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My friends and I are asking this question about the standard model and general relativity to put the discussion on a firmer footing:

Does some experiment show that the two theories contradict each other?

It is obvious that the two theories really do contradict each other - but only on paper. Their mathematical descriptions are not compatible and contradictory. In reality, it seems that no experiment contradicts these theories, and no experiment shows any contradiction between the two theories.

What is the exact status? Is there a discussion of this point somewhere?

ADDED:

(1) The incompleteness of either theory is clear and due to their different domains of application. But that does not show that they contradict each other. In nature, inertial and gravitational mass are equal; so letting something fall does not contradict the standard model. Just let the observer fall near the experiment, as a check.

(2) The mathematical formulations of the two theories do contradict each other, because general relativity is not probabilistic (e.g. the mass-energy tensor) whereas quantum theory is. But it seems that no experiment has observed the contradiction.

(3) Is there a thought experiment showing a contradiction?

(4) Any experiment (real or thought) confirming one theory and contradicting the other would qualify. In the meantime, a number of experts have confirmed to us that as of November 2022, no such experiment is known. Following the most recent reviews, general relativity and the standard model have no confirmed anomalies or exceptions. (Falling apples, quantum superpositions or double slit experiments do not qualify: they do not contradict the other theory.)

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    $\begingroup$ For one thing, the Standard Model doesn't have gravity in it, so every time you drop something it's an experiment "contradicting" the Standard Model. $\endgroup$
    – knzhou
    Nov 17, 2022 at 18:00
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    $\begingroup$ "It is obvious that the two theories really do contradict each other..." Why is it obvious? $\endgroup$
    – hft
    Nov 17, 2022 at 18:01
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    $\begingroup$ "My friends and I are asking..." You can ask a question for yourself, it's OK, no need to invoke your "friends" for emotional support. On a more serious note, it is usually better to not clutter up your question with such superfluous details. See: meta.stackexchange.com/q/2950 $\endgroup$
    – hft
    Nov 17, 2022 at 18:06
  • $\begingroup$ I don't think there is a contradiction between GR and the standard model, because in GR gravity is not a force, so there is no need to put a particle of gravity in the standard model. However, the problem is between GR and QM, which only experts could explain to you exactly what it is. (maybe gravity turns out to be a real force and not just spacetime curvature) $\endgroup$
    – user348262
    Nov 17, 2022 at 18:07
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    $\begingroup$ For theoretical physicists, thought experiments suffice to convince them. $\endgroup$
    – Ghoster
    Nov 17, 2022 at 21:58

3 Answers 3

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From the standpoint of accelerator physics, the energy levels required to look at where gravity begins to muscle in on the standard model are unattainable now and will probably remains so forever (i.e., requiring an accelerator that was light-years in length), so there is no hope of ever performing an experiment that would, for example, sprinkle gravitons into a warm bowl of quark soup and let us taste the result.

Although the graviton/quark soup recipe was on the menu in the early stages of the big bang, there is no telescope that can reach earlier lookback times than the recombination era because the universe was opaque to electromagnetic radiation before then, so that path to understanding is blocked too.

This is why we have no direct experimental result on hand today that proves GR and QM incommensurable.

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  • $\begingroup$ I tend to agree, but in contrast, all the people of the most upvoted comment under the question do not ... $\endgroup$
    – KlausK
    Nov 17, 2022 at 19:27
  • $\begingroup$ My friends and I agree; but your first sentence is too narrow . the answer is true from every standpoint. (In a sense, this was the real question behind the question. Thank you.) $\endgroup$
    – KlausK
    Nov 19, 2022 at 4:33
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As pointed out in the comments, the Standard Model does not contain gravity. So the Standard Model cannot explain apples falling from trees.

However, there are ways to "glue together" classical gravity and the Standard Model, at least approximately. In modern language, this is the effective field theory of gravity. Essentially, since we expect quantum effects associated with the gravitational field itself to be small below the Planck scale, we can (to a very good approximation) treat the gravitational field as a classical background in which other quantum fields act.

On theoretical grounds, we can estimate the regime of validity of this approximation. Essentially we would only expect it to break down when the curvature scale becomes of order the Planck length; so, for instance, very close to the singularity of a black hole. There are no experiments that have been done, or conceivably could be done on any reasonable time scale, that would fall outside this regime of validity. So, there are no experimental results able to show this approximation breaks down.

