Both Ends of the Quantum Gravity Spectrum

Discovering Physics’ Most Infamous Clash

Conjecture Institute Fellow Antonia Weber’s love of physics began in her high school class with problems whose solutions are well-understood such as, “Why don’t electrons fall into the nucleus?” Now she spends her days investigating problems at the cutting edge of fundamental physics: “How can we unify quantum mechanics and general relativity? What tests can we perform that may tell us whether or not general relativity needs to be quantized in the first place?”

Although Antonia first discovered the concept of quantum gravity in one of the many popular science books she’d read as a teenager, she was not yet certain about which topic in physics she wanted to pursue after high school.

“My favorite university courses were about quantum mechanics, general relativity, and cosmology,” Antonia says about her time at ETH Zurich, Switzerland.

During her cosmology internship, Antonia noticed that her project focused on phenomenological models that described observational data. While she appreciated the importance of empirical work, she wanted to understand the underlying explanatory principles of the field more deeply. “There were so many open questions in cosmology, and I realized that studying the foundations of quantum mechanics could shed light on some of them.”

During her course on the foundations of quantum mechanics, she discovered the proposed Bose-Marletto-Vedral (BMV) experiment that aims to test whether or not gravity has quantum features.

General relativity, first proposed by Einstein in 1915, has been our deepest theory of spacetime, gravity, and the universe as a whole ever since. Its account of reality is radically counterintuitive and yet has passed every experimental and observational test that scientists have thrown at it, such as correctly predicting the bending of light around the Sun, the existence of gravitational waves, gravitational redshift (whereby electromagnetic radiation loses energy as it pulls away from strongly gravitating objects like black holes or stars), and many more.

The two primary physical objects in general relativity are a dynamic spacetime, the arena of the universe, and matter and energy, the entities that roam around spacetime. In pre-Einsteinian (that is, Newtonian) physics, space and time were thought to be both independent of each other and also implacably static. They had simply been background ‘givens’ that all observers would agree upon.¹ In general relativity, spacetime curves and stretches in accordance with the distribution of matter and energy (which are themselves interchangeable in a way that Newton had never predicted). Not only do matter and energy distort the shape of spacetime, but the shape of spacetime determines how matter moves about—systems take the straightest possible paths under the constraints of a curved spacetime, and gravity just is this spacetime curvature.

While general relativity explains gravity in terms of matter-energy distributions in a dynamical spacetime, quantum mechanics accounts for the physics of nearly everything else. The theory can be thought of as a set of principles that constrain how a system can possibly behave and evolve. These principles imply the following features for any system:

1. Superposition—a quantum system can exist in many different states simultaneously. For example, it might exist in multiple locations or have multiple velocities at once. Similarly, an electron can exist in a superposition of ‘spin up’ and ‘spin down’. Under the Everett interpretation, when this system interacts with an observer, the combined system branches into parallel worlds—one where the spin is measured as ‘up’ and another where it is measured as ‘down’.
2. Interference—the aforementioned instances can interfere with one another such that the distribution of a quantum system’s states across the multiverse is different from what it would be absent any interference. For example, the famous double-slit experiment relies on a single photon going through two slits simultaneously, which interfere with each other upon reaching the screen. As more single photons are sent through, this self-interference builds up a pattern on the detector: bright bands appear in some spots where the photons interfere constructively, and dark bands appear in other spots where they interfere destructively.
3. Entanglement—the phenomenon whereby the quantum states of multiple systems are correlated. Under the Everett interpretation, measurement is simply the process of entangling the observer with the system. For example, when a scientist measures an electron that had been initially prepared in a superposition of ‘spin up’ and ‘spin down’, he will measure ‘spin up’ in some branches and ‘spin down’ in other branches. In other words, the scientist’s own superposition of ‘measured “spin up”’ and ‘measured “spin down”’ is correlated with the electron’s superposition—which of the two states he is in correlates with which of the two states that the electron is in.
4. Noncommutativity—the phenomenon whereby two attributes of a system cannot be measured to arbitrary accuracy simultaneously. For example, a system’s position and momentum do not commute, which means that the more precisely we measure one of them, the less precisely we can measure the other.

Now, all of these quantum features are utterly alien to the mathematical language, conceptual framework, and physical picture of general relativity. Einstein’s theory is a classical theory—exotic as it may be to our intuitions, there is still only a singular spacetime, a singular distribution of matter and energy, and a singular trajectory of any system it describes. According to the Everett interpretation, quantum theory, meanwhile, not only implies that systems exist in multiple instances across the multiverse, but it also details a number of phenomena that this multiplicity gives rise to, as briefly described above.

