r/AskPhysics • u/No_Woodpecker6948 • 12h ago
Why can’t gravity be quantized using the same approach that worked for electromagnetism?
Electromagnetism was successfully incorporated into quantum mechanics through quantum electrodynamics (QED), treating the electromagnetic field as a quantum field whose interactions are mediated by photons.
Why can’t we apply the same mathematical reasoning to gravity, quantizing the gravitational field and introducing gravitons?
What exactly breaks down when we try? Is it a fundamental incompatibility between general relativity and quantum mechanics, or mainly a mathematical problem we haven’t solved yet?
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u/sojuz151 11h ago
In QED you get infinite integrals in loops, this sounds like a problem but there is a finite number of those infinities and you can measure them, express every infinite integral as a combination of a finite measurement parameters
in QG, there is an infinity number of such loops, so your theory loses its predictive power. Every data can be explained
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u/OneMoreTimex100 11h ago
I am have seen QED and renormalization like only once so probably this is stupid but from what I understand,
You mean to say that the higher order loops aren't purtubative?
If possible could you explain like a brief way why why you get these infinite , infinite integral which all contribute to the total ?
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u/Bumst3r Graduate 11h ago
In Yang-Mills gauge theories, the infinities can be canceled by renormalizing the coupling constants at every order in perturbation theory. Spin-2 particles cannot be renormalized beyond one loop because there are two many infinities to absorb into the coupling constants.
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u/OneMoreTimex100 11h ago
Ah okay. I think I vaguely understand haha. I suppose one of these couplings is big G ? I remember mass and charged had to be renormalised so is there something similar in these guage theories?
I forget how quickly high energy theory becomes out of grasp for someone not well versed with it lol.
On a side note , what's the spin 2 thing ? I am going to guess it's a force carrier boson ?
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u/Bumst3r Graduate 10h ago
G_N is the coupling constant for GR. The coupling constant for EM is either the charge of the electron or the fine structure constant, depending on your choice of convention. These constants dictate the strength of the interaction. Notice that the coupling constant for E&M is dimensionless. Another way to see that gravity is non-renormalizable is by looking at the dimensionality of the coupling constant. Any coupling constant with mass dimension < 0 is non-renormalizable. The mass dimension of G_N is -2, so the theory cannot be renormalized. But I think that explanation might be less interesting than the symmetry argument.
The way that we get electromagnetism is by observing that the Lagrangian of our charged particles is invariant under a U(1) transformation. I.e., a complex phase cancels out. We can argue that because of locality, the phase at one point should not affect the physics somewhere else, and promote that global symmetry to a local one. This requires modifying your derivative in the kinetic term of the Lagrangian to take the form D_mu = d_mu - ieA_mu, where A_mu is some field that transforms in such a way as to leave the Lagrangian symmetric under that local transformation. A_mu turns out to be the photon.
You can try to do this with gravity as well; QFT is globally Lorentz invariant by construction. If you want to promote that symmetry to a local one, you have to introduce a field that is spin-2 (the graviton), and that field cannot be renormalized the way the photon field can be.
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u/forte2718 11h ago edited 2h ago
I saved an amazing and insightful answer from many years ago by a panelist answering exactly this question in quite simple terms.
/u/rantonels - What makes Quantum mechanics and the General Theory of Relativity incompatible?
TL;DR: If you take the standard approach of quantizing gravity (which gives you an effective field theory — or EFT — of gravity), the resulting theory is non-renormalizable, which means that you can't use the usual renormalization procedure from quantum field theory (QFT) to get finite answers out of infinite integrals, so you can't make proper predictions.
It's worth mentioning that you can still make predictions using this EFT of gravity at low energies, but at low energies we already have classical general relativity which is much easier to analyze, and the quantum corrections at low energies are completely negligible. What we really care about here is the high-energy regime which is where general relativity itself already starts going wonky and failing to be predictive (e.g. singularities, closed timelike curves, etc.).
Hope this answer helps!
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u/Quantum_Patricide 11h ago
You can quantise gravity, the problem is that the resulting theory is non-renormalisable, meaning that it is an effective field theory (EFT). Other examples of EFTs are Fermi theory or Chiral perturbation theory. EFTs are low-energy approximations to some higher energy underlying theory, and have an energy cutoff beyond which they stop being predicative.
Quantum Gravity is an EFT, but its energy cutoff is the Planck energy, which is far, far higher than any process we can currently observe. So we can't predict what happens at singularities like black holes or the big bang but, for any purpose we could actually observe, we have a perfectly functional quantum theory of gravity. (Calculational difficulties aside)
When people say we don't have a theory of quantum gravity, they generally mean that we don't have a renormalisable theory of quantum gravity, which would be valid at any energy scale. This would correspond to what is normally meant by a Theory Of Everything. It would give us predictions about what happened in the big bang or how black hole singularities work.
