In string theory gravity is described by a condensate of a gravitons between (and around) masses, modeled in accordance with the interactions of the three basic forces, the EM-, the strong color- and the weak nuclear force (in contrast to its competitor Loop Quantum Gravity which takes General Relativity as a starting point). The condensate of gravitons between two masses contains "the message" for the masses to get closer to each other.
In flat Minkowski spacetime, as assumed in string theory, a geodesic is a straight line between spacetime points. The gravitons though cause an object to deflect from this straight line. This would mean the object will deviate from the geodesic and according to GR, this means the object "feels" an acceleration (just as the deviation from a geodesic in the curved spacetime in GR will cause an acceleration of the object, which we would feel when attached to the object), say by putting a constraint on the movement of the mass.
So why don't we feel an acceleration when we are attached to an object that moves on this non-geodesic path?

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    $\begingroup$ Photons do not form condensate. This should be also true for gravitons that represent a linear approximation for general relativity. $\endgroup$ – Jon May 3 '18 at 12:02
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    $\begingroup$ What do you mean by the word feel? We don't feel gravity. We observe the effect of a gravitational force as an acceleration of our body's rest frame. When we sit in a chair, our nervous system tells us the chair is pushing up, and we interpret that as "gravity," but it's really the EM-based normal force from the chair. $\endgroup$ – Bill N May 3 '18 at 12:19

The reason you do not feel gravity in free-fall has very little to do with the quantum nature of gravity (whatever that may be).

The human body can't really feel acceleration directly. What it can feel is tension and compression caused by non-uniform acceleration. It's similar to how you can't feel air pressure around you, despite the fact that one atmosphere of pressure applied to just one part of your body can cause some serious damage.

A uniform gravitational field always provides a uniform acceleration. No matter your quantum mechanical model for gravity, it doesn't change the fact that whatever force is applied to each individual molecule in your body produces the same acceleration, and so there's no non-uniformity to feel.

Since humans don't have access to any significantly non-uniform gravitational field, you can never feel its force in free fall.

  • $\begingroup$ "The human body can't really feel acceleration directly" - Sure it does, try skydiving some time (C-license, Instructor-B, Coach-2). Or a rollercoaster. The inner ear is there for a reason. $\endgroup$ – Maury Markowitz May 3 '18 at 19:12
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    $\begingroup$ @MauryMarkowitz The acceleration is non-uniform in both cases, due to air resistance and the force of the car on you. Gravity accelerates your inner ear at the same rate as the rest of you. Otherwise astronauts in the ISS would go crazy ;) $\endgroup$ – Chris May 3 '18 at 21:20

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