Many physicists argue that the idea that quantum theory only applies to very small objects like electrons or atoms is a myth. Any massive object, be it an ounce of water or an entire star, would itself be a quantum object and should therefore be capable of manifesting the same bizarre properties that photons and electrons display in a controlled laboratory setting. This already poses a problem, since general relativity tells us that matter behaves classically, that is, has only one value for each of its attributes.

The situation is even thornier than that. Consider that quantum theory predicts that, say, our Sun exists in a superposition of locations. Since spacetime is distorted according to the distribution of matter (and energy), then the shape of spacetime should be slightly different in each branch of the universe. But, again, general relativity insists on a singular spacetime, a singular gravitational field.

Some physicists think that quantum theory stops applying at some scale, at which point the world is once again classical. General relativity could then reign supreme, and gravity need never concern itself with the multiplicity of the quantum world. But there is nothing in quantum theory proper that indicates such a cutoff, contrary to advocates of such ‘collapse’ interpretations.

Other physicists think that the principles of quantum theory are universal and that gravity must somehow be made to conform to them.

Probing Gravity’s Quantum Features

Roughly speaking, there are two broad categories of proposals for unifying general relativity and quantum mechanics: those who think that classical gravity will survive the unification, and those who think that gravity will be quantized in the unification.

Because gravity couples only extremely weakly to matter, directly testing any such proposals is well beyond current technological capabilities. For example, theories that assume that gravity is quantum predict the existence of the graviton, but they are predicted to spontaneously emit from matter so infrequently that detecting such an event would take longer than the age of the universe. And trying to provoke a graviton in the laboratory would require far more energy than humanity is currently capable of harnessing.

“There is…the extreme difficulty of experimentally probing the relevant scales at which quantum gravitational effects are expected to become significant,” Antonia writes. “This is because the gravitational interaction is extremely weak compared to the other fundamental interactions. While electromagnetic interactions are roughly 1/137 of the strength of the strongest of all fundamental interactions, the strong force, gravity is weaker by a factor of about 6 × 10⁻³⁹.”

However, Conjecture Institute Scientists Chiara Marletto and Vlatko Vedral, and, independently, Sougato Bose, recently proposed an experiment that would not discriminate between any two individual theories of quantum gravity but would instead discriminate between the two categories of proposals—the BMV experiment may tell us whether or not gravity needs to be quantized in the first place. This test does not require a record-breaking particle collider nor a comically sized telescope but can be executed in an ‘ordinary’ laboratory at a cost orders of magnitude less than the cost of running the famous Large Hadron Collider at CERN.

Using constructor theory, a new theory in fundamental physics, Marletto and Vedral have proven the so-called General Witness Theorem (GWT):

By ‘non-classical’, they do not mean that system G conforms to all of quantum theory’s formalisms. On the contrary, the whole point of investigating how to unify general relativity and quantum mechanics is to discover their eventual successor theory, which will be deeper than either’s formalism! To test whether or not gravity is quantum, then, requires first isolating those features of quantum theory for which we have good reason to expect will survive unification with gravity, and then thinking of a test by which we can probe whether or not gravity also possesses those features.

Constructor theory has allowed Marletto and Vedral to express in exact terms the defining property of all non-classical systems, whether they conform to quantum theory’s formalism or whether they conform to quantum theory’s (and general relativity’s) eventual successor:

If constructor theory is right that this really is the key feature that distinguishes the classical world from the non-classical world, and that this feature will survive in whatever theory eventually unifies general relativity and quantum mechanics, then we should expect gravity to possess at least two non-commuting variables. Just as time only seems observer-independent in pre-relativistic physics but whose underlying observer-dependence is revealed under more extreme conditions, so too gravity only seems classical but whose underlying non-classicality should be demonstrable under clever experimental conditions.

At least, that is what constructor theory predicts.

The General Witness Theorem states that any system G that causes entanglement between two systems must be non-classical. Therefore, if one can devise an experiment whose outcome is a pair of entangled objects, and whose cause of entanglement could only possibly be gravity, then one will have demonstrated that gravity must be non-classical in the constructor theoretic sense defined above.

“Using the general witness theorem, we can conclude that if entanglement between the masses is measured in the BMV experiment, then the gravitational field must be non-classical,” Antonia writes. “This argument is often referred to as gravitationally induced entanglement.”