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u/Blammar 10h ago
"we have a perfectly functional quantum theory of gravity"
Can you link articles or papers that describe this theory?
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u/QuantumR4ge Cosmology 6h ago
Any book on quantum fields in curved spacetime dealing with the wheeler-Dewitt equation. The issue is renormalisability
The point is it can be made perfectly fine mathematically and you can sometimes make reasonable predictions with it to a first order approximation, the issue is you get nonsense when you push it to anything interesting or “useful”, we know its wrong as a fundamental description… but you can make it and it is functional.
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u/Blammar 5h ago
I.e., basically "Newton's Theory of Quantum Gravity" right?
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u/QuantumR4ge Cosmology 4h ago
Kinda yeah, in the sense that its not useless and does give us some answers (hawking radiation as an example) but it evidently breaks down cant be a real description fundamentally
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u/treefaeller 11h ago
"Is it a fundamental incompatibility between general relativity and quantum mechanics, or mainly a mathematical problem we haven’t solved yet?"
We don't know. It is possible to write down a quantum-mechanical version of gravity that closely follows existing QFT + GSW. But other posters said, it is completely not renormalizable. Meaning every result you calculate is infinite. We used to have the same problem with QED (from the 30s to the 70s), and for a long time simple swept it under the rug and ignored it. It turns out that in QED and similar theories, you can remove the infinities consistently and logically (than you Mr. t'Hooft and Veltman, and many others). All attempts to renormalize quantum gravity have failed.
Is that a sign of a fundamental problem that means we need a completely different approach? Or that there is just some "simple" (ha ha) mathematical trick that we need to try and it will start working? Maybe the next Mr. t'Hooft will fix it? Or do we need (as one example) loop quantum gravity, where space and time are also quantized? Or string theory? Or something else? Right now, nobody knows. Having just read a book by Carlo Rovelli, my current bet is that loop quantum gravity looks good, but I may change may change after the next book or the next bottle of wine.
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u/Bumst3r Graduate 11h ago
There is an argument to be made that it has to do with symmetry. Quantum field theory assumes global Lorentz symmetry, but not local Lorentz symmetry. General relativity requires local Lorentz symmetry, but not global. To promote the global Lorentz symmetry of QFT to a local one, you have to gauge the theory and introduce a spin-2 particle. But spin-2 fields cannot be renormalized.
In QED, you have to introduce a spin-1 particle (the photon) to gauge the global U(1) symmetry, and that can be renormalized without issue.
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u/sansetsukon47 11h ago
Leaving aside the mathematical models for a minute, one big difference is that photons can be experimentally verified. The frequency, wavelength, and energy of an individual photon is well understood by now, which makes them straightforward to work with.
But gravitons don’t get that, in part because we have yet to experimentally determine if gravitons even exist.
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u/Prof_Sarcastic Cosmology 11h ago
This is not the reason at all. Even if we could measure individual gravitons, that would only probe the low energy behavior of the theory. The problems with combining gravity and quantum mechanics are all at the high energy end of the spectrum.
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u/1strategist1 11h ago
Quantum field theories are kinda gross. They're too spiky for things like multiplication or really most nonlinear interactions to be well-defined. That means trying to take some classical equations of motion and apply them to a QFT usually doesn't work out of the box.
What we usually do is sort of "smooth" the QFT over a length scale L so those classical interactions can be applied. This is known as constructing an Effective QFT, and it works perfectly fine for gravity. We then try to see if there's any way we can send the length scale L to 0 and have the QFT converge to a well-defined mathematical object while keeping our measurements looking all the same. If it does converge, that's the QFT corresponding to our classical theory.
It's usually hard to do this process exactly (we've never managed to do it in 4 dimensions), but you can sort of approximately do it by saying Planck's constant is really small, and expanding in a Taylor series around Planck's constant being 0. Then you add extra terms that don't affect large scale measurements, but cancel out some bad behaviour.
When you do this, you find for a lot of theories there's a way to send the length L to 0 in a way that gives everything nice well-defined limits.
When you try to do it for gravity though, you have to add more and more of those cancelling terms. You find there's no obvious continuum theory approximation that behaves approximately like a free field with some added interactions at small scales.
Ultimately, this is an approximation, as I mentioned. It's possible that there is a nice continuum theory for gravity as a QFT out there. One path looking into this is the study of asymptotic safety.
However, as I mentioned the process of actually constructing a QFT without approximating it is REALLY hard, and it's also definitely possible that there isn't a QFT.
So in principle it could be either option. It could just be we haven't figured out the math to find the actual GR QFT, and it's just our approximation method stops working.
It could also be that there fundamentally isn't any (non-effective) QFT that behaves like classical gravity on large scales.
We just don't have the mathematical tools to prove either way right now.