Leaderboard

So a predetermined sense of free will for all sane individuals?

The smooth change of refractive index condition is exactly what happens in marine acoustics. (It is not the only thing though.) In this context the eiconal equation is discussed chapter 2 page 5 et seq of the book most people refer back to by R J Urick Sound Propagation in the Sea. Originally written in 1979., but is now availble as a free pdf. Alternatively the eiconal equation for optics and many other uses such as the propagation of discontinuities is discussed in Erich Zauderer's book Partial Differential Equations of Applied Mathematics Wiley 1989

I think this is the way it is with most any subject. Before we learn, we make guesses using only what we know. Those guesses live in the gaps in our knowledge, and get forced out as we learn more and more about a subject.

I used to have these kinds of wild thoughts before I learnt about this subject. Either you swallow your pride and learn what has already been discovered, or you will plug away in your own imaginary reality that nobody agrees with.