Bohr model and Quantum Mechanics stabilize the atoms in order to have a minimum state (due to some effective or centrifugal force) avoiding electrons to hit the nuclei. Thus, electrons (accelerated charges) do not emit electromagnetic waves, losing energy until they fall down into the nucleus.

Quantum gravity: we know that classical gravity emitting GRAVITATIONAL waves, inspiral (just like classical atoms emitting electromagnetic waves), but...Shouldn't quantum gravity avoid this? That is, when (small) bodies theoretically approach Planck length, are they stabilized? Should we expect a similar stabilization from quantum gravity? What string theory says about this problem (2 particles, in strong gravity, with a radius when radiation and backreaction are important)? And LQG?

  • $\begingroup$ Well, when the Schwarzschild radius of a small black hole recedes behind its Compton wavelength (at the Planck length, as you indicate) a workable consistent theory of gravity should strive to describe the system. You surely are not proposing a semi-realistic one such, are you? $\endgroup$ – Cosmas Zachos Mar 15 '18 at 16:58
  • $\begingroup$ No, but as string theory is generally considered finite (even SUGRA N=8 could be even finite), I was wondering if it (they) have a consistent answer of what happens with gravitational radiation just as Bohr model cheated and stated electrons were "stationary" and "non radiant" until QM was built. I mention string theory as I know the theory but, as far as I know, I have never seen an answer to this type of question (unless I missed some paper on gravitational wave emission and backreaction in string theory, another option). $\endgroup$ – riemannium Mar 15 '18 at 17:01
  • $\begingroup$ Oh, if you wanted the analog Bohr-like radius of a semiclassical gravitational "atom" of a neutron and an electron, it would be x times larger than the Hydrogen atom Bohr radius, where $x\sim (m_{pl}^2/m_e m_n 137)\sim 2\cdot 10^{39}$. $\endgroup$ – Cosmas Zachos Mar 15 '18 at 18:52
  • $\begingroup$ Yes, that is part of my puzzle...Because it works for light particles as electrons or neutrons, not for massive particles...Take two very massive objects instead of elementary particles...I find the question shocking... I know about gravitational atoms, I wrote about them in my blog... $\endgroup$ – riemannium Mar 15 '18 at 18:56
  • $\begingroup$ I have trouble thinking of a stringy model of a purely gravitationally bound state of a small number of entities (massive D0-branes?), because other forces always come into play ("gravity is the weakest force"). $\endgroup$ – Mitchell Porter Mar 15 '18 at 23:53

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