Antonia had become so fascinated by the BMV experiment and its potential to probe quantum gravity that she reached out to Vlatko and asked if she could complete her master’s thesis under his co-supervision alongside her supervisor from ETH, Renato Renner. Antonia and Vedral would collaborate on some of the theoretical aspects of the BMV experiment and its implications. The question was (and, in many ways, still is): if the BMV experiment indeed demonstrates that gravity is non-classical, then which of its variables in particular do not commute with each other?

In the gravitationally weak regime in which the BMV experiment operates, general relativity tells us that the shape of any region of spacetime can be thought of as the sum of three ‘modes’: the so-called scalar, vector, and tensor modes. The scalar mode describes fluctuations in the density and pressure of the region, the vector mode describes rotational, vortical, and shear-like disturbances in spacetime, and the tensor mode corresponds to ripples in the spacetime region, otherwise known as gravitational waves. Antonia and Vlatko would demonstrate that if the BMV experiment succeeds, then gravity’s vector modes (not just its scalar modes, as one may have naively assumed) must be non-classical. These vector modes consist of several variables, and which of them do not commute with each other remains an open question.

“I’m truly impressed with her original contribution,” Vedral says. “She is an exceptional young researcher.”

After completing her Master’s, Antonia applied to a PhD program under Vedral, became a Conjecture Institute Fellow, and then matriculated at Oxford, where she continues to work with Vedral and others.

The Quantum Seeds of the Universe

“The BMV experiment focuses on the low-energy regime when it comes to quantum gravity,” Antonia says. “Having already worked on that, I then wanted to explore the high-energy regime. This is very important for understanding the early universe, which was extremely hot and dense, and so you can’t ignore either quantum effects or gravitational effects.”

Cosmology has a wealth of open problems that demand explanation, such as:

1. The horizon problem: the temperature of the Cosmic Microwave Background radiation (CMBR), the oldest observable light in the universe and perhaps our best window into the Big Bang itself, is extremely uniform across the sky, despite the fact that some regions had never been in causal contact according to the Big Bang model.
2. The flatness problem: general relativity does not predict any particular geometry for the universe as a whole. Physicists have developed various models that correspond to different topologies, such as flat, spherical, or hyperbolic. For our universe to be flat, its energy density must be about 9 × 10⁻²⁷ kilograms per cubic meter in terms of mass, or about 8 × 10⁻¹⁰ joules per cubic meter in terms of energy (recall that the distribution of matter and energy determines the shape of spacetime). If the mass/energy density is even slightly greater or lesser than this critical value, then the shape of the universe readily becomes spherical or hyperbolic, respectively. And yet our universe does seem to have precisely the mass/energy density required to maintain a flat topology.
3. The monopole problem: many so-called Grand Unified Theories, proposals that aim to unify the strong, weak, and electromagnetic forces, predict (or retrodict) a barrage of newly created magnetic monopoles during the early universe. None have been detected.

The theory of inflation, often called ‘cosmic inflation’, was initially introduced by Alan Guth in 1980 to solve the monopole problem, though he would go on to discover that it might solve the horizon and flatness problems as well. The idea is that the universe underwent a period of rapid, exponential expansion from about 10⁻³⁶ to 10⁻³² seconds after the Big Bang, after which the universe evolves in accordance with conventional models of cosmic evolution.

1. Solution to the horizon problem: inflation implies that all of those causally disconnected regions of the CMBR were, in fact, close enough to interact and equilibrate (reach the same temperature) before the inflationary epoch. Inflation then pushed them far enough away from each other that they could never interact again.
2. Solution to the flatness problem: one can show mathematically that inflation’s exponential stretching of spacetime ‘smooths out’ any deviations from flatness such that, no matter what the universe’s topology may have been prior to the inflationary period, inflation would guarantee that the universe would become and remain flat.
3. Solution to the monopole problem: inflation’s intense expansion diluted the density of magnetic monopoles such that they are too sparse across space to be detected in the present moment.

Guth hypothesized that inflation was driven by a quantum field called the inflaton. Quantum fluctuations of this field are thought to be the origins of many asymmetries of the universe, such as the (very tiny) discrepancies among regions of the CMBR. These fluctuations are also thought to be the origins of galaxies and other large-scale structures, which, after all, are quite inhomogeneous relative to the empty space around them.

