# Why quantize gravity?

Lapidus
What rational says that gravity at the Planck scale needs to be quantized? I often read just the rather vague statement that it is because when all Planck constants become relevant we need an unification of quantum theory and gravity at this scale.

But why does that unifcation have to mean quantization of gravity?

Of course, there is the Einstein field equation. If the stress-energy tensor is the expectation value of some quantum state, but spacetime and the metric are classical entities, then this will lead to difficulties when we measure the quantum states of matter (see Wald's GR book p.382).

But on the other hand, since probing distances shorter than the Planck length is already forbidden by classical GR (creations of black holes in ultra-high energy scattering, all singularities are hidden via the censorship theorem for black holes and inflation for the big bang), might there not some conspiracy by Nature that sweeps these inconsistencies under the rug?

In Zee new GR book (p.766) I even read there is a "classificalization of gravity" program, which claims "..it maybe that when quantum gravity enters into Planck distance scales, quantum physics will inturn be replaced by classical physics somehow."

So my question again: why do we need to quantize gravity?

thank you!

Mentor
From a math standpoint, quantizing gravity means it'll use the same mathematical structure as QM. There is a problem when factoring GR gravity into the mix where things can't be renormalized which result in infinities and so the search for how to quantize gravity so it can work with QM.

See wikipedia:

http://en.wikipedia.org/wiki/Quantum_gravity

Conceptually to me, its basically the question of whether nature is smooth at all scales of investigation or does it becomes pixilated at plank lengths. QM implies the pixilated approach but this is just speculative thinking on my part (and others).

yavenchik and Lapidus
The basic problem is that General Relativity and Quantum theory are in conflict where they both have apply. Quantum gravity is an attempt as resolving this problem.

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Gold Member
Dearly Missed
... I often read just the rather vague statement that it is because when all Planck constants become relevant we need an unification of quantum theory and gravity at this scale.

But why does that unification have to mean quantization of gravity?

Of course, there is the Einstein field equation. If the stress-energy tensor is the expectation value of some quantum state, but spacetime and the metric are classical entities, then this will lead to difficulties when we measure the quantum states of matter (see Wald's GR book p.382).

But on the other hand, since probing distances shorter than the Planck length is already forbidden by classical GR (creations of black holes in ultra-high energy scattering, all singularities are hidden via the censorship theorem for black holes and inflation for the big bang), might there not some conspiracy by Nature that sweeps these inconsistencies under the rug?
...

So my question again: why do we need to quantize gravity?
...

I like the way you put the question. It's an interesting one. But we don't know with certainty that we HAVE to quantize geometry. The question is really what is the rationale for thinking it is a good idea to try to quantize geometry. Why do some people think it is a good idea to try to find a quantum theory of how geometry behaves (in response to measurement or interaction with other systems).

Like you say, there might be some as-yet-unimagined CONSPIRACY that harmonizes the LHS and RHS of the Einstein GR equation. Or one can speculate that there is some deeper theory more fundamental than EITHER QM or GR!

It is only some people who are motivated to try to develop a quantum theory of geometry. You seem to be asking to understand their motivation. I'm not expert but I watch QG and what I think is this:
These are people who think that it is a good bet to take both QM and GR core ideas seriously and try to develop the tools for general covariant quantum field theory. So far QFT is only special relativistic. Maybe there should be a general relativistic QFT.

Obviously I don't mean QFT on a prior fixed "curved spacetime" because that is not how nature works. The geometry responds to what matter does.

Rovelli has pointed to some historical precedents supporting the idea that it might be a good bet to do this (instead of trying to guess or make up a completely new more basic theory underlying both, or imagining a conspiracy). When Newton put the parabolas of Galileo and the ellipses of Kepler together into a combined theory of motion he didn't need any new observational data. It is a conservative idea: to take seriously and be guided by two established successful theories which appear disjoint. There is no guarantee but sometimes this works.

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Rovelli has pointed to some historical precedents supporting the idea that it might be a good bet to do this (instead of trying to guess or make up a completely new more basic theory underlying both, or imagining a conspiracy). When Newton put the parabolas of Galileo and the ellipses of Kepler together into a combined theory of motion he didn't need any new observational data. It is a conservative idea: to take seriously and be guided by two established successful theories which appear disjoint. There is no guarantee but sometimes this works.

