The odds of the bet Jonathan Oppenheim made in 2023 are generous, even at 5000 to 1. But if he wins, it could transform our view of the universe. The physicist is wagering that space-time, and therefore gravity, isn’t governed by quantum theory. That swims firmly against mainstream physics, which says gravity must ultimately be quantum, like the rest of the fundamental forces – even if we can’t currently work out how.
The wager is playful, but the question is serious, representing perhaps the most intractable puzzle in modern physics. And although Oppenheim is still out on a limb with his “post-quantum” theory of gravity, he is increasingly convinced his peers should take notice – not least because of the complexity of the alternatives. “There are all these people who think that we live in 11 dimensions and there are superstrings and space-time is emergent, looking at this theory and calling it radical,” he says. “But if you step away and think about it objectively, it’s sort of the opposite – it’s the most conservative theory you can have.”
And that’s not all. Accept the model’s perhaps most controversial innovation, and Oppenheim’s calculations show that it might elucidate another great mystery of modern physics: the nature of the invisible dark matter that seems to provide most of the gravitational oomph in the cosmos. Might he just be on to something?
For decades now, scientists have been trying to reconcile the two pillars of modern physics: quantum theory, which governs the behaviour of particles and forces on small scales, and Albert Einstein’s general theory of relativity, which describes gravity and determines how the universe works on the largest scales. Each of these pillars has been extensively stress-tested and stood strong. Yet, according to our current understanding, the two are fundamentally incompatible.
Quantum theory explains the workings of three fundamental forces – electromagnetism and the strong and weak nuclear forces – through the exchange of quantum particles that bind matter together in different ways. But according to general relativity, massive objects generate gravity not by exchanging quantum particles, but by warping space and time around them, causing them to “fall in” towards each other.
Each theory works spectacularly well in its domain: quantum forces explain how the matter that makes up the chair we are sitting on holds together; gravity explains why our bodies fall to Earth with a bump if we miss the chair when we try to sit. But this coexistence breaks down where large scales meet small ones: when quantum particles cross over the event horizon of a massive black hole, for instance, or in the very first instants of the big bang, when our known universe began as a tiny pinprick of mass and energy.
The vast majority of physicists think that the most likely solution will be some form of quantum gravity, in which gravity is built out of tiny quantum pieces like the other forces. At extraordinarily small scales, the smoothly warping space-time of Einstein’s theory would break down and pixelate, like an image zoomed in too far.
There are many different ways to quantise gravity and space-time. Perhaps the best known is string theory, which proposes the existence of tiny, curled-up extra dimensions. Another favoured contender, loop quantum gravity, depicts a smooth space-time as emerging from a deeper fundamental network of geometric “grains”.
Post-quantum gravity
Oppenheim, a physicist at University College London, isn’t sold on any of this. “In quantum gravity, the notion that gravity is describable in terms of space-time breaks down, but still everyone believes it’s quantum rather than a theory of space-time,” he says. He thinks that, if any successor theory is to reproduce the successes of general relativity, it’s crucial it should maintain that theory’s picture of gravity as a force acting between masses in a continuous, indivisible space-time. Post-quantum gravity does just that. “If you believe that, fundamentally, gravity is a theory of space-time, this is the theory for you,” says Oppenheim.
The model and its underlying mathematics are complex, but its goal is simple: start with what we know for sure about the various quantum fields, don’t quantise space-time and then see what happens. After years of painstaking work, Oppenheim has found that it actually seems to describe reality surprisingly well, so far. Crucially, gravity matches with quantum mechanics on small scales and behaves as general relativity predicts at larger ones.
In his latest paper, published in July, Oppenheim and Zachary Weller-Davies at the Perimeter Institute in Canada found that certain space-time symmetries that are crucial features of general relativity can also be applied to post-quantum gravity.
