The theme for this year's FQXi contest topic is "Questioning the Foundations: Which of Our Basic Physical Assumptions are Wrong?". I had some difficulty to start with this topic (I didn't seem to be the only one, see Ajit Jadhav's blog here and there). I had a lot of things to say about what has gone wrong with physics, which assumptions had to be reconsidered. So, since the opening of the contest, I regularly put some ideas in a draft, being confident that I would be able to arrange them into a coherent thesis for the essay. However by the 20th of August (ten days before closing), I still didn't know how I could write them together into an essay without being suspected of "trotting out my pet theory" (see warning in the Evaluation Criteria).
My "pet theory" is simple: the fundamental entity in physics is "THE quantum particle" which you can represent as an arrow (a vector, a ket). From the mechanical interactions between such rod-like particles, you may deduce all of physics, provided that you assume some complementary parameters (such as the velocity at which two particles fly one from another = c, the length of the rod = Bohr diameter of hydrogen). No mass, no force, no charge, etc. Just paths of rotating arrows that interact with each other through contact (collision). This is the way I reason about photons, electrons, quarks, fields, waves, etc. But I can't reasonably write it that way in an essay. I would need to recall a lot of history of science. So I chose to bring up some ideas that have emerged in history of science that we could reconsider, not necessarily in the same way, but gaining insight with hindsight.
Also I prefer to avoid abstract mathematics when talking physics. Mathematics is just a language, very convenient though, but really just a language that can hinder us in our intuitive understanding. Instead of math, scientists could as well use words, fantasy, dreams, pictures, poems maybe. It is an art and sometimes it is necessary to change the expression of this art. I hope you'll enjoy my dreaming in Geneva.