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R. Feynman was troubled by this question. He claimed there was no classical explanation. In fact by his classical analysis, the electron would spiral into the proton in approximately one nanosecond.This problem is formally the referred to as "atomic stability", in this case of "the atomic stability of the hydrogen atom". In 1911 Planck proposed his second quantitation theory where he introduced the concept of an energy sea that we now refer to as Zero-point radiation. after a rocky start. it is now mainstream research that is used to in QED, "Lamb shift", the "anomalous g-factor of the electron" and "atomic stability of hydrogen" I suggest a look at the following link as background: https://en.wikipedia.org/wiki/Zero-point_energy

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    $\begingroup$ I'm puzzled that Feynman was troubled by that. Do you have a relevant quote? Perhaps he was speaking rhetorically, and was explaining that because atoms don't behave classically we had to develop a theory (quantum mechanics) that gives us a better model for atoms. $\endgroup$
    – PM 2Ring
    Jun 18, 2021 at 11:17
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    $\begingroup$ @PM2Ring, I too am puzzled. The claim that there is no classical explanation is a statement of fact, but not one of being troubled. I would like to see a quote too but the OP seems unwilling to back up these statements, and keeps having conversations deleted. $\endgroup$
    – user196418
    Jun 19, 2021 at 15:09
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    $\begingroup$ If the question here is about Feynman’s mental state (“troubled” or not), or about Feynman’s hyperbolic style of describing interesting and surprising results, then the question is off-topic for Physics. The calculation that a classically-orbiting electron would crash into its nucleus predates Feynman: the axiom “let’s just assume that doesn’t happen” is fundamental to the Bohr model. $\endgroup$
    – rob
    Jun 19, 2021 at 18:04
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – ACuriousMind
    Jun 20, 2021 at 10:22

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No, there is no classical explanation of atom/matter stability. Classical physics (a combination of Newtonian mechanics + electrodynamics - Larmor) predicts the total loss of energy of the electron in orbit by radiation, therefore the "classical elementary atom" proposed by E. Rutherford in 1911 would not exist. So the question in the title has a very simple almost trivial answer.

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    $\begingroup$ Hence the need for quantum mechanics… $\endgroup$
    – Jon Custer
    Jun 18, 2021 at 10:56
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If there was a classical explanation for the stability of the Hydrogen atom there would be no reason for a quantum mechanical description. Classical mechanics simply cannot provide explanations for several observed phenomenon and theoretical descriptions of atomic systems.

In short, classical electrodynamics predicts that an accelerating charge will emit radiation. Conservation of energy states that if energy appears in the radiation field, the accelerating charge must lose mechanical energy. Along with other reasonable assumptions there is no other conclusion than the particle orbit gets smaller, eventually collapsing on the other particle.

There are a lot of things one can question to try and fix this. For example, both the electron and proton are moving, as current loops, about the center of mass. Could they be exchanging classical radiation? I don't think so. People have tried for quite some time to look for issues with the early classical descriptions of atoms to see if adding more physics would lead to a stable state. This has failed. Much like Mercury's orbit not following Newton's law of motion using his gravity model. Eventually Einstein had to develop General Relativity to describe this.

This inability to describe the stable atom with classical physics, and the ability to do so with QM, is one of the major achievements of QM.

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    $\begingroup$ Just as an aside, I'd argue that the precession of mercury's perehelion was not the reason general relativity was needed (the inconsistency of newtonian gravity and special relativity was the big motivator here), but rather, the anomaly in mercury's orbit was a nice confirmation, available in 1916, that general relativity could be right. $\endgroup$ Jun 19, 2021 at 16:56
  • $\begingroup$ @Jerrie Schirmer....I'm always wrong , but did Newton know that gravity travels at the speed of light and the lines of force between the sun and Mercury are therefore curved? $\endgroup$
    – barry
    Jun 19, 2021 at 17:09
  • $\begingroup$ @barry In Newtonian physics, gravity propagates instantly, and if you try calculating orbits with gravity propagating at c (as it does in GR), Bad Things happen, as Laplace discovered. Please see physics.stackexchange.com/q/5456/123208 especially the answers by hawkeye & user154997, as well as various other questions linked on that page. $\endgroup$
    – PM 2Ring
    Jun 19, 2021 at 18:54
  • $\begingroup$ @JerrySchirmer, while you are correct that this anomaly did not necessarily require GR every attempt to estimate it using Newtonian gravity failed. My point with that example was that there was no saving Newtonian Gravity, even in Newton's day. $\endgroup$
    – user196418
    Jun 19, 2021 at 20:58
  • $\begingroup$ I think the core point is that no one would throw out as well-established theory as Newton's gravity over an anomaly as small as 73 arc seconds of unexplained precession per century, without a bunch of other good reasons -- a small systematic error of some form or another would be enough to fix that. $\endgroup$ Jun 19, 2021 at 21:48
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There is no classical explanation for it for a lot of reasons, one of them being that in classical physics (and in chemistry, etc.) words like electrons, atoms, etc are just that: words, placeholders, wildcards...

In classical physics, an electron is defined as the theoretical smallest part of a charge or as a « grain » of charge or as the particle making up electrical currents, charges, etc.

That kind of macroscopic definition says nothing about the behavior of a single electron.

Therefore, the popular / classical image of the electron as a very tiny spherical ball of electricity is just plain wrong. That’s why it leads to apparent paradoxes.

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  • $\begingroup$ You are right on the money with this. The very paradigm of "what matter is made of" is what is at stake here. Your answer is one of the first times I have seen another scientist express this. $\endgroup$
    – user196418
    Jun 19, 2021 at 22:17
  • $\begingroup$ @ggcg....I have given a cogent Maxwellian / Planckian explanation of atomic stability that has failed to be critiqued in matters of fact. Many of my comments and answers are removed, "poor quality", "off topic", disguised rant","go to a history site", "not mainstream" I'm currently banned from asking question? $\endgroup$
    – barry
    Jun 23, 2021 at 2:36
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The closest thing to a classical explanation is a calculation that indicates that electron orbitals in a hydrogen atom correspond to resonant 3D standing wave patterns, with the wave packet associated with an electron being bounded by the E field from the nucleus. Though some of the patterns do have a non-zero amplitude at the position of the nucleus, the probability of an interaction within that very small volume is quite low. There are some unstable nuclei that have the ability to do a “K capture”.

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  • $\begingroup$ @R. W. Bird...Zero-point radiation provides the energy to keep the electron away from the proton. There is also a enormous (relative to coulomb force) short range nuclear force that prevents the electron from entering the proton. This is current mainstream physics. $\endgroup$
    – barry
    Jun 21, 2021 at 17:50
  • $\begingroup$ @R. W. Bird..."K capture is totally irrelevant for the hydrogen atom" the spiraling electron cannot radiate into the energy sea of the Zero-point energy, Maxwell forbids this, it is equivalent to a dipole trying to radiate into a closed cavity, the radiation resistance goes to zero the input impedance becomes purely imaginary. this technique can be used to extend transition times of particles indefinitely even the so called uncertainty of nuclear decay can be extended using this technique. I refer you to the to the wiki link in the original post, on Zero point. $\endgroup$
    – barry
    Jun 23, 2021 at 2:55
  • $\begingroup$ I did not say that K capture occurred in hydrogen. I was just pointing out that in some cases, electrons do get sucked into the nucleus. $\endgroup$
    – R.W. Bird
    Jun 23, 2021 at 13:12
  • $\begingroup$ @R. W. Bird... No comment on the Wikipedia link re: Zero-point radiation that is the question? $\endgroup$
    – barry
    Jun 23, 2021 at 13:28

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