[trhway]

>Say we have an experiment which puts an object with non-negligible stress-energy into a superposition of being in two different positions (for example, we make its position depend on the outcome of a spin measurement on a qubit). QM would say that spacetime would then need to also be in a superposition of two different geometries.

The energy to move the object into a given position is an additional element here unaccounted for in your model. 2 different positions to move object into - 2 different energies (more specifically 2 different changes to the starting, before the experiment, stress energy distribution of the Universe). When corresponding moving energies (ie. their GR effects) are accounted for in those 2 cases it may as well be that those 2 cases are indistinguishable from the GR point of view, ie. those 2 supposedly different spacetime geometries happen to be the same. The superposition of 2 indistinguishable cases - it doesn't really matter is it superposition or not.

[qnleigh]

There is an entire sub-field of experimental science that involves putting ever larger objects in superpositions of different locations. These experiments are no closer to testing quantum gravity, but they falsify whatever it is you're trying to say here. See https://www.nature.com/articles/srep13884 for a random example.

[pdonis]

> The energy to move the object into a given position is an additional element here unaccounted for in your model.

You can set the experiment up so the energy is the same in both cases (for example, both positions at the same height, just horizontally separated). If you don't, then yes, you have to include the effects of the different energies in your model.

> When corresponding moving energies (ie. their GR effects) are accounted for in those 2 cases it may as well be that those 2 cases are indistinguishable from the GR point of view, ie. those 2 supposedly different spacetime geometries happen to be the same.

I'm not sure how this would work if the energies were different, since "different" means a different source for the spacetime geometry.

But in any case, yes, for such an experiment to be relevant at all to the question I was discussing, the spacetime geometries being superposed would have to be different.

[trhway]

>You can set the experiment up so the energy is the same in both cases (for example, both positions at the same height, just horizontally separated)

The action of placing them, say with your hands for simplicity, into different horizontal positions means differently pushing the Earth with your legs. For more cleaner illustration - let's say in our experiment a space ship is placed into orbit clockwise or anti clockwise. We can't just teleport the ship, so let's say we move it by rocket engines. So the ship goes in one direction, rocket engine exhaust goes in the other. The exhaust does have mass and speed. Even if it wouldn't eliminate the superposition gap, it will definitely decrease it, and decreasing the superposition gap increases the chances that some other unaccounted for factor(s) (for example gravitational waves caused by all these movements) will eliminate it or decrease further. Even if ultimately we still can't fully eliminate the gap, significantly decreasing it may eliminate various divergencies arising from quantization or make them very smallscale/localized (an observer from Alfa Centauri wouldn't care about the ship's orbit direction like we don't care about the spin of a given particle in the air around us) and average-able out on larger scales.

[pdonis]

> The action of placing them, say with your hands for simplicity, into different horizontal positions means differently pushing the Earth with your legs.

This might change the momentum, but not the energy if the heights are the same. But if your point is that there will always be some difference in a conserved quantity, yes, that's a fair point.

But it also means that there will always be some difference in the spacetime geometry. None of the other factors you talk about would eliminate the "superposition gap", because none of them cancel out any changes in the spacetime geometry; they just add more changes to it.

> average-able out on larger scales

But if you don't have a theory that can represent the variations you're going to average out, you can't do the averaging. That's the problem: classical GR cannot represent "variation in spacetime geometry" at all. It can only represent one spacetime geometry. It can't represent a superposition of them, not even to do an average.