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I am generally wondering how useful new more ambitious theories would be considering that even with standard non-relativistic electrostatic QM one usually has to employ unsatisfyingly crude approximation, if one wants to calculate anything for a system with more then 2 particles, like ignoring quantum effects, ignoring pair interactions, assuming ground state or guessing some exchange correlation potentials.

More recently I was wondering though: Independently of the complexity of the calculation, for what kind of system would a description by a quantum gravity theory actually be needed?

If we want to describe quantum particles extremely weakly interacting via gravity, QM with static Newtonian potentials should yield perfectly fine results. If we want to describe stronger gravitational actions generated by allot of particles, we should be far away enough from them to ignore their quantum nature. If we want to describe a particle close to a black hole, doing QM in curved space time should be sufficient, so no quantization of gravity itself would be needed. Maybe QCD in a neutron star would be a use case? But shouldn't there also QM in curved spacetime be sufficient as the gravitational retroaction of individual QM-particles on the neutron star should be negligible? Maybe if one wants to describe singular quantum particles with macroscopic masses, perhaps some kind of high energy photons, but do such particles actually exist? Do they play a significant role in our universe?

I understand that one might hope to get some kind of insight over dark matter or dark energy problems. But shouldn't a theory of quantum gravity by construction reproduce general relativity at large distances and therefore yield the same dark matter and dark energy problems? In other terms to make general relativity work with QM one would need a modification of the theory at small distances, but to solve dark matter and dark energy problems one would need a modification at large distances?

So: For the description of what kind of systems would one actually need a theory of quantum gravity?

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    $\begingroup$ What about the very beginning of the Universe or the supposed singularities inside black holes? $\endgroup$
    – Jeanbaptiste Roux
    Commented May 13 at 11:11
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    $\begingroup$ Also for the description of particles near black holes, the description of quantum field theory in curved backgrounds is not sufficient. E.g. the information paradox or complexity calculations in this setting yield results which we believe to be incorrect. Further a lot of questions on what observers actually experience as they fall into a black hole need a full QG description $\endgroup$
    – Thomas Tappeiner
    Commented May 13 at 12:03
  • $\begingroup$ @ThomasTappeiner If one looks at such a tiny perturbation as the gravitational influence of a quantum particle on the gravitational action of a black hole I would naturally assume it to be negligible. Your comment suggests, there are reasons to believe, that this is not the case. Would it be possible to elaborate on those or would that be too complicated for this frame? $\endgroup$
    – Zaph
    Commented May 14 at 20:36

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The two standard answers are:

  • Resolving the singularity at the Big Bang
  • Resolving the singularity in Black Holes

Both of these have large spatial curvature within very small regions.

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Suppose you have an electron in a superposition of two measurably different locations. The electron has mass so it interacts with the gravitational field, so what does the gravitational field look like in this situation? Situations like this are very common so in some sense there is a very common motivation for wanting a quantum theory of gravity.

In practice gravity is very weak so in many situations any effects of the quantisation of gravity would be washed out by other effects. For example, an electron will interact with the electromagnetic field more strongly than with the gravitational field.

However, some experiments to indirectly test whether gravity is quantised have been proposed. The basic idea is that you put two masses into a superposition state and get them to interact gravitationally. If the gravitational field is quantised and decoherence from other sources is weak enough they end up entangled and otherwise they don't:

https://arxiv.org/abs/1803.09124

https://arxiv.org/abs/2309.16312

https://arxiv.org/abs/2012.06230

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Currently, the conceptual need for a quantum theory of gravity (or a theory that combines gravity and quantum physics) is to a large extent induced by the fact that we don't know what gravity does with a superposition of different mass distributions. We know how gravity reacts to a classical mass distribution; Einstein's field equation allows us to compute the resulting curvature of spacetime. But when we bring in quantum physics, we can imagine superpositions of different mass distributions. For example, imagine a massive object in a superposition at two different locations: $$ |\psi\rangle = |M(x_1)\rangle\alpha + |M(x_2)\rangle\beta . $$ Does gravity work with the average of the two or does it cause spacetime to become entangled with the object? There has been some proposals and there are several people working on this problem.