This comes at a price, however. If Oppenheim’s model is to fit with quantum mechanics, it must adopt certain features of it. In particular, it must allow all objects to be in a superposition of two states at once, resolving to a single state only when the quantum wave functions that describe them “collapse” on measurement.
These states include the position of the object – but herein lies the difficulty. If an object in two positions at once produces a gravitational pull from both, this would indicate that gravity is fundamentally quantum. Yet if only one position creates a pull, this would indicate that gravity “knows” which position the object will end up at once its wave function collapses. That would violate the uncertainty principle, a key and broadly accepted precept of quantum mechanics.
The only way to resolve this, according to Oppenheim, is to introduce a degree of randomness in the form of fluctuations in the coordinates of space-time. This effect is itself small, but its consequences are significant: it would mean that, at least on very small scales, both space and time are unpredictable. The ticks of a clock, for example, would no longer be at exactly equal intervals, but wobble slightly. It is a glitch, if you will, in space-time.
Messing with the nature of time in particular isn’t something to do lightly. “When we describe a system, we describe how it evolves in time, so the nature of time is a big question,” says Oppenheim. Time becoming random, even in a small way, makes it very difficult to work out how we should describe systems evolving – potentially throwing a wrench into the workings of physics itself.
The fact that this randomness doesn’t have a known physical source troubles some researchers. “I think he’s sort of going around the main thing, which is an explanation of why it is [random],” says Ivette Fuentes at the University of Southampton in the UK.
Oppenheim actually agrees. “I don’t like the fact that there are these unpredictable fluctuations,” he says. “It conflicts with the idea that everything should have a cause and we should be able to physically describe the world.” But something has to give if we are to reconcile quantum mechanics and gravity, he says. “We’ve tried all the easier approaches, and nothing has worked out, so there is a price we have to pay.”
And there might be reasons not to discount the existence of the fluctuations. One comes in the shape of a foundational postulate of quantum mechanics known as the Born rule. This is a formula that gives the probability of obtaining a particular value for a quantum system’s state when measuring it, and it is central to making the mathematics of wave function collapse work. The rule has held up to a century of scrutiny, but we still don’t know where it comes from. In Oppenheim’s model, it pops out as soon as the fluctuations in time are introduced, even though it wasn’t included as a premise of the model.
Phantom dark matter
What’s more, in work published this May, Oppenheim and his colleagues found that post-quantum gravity can reproduce some of the gravitational effects currently attributed to dark matter. Observations suggest that dark matter outweighs normal visible matter in the cosmos by 5 parts to 1 – but we have no clue what it consists of.
“Phantom” dark matter caused by space-time fluctuations might sidestep this massive problem. This part of the model is still in its infancy, says Oppenheim: “We know that there’s an effect that looks like dark matter, but we don’t know if it’s big enough to explain anything or if it has the right properties.” He is now working to nail down the possible connection in more detail.
His peers remain largely unmoved. Carlo Rovelli at Aix-Marseille University in France is one of the originators and leading proponents of loop quantum gravity. Along with string theorist Geoff Penington at the University of California, Berkeley, he struck the bet with Oppenheim back in 2023. The exact terms are that, if gravity is proved to be quantised, Oppenheim has to buy Rovelli and Penington something worth 20p; if it is proved to be not quantised, they are on the hook for an item worth £1000.
Rovelli says the model violates both quantum mechanics and general relativity. “Why should progress be walking back on what we have understood?” he says. “It is like proposing theories in which the Earth does not rotate around the sun.”
Not so, says Oppenheim. The model fits perfectly well within general relativity and, by proposing a physical origin for the Born rule, provides a necessary update to quantum mechanics. “It’s not that it breaks quantum mechanics; it actually solves one of the vexing issues that has plagued quantum mechanics since its inception,” he says.
A third view is that you simply can’t make an omelette without breaking a few eggs. “When you quantise gravity, and you quantise space-time, you’re also breaking general relativity,” says Fuentes. “I think you have to break both relativity and quantum mechanics to unify them.”