There are theoretical possibilities that this approximation might break down in other ways, but these require some luck (they might just not be true) and the experiments have not been kind to these ideas. Some examples are:

  • We could be living in a world with "large" (millimeter sized) extra dimensions, such that the true Planck length is actually much larger than the one we would naively guess confined to our four dimensional world. If this were true and the extra dimensions were large enough, we could detect deviations from the inverse square law at millimeter scales, or produce black holes in particle accelerators. Both experiments have been tried and found nothing.
  • There are theories of quantum gravity where fundamental symmetries like Lorentz invariance are broken, and these broken symmetries could potentially manifest themselves observationally. Again, searches for these effects have been done, and not found.
  • There are hints from the information loss paradox that the effective field theory of gravity should break down around the scale of the horizon of a black hole, rather than near the singularity. However, these effects imprint themselves in subtle ways on Hawking radiation, which is observationally very far out of reach. (In that sense this example is not like the other two; there are no searches for Hawking radiation of astrophysical black holes because it is just pointless).

To summarize: there is no direct experimental evidence contradicting the effective field theory of gravity coupled to the Standard Model. However, we also would not expect any experiment done to date (or in the conceivable future) to lie outside the regime of validity of this framework, barring a scenario like large extra dimensions. Nevertheless, the effective field theory of gravity coupled to matter does have a finite regime of validity, so on theoretical grounds we expect that it must be an approximation to something more fundamental.

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  • $\begingroup$ Is it true that the EFT treats gravity classically? I thought it treated Gravity Quantum mechanically and it's just that the perturbation series was renormalizable below the Planck energy. $\endgroup$
    – Ryder Rude
    Nov 19, 2022 at 1:34
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    $\begingroup$ @RyderRude You're right that the EFT of gravity allows you to include quantum corrections in a systematic way, to any desired order in $E/M_{\rm Pl}$ (where $E$ is the energy of the process being considered). However, the net result is that quantum corrections are negligibly small until you reach the Planck scale. $\endgroup$
    – Andrew
    Nov 19, 2022 at 13:00
  • $\begingroup$ indeed, Schwartz's book said it predicts some horribly tiny correction to Mercury's tilt or something. Still, it's satisfying to know that we have a theory which treats the metric as probabilistic. $\endgroup$
    – Ryder Rude
    Nov 19, 2022 at 13:03
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    $\begingroup$ @RyderRude Well, in the EFT approach, it is just the fluctuations around a fixed classical background that are quantized. The causal structure still comes from the background. So it doesn't solve some of the hard conceptual problems of quantum gravity. $\endgroup$
    – Andrew
    Nov 19, 2022 at 13:09
  • $\begingroup$ Yeah, it doesn't preserve the beauty of general relativity by treating it perturbatively like a force. General Relativity allows non-trivial spacetimes (like loops) which can't be taken as a perturbation on flat space. It'll take some huge conceptual leap to quantum mechanically account for the nature of time in GR. $\endgroup$
    – Ryder Rude
    Nov 19, 2022 at 13:33
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Pretty much every single quantum mechanical experiment contradicts General Relativity. Take the double slit experiment. General Relativity predicts that Newtonian mechanics should hold in the double slit experiment, because General Relativity reduces to Newtonian mechanics in these approxomations.

So, the double slit experiment is one experiment that shows contradiction between the two theories.

Similarly, pretty much every observation in cosmology contradicts the Standard Model, because the Standard Model predicts no such thing as gravitation in its macroscopic limit.

EDIT I want to correct the last paragraph. The Standard Model can include an Effective Field Theory of Gravity, like explained here

This theory does reproduce General Relativity in the macroscopic limit. You could say that this theory accurately models all experiments until around the Planck scale.

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  • $\begingroup$ The last paragraph is the exact opposite of the first sentence. Which of the two do you mean? $\endgroup$
    – KlausK
    Nov 18, 2022 at 20:08
  • $\begingroup$ @KlausK Both. First paragraph says that there are experiments which violate general relativity. The last paragraph says that Standard Model (plus Effective gravity) can reproduce General Relativity in its macroscopic limit. Why is this contradictory? $\endgroup$
    – Ryder Rude
    Nov 19, 2022 at 1:19
  • $\begingroup$ An experiment that violates general relativity would be an answer to the original question. No such experiment is known. The double slit experiment does not violate GR. In your last paragraph you even confirm this. That confused me. Violating GR means violating the field equations. The double slit does not achieve this. Nobody has been able to measure the curvature of space-time in a double slit experiment (though some are trying). $\endgroup$
    – KlausK
    Nov 19, 2022 at 4:30
  • $\begingroup$ @KlausK I don't know what you're talking about. In my last paragraph, I'm talking about a different theory from GR. That theory is Standard Model + Effective Field Gravity. This theory isn't violated in any experiment until the Planck scale. GR is absolutely violated in the double slit experiment because GR predicts that the double slit experiment should be in agreement with Newtonian mechanics $\endgroup$
    – Ryder Rude
    Nov 19, 2022 at 5:19

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