Before Guth’s theory, physicists recognized that quantum theory ought to play a role in some subtopics of cosmology, such as the Big Bang itself. But Guth’s inflation forced physicists to consider the role of quantum mechanics in shaping macroscopic structures of today’s universe. And, because gravity plays an indelible role in the evolution of the universe, anyone who takes inflation seriously must grapple with how quantum mechanics and gravity interface.

However, physicists before and since Guth’s proposal have been making progress armed with only the tools of general relativity, accurately modeling the structures of the universe without appealing to quantum mechanics. Absent any cosmological observations that could only be explained by invoking some quantum mechanical effects, one could reject inflation on the grounds that quantum mechanics simply could not possibly be the origins of large-scale structures.

Do we need quantum mechanics to explain the CMBR and the flatness of the universe, as Guth’s inflation would have it? Or are the classical mechanisms of gravity enough?

The logic is similar to that of the BMV experiment in that, to discriminate between two classes of theories (rather than between two actual theories), one requires an observation that can only have been brought about by a quantum mechanical process. If such an observation is made, then fully classical theories that purport to solve all of the aforementioned problems in cosmology are ruled out, and inflation is ruled in (though it could still have rival theories that also invoke quantum mechanics).

“The problem is that we’re limited by observational data,” Antonia says. “With cosmology, we can’t run an experiment over and over, and we can’t change parameters at will. So thinking of how to test for quantum effects in cosmology is an altogether different problem than when we probe gravity for quantum features in the laboratory.”

Just as one of the masses in the BMV experiment serves as an indirect witness of gravity’s quantum features, Antonia wondered whether there might similarly be cosmological witnesses out there to observe.

Inflation’s hypothetical quantum fluctuations are extremely difficult to measure directly, since the inflationary field decayed away after the short period of rapid expansion billions of years ago, and its energy has been converted into generic particles and radiation. However, over the last twenty years scientists have developed so-called Bell tests on the CMB, which is far easier to gather data on and analyze than the inflaton itself.

A Bell test does not discriminate between two theories but rather tells you whether or not the system under investigation is classical. To run a Bell test, the system must have (at least) two variables that could be entangled if the system is indeed non-classical. If the inflaton is non-classical, then correlations between these two variables should violate a particular bound. If the inflaton is classical, then these correlations should not violate this bound.

Although a Bell test on the CMBR should tell us whether the inflaton is classical or non-classical in theory, many practical challenges remain:

1. The correlations are ‘contaminated’ by historical and contemporary cosmological processes, making the signal-to-noise ratio lower than preferred.
2. The instruments used in conducting this Bell test are classical, so if there are non-classical correlations in the CMBR, they need to be captured without being destroyed by contact with classical devices here on Earth.
3. Statistical sampling (taking many measurements of the same variables across different regions of the sky) is limited by the fact that there are not infinite regions of the CMBR to gather data on.
4. Strictly speaking, Bell tests might only work for certain, more elaborate models of inflation. For simpler models, one would need to measure curvature perturbation—the uneven wrinkles in spacetime’s geometry as caused by inflation—and the ‘momentum’ of the inflationary field. However, we do not have empirical access to this momentum (due to the inflaton’s aforementioned decay), making a Bell test that would require this particular pair of variables impossible. Physicists are currently investigating alternative candidate variable pairs that could be used to perform a Bell test on simpler inflationary models. For both simple and complex inflationary models, the search for more accessible Bell test variables is an active area of research.

“I’m looking into different proposals to witness the non-classicality of these cosmological primordial perturbations at the moment,” Antonia says. “There have been some promising proposals. For example, some are looking into temporal Bell tests on the CMBR, which seek to measure variables at different times rather than at different points in space. Beyond Bell tests, there might be entirely different ways we can probe the CMBR for quantum signatures, such as by leveraging tools from quantum information theory.”

Antonia is in the early stages of collaborating with Vlatko, Aditya Iyer, and others on the problem of testing whether or not inflation—and, therefore, quantum theory—played an indelible role in the evolution of our universe.

Antonia’s career as a professional physicist is scarcely two years old, and already she has journeyed to both extremes of quantum gravity. With her work on the BMV experiment, Antonia contributed to our understanding of how quantum theory and gravity interface in the low-energy domain. In her current work on investigating quantum theory’s role in cosmology, she intends to solve problems in the high-energy domain of quantum gravity.

She has entered the field at an exciting time, when testing both ends of the quantum gravity spectrum is increasingly within reach. Antonia’s ability to contribute theoretical insights has already borne fruit, and that is before any such tests. Informed by future experimental results, her work on quantum gravity is sure to be that much more penetrating.