Rade said:
At this link:
http://www.geocities.com/ptep_online/PP-04-07.PDF
is a recent paper by Carlos Castro on a new nonlinear Schrodinger equation--for those that work in this area.
I have red your paper and, if you give me the permission, I shall give you now my sensations about it.
1) Firstly, I got a surprise with the datum: January 2006, because we are in November 2005;
2) It seems to be a new review of physics because it is volume 1 and there is no page. These two first points are acting on me like a warning signal: what is this? Where does it come from? Certainly a quantum experiment (smile), I mean a work coming from the future … (smile)
3) The idea of fractal trajectories is (at least in my mind) a great one because it could be an elegant way of reconciliation between a classical and a quantum point of view; and (personal remark) is in someway what I am personally working about when I speak from photons springing from a piece of geodesic to another one (etgb28.pdf); the only point was: I didn’t knew that I was dealing with fractal trajectories as Mister Jourdain in Molières work (French writer in the 1700…) didn’t knew that he was doing “prose” when he was writing and speaking.
4) I remark that the Schrödinger equation is obtained with a classical formulation of the Newton’s Law (which is avoiding a relativistic approach before any calculation has been done) if one considers the left part of equation (7) page 2, but with a special (due to Nottale) formulation of the acceleration if one observes the middle part of the same equation; so, it is not really the classical Newton’s Law but an extension of it including a “complex-time” derivative operator (page 2 relation3). Why not?
5) One point is not clear for me; does the introduction of a complex number D (instead of the use of a real one at the beginning of the article) allows an extension of the work of Nottale and all to non-flat universe?
6) One other point is not clear: is not the middle term page 6 in (40 on the left hand) and in (42; the integrand) equal to zero if the particle-wave following a geodesic (as required by GR in a 4D space)?
Thank you for explanations.
