If the concept of superposition can ever challenge our understanding of space-time in general relativity..
I.e. it does so by introducing scenarios where objects can exist in multiple states simultaneously, having indefinite positions and being in a mixed state
which conflicts with the classical view of spacetime, which is deterministic and absolute.
I.e. if massive bodies are in superposition, it raises questions about the validity of Equivalence Principle as their gravitational effects could vary depending on their states[1].
On an am even more subtle level, superposition suggests that spacetime itself may also be in a state of superposition, meaning it is not the clear cut thing we expect but an emeregent effect of more fundamental ontologically same or not entities,
thus complicating the relationship between quantum mechanics and gravity[2], indicating that our classical notions of spacetime may be emergent rather than fundamental, necessitating a reevaluation of how we understand gravity and quantum phenomena. This idea captured scientists in early 2000s (Smolin, Markopoullou) while some like Rivelli continue to enertain it.
Citations:
[1] Quantum superposition of spacetimes obeys Einstein's Equivalence ... https://arxiv.org/abs/2109.01405
[2] Marios Christodoulou: Spacetime in Superposition, in the Laboratory https://www.youtube.com/watch?v=1MGU6o6pIgo
The superposition principle is about what we can know about the outcomes of measurement. It arises in the pre-conditions for a measurement, where, rather obviously, we do not have concrete knowledge of the value we will measure. This does not on the face of it have much to say about the geometry of space-time which being geometrical is all about the extension of what we know into pasts and futures. In this scheme mass reduces uncertainty. Penrose was forced to acknowledge this. So it is hard to see how superpositions are needed to occur in space- time. Even vast masses do not create uncertainty, rather the opposite in fact, which is why the information problem of black holes has not really been solved. All this is to say the equivalence principle is just that, an equivalence In our measurement values. A superposition of accelerations don’t make much or indeed any sense since if time varies between locations you get different actual locations rather than undecohered ones.
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