# Can Gravity alone produce a simple Hydrogen or Helium atom?

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

• Does this address the question? physics.stackexchange.com/q/27498/180843
– Sten
Commented Sep 10, 2023 at 1:23
• 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
Commented Sep 10, 2023 at 1:28
• Starting far apart, there is no way to lose energy and end up in a stable, small orbit. Commented Sep 10, 2023 at 1:33
• 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
Commented Sep 10, 2023 at 1:50
• @JonCuster, there is a way: gravitational waves. See answers to this question physics.stackexchange.com/questions/275619/… BTW I find odd that somebody proposed to close this question as non-mainstream physics. I would close as a duplicate. Commented Sep 10, 2023 at 11:35

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.

• 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. Commented Sep 10, 2023 at 9:44
• @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
Commented Sep 10, 2023 at 9:47
• 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. Commented Sep 10, 2023 at 9:53
• @JeanbaptisteRoux Thanks. I have modified the text. Frankly, it is a statement made in passing and not to be taken seriously.
– S.G
Commented Sep 10, 2023 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
Commented Sep 10, 2023 at 11:41