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What Are Some Theories on Quantum Gravity?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

While no definite working theory for quantum gravity exists, scientists and theorists are hard at work trying to uncover this Holy Grail. If you can figure it out, physics is likely unified and many dominos holding up mysteries would topple with ease. So let’s look at a few major theories to learn about the frontiers of unification.

Loop Quantum Gravity

The heart of quantum mechanics (QM) lies in probability functions, and this especially becomes interesting when we get to the meeting ground it has with special relativity courtesy of electromagnetism. QM gives you a roadmap to calculate the probabilities of quantized energies in a given field and how the interactions between fields act like the classical particles we recognize.

It demonstrates how information is finite and therefore discrete, how we have uncertainty in our measurements, and that relational dependences are afoot. When we look at QM and special relativity acting together, we arrive at quantum field theory, where “particles are quanta of a field.” This led to many accepted theories of today such as the standard model and the Higgs boson (Rovelli 126-130).

Lev Landau took this field theory and wondered what would happen if we looked at a small region of space-time. He theorized that the fields inside the region would fail because of the probabilistic nature of quanta creating a flux that would inhibit us from finding any values. Niels Bohr was able to show that this isn’t true for electromagnetic fields. But Matvei Bronstein wondered about gravity fields for the region, and it turns out Landau was right for that classification (151-3)

The trick was to see the relationship between the size of the space and the escape velocity required to leave it. As we try to confine an object, the chance of it leaving grows and its energy potential increases, causing space-time to change as well as our object moves. If this keeps up, we will end up with a black hole, a singularity that has a definite location and therefore violates our quantum aspects. This led to the discovery of the Planck length, which is the smallest distance for which I can still have relevant quantum information. Nothing can get smaller than this scale, so this is the most basic piece of space-time we can look at (Ibid).

At the Planck length, quantum effects should be quite prominent, but gravity is also present, so this is the launching point from which quantum gravity investigations start. But right away we are in an interesting dilemma: If QM allows for quanta of information, what would quanta of gravity look like? We don’t associate gravity with a basic unit because it’s seen as a consequence of matter displacing space-time (153-4).

That is often visualized as a fabric made of infinite lines, something that quantum mechanics doesn’t allow for. Space-time has to have a base unit, but what would that be? We could approximate the math, but it doesn’t necessarily yield the truth of the situation either (Ibid).

Richard Feynman attempted to extend his work on the basic atomic particles (neutrons, electrons, and protons) and apply it to general relativity in an attempt to gleam insight but no such luck because of the inability to get to that basic quanta. John Wheeler, Feynman’s teacher, attempted to look at space at small scales and work his way down. After looking at the superposition of various geometries, he developed the idea of quantum foam, just like what one would see at a beach but at a very tiny scale. This would pop in and out of existence and act like the source from which space originated (155-160).

To explain the structure of this foam, Wheeler along with Bryce DeWitt developed the Wheeler-DeWitt equation, which is complicated because it deals with potential orbitals and probabilities of curved spaces. It does have some issues, including its independence of time and the infinite solutions it can generate but which have no real correlation to them (Ibid).

Despite this, it does offer some promising results and has ties to QM and relativity, especially with causal loops. These deal with closed and open timelines, and for the Wheeler DeWitt equation we end up with closed, complete loops of quantum foam. This has led to the loop quantum gravity theory, one of the best candidates so far (Ibid).

From shapes to spin networks.

From shapes to spin networks.

Just how do these loops arise? Well, when we talk about gravity field lines, these end up being potential Wheeler DeWitt solutions. Ken Wilson in 1976 modeled space time using points, lines, and lattices. It was one of the first discrete space-time models known to be developed for physical processes.

In it, lines connecting points are much smaller than a diameter of a proton and so is hard to spot but this allows for the lines to act much like fields in physics. The line are space itself and not a displacement caused by objects resting in it. The fabric that we are used to talking about is instead a set of nodes, or locations where lines intersect. The distance between two nodes is referred to as a link, and the set of nodes and links present forms a graph of space (Rovelli 161-6, Smolin 115-8).

Essentially, the nodes in our graph provide the volume we associate with space and our links give definition to our distance parameters. Recall that the volume of space we have at any given moment is correlated to the gravity field. With smaller and smaller volumes present, our quantum effects stack up and our nodes fluctuate, creating a “spectrum of the volume” possible to us. And this set is discrete, quantized. There are no infinite possibilities, but a fixed number of possibilities provided by the nodes of our graph. Those links end up being field lines between our volumes, and the areas bounded by links determine the regions of space that we conceptualize as the fabric or lattice of space time (Ibid).

This finally leads to our quanta of gravity. Smolin took this lattice idea and other pieces from Polyakov, t’Hooft, Peskin, and Shenker to develop a model for quantum gravity. His first go at it didn’t work because he made the lattice too rigid and not in line with general relativity. To resolve this, he needed a flexible, changeable lattice structure that could adjust according to the passage of time (Smolin 118-21).

