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As I see it, the biggest pressing problem is how to make sense of QM and GR in the same consistent framework. (I’m not sure if this counts as a “practical purpose” in most people’s accounts, but it does in mine.) Certainly, many people don’t think we need to wait for an ability to collect empirical evidence in situations where both QM and GR are relevant before we try to develop such a theoretical framework.
Now, most people don’t see this as a challenge for Quantum Foundations; they view it as a challenge for people figuring out how to quantize gravity, extending the QM/QFT formalism into GR’s domain. But the most plausible steps along this path seem to give up on the most cherished lessons of GR (choosing some global foliation, denying the reality of spacetime, etc.), and have generally failed to make it work. This raises the question of whether the key to cracking this problem is a Quantum Foundations issue after all. (Smolin mentioned this as a possibility near the end of ‘The Trouble with Physics’.)
Hardly anyone will even acknowledge there is another path towards solving this big QM/GR problem, but there clearly is. This other path starts with foundational approaches that explain quantum phenomena via some ontology that lives in ordinary spacetime. Given this starting point, GR-based approaches could in principle be applied to even entangled particles; it would not be “quantizing gravity”, it would be “spacetimeing quanta”. Bob Griffiths thinks this can essentially be done with consistent histories; Travis Norsen is trying to do this by extending lessons from Bohmian mechanics; I think it can be done with retrocausal hidden variable models. (For my account, see https://www.youtube.com/watch?v=qVUdrCooGA8 )
Quantum Gravity has gotten all the attention on this front, but it could be that the solution to this pressing problem will lie in the very foundational issues that have been discussed in this forum.
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