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I understand that one might hope to get some kind of insight over dark matter or dark energy problems. But shouldn't a theory of quantum gravity by construction reproduce general relativity at large distances and therefore yield the same dark matter and dark energy problems? In other terms to make general relativity work with QM one would need a modification of the theory at small distances, but to solve dark matter and dark energy problems one would need a modification at large distances?

Not necessarily. Dark matter would be solved by finding evidence of the existence of extra particles/fields with little interaction with the known standard model. This by its very nature is a short distance modification to our understanding of nature. Many UV extensions to our current understanding (like string theory) also predict lots of extra fields.

Similarly with dark energy. The existence of a vacuum energy that scales with volume is not the really mystery here. Almost any quantum field theory predicts this. The real mystery is why this vacuum energy is so small? It is not unreasonable to expect a UV completion of standard model+gravity to answer this question.

If we want to describe a particle close to a black hole, doing QM in curved space time should be sufficient, so no quantization of gravity itself would be needed.

It is not at all clear that this is the case. Various results surrounding the black hole information paradox point out that we will have to give up something about our assumptions of how nature works. One of those things could be that the semi-classical gravity description is valid on the horizon scale (others including giving up unitarity, or locality, or other things dear).

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  • $\begingroup$ If I imagine a quantum particle, who's gravitational field is so small, we can’t measure it, next to a black hole, which produces the largest gravitational effects, we can observe in the universe I would naturally assume, that the perturbation of the black holes gravitational action caused by the particle would be negligable. You claim that might not be the case. Could you eleborate, how the gravitational action of the particle could be relevant in that context? If you don’t want to do that here, could you at least confirm I understood you correctly? $\endgroup$
    – Zaph
    Commented May 14 at 13:33
  • $\begingroup$ @Zaph, the black hole (when talking about star-massed BHs) has no particularly large gravitational effect. In fact unless you are (very) close to the singularity - well past the Schwarzschild radius - where all the fun stuff happens (objects becoming seemingly slower and fading out, instead of disappearing instantly; or the "bleeding out" of the black hole via pairs of particles spontaneously appearing right on the radius), it behaves exactly like any star with the same mass. Still, the regime seems to change a lot at the Schwarzschild radius... $\endgroup$
    – AnoE
    Commented May 16 at 10:50
  • $\begingroup$ @AnoE Well it behaves like a star with the same mass only if looked at from outside of the stars Volume, but that is far away from its Schwarzschild radius. Anything said in this answer or my comment unless I missunderstood it was about the regime close to but outside of the Schwarzschid radius, in which I would expect significantly larger gravitational effects then outside of a regularly dense star. $\endgroup$
    – Zaph
    Commented May 16 at 15:32
  • $\begingroup$ @Zaph It is not the gravitational interaction with the gravitational field generated by the particle concern. It is the interaction of the particle with the vacuum fluctuations of all the other fields (which may not behave in the way suggested by the semi-classical approximation). This not guaranteed to happen, but is certainly considered see e.g. discussions about "firewalls" or "fuzzballs", etc. $\endgroup$
    – TimRias
    Commented May 16 at 16:18
  • $\begingroup$ @zaph, sure, if I fall into a small BH (say, Earth's mass, with 9mm SR) my experience will be a little different than if I fall into a Supermassive BH which Wikipedia lists some with a SR the size of Uranus' radius around the sun. My point is that "in principle", for a large enough SR, you as an observer will not notice that you're crossing the SR at all (at least not using gravitational effects, which we're talking about - the visuals will probably be stunning and give it away... ;) ). While the singularity at r=0 is "real", the border at the SR is just a "mathematical" singularity... $\endgroup$
    – AnoE
    Commented May 17 at 9:16
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The first case is more of a "particle physics–like approach". We just want to understand what things are made of, and this involves reaching larger energy scales. The Planck scale surely involves quantum gravity, and we would like to understand what's lying there. It is a matter of curiosity, not of necessity, I would say. Furthermore, there are many hopes that quantum gravity may bring information about things that happen in more generality: the holographic principle introduces limits on the entropic content of everything (which is a non-gravitational observable), some approaches for quantum gravity could have less free parameters than the standard model, some ideas related to quantum gravity (such as the Schrödinger–Newton equation) try to explain how the classical world is so different from quantum mechanics, and the list goes on.