If two theories work quite perfectly, as it is the case for GTR and QT, perhaps is it just a clear indication: we don't yet have really understood the (mathematical) logic connecting them (no conspiracy, just our collective low intellectual level!). The nature unifies these two faces permanently in front of our eyes. Gravitation acts everywhere at any time, inclusively when the curvature appears to be very tiny as it is the fact in interstellar vacuum. This doesn't empeach the propagation of EM waves which (as we also know) are "carrying" a quantized energy. Why do we see a frontier where there is none? Dirac's equations are the first historical example where covariance (inherited from the GTR considerations) works perfectly in a QT context. I think that the fictive "dichotomy" between matter, wave and geometry is obscurcing our vision and our understanding. We want a mathematical unification for objects which we presuppose are of different nature (particles and geometry for example); but are they really of different nature?

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Gold Member
Dearly Missed
... Dirac's equations are the first historical example where covariance (inherited from the GTR considerations) works perfectly in a QT context...
I thought the Dirac equation was special relativistic, not relativistic in the full sense.
I think that is part of the motivation: why should QT be stuck half way?

And the electron obeying Dirac equation is not influencing the geometry around it (which is typically flat Mink'ski space). But we know that all matter is interacting with the surrounding geometry.

So I think the picture strikes some people intuitively as incomplete.

But maybe it does not seem so to YOU. That's perfectly fine, there is plenty of room for differing opinion. I think the original thread question was about trying to understand the rationale or motivation of those people who think QG is a good bet, a good research direction to pursue. We are not talking about certainties, because we don't know what new mathematical tools and ideas may appear, or how things will turn out in the end.

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Gold Member
Dearly Missed
Maybe we need to stop thinking of differential manifolds as real. We don't know that spacetime IS a smooth manifold. What we have are discrete measurements (of angles, distances, momenta...) and a manifold is a convenient device to keep track of and interrelate this large finite number of measurements.

Personally I suspect that at a small enough scale some geometric measurements do not commute.
If you try to measure the six edgelengths framing a small enough tetrahedron you could keep on measuring one after the other and keep getting new answers

It wouldn't let you permanently pin down its shape, I suspect. The order you measure in would matter---whether you measured one first, before the other five, or last.

And I imagine that probably in the long run the REGGE model of geometry where space geometry is described by a bunch of tetrahedra, and spacetime by a bunch of pentatopes (the 4d analog of a tet) is probably more basic. Because corresponding more closely to the idea of a large finite number of discrete measurements.

A poster named Nugatory had this to say recently. I liked it so much I want to quote it. He is explaining that you shouldn't think of space or geometry as a material/substance/fabric etc. It is a bunch of geometric relationships.

Take three small objects, not all located on the same line. They're real solid material objects.

Stretch strings between them. These strings are also real solid material objects, and they form a triangle.

Measure the internal angles of that triangle. Do they add to 180 degrees? If not, our three objects are set in a curved space... And I worked this out without ever having to consider whether the space is a material object.

...And curvature is [also] a property of the relationships between these distance measurements, such as whether the distance between two parallel lines is the same everywhere. Where's the real material thing there?

What we know and observe are material objects and the geometrical relationships between them. If the interior angles of the triangle added to 180 degrees, we wouldn't jump to the conclusion that space is a material object that happens to be flat; so if they don't add to 180 degrees we don't have to conclude that space is a material object that happens to be curved.

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But why does that unifcation have to mean quantization of gravity?

Of course, there is the Einstein field equation. If the stress-energy tensor is the expectation value of some quantum state, but spacetime and the metric are classical entities, then this will lead to difficulties when we measure the quantum states of matter (see Wald's GR book p.382).

thank you!

It doesn't, and in fact I would say the current belief is that you can't quantize gravity in a straightforward way, at least as conceptualized by 20th century physics methods. As far as we can see, the canonical quantization and path integral methods and programs have essentially been failures, and the underlying objects probably do not exist mathematically.

