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Mudassir Ali

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A2A.: Mu. (No.)

Absence of proof is no proof of absence.

We do not have proofª that “gravity has no quantum properties”;

we (“merely”) have no proofª that gravity does have quantum properties.

So, where/how might we possibly see any proof of absence (or presence) of quantumness in gravity?

The simplest “back of the envelope” estimates stem from simply extrapolating general relativity and quantum mechanics to where they might meet, and that yields distances of the order 10−35m, and notice that this is some 13 orders of magnitude (ten-million-million times) smaller than the currently teensy-tiniest experiments we can muster (Penning trap, trapping electrons to within aboutº 10−22m).

Thus, we have no proof of quantum properties of gravity because our best experiments do not have good enough resolution.

Kind of like how we cannot see “sunspots” on V762 Cas in Cassiopeia (see How To See The Farthest Thing You Can See).

BTW, one such simplest “back of the envelope” estimate is as follows: A probe with the de Broglie (quantum) wavelength λdB=h/mv=h/2mEkin−−−−−−√ (λdB=hc/Ekin, for ultra-relativistic probes) hits a target, which we are trying to probe. The probe and the target interact, forming composite system. For the probe to be able to leave the site of interaction so as to provide information about the interaction and target, the escape-velocity of the probe+target composite system† should not be bigger than the speed of light. This is equivalent to requiring λdB to be no smaller than the (general relativity) horizon radius, rh, which generally grows linearly with the mass‡ of the probe+target composite system. Since λdB diminishes with the energy of the probe while rh grows with the energy of the probe, they must meet somewhere. The numerical value of this critical distance (~ Planck length) is obtained by extrapolating the quantum and general-relativistic formulae that are well established in their respective regimes.

There are other, variously set-up and analyzed “back of the envelope” estimates, but they all yield the same ballpark estimate.