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I have seen Newton derived from Schroedinger (Ehrenfest) and I have seen Newton derived from the General Relativity equation. I assume that it has been tried to derive GR from QM. Is this the main stumbling block where infinities arise?

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  • $\begingroup$ I'm unaware of any attempt to derive GR from QM. When quantising gravity, we want to quantise it as a field theory like electrodynamics. So it's not like QM with the Schroedinger equation (which is not relativistic, as you probably know). The main issue as far as I'm aware is that Gravity isn't renormalisable. When quantising electrodynamics, there are infinities too, but we can get rid of those with some maths tricks. The same techniques don't work on gravity. I'm putting my answer in here because I haven't seen the attempt at quantising gravity, but my lecturers have spoke about it a little $\endgroup$
    – baker_man
    May 8, 2020 at 21:34
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    $\begingroup$ @Nick There is much ongoing research attempting to derive GR from QM. Google “It from Qubit” for a start. $\endgroup$
    – d_b
    May 8, 2020 at 22:04
  • $\begingroup$ @d_b Thanks, interesting site. I think I may have actually heard about this in a podcast from steve carrol, or something similar $\endgroup$
    – baker_man
    May 8, 2020 at 22:19
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    $\begingroup$ An addition to @d_b's comment: the AdS/CFT correspondence is a huge research industry (has been for 20+ years) largely focused on the mathematical discovery that some quantum field systems automatically include GR (as an approximation) albeit in a higher-dimensional spacetime. The collection of ideas called ER=EPR is another (related) example. $\endgroup$ May 8, 2020 at 23:04

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Quantum mechanics is explicitly non-relativistic, so no, it hasn't been tried because it's clear that it won't work. In order to incorporate relativity, quantum field theory must be used. The main difficulty with incorporating gravity into quantum field theory, and in particular into the Standard Model, is: in order for general relativity to work correctly, the "graviton" (the force carrier for gravity) must work differently than, for example, the photon (in particular, the graviton must be spin-2 while the photon is spin-1), and it turns out that this makes the theory non-renormalizable, which is where the non-resolvable infinities come in.

There are various modifications to the Standard Model that attempt to resolve this problem (generally they fall under the umbrella term "quantum gravity"), but experiments have not yet demonstrated that the predictions of any of them are correct.

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    $\begingroup$ I take your point, but arguably quantum field theories are a particular subset of quantum mechanical theories. (Confusingly, this subset of QFTs includes as a subset “ordinary,” non-relativistic quantum mechanics.) I think your comment that it is clear that such a program will not work would be a surprise to the many researchers currently involved in carrying out said program. $\endgroup$
    – d_b
    May 8, 2020 at 22:10
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    $\begingroup$ @d_b As far as I can tell, the term "quantum mechanics" is very different from the term "quantum mechanical theories". Quantum mechanics, in the usages I've encountered, specifically means the theory centered around solutions to Schrodinger's Equation, which is explicitly non-relativistic, whereas the term "quantum-mechanical theories" is usually used in a broader sense. That said, the more common term for this broad category, in my experience, is "quantum theories", which avoids some of the ambiguity, as it's less easily confused with the term "quantum mechanics". $\endgroup$ May 8, 2020 at 22:39
  • $\begingroup$ Good point, thanks. $\endgroup$
    – d_b
    May 9, 2020 at 23:04

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