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The current foundation of physics is not complete because two parts of it, namely General Relativity (GR) and Quantum Mechanics (QM), are not compatible. But why should we believe that it can be completed?

Question: What are the best facts and citations about this belief (for, against or neutral)?

Perhaps we can prove a result stating that any theory of physics from which we can recover GR and QM (and Standard Model) is inconsistent. But such a result would require to fix what we mean by "theory of physics" and "recover", which can be a deeper problem...

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  • $\begingroup$ Aren’t both string theory and Loop Quantum Gravity consistent with both quantum mechanics and General Relativity? I think you are worried about a nonexistent “incompatibility”. $\endgroup$
    – G. Smith
    Commented Jan 10, 2020 at 15:39
  • $\begingroup$ @G.Smith Are they really consistent? If so, how they solve the problems pointed out here and there. And more importantly, can we recover the standard model from each of them? $\endgroup$
    – Sebastien Palcoux
    Commented Jan 10, 2020 at 16:11
  • $\begingroup$ Not being an expert on string theory or LQG, I can’t explain how they solve the two problems that you mention. If either obviously led to the Standard Model, we would no longer be looking for the correct theory of quantum gravity. My point is that there are already multiple theories marrying QFT and GR and I see no reason to be pessimistic about eventually finding the right one. I do NOT believe that there is any fundamental incompatibility. $\endgroup$
    – G. Smith
    Commented Jan 11, 2020 at 10:40
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    $\begingroup$ @SebastienPalcoux A physical theory does not begin its development based on some well-defined foundations. The methods of the new physical theory are initially intuitively conceived and applied. The theories usually encounter contradictions on the way, and the discovery of the cause of these contradictions develops the theory further. These clarifications for the contradictions help us avoid them in the future. The contradictions are crucial to the development of any physical theory. It is these clarifications that become the foundations of the said physical theory. $\endgroup$
    – user29978
    Commented Apr 17, 2020 at 23:42

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We should believe it can be completed because we believe that nature behaves in a predictable way, even if we do not yet know what that way is.

Inductively, we also know that historically, successful theories of physics have always served as limiting cases of more general theories whose domains had not yet been accessed and there is no reason to think that GR and QM are exceptions.

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