Reality will ultimately be the decider. There aren’t that many models of non-quantised gravity, and the selection is even sparser if you get rid of those that aren’t testable. That makes Oppenheim’s theory noteworthy, says Daniel Carney at Lawrence Berkeley National Laboratory in California: he likes that there are ways to check its predictions. “This model, in my mind, is mostly useful as a test case – it says, what if we’re wrong? Yeah, gravity is probably quantised like electromagnetism, but what else could happen is a shockingly difficult question to answer,” says Carney. “For that, it’s incredibly valuable.”
Already, observations are placing some constraints on the model. For example, if it is correct, there should be random gravitational waves with a particular range of frequencies and strengths that permeate the entire universe, emanating from random space-time fluctuations early in cosmic history. Gravitational wave observatories, such as the US-based Laser Interferometer Gravitational-Wave Observatory, measure ripples in space-time caused by the movements of highly massive objects such as black holes, and have also begun to make measurements of this weaker “stochastic gravitational wave background”.
Results so far have greatly constricted this background signal’s possible properties, likewise constricting the possibilities for post-quantum gravity. Meanwhile, laboratory experiments using ultracold atoms to measure gravity are providing constraints to the model at smaller scales. “There’s not a lot of wiggle room, not a lot of ways to hide if there are problems with it,” says Oppenheim.
Ultimately, what’s needed are more direct experimental tests – and recent improvements in theory and quantum sensing technologies mean they could be on the cards. The first such test would be to place a tiny mass, such as a nanoscale crystal, into a quantum superposition of two locations at once. Researchers would then try to entangle it with another crystal so that measuring the position of one instantaneously affects the result of measuring the other. Entanglement is a purely quantum effect, and so if gravity isn’t quantum, it would disrupt any entanglement between the two masses. Measuring any entanglement would immediately rule out post-quantum gravity, along with all other classical models of gravity.
A second test is to subject the superpositioned mass to a gravitational field and measure its response many times in a row. If gravity is quantum, the measurement should be about the same each time. If it is post-quantum, the tiny fluctuations in space-time should create inconsistencies between different runs of the experiment.
The same set-up can also be used to measure how long such a superposition lasts. “If classical gravity is coming from a quantum object, that really spoils the superposition of the mass in two places at once,” says experimentalist Sougato Bose, also at University College London – the mass will quickly collapse to a single location. Carney compares it to Schrödinger’s cat, the classic thought experiment in which a cat is trapped in a box, in a superposition of being both alive and dead until the box is opened and the cat is observed. “Instead of the cat being alive and dead, the cat will just become alive or become dead on a short time scale,” he says – with, in this instance, the cat being Oppenheim’s model.
University College London has just announced a new organisation, the David Potter Institute for Quantum Information and Spacetime, headed by Bose and Oppenheim and dedicated to testing theories such as post-quantum gravity. Actually doing the experiments is still extraordinarily fiddly, and it could be a decade or more until researchers have answers. “If we thought that gravity was quantum beyond question, then it wouldn’t make sense to even do these experiments,” says Bose. “But having these alternative theories is a very strong motivation to test this.”
“Worth testing” is, of course, not the same as “likely to be true”. Until the tests are actually performed, Oppenheim’s post-quantum gravity will probably remain on the fringes. “Does anybody really believe that the world could work the way he’s proposing? I’m sure some people do, but they would be hard to find,” says Carney.
Oppenheim sticks with the defence that his model requires far fewer assumptions, fewer tweaks to the existing models of the cosmos and the quantum world, and fewer carefully selected values and variables than many, or even most, quantum gravity models that have yet to gain experimental support, such as string theory.
Fuentes thinks that is a valid point. “We’ve had the last decades of just theory and theory and theory, mathematics without any real connection with what can be tested,” she says. “Yes, [Oppenheim] has a crazy idea, but he proposes an experiment. This is the sort of science that we should be doing at the moment.”