>>13518581You don't need all that to get to E=mc^2. But we can pretty reasonably guess that all the "low-hanging fruit" has been picked. The simplest relations between measurable quantities have already been mathematically characterized. So you'll probably have to get into the weeds a bit to come up with something novel.
Re: Newton, The first and third laws are kind of contained in the second, F_net = ma, if you also assume that mass is conserved and F_net = 0.
