It appears that some new formulation is required satisfying the requirements of both Classical mechanics & Quantum mechanics, QM is the theory of the day while CM is the theory of Night and for simple reasons we cannot ignore these two. QM is applicable only to confinements only, while, at large, CM does not require any such things. All the above mathematical fantasy is not required. Solution lies in origin, not in elaborate mathematical structures. My simple question at this is this, whether all these QFT, QED, SRT, GR...... say any thing with which we started e.g. Blackbody emission spectra, photo electric effect, and the photon itself...? All the explanations existing in these theory just try to express their outer manifestation they even did not touch the ground of very cause. If we see and try to understand CM: everything is explainable.

All: Forget classical mechanics as soon as possible. Maxwell equations depend on the existence of classical waves, but they and particles (in any mixture) are denied by QM. Only quantum waves exist in Nature.

With Maxwell equations, this is similar to watching a game of Go, yet describing it using the rules of Chess.

All: For example, according to classical mechanics there can be no diamagnetism and no paramagnetism at all, using Maxwell equations. Yet, paramagnetism, diamagnetism, precessing orbits, and so on, exist in Nature.

Referring to your statement: "... the answer lies not in physics per se, but in the use of conventional mathematics, which predicates a supposed Newtonian "continuity", "infinitesimal", and "infinity" that, however, do not exist in Nature -- and then we modified and extended GR to be compatible with QM, by using proper mathematics... ", it seems that my old research into Foundations of QM / Quantum Logic Article Nonstandard extension of quantum logic and Dirac's bra-ket f...

@Ed

What are quantum waves? Please elaborate on it. I never heard of it.

DKM and all: I found about 64,300 results for an exact search in google, after "quantum waves". In physics, "quantum waves" usually denotes the third case of the three hypotheses for the double slit experiment, the only hypothesis that explains all experiments including at low intensity when only one photon is in the apparatus. The other two possibilities are classical, and fail, of particle or classical waves.

This is explained in the references given (including a video from Feynman):

1. https://www.researchgate.net/post/Is_it_better_for_students_to_view_the_double_slit_experiment_as_three_different_cases_or_two

2. https://www.youtube.com/watch?v=GzbKb59my3U

@Ed

The video part is wrong explaination of the interference pattern. It aslo uses the word single photon which is severely wrong. Single photon has never been detected, instead they occurs in pairs, it is common to see wrong vocabulary used by optical researchers.

And the second link also does not corroborate it.

DKM: You diverge from physics, and optical researchers have been at the forefront of quantum physics, for example with the laser. History is not yours, to be made up. Please delete your answer and respect the RG ToS.

@Ed

Another mistake in that forefront, plane of plarization = spin direction, what about this? Thank you

All: More than challenge the status quo, which often just makes people mad as one often sees, one can try to offer a way forward, out of the quagmire of "classical physics" that once served a purpose but today prevents new horizons  to be seen.

JL: You diverge from physics. History is not yours, to be made up. Please delete your answer and respect the RG ToS.

All: It strains me to see a connection between some comments still above, and this thread -- it's all off-topic here.

These "points" are also not allowed under free speech rules -- a theater is not free speech, NO audience member can yell "FIRE". It is a crime (US). As another counter-example, ad hominem attacks are not allowed in research, nor here. We also should NOT consider at all that there is presently a king in France.

It thus strains me to see a connection with these "comments" in this thread -- it's off-topic. These are also not allowed under free speech rules. Please delete any message that is off-topic here.

All: See Preprint On the Sun's Gravity and the Topology of Mercury's Orbit

You are wrong, Maxwell eqs. are perfectly relativistic in the sense of SR.

That they are Classical and may miss out on QM, is another issue altogether.

This is remedied usually by replacing p by p-qA, and translating to QM by means

of p= -i hbar grad ,as operator, in a Hamiltonian, as well as energy going to

i hbar d/dt. Then you could ask if the corresponding QM treatment is relativistic or not, according the the choice of Hamiltonian. This proceedure is enough to discuss the ABeffect you mention, or the energy spectrum of electrons in a magnetic field.

Of course the AB and levels of a particle in a magnetic field (Landau levels) refer

specifically to a particle in external fields, and not fields themselvs, as in the Maxwell equations. These later, the fields, are quantized from the proceedure of field quantization, which do not require a modification of Maxwells equations themselvs.

JW: Again, this is not physics - it does not happen this way in Nature -- no matter how often it is said, or who said it. This is not humanities. EM is quantum, not classical. There is a gulf between both behaviors, both micro and macroscopically.

The laser in EM is now 60 years old, certainly a macro phenomenon, but utterly quantum. In May of 1960, Ted Maiman fired the first laser, a low powered ruby laser.

EM is also not according to Einstein SR, but to Minkowski SR.

To some extent you are correct, if you deal with photons or lasers.

However if you just deal with Maxwell equations by themselvs, this is

considered classical and comes from a time prior to the quantum age,

the ninteenth century. Maxwell did not know quantum stuff.

I use classical from its historical sense.

To say its quantum you disrespect history. It is clearly older than just 60 years.