### Einstein’s gravity and quantum mechanics

Modern physics is founded upon two pillars. One is quantum theory, which governs the smallest particles in the universe. The other is Einstein’s theory of general relativity, which explains gravity through the bending of spacetime. But these two theories are in contradiction with each other, and a reconciliation has remained elusive for over a century.

The prevailing assumption has been to modify Einstein’s theory of gravity, or “quantized” to fit within quantum theory. This is the approach of two leading candidates for a quantum theory of gravity, string theory and loop quantum gravity.

But Jonathan Oppenheim at University College London Physics & Astronomy has developed a new theory. In a new paper in the peer-reviewed open-access journal *Physical Review X* (PRX), he challenges that consensus and takes an alternative approach by suggesting that spacetime may be classical. That is, not governed by quantum theory at all.

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### Here’s how Einstein’s gravity and quantum mechanics works

Instead of modifying spacetime, the theory – dubbed a “postquantum theory of classical gravity” – modifies quantum theory. It predicts an intrinsic breakdown in predictability that is mediated by spacetime itself. This results in random and violent fluctuations in spacetime that are larger than envisaged under quantum theory, rendering the apparent weight of objects unpredictable if measured precisely enough.

A second paper, published simultaneously in the peer-reviewed, open-access journal *Nature Communications* and led by Oppenheim’s former Ph.D. students, looks at some of the consequences of the theory. It also proposes an experiment to test it: to measure a mass very precisely to see if its weight appears to fluctuate over time.

For example, the International Bureau of Weights and Measures in France routinely weighs a 1 kilogram mass, which used to be the 1kg standard. If the fluctuations in measurements of this 1kg mass are smaller than required for mathematical consistency, they can rule out that theory.

### A 5,000:1 odds bet

The outcome of the experiment, or other evidence emerging that would confirm the quantum versus classical nature of spacetime, is the subject of a 5,000:1 odds bet between Professor Oppenheim and theoretical physicists Carlo Rovelli and Geoff Penington. Rovelli and Penington are leading proponents of quantum loop gravity and string theory, respectively.

For the past five years, the UCL research group has been stress-testing the theory and exploring its consequences.

Professor Oppenheim said:

Quantum theory and Einstein’s theory of general relativity are mathematically incompatible with each other. So it’s important to understand how this contradiction is resolved. Should spacetime be quantized, or should we modify quantum theory, or is it something else entirely? Now that we have a consistent fundamental theory in which spacetime does not get quantized, it’s anybody’s guess.

### The experimental proposal

Co-author Zach Weller-Davies, who, as a Ph.D. student at UCL, helped develop the experimental proposal and made key contributions to the theory itself, said:

This discovery challenges our understanding of the fundamental nature of gravity but also offers avenues to probe its potential quantum nature.

We have shown that if spacetime doesn’t have a quantum nature, then there must be random fluctuations in the curvature of spacetime which have a particular signature that can be verified experimentally.

In both quantum gravity and classical gravity, spacetime must be undergoing violent and random fluctuations all around us, but on a scale which we haven’t yet been able to detect. But if spacetime is classical, the fluctuations have to be larger than a certain scale, and this scale can be determined by another experiment where we test how long we can put a heavy atom in superposition* of being in two different locations.

The analytical and numerical calculations of co-authors Carlo Sparaciari and Barbara Šoda helped guide the project. They expressed hope that these experiments could determine whether the pursuit of a quantum theory of gravity is the right approach.

### More about the proposal

Šoda (formerly UCL Physics & Astronomy, now at the Perimeter Institute of Theoretical Physics, Canada) said:

Because gravity is made manifest through the bending of space and time, we can think of the question in terms of whether the rate at which time flows has a quantum nature, or classical nature.

And testing this is almost as simple as testing whether the weight of a mass is constant, or appears to fluctuate in a particular way.

Sparaciari (UCL Physics & Astronomy) said:

While the experimental concept is simple, the weighing of the object needs to be carried out with extreme precision.

But what I find exciting is that starting from very general assumptions, we can prove a clear relationship between two measurable quantities, the scale of the spacetime fluctuations, and how long objects like atoms or apples can be put in quantum superposition of two different locations. We can then determine these two quantities experimentally.

Weller-Davies added:

A delicate interplay must exist if quantum particles such as atoms are able to bend classical spacetime. There must be a fundamental trade-off between the wave nature of atoms, and how large the random fluctuations in spacetime need to be.

### Einstein’s gravity and quantum mechanics background

**Quantum mechanics**. All the matter in the universe obeys the laws of quantum theory, but we only really observe quantum behavior at the scale of atoms and molecules. Quantum theory tells us that particles obey Heisenberg’s uncertainty principle, and we can never know their position or velocity at the same time. In fact, they don’t even have a definite position or velocity until we measure them. Particles like electrons can behave more like waves and act almost as if they can be in many places at once (more precisely, physicists describe particles as being in a “superposition” of different locations).

Quantum theory governs everything from the semiconductors that are ubiquitous in computer chips, to lasers, superconductivity and radioactive decay. In contrast, we say that a system behaves classically if it has definite underlying properties. A cat appears to behave classically: it is either dead or alive, not both, nor in a superposition of being dead and alive. Why do cats behave classically, and small particles quantumly? We don’t know, but the postquantum theory doesn’t require the measurement postulate, because the classicality of spacetime infects quantum systems and causes them to localize.

### About gravity

**Einstein’s gravity**. Newton’s theory of gravity gave way to Einstein’s theory of general relativity (GR), which holds that gravity is not a force in the usual sense. Instead, heavy objects such as the sun bend the fabric of spacetime in such a way that causes Earth to revolve around it. Spacetime is just a mathematical object consisting of the three dimensions of space, and time considered as a fourth dimension. General relativity predicted the formation of black holes and the Big Bang. It holds that time flows at different rates at different points in space, and the GPS in your smartphone needs to account for this to properly determine your location.

### Illustration at top

At the top of this article is an artistic version of Figure 1 in the PRX paper. It depicts an experiment in which heavy particles (illustrated as the moon) cause an interference pattern (a quantum effect), while also bending spacetime. The hanging pendulums depict the measurement of spacetime. The actual experiment typically uses Carbon-60, one of the largest known molecules. The UCL calculation indicates that the experiment should also use higher density atoms such as gold. Image via Isaac Young/ University College London. Used with permission.

Physical Review X paper

Nature Communications paper

Public lecture by Professor Jonathan Oppenheim in January 2024

Professor Oppenheim’s academic profile

UCL Physics & Astronomy

UCL Mathematical & Physical Sciences

Bottom line: Einstein’s gravity and quantum mechanics are the two bases for modern physics. But these two theories contradict each other. Have we reached a reconciliation?