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Padmanabhan (and also Klinkhammer and others) argues that even classical gravity is already "quantum"...since:

$$F=G\dfrac{Mm}{r^2}=\dfrac{L_p^2 c^3 Mm}{\hbar r^2}$$

Is this "naive" argument right? And related to this, how should we understand holography in newtonian gravity, provided it makes sense?

References:

  1. https://arxiv.org/pdf/0912.3165.pdf
  2. https://arxiv.org/pdf/gr-qc/0703009.pdf
  3. https://arxiv.org/pdf/1006.2094.pdf
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  • $\begingroup$ What's the reference? $\endgroup$ – Avantgarde Oct 9 '18 at 18:07
  • $\begingroup$ References added $\endgroup$ – riemannium Oct 9 '18 at 19:54
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As the Planck length $\ell_{\mathrm {P}}$ is defined in terms of the gravitational constant: ${\displaystyle \ell _{\mathrm {P} }={\sqrt {\frac {\hbar G}{c^{3}}}}}$, then yes, trivially we have $G = \ell_{\mathrm {P}}^2c^3/\hbar$. This is no way implies that classical gravity is 'quantum', at least not in any sense that the term quantum is normally used.

And it doesn't seem like those papers are suggesting that. Instead it is talking about an alternative perspective where the Planck length is fundamental instead of $G$. Quoting from the third paper:

Moreover, having a new fundamental constant $l$ may help in resolving a potential problem of Verlinde’s approach regarding the total entropy of a general equipotential screen.

Being able to reconstruct the classical limit would be that minimum that would be possible if entropic gravity is true.

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