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Imagine there is no EM or Nuclear Force, and Gravity is the only force.

Can gravity alone produce an atomic structure similar to a basic atom?

In this scenario, the nucleus is just a single particle. The electron is another particle with only mass and angular momentum, like a planet orbiting a star.

How feasible is it for Gravity alone to produce such a structure and hold it together, with energy and mass equivelent to those of simple hydrogen nuclei, electrons and matching speed/energy of orbits and angular momentum

Qmechanic
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kvi
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    Does this address the question? https://physics.stackexchange.com/q/27498/180843 – Sten Sep 10 '23 at 01:23
  • Im sorry im kinda of more a lay-person in this area. That response is too complex for me.

    I mean, i know its not a simple question, but if experts can sufficiently comprehend my query. I am basically asking could the simplest atoms hypothetically exist using only gravity, if the nuclei and electrons were just basic particles with mass but no charge.

     – kvi Sep 10 '23 at 01:28
  • Starting far apart, there is no way to lose energy and end up in a stable, small orbit. – Jon Custer Sep 10 '23 at 01:33
  • We know the mass of electrons and protons, and the bohr radius for hydrogen. So is it possible for those masses, for an electron to orbit a proton at the borh radius using jus gravity.

    Im just tring to understand how differntly would a simple hydrogen atom behave, if it was just a nucleus with mass, an electron with mass, at the base orbit, and only gravity and no other forces,

     – kvi Sep 10 '23 at 01:50
  • @JonCuster, there is a way: gravitational waves. See answers to this question https://physics.stackexchange.com/questions/275619/are-gravitational-atoms-stable-without-quantization?rq=1 BTW I find odd that somebody proposed to close this question as non-mainstream physics. I would close as a duplicate. – GiorgioP-DoomsdayClockIsAt-90 Sep 10 '23 at 11:35

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In a universe where only gravity exists, every form of mass would eventually collapse to a region that is within its own event horizon. So naively, one may assume the particles in question to be tiny black holes, although, at these tiny scales, general relativity would likely need to be modified.

However, if naively one thinks of the atom using the simple Bohr model. Analogous to electromagnetic radiation, here we will have gravitational radiation that will remove energy and angular momentum from the orbit of the two-particle system. However, we might postulate certain configurations to be stable, as is done in the Bohr model.

Unfortunately, these configurations would have a very large radius as $$ r_n = \frac{n \hbar}{mv} \,, $$

$n$ being the quantum number, and $v$ is the orbital velocity for a circular orbit. This can be further shown to be (check the link above and calculate)

$$ r_n = \frac{n^2\hbar^2}{G m_\mathrm{e}^3} $$

which will give very large radius.

S.G
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  • Can you provide references for your first paragraph? That the earth collapses into a black hole if we "turn off" interactions other than gravity, I'm fine with this. But that a single particle, say an electron, would collapse into a tiny black hole, seems fishy to me as an electron does not have any substructure (as per our current understanding of the standard model). Moreover, this electron would be an over extremal BH which is problematic. – Jeanbaptiste Roux Sep 10 '23 at 09:44
  • @JeanbaptisteRoux I can't provide a reference. It is more of an opinion. But with only gravity around, we would not have a standard model, I think. I wrote that paragraph assuming that there is a particle with the mass of an electron but otherwise does not have the properties one would expect for an electron. – S.G Sep 10 '23 at 09:47
  • I think you should explicitly write that this is an opinion. We don't even know if General Relativity still holds at such a scale: maybe it is emergent, maybe it is non-commutative at the Planck scale, or maybe geometry is quantized, etc. – Jeanbaptiste Roux Sep 10 '23 at 09:53
  • @JeanbaptisteRoux Thanks. I have modified the text. Frankly, it is a statement made in passing and not to be taken seriously. – S.G Sep 10 '23 at 10:05
  • Oh thanks, that helped to clarfy things. I understand the 'orbital' distance would need to be massive, much more than current hydrogen atoms.

    You say without the other forces mass particles would collapse into themselves. Thats an interesting idea.

    I was looking at the feasibility of EM and smaller forces 'coming into existence' after Gravity and Mass had already produced large structures like Galaxies, Stars and Planets. In that scenario, specific qualties of Mass would balance Gravity and stop collapse in some configurations, while other configurations would collapse into black holes.

     – kvi Sep 10 '23 at 11:41
  • This would be some property of matter. So looking at this way, it maybe that this property or mechanism that may have been a part of matter, became 'codifed' as part of the 'later' forces, perhaps removing this mehcanism from matter itself. Thanks. Let me know if you further thoughts on this. – kvi Sep 10 '23 at 11:42
  • @kvi Without other forces structure formation like planets etc. won't be possible I think. Anyway, if you found the answer helpful please consider voting/approving it. – S.G Sep 10 '23 at 11:50
  • @S_G Upvoted. How can I learn more about the mechanisms by which other forces act against gravity to stop collapse at larger scales? You mean they can form, but will collapse, rather than not form at all? – kvi Sep 10 '23 at 11:58
  • @kvi structure formation happens over time. But gravity by itself would prevent the formation of a stable structure like a proto-planet due to its attractive nature. – S.G Sep 10 '23 at 12:05
  • @S_G "But gravity by itself would prevent the formation of a stable structure like a proto-planet due to its attractive nature". Sorry to keep asking, but it seems counter-intuitive that gravity would prevent teh formation of stable structures like planets. I always understood it is gravity causing these structures. Do you mean that Gravity would clump everything together in a big mess, like a uniform mass rather than distinct planets, and other mechanisms like perhaps EM is required to form distinct planets from the earlier universe – kvi Sep 10 '23 at 12:28
  • Yes, the reason our planet is in a stable configuration is due to the EM repulsion between its constituents. If you remove that, then it will collapse (although QM degeneracy will halt it eventually, but that again requires fermions to exist) – S.G Sep 10 '23 at 12:33