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I hear this sentence sometimes: "quantum theory is inconsistent with relativity theory".

Is it possible to interpret this really in a formal system logically? I tried to understand the term "to be consistent with" to be implying that all the first order theory extension of these two in mathematical proofs gives a contradiction.

However, when I think that this theory has to be formalized on some mathematics like ZFC, it seems to have consistency relative to that. But this doesn't seem to be right.

And also, what kind of a theoretical framework should resolve these inconsistencies between the two?

Ishika_96_sparkle
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Lost definition
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  • Welcome to Physics! I've removed some comments that answered the question; their authors are invited to post answers instead. – rob Jun 19 '20 at 15:14
  • Essentially a duplicate of https://physics.stackexchange.com/q/387/2451 – Qmechanic Jun 19 '20 at 15:33
  • Qmechanic, this isn't the same question you are saying it is duplicated. And I don't know why it was moved to physics in first place. I am questioning about a possible formalization of physics. Such as on the sixth Hilbert problem. If it is possible to formalize such fields, I think it would have to incorporate ZFC, or something like it, because the mathematical structures like Hilbert Spaces seems to need things as infinite dimensions, and then you would need something like the choice axiom. I would like to know if I am saying something wrong, or be answered, and not simply be closed. – Lost definition Jun 19 '20 at 22:39
  • I would like someone who is versed on both logic and physics to say if this question makes sense. If it doesn't, why? – Lost definition Jun 19 '20 at 23:04
  • But the physics inconsistency between GR & QM is not at the level of formalized logic per se, cf. e.g. this Phys.SE post. – Qmechanic Jun 20 '20 at 10:09
  • Yes, Qmechanic, thanks for the link, this now is a little bit clearer for me. I would like to know what this incompatibility between GR & QM means at level of logic if you suppose you have something like the solution of the Hilbert problem for both this theories. But I think I have to understand better the works done on logical formalization of physics. – Lost definition Jun 21 '20 at 05:29

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The special theory of relativity is incorporated into the Quantum theoretical framework. The relativistic quantum mechanics (RQM) gave the first insight into the existence of antiparticles-the pair productions, the decay rates, spin magnetic moment etc. What you are asking is, perhaps, why General theory of Relativity (Gravitation) is incompatible with the Quantum mechanics, right?

The problem is the quantisation of the highly non-linear gravitational field equations and to make meaningful operators out of them. One needs to find a way to have quantized space-time structure and then the smooth manifolds over which the general relativistic equations are defined cease to exist. In the general relativistic description the space-time is a dynamical background (field energy content changes the nature of spacetime, sort of a back-effect) affecting the fields while in the RQM/QFT its a static stage on which various fields/operators live and interact.

Then there is a problem of carrying over the parameter time in quantum mechanics to general relativity. The notion of absoluteness of time (non-local) leads to the stationary states as solutions of Schroedinger's equations. How to arrive at an unambiguous definition of time (local) in a quantized version of gravity could be one problem.

There could be many other deeper layers to the problem of compatibility of the two and those probably will be discussed here by some physicist working with quantum fields on a curved space-time.

Ishika_96_sparkle
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  • I appreciate your answer, but it is not really what I was asking. I was thinking about a formal system property: inconsistency. And if this property simply does't make sense to this problem, then what this "inconpatibility" means formally? What means to say the general relativistic equation cease to exist in formal terms? Or simply this subjects don't have a formalization? – Lost definition Jun 19 '20 at 23:01
  • Ahh... Ok! i edited your question. Please check if you agree to the editing and see if it retains the spirit in which you asked the question. It should be opened for discussion after that. – Ishika_96_sparkle Jun 20 '20 at 03:19
  • Thanks for the edition. – Lost definition Jun 20 '20 at 08:02