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## Main Question or Discussion Point

I often encounter statements to the effect that classical physics cannot describe processes at the atomic and subatomic level. I also understand fully well that no one ever has to date successfully described these quantum processes, even the most basic ones, using classical physics. But that something has never been done is not a proof of impossibility, obviously. So, what are the best arguments for the universe being essentially non-classical? I would like to find out if there are some I don't know, and whether I can sustain an argument that the position that quantum theory is unique and essential is no more than an observation that there is no classical description that works.

To start it off I will offer the problem of radiative decay of the classical atom. This is one of several arguments for essentialness of quantum theory I can think of off the top of my head. If we consider the Rutherford (i.e., planetary) model of hydrogen where the electron orbits the proton under Coulomb attraction, in Keplerian orbits, it is commonly claimed that this system must decay due to radiation damping. For highly-excited states, such as in Rydberg atom experiments, this type of radiative decay is a good description of observations. Yet obviously atoms do not decay beyond a ground state. You are probably wondering how I could possibly rationally propose that classical physics could nonetheless result in a stable and nonradiative atom. Yet not only do I think it plausible, I even think there is a fair amount of progress in constructing just such a model.

The reason I believe it's rash to conclude quantum theory is unassailably fundamental to describing the atom, is that even the simplest atom, hydrogen (or even simpler still, positronium) has not been solved in classical electrodynamics. This is not disputed in the literature. The electromagnetic two-body problem has not been solved and people are publishing papers on it in Physical Review E and Jour Math Phys and on arxiv.org as recently as a few weeks ago. The problem is rigorously handling the effect of propagation delay, as well as the radiation damping force. The former leads to functional differential equations of motion rather than ODEs, while the latter leads to third-order-in-time equations and run-away solutions. The latter problem is in Jackson (see the last chapter, the Abraham-Lorentz equation, or for that matter Abraham-Lorentz force on wikipedia). Raju is openly suggesting in a 2004 Foundations of Physics paper (here as #4 with his new one as #3: [I had to remove the links due to not enough posts yet but search c k raju on arxiv dot org]) that the origin of quantum behavior is potentially due to that the proper equations of motion of the EM two-body problem are functional differential equations, not ordinary ones. De Luca has done a series expansion of the full classical electrodynamic Lagrangian for hydrogen and kept only the linear terms and solved it to find stable (i.e. non-radiative) orbits at approximately the proper energy levels, and an explanation for monochromaticity of transition radiation, and all without introducing Planck's constant. This was in Phys Rev E in 2006, also on arxiv here: [search Jayme De Luca on arxiv dot org]. What De Luca did seems to me is essentially what was proposed by Hestenes at least as early as the 90s, that zitterbewegung resonances could explain both atomic stability and monochromaticity of transition radiation (these links are tougher although Hestenes has two recent posts to arxiv I intended to post links to some papers elsewhere. The first is "Zitterbewegung in Radiative Processes" which I did link to in my blog entry #2. The other is a page with about 10 different quantum-theory and zitterbewegung related papers on Hestenes' personal cite, which I found from the wikipedia article on him.)

So, seems to me, the facts that no one has done it, and that until recently no one had any ideas for how to do it, isn't a safe basis for claiming that classical physics can't yield up quantum behavior. Personally I suspect it can and will but I am interested to know if there are some convincing arguments I am overlooking. I look forward to your responses.

To start it off I will offer the problem of radiative decay of the classical atom. This is one of several arguments for essentialness of quantum theory I can think of off the top of my head. If we consider the Rutherford (i.e., planetary) model of hydrogen where the electron orbits the proton under Coulomb attraction, in Keplerian orbits, it is commonly claimed that this system must decay due to radiation damping. For highly-excited states, such as in Rydberg atom experiments, this type of radiative decay is a good description of observations. Yet obviously atoms do not decay beyond a ground state. You are probably wondering how I could possibly rationally propose that classical physics could nonetheless result in a stable and nonradiative atom. Yet not only do I think it plausible, I even think there is a fair amount of progress in constructing just such a model.

The reason I believe it's rash to conclude quantum theory is unassailably fundamental to describing the atom, is that even the simplest atom, hydrogen (or even simpler still, positronium) has not been solved in classical electrodynamics. This is not disputed in the literature. The electromagnetic two-body problem has not been solved and people are publishing papers on it in Physical Review E and Jour Math Phys and on arxiv.org as recently as a few weeks ago. The problem is rigorously handling the effect of propagation delay, as well as the radiation damping force. The former leads to functional differential equations of motion rather than ODEs, while the latter leads to third-order-in-time equations and run-away solutions. The latter problem is in Jackson (see the last chapter, the Abraham-Lorentz equation, or for that matter Abraham-Lorentz force on wikipedia). Raju is openly suggesting in a 2004 Foundations of Physics paper (here as #4 with his new one as #3: [I had to remove the links due to not enough posts yet but search c k raju on arxiv dot org]) that the origin of quantum behavior is potentially due to that the proper equations of motion of the EM two-body problem are functional differential equations, not ordinary ones. De Luca has done a series expansion of the full classical electrodynamic Lagrangian for hydrogen and kept only the linear terms and solved it to find stable (i.e. non-radiative) orbits at approximately the proper energy levels, and an explanation for monochromaticity of transition radiation, and all without introducing Planck's constant. This was in Phys Rev E in 2006, also on arxiv here: [search Jayme De Luca on arxiv dot org]. What De Luca did seems to me is essentially what was proposed by Hestenes at least as early as the 90s, that zitterbewegung resonances could explain both atomic stability and monochromaticity of transition radiation (these links are tougher although Hestenes has two recent posts to arxiv I intended to post links to some papers elsewhere. The first is "Zitterbewegung in Radiative Processes" which I did link to in my blog entry #2. The other is a page with about 10 different quantum-theory and zitterbewegung related papers on Hestenes' personal cite, which I found from the wikipedia article on him.)

So, seems to me, the facts that no one has done it, and that until recently no one had any ideas for how to do it, isn't a safe basis for claiming that classical physics can't yield up quantum behavior. Personally I suspect it can and will but I am interested to know if there are some convincing arguments I am overlooking. I look forward to your responses.