyze, support, and disseminate research on questions at the foundations of physics and cosmology.” It was founded in 2005 by cosmologist Max Tegmark, who holds the position of Scientific Director. It has run four worldwide grant competitions (in 2006, 2008, 2010, and 2013), the first of which provided US$2M to 30 projects. It has also run four essay contests open to the general public, with $40,000 in prizes awarded by a jury panel. FQXi is an independent, philanthropically funded non-profit organization, run by scientists for scientists, with a Scientific Advisory Board including John Barrow, Nick Bostrom, Gregory Chaitin, David Chalmers, Alan Guth, Martin Rees, Eva Silverstein, Lee Smolin, Frank Wilczek, and Dieter Zeh. The seed funding was donated by the John Templeton Foundation.