Now, what is of course manifestly inconsistent is choosing to do nothing, and keeping geometry exactly classical. This is of course forbidden by Walds thought experiment, as well as many others. Therefore either gravity needs to be quantized (eg by putting hats over the Ricci tensor and assorted metric field) in some way, or the equations must be replaced by more convoluted objects in some way (think of trying to ask how to quantize fluid mechanics)

The classicalization program you refer too is a neat idea by Dvali and coworkers, that exploits what is known as the UV/IR correspondence in a clever way. It relies on some tricks that are controversial at this time, but despite its name, is still highly quantum mechanical.

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Jim Kata
I agree with Haelfix. I think the current consensus among most Physicist is that GR is an emergent theory, and quantizing it is just quantizing an effective field theory. Not to mention that all attempts to do so have generally been almost a complete failure. So why quantize gravity? I think the mundane answer is because nobody knew what else to do.

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Gold Member
The feeling that QM is THE theory of reality, and GR is emergent is strong. One problem is no one has even figured out exactly where any conflict arises. The current consensus is the Planck scale.

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The feeling that QM is THE theory of reality, and GR is emergent is strong. One problem is no one has even figured out exactly where any conflict arises. The current consensus is the Planck scale.

I thought that the interior of a black hole and the beginning of the big bang are examples of conflict.

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Dearly Missed
I thought that the interior of a black hole and the beginning of the big bang are examples of conflict.
I think that's right, and there is also a scattering amplitude regime for nearly headon collisions where the energy is not high enough for the colliding particles to form a black hole but still high enough that geometry is being affected and ordinary QFT does not apply. I'm told we don't have predictive theoretical coverage of that "No-Man's Land" region of parameter space between QFT and GR.

I was talking about that, and also other motivations for studying quantum geometry in a Cosmo forum thread:
... i don't see a mechanism here. I was trained in mechanisms.

You are right to see a gap. This gap (an undiscovered mechanism by which geometry can guide matter and matter can, in turn, bend geometry) fascinates and attracts researchers to QG.

One wants to find out how, at their roots, matter and geometry are related, so it will seem natural that they interact.

As an inexpert bystander just watching the ongoing research in quantum geometry/gravity I would say that Einstein 1915 GR is merely DESCRIPTIVE of the manner in which matter and geometry interact. The reason people are drawn into QG research is they want to understand the mechanism of that interaction.

The LHS of 1915 GR equation is purely geometric, a package of numbers describing curvature.
The RHS of the equation is about matter a package of numbers describing energy and momentum.
So it is saying that, at any given point, LHS = RHS, meaning that matter is determining how the geometry is bending/changing...So it is DESCRIBING the interaction that we see occurring in reality. We see matter and geometry behaving like that. But the equation is not saying why they interact like that.

So the quantum relativists, or quantum gravitists if you prefer, seem to be expecting that if they can delve down into the quantum roots of geometry, they will be able to find a connection between the quantum description of matter and that of geometry. A way to put BOTH into the same Feynman path integral, or if you like both into the same Lagrangian (a mathematical machine that physicists customarily use to describe dynamics). That would be lovely! quantum matter and geometry working together in the same mathematical machine which is cranking out combined TRANSITION AMPLITUDES between initial and final combined quantum states of geometry and matter! (You can see how this would excite and motivate some researchers.)

I don't want to overstate this, but I think you are pointing out an interesting and attractive gap in the current picture that people have.

There is also the thing of people wanting to understand how geometry and matter behave at extremely high energy density---what could have been happening around start of expansion? could there have been a bounce when the energy density was very high?
And I gather some people would like to be able to compute scattering amplitudes for head-on or nearly head-on particle collisions where the energy is not high enough to form a miniature black hole but is nevertheless high enough that ordinary QFT doesn't work because geometry does get involved. So there's a bunch of other motivations, things people are curious about besides what you suggested.

friend
I think that's right, and there is also a scattering amplitude regime for nearly headon collisions where the energy is not high enough for the colliding particles to form a black hole but still high enough that geometry is being affected and ordinary QFT does not apply. I'm told we don't have predictive theoretical coverage of that "No-Man's Land" region of parameter space between QFT and GR.

How does the "running of the constants" at higher energies fit into this picture of QFT in curved spacetimes? How much "running" do we see at LHC energies? Do we need to get into the realm of curving spacetime to see this running effect? Thanks.