A more direct answer is to consider the situations in which quantum gravity is absolutely necessary to describe the relevant physics. These would be near black hole singularities and at the very early universe. In this case, the scales are way too small for quantum field theory in curved spacetime to make sense, way too energetic for gravity as an effective field theory to be useful, and the curvature is way too strong for any Newtonian approach to be applicable. These limits are interesting because they let us understand more deeply how black holes truly behave, whether information is lost or not through black hole evaporation, and how everything started. In particular, there is much hope that quantum gravity would get rid of the singularities of general relativity, so perhaps quantum gravity will change our picture of the Big Bang for something different, like a Big Bounce.

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    $\begingroup$ @AlbertusMagnus I don't work directly with quantum gravity, so I'm not sure at all hahaha. However, I've heard that there are some expectations of measuring consequences of quantum gravity at the early universe by means of gravitational waves with LISA, for example. You'd have to ask someone more used to quantum gravity phenomenology for a better answer $\endgroup$
    – Níckolas Alves
    Commented May 13 at 12:33
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    $\begingroup$ "some approaches for quantum gravity (like string theory) have way less free parameters than the standard model" I thought we had more or less moved past that notion, with the discovery of the seeming endless landscape of string vacua? $\endgroup$
    – TimRias
    Commented May 13 at 15:01
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    $\begingroup$ So perturbative string theory in 10 dimensions has essentially no free parameters (just the scale of the string tension). Coupling constants are determined by the background values of fields (in the low energy limit where string theory looks like a bunch of fields). But then you need to compactify the theory to 4 large spacetime dimensions, and this is where things blow up. First, there are many different Calabi-Yau manifolds that can be used to compactify. Then, you need to introduce background fields to "stabilize the moduli". In other words, the Calabi-Yau's have continuous parameters... $\endgroup$
    – Andrew
    Commented May 14 at 3:46
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    $\begingroup$ ...describing their geometry, which turn into massless fields in the low energy limit. Massless fields are a disaster, because they correspond to long range forces we don't observe. So you need a mechanism to get rid of those. Then there also needs to be some mechanism to generate a positive cosmological constant, which is also not easy to do, and leads to additional background fields. So all these different combinatoric choices for compactifcations and background fields explode into effectively a huge number of parameters. A qualitatively similar thing happens in low-energy supersymmetry... $\endgroup$
    – Andrew
    Commented May 14 at 3:48
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    $\begingroup$ ...where a supersymmetric theory by itself is quite constrained and has few parameters, but then we need to break supersymmetry to account for what we observe, and there are many more parameters describing the possible ways to break supersymmetry than there are parameters in the standard model. Many beautiful ideas with few parameters in the abstract start becoming very complicated once you require that they connect with observed reality. But, on the other hand, there probably is a theory of Nature that unites gravity and quantum mechanics, and string theory does do that. $\endgroup$
    – Andrew
    Commented May 14 at 3:50
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You've (re)discovered a somewhat awkward fact: even if one day we do discover the correct theory of quantum gravity, and we develop vastly more precise experimental apparatuses than exist today, then it's still possible (and maybe even likely) that we will never be able to test that theory experimentally.

As other answers have pointed out, the only known systems where quantum gravity is definitely important are the Big Bang and the singularities at the center of black holes. Neither of these systems are directly accessible by controlled experiments: the Big Bang is, well, already done, and the singularities in black holes may well be out of direct experimental reach, even in principle, if the cosmic censorship hypothesis is true. (There's also the practical issue that all existing black holes are presumably very, very far away from us. But that problem could in principle be solved, either by traveling to existing black holes or by creating new ones nearby.)

