The big challenges to make independent research possible are: money and creating independent communities away from the established mainstream academia.
Of all the communities available to us there is not one I would want to devote myself to, except for the society of the true searchers, which has very few living members at any time.Albert Einstein
It is no measure of health to be well adjusted to a profoundly sick society.Jiddu Krishnamurti
Two possibilities to finance independent research are crowdfunding and anti-sabbaticals:
“Anti-sabbatical: A job taken with the sole intention of staying only for a limited period of time (often one year). The intention is usually to raise enough funds to partake in another, more personally meaningful activity such as watercolor sketching in Crete or designing computer knit sweaters in Hong Kong. Employers are rarely informed of intentions” Douglas Coupland
See Flexible working: Solo scientist by Amber Dance (Nature)
“If you want to bring a fundamental change in people's belief and behavior…you need to create a community around them,“ The Tipping Point by M. Gladwell
“a physicist and philosopher who lives in a little village near Oxford. Julian hadleft the academic world after his Ph.D. in order to have thefreedom to think deeply about the nature of space and time. He supported himself by translating Russian scientific journals into English and, away from the usual pressures of academic life, heused his considerable linguistic skills to read deeply into the history of our understanding of space and time. He had understood from his study the importance of the idea that space and time are relational, and he had then applied this wisdom to modern physics. He was I believe the first person to gain a deep understanding of the role this idea plays in the mathematical structure of Einstein's theory of relativity. In a series of papers, first alone and then with an Italian friend, Bruno Bertotti, he showed how to formulate mathematically a theory in which space and time were nothing but aspects of relationships. Had Leibniz or anyone else done this before the twentieth century, it would have changed the course of science.” Three Roads to Quantum Gravity by Lee Smolin
Got rich by buying apple stocks, now does research independently on his own pace. Founded pacificscienceinstitute.org, an independent research facility.
If you are going to break with the community it’s very difficult to keep up with that level of neural horsepower if you have any other commitments on your time. So in some sense if you choose the path of the dissident or the heterodox or the crank, you will find that your only hope and chance is to have a really novel idea about how this game goes so that you have some time and some breathing room for everyone else.
And, of course, nobody’s very optimistic about that prospect because it’s very difficult to do work on one’s own as Einstein did in the patent office. In fact we haven’t seen a second version of his story since his famous emergence from the patent office.
However, the fact is that the traditional community is also stalled out. So you have two horses, neither of which seems to be capable of finishing the race, and the question at this moment is should we be looking more to the heterodox—running the risk of craziness and cranks—or should we be looking more to the traditional community which seems to have gotten itself in a cul-de-sac that we call string theory, M-theory and super symmetry?
The jury is out but I think it’s become a much more interesting question because traditionally we would have bet on the experts.
But the experts have taken more time researching this theory than any group I think has ever taken to research a theory. And the fact that they have been unable to find anything, in fact, means that perhaps the odds have changed in that race.