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In quantum gravity, it's tried to quantize the gravitation. However, if I got it correctly, most quantum gravity approaches try only to quantize gravity as a force, the curvature of spacetime, not the spacetime itself. (Please correct if this is wrong.) The quantum effects of such theories are studied at the centres of gravity, where gravity is really strong.

In contrast, I would like to think about "how would it look like if the spacetime itself was the thing that we have to quantize to describe nature better?" In the general spherically symmetric solution to the Einstein Field Equations, the prefactor in front of the $dr^2$-component is always bigger than 1. And it is growing when mass increases. That can be written as 'with more mass, there is more space'. Therefore, for me, it seems plausible and reasonable that spacetime itself is something which adds up and needs to be quantized. The effects of such a theory could be studied at the far distance from the centres of gravity, where gravity is expected to be weak.

Are there theories which build up on that?

Or is there a reason not to look this way round?

Or do indeed the quantum gravity theories look this way round and I only got it wrong?

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  • $\begingroup$ There are plenty of them, take a look at Hossenfelder's article on them. $\endgroup$ Mar 31 at 7:53
  • $\begingroup$ It's an interesting article. But looking for a minimal length scale is high energy gravity, densest possible packing of spacetime. "testing short distances requires focusing large energies in small volumes, and when energy densities increase, one finally cannot neglect anymore the curvature of the background." (in your link, introduction) - - - What I'm craving for instead is real background independence. $\endgroup$ Mar 31 at 8:39
  • $\begingroup$ I deleted the edits which were done to my question. In detail, I deleted the word "discrete". The word "discrete" leads the question in direction to small scales, granular spacetime, high energies and high curvature, black-holes-related. However, my question is about spacetime itself without any other background, where there is low energy, no energy-related curvature, empty-space. $\endgroup$ Mar 31 at 9:01
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    $\begingroup$ It seems likely that any theory of quantum gravity would regard spacetime as quantum in nature. Or do you mean something more specific with the phrase? $\endgroup$
    – Qmechanic
    Mar 31 at 9:01
  • $\begingroup$ I have something in mind that is infinite in extension (radius) but finite in volume. $\endgroup$ Mar 31 at 9:09

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I know only of loop quantum gravity:

It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. As a theory LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale above the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.

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"Loop quantum gravity" is the theory you are looking for. At its most basic, space itself is particulate with each particle being about Planck length. LQG is being studied by many physicists as an alternative to string theory. You can get started by looking at Carlo Rovelli's book Covariant Loop Quantum Gravity

In notes from my own speculative paper: Carlo Rovelli noted, “The physics of quantum gravity is the physics of the quantum fields that build up spacetime… A region of space can be described by a set of interconnected grains of space… The length of these links is determined by the field itself because geometry is determined by gravity.” Likewise, physicist Jim Baggott noted “LQG suggested that at the Planck scale, space is discrete, composed of individual units or quanta – the loops themselves. These represent the building blocks of space, which is formed from a weave, but more like chain mail produced by linking individual loops of steel than linen produced by weaving continuous threads. This kind of model suggests that space cannot be continuously variable. At the Planck scale, there must be some kind of ultimate area or volume which cannot be transcended. There can be no area smaller than the smallest area; no volume smaller than the smallest volume.”

And further on in my paper: Dr. Don Lincoln from Fermilab said “When you add mass and energy, you can distort the shape of the little volumes of quantum space… Bending space and time has a property that you can distort the local definition of space.” Likewise Arvin Ash noted “How do particles traverse this quantized space? When mass and energy are added to the spin foam the shape of the volumes of the spin network is distorted. This distorts space and time… This distortion of space and time is what we perceive as gravity.”

So in answer to your basic question about quantum spacetime rather than just quantum space, it appears that adding energy to this particulate space leads do a dilation of space and thus a dilation of time - and becomes the ultimate source of gravity - at least in this theory.

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