About this time, Smolin heard of work by Julian Barbour and Bruno Bertolli which demonstrated space-time as nothing more than components of relationships. Smolin realized that general relativity was just one type of relation out there and so applied the approach to gravity to develop the dynamic lattice theory (Ibid).

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If we envision a loop made by tracing nodes and links in a route, we have achieved a quantum state for our gravity field. Unlike normal quanta, which are dependent on their location, our gravitational quanta are where something is happening as defined by my links. It’s really quite amazing. “Quanta of gravity…are not in space, they are themselves space,” and that is a radical new way to explore QM (Rovelli 167-9, 173-4).

Spin networks are spaces, formally defined. When I complete a loop, I have made a circuit and therefore have established my quanta of gravity. Our loops can interact with each other, creating the probabilities we associate with QM and at the Planck length we get the probability cloud of loops that is ultimately space. Yes, it’s a lot to process (Ibid).

But we haven’t addressed the time component here. In relativity, we have funny business with time dilation caused by gravity effects, so clearly a relation does exist. But when you look at the Planck scale, time seems to practically disappear, yet clearly we know this not to be the case. But this refers only to Newtonian time that vanishes, not relativistic time. That aspect pertains to frames of reference, which we mainly look at the macro scale to appreciate the underlying physics and consequences. We have events happen and the process of going from event to event (reference frame to reference frame) can be extended to our spin networks also (177-190).

This implies that time is really just a process of space, with our size diminishing until we get some Heisenberg considerations. If we limit the borders of which our event can transpire, we have confined ourselves and so enter a probability cloud of events happening, a “quantum cloud.” How this cloud changes our spin network can create a history of it, which leads to a spin foam appearing to compensate for this (Ibid).

It allows us to see how nodes have moved along a link, creating and destroying networks as we go along. “The boundary of a spin foam is a spin network and the matter on it,” defined by planes of area made by the links themselves. Thus, we have finally arrived at the ultimate goal of space and time being described by QM. Now, it’s up to experimenters to verify the theory (Ibid).

Asymptotically Safe Gravity

Of course, other theories are out there. Developed in 1978 by Steven Weinberg, Asymptotically Safe Gravity deals with the energy aspects of gravity. In QM, energy like all things is quantized, and depending on how much energy of a given type I have there will be a corresponding reaction. With gravity, high energies pose a problem for QM because of their infinite implications. But what if this doesn’t actually come to pass courtesy of a parameter tied to gravity? If so, then we could say gravity is asymptotically safe (that is, it won’t approach infinity as energy increases) (Hossenfelder).

This is important because gravity at low energies can be easier to reconcile with QM than high energies. In the late 1990’s, work by Christof Wetterich (University of Heidelberg) and Martin Reuter led to a mathematical start to talk about QM and gravity at higher energies. By progressing with the lower energy levels and building from there the hope is to scaffold to the quantum gravity description for all energy levels. The work has shown other models to be asymptotically safe and it works for known low energy situations (Ibid).

If theorists can move beyond the confines of the small spaces and work with larger ones without approximating, we may be able to find it too is an asymptotically safe scenario and therefore reconcilable with QM. As a bonus, it predicts the lack of success that supersymmetry has encountered so far, showing the superpartners to be impossible because of the energy levels needed to isolate them (Ibid).

Remaining Possibilities

Of course there are more quantum gravity ideas out there which will require more exploring than we have room for here (and so hopefully will be discussed in a future article of mine”. Freeman Dyson’s theory says the universe could exists as a dualistic cooperation where Einstein’s gravity “‘is a purely classical field without any quantum behavior’“ that happens to share a universe where QM rules for the particle land. That would imply we have no business trying to quantize gravity, but if true then a theory of everything would be unachievable (Wolchover “Physicists Find”).

For Roger Penrose/Lajos Diosi, their theory states that space-time is incapable of being superimposed, for it is classically impossible to take a curved region and give it superimposed properties, but it does cause particles to collapse because they must match their environment. This is otherwise known as gravitational decoherence, and it does show some promise (Ibid).

So there you have it, a brief tour of some quantum gravity fun. I’m glad I was able to pull you in and I hope you enjoyed.

Works Cited

Hossenfelder, Sabine. “Why an Old Theory of Everything is Gaining New Life.” Quantamagazine.com. Quanta, 08 Jan. 2018. Web. 28 Aug. 2019.

Rovelli, Carlo. Reality is Not What It Seems. Riverhead Books, New York. 2017. Print. 126-130, 151-169, 173-4, 177-8, 182-190.

Smolin, Lee. Three Roads to Quantum Gravity. Basic Books, Great Britain. 2001. Print. 115-121.

Wolchover, Natalie. “Physicists Find a Way to See the ‘Grin’ of Quantum Gravity.” Quantamagazine.com. Quanta, 06 Mar. 2018. Web. 05 Mar. 2019.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2021 Leonard Kelley

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