What if atoms obeyed an inverse-cubed law

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In a universe governed by an inverse-cubed law, atoms would be impossible due to the lack of stable electron orbits. This instability arises because such a potential does not allow for a ground state, which is essential for atomic structure. Additionally, the conservation of flux, a key feature of the familiar inverse-square laws, would be compromised. The discussion highlights that these principles are often overlooked but are critical for the existence of stable matter. Ultimately, the implications of an inverse-cube law would fundamentally alter the nature of atomic and molecular formation.
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atoms would be impossible in a universe ruled by an inverse-cube law because there would be no stable orbits for electrons.

The above sentence comes from Rees' book Just Six Numbers. I don't get it. Why would an inverse-cube law affect the stability of electron orbits?
 
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Because for an inverse-cube potential, there is no ground state!
 
they will obey inverse cube law if universe had 4 space dimensions
 
Bill_K said:
Because for an inverse-cube potential, there is no ground state!

Not to mention flux is no longer conserved. That's a special property of 1/r^2 laws that we often take for granted.
 

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