There are certainly some theories of quantum gravity that do have experimental signatures that are detectable in more prosaic and accessible settings. But (while this question necessarily gets a bit philosophical) I don't see any reason why such theories are likely to be true. If they are, then in some sense we will have gotten lucky.

Of course, if our experimental apparatuses (and quantitative modeling capabilities) get really accurate in the far future, then presumably we could detect the deviations of the final theory of quantum gravity away from the predictions of the Standard Model on classical curved spacetime (plus whatever new physics we discover before then) somewhere out in the 35th significant figure of the experimental data, even in "gentle" regions of spacetime like the outside of a black hole. But it's far from certain - to say the least - that our technology will ever reach that capability.

As Sean Carroll often points out: as far as we know, the Standard Model on curved classical spacetime is a phenomenally good theory with an incredibly wide regime of applicability, even if it doesn't quite hold in every physical regime.

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Others have answered in terms of theoretical achievements. But there also could be practical, technological benefits.

What would they be? Who knows? Could the early researchers into quantum mechanics have anticipated lasers, transistors and other modern technologies that depend on understanding the nature of the subatomic world? Even if lasers and transistors were the only beneficiaries, think about how much depends on those two -- mini- and microcomputers (and all the devices that incorporate computers) could not exist without transistors, and high-speed optical communication depends on lasers.

The history of science and mathematics is full of examples of theoretical discoveries that initially seem to have little practical application, but are eventually found to be useful, sometimes very important (Einstein applied the topological theory of 4-dimensional manifolds to general relativity). But we'll never know if we don't work on the theory.

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  • $\begingroup$ There may be more subtle benefits. The concept of the Global Positioning System doesn't depend on General Relativity: people thought of building the system without an input from GR. The GPS, however, would have been inaccurate without correcting for the effects of GR, which luckily were anticipated. Maybe there will be some technology that doesn't depend on Quantum Gravity, but needs it in order to work. $\endgroup$
    – Simon Crase
    Commented May 15 at 18:13
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I want an anti-gravity machine. When we get a workable theory of quantum gravity, I expect that it well tell me that I can't have the machine; it would be nice, however, if it gave us some insights into how to build it instead.

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    $\begingroup$ The questions was: "What would one use a theory of quantum gravity for?" That is what I would want to use it for. It is the precise reason that I learned enough general relativity to learn that existing theories couldn't do what I wanted, and to suspect that it is impossible. $\endgroup$
    – Simon Crase
    Commented May 14 at 9:29
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I suggest you take a look at Oriti's discussion of the Bronstein hypercube of QG meta-thelries. The different vertices of the cube correspond to the target theory one gets based on the number of particles one is considering, the strength of the interactions, the inclusion of fields, and so on. I reproduce the abstract of the paper below:

We argue for enlarging the traditional view of quantum gravity, based on "quantizing GR", to include explicitly the non-spatiotemporal nature of the fundamental building blocks suggested by several modern quantum gravity approaches (and some semi-classical arguments), and to focus more on the issue of the emergence of continuum spacetime and geometry from their collective dynamics. We also discuss some recent developments in quantum gravity research, aiming at realising these ideas, in the context of group field theory, random tensor models, simplicial quantum gravity, loop quantum gravity, spin foam models.

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A bunch of areas in which QG would be needed:

  • Primordial Cosmology

  • Black hole singularities

  • Development (or finding a no-go theorem against) of time-machines and faster-than-light travel.

  • Manipulation of negative energies for anti-gravity devices (or finding a no-go theorem against macroscopic use of those)

  • Construction of maximally powerful computing devices (black-hole computers)

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Has anyone mentioned the graviton? A QG would showcase this as a fundamental force. It would then be left to delineate the limit of GR as a geometry to the discreteness of this fundamental particle of the Standard Model. The marriage of Wood and Marble.

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    $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented May 17 at 16:25
  • $\begingroup$ As stated the question itself is not exactly clear on what is meant by use a theory of quantum gravity for. $\endgroup$
    – Mark Thomas
    Commented May 17 at 16:37

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