Recent content by PhilDSP

May I ask: what does 't Hooft mean by "fast moving classical variables"? Is he including or requiring or implying superluminal transportation of some form of information for his argument?

Okay, thanks. That is a very worthy contribution - more or less what I understand from what I've read so far. On the other hand, Bohm's take is philosophically a bit apologetic possibly. He is saying, in effect, that the formulations that de Broglie and Schrödinger created, with extension...

I'm investigating some newly conceived Hamiltonians using the approaches of de Broglie and Schrödinger as jumping off points. Lanczos in "The Variational Principles of Mechanics" p. 278 describes and analyzes them. Neither de Broglie nor Schrödinger really completed the program of the H-J...

Yes, you're right. It's the unmagnetized case. Early in the book they start with more simple cases and later derive equations for other conditions. They even analyze shock waves with interesting insights later in the book. It's a great textbook!

An interesting alternate example of where the breakdown of Es and Em leads to both scientific and engineering insights is detailed in Introduction to Plasma Physics: With Space, Laboratory and Astrophysical Applications by Gurnett and Bhattacharjee. If I remember correctly it is described...

For that matter, we might very well find in the long run that light, charge, electric fields, magnetic fields, mass, even quantum behavior are all manifestations of the same underlying phenomena each having a particular local (or non-local) context or configuration. One major problem with 4...

P.S. This paper by Claude Daviau and Jacques Bertrand shows how influential de Broglie continued to be and how his discoveries continue to be developed in ways that bring rather important principles into the foreground. https://file.scirp.org/pdf/JMP_2015112314063920.pdf

Fortunately there are several textbooks he wrote in French that have been translated to English. One is a general textbook that isn't oriented towards specialists. Others that I know about and have copies are: Nonlinear Wave Mechanics...

Assuming you have valid and accurate classical field equations, couldn't you essentially apply the Lorentz Transformation with the gamma factor separated out? It seems to be a mystery to many how both the derivation and application of the de Broglie relations can be done without invoking a...

Would those unobservably fast oscillations include the phase of "matter waves" from De Broglie's theory (which become extremely rapid as a particle's velocity approaches rest)? Granted they aren't physical waves as we know them.

However, if you do not limit yourself to using scalar values for ## \epsilon_0 ## and ## \rho_0 ## then there is very much that can be accomplished with materials. For example, you can generate a negative index of refraction. https://www.sciencedirect.com/science/article/pii/S1369702106715735...

It could also be worth looking at the Ewald-Oseen Extinction Theorem. This describes what is going on in terms of the fields and shows how the electrons in the transparent material or media are set into motion or oscillation. A recursive effect is set up between the moving electrons and the...

Oh. Thanks for that additional insight!

Thanks so much for your attention and suggestions Charles! My immediate inclination is to approach the problem from a bit different mathematical foundation. I hope I'll have time to see it through to complement your observations. Of course we all have different conceptual foundations and have...

But don't the EM waves interacting with either a beam splitter or a dielectric interface essentially mean that you're dealing with media and therefore have multiple values of ## \rho ## for example? That's where I believe I see the non-linearities arise.