*Much of the physics world, and millions in funding, is spent on the ceaseless hunt for a theory of everything which unites general relativity and quantum mechanics. Quantum gravity – a description of gravity that obeys the principles of quantum mechanics – is held up as the holy grail that will lead our discovery, however Isaac Layton argues this search is misguided.*

In 1905, whilst working in a patent office, Albert Einstein published four ground-breaking papers, setting the stage for half a century of rapid progress in theoretical physics.

Two of the papers laid the basis for what is now known as general relativity. Completed a decade later in 1915, general relativity provided a new understanding of gravity, explaining the apparent force we feel from massive objects in terms of the bending of space and time. To this day, general relativity provides our best theory of gravity, and has been extensively tested, most recently with the detections of gravitational waves.

Although general relativity provided a radical conceptual shift from the earlier work of Newton, it is still what physicists would call a classical theory. Classical theories are those which build on the basic intuitions that we all have about the natural world: that objects have definite positions in space, and that these don’t change when we look at them.

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On the other hand, Einstein’s first paper of 1905 helped push scientific progress in a completely different direction – to that of quantum theories.

In contrast to the classical theories, quantum theories throw away the notion that everything has a definite state of existence. The most famous example of this is the now infamous Schrodinger’s cat, which stays in a state of simultaneously being alive and dead inside its box, until the box is opened and the state of the cat is measured.

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This collapse is random: when Schrodinger’s cat is measured, 50% of the time it instantly goes to the state of being alive, while 50% of the time it becomes dead.

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The strangest property of quantum theories compared to classical theories is that every measurement must be accounted for in the theory explicitly – like if the weather forecast for tomorrow depended on whether or not you looked up at the sky today. In quantum theory this appears as the so-called “measurement postulate”, which says that every time a measurement is made of something quantum, the quantum system instantly “collapses” into a definite state of being. This collapse is random: when Schrodinger’s cat is measured, 50% of the time it instantly goes to the state of being alive, while 50% of the time it becomes dead.

Replacing the classical notions of determinism and objectivity, quantum mechanics provided a broad new framework with which to understand the world. The development led to a new rush to understand reality through a quantum lens, and "upgrade" existing classical theories to quantum ones. Technically known to physicists as “quantisation”, the quest to upgrade the classical theory of electromagnetism to a quantum one took the efforts of many of the best physicists of the century, and was ultimately successful. The resulting theory of quantum electrodynamics provided a new viewpoint on electromagnetism; while it may look regular and classical on the surface, the underlying theory is fundamentally unexpected, with subatomic particles continually popping in and out of existence. This theory was subsequently followed by the successful unification of electromagnetism with the strong and weak forces into a single combined quantum theory.

The early success of the quantisation of the known forces lead to one overwhelming conclusion amongst physicists: that gravity should too be upgraded to a quantum theory. Early attempts at doing so began in earnest in the 1950s, and have since evolved and branched into multiple directions, the most famous of these being string theory and loop quantum gravity. Today, the field is largely focused on broad, model-independent concepts such as “holography”, and is making good progress at providing connections between many of the ideas that have been generated along the way. However, in contrast with the success of either general relativity or quantum theories of matter, there has been no clear winning contender of a quantum theory of gravity, nor any experimental evidence for those which were favoured early on.

The ongoing difficulty of constructing a quantum theory of gravity begs an obvious question: does gravity really require upgrading to a quantum theory?

The core argument against leaving gravity classical was a simple one: no one could see how to make classical theories coexist with quantum ones. To see why this might be the case, imagine what would happen if Schrodinger’s famous quantum cat met a regular, classical mouse. When the cat is alive, the mouse will be eaten; but if the cat is dead, the mouse will remain alive. In this way, the quantum cat’s state of being simultaneously alive and dead also seems to infect the mouse, leading it too to become quantum. For this reason, classical and quantum theories seemed destined to be un-reconcilable. Given that quantum theories of electromagnetism and matter were already mainstream, it seemed impossible to include gravity in these theories without also upgrading to a quantum theory.

However, it turns out that it is possible to make classical and quantum theories coexist. An example is provided by imagining Schrodinger himself, looking inside the box at his cat. When he does so, the cat is found randomly to be either alive or dead, and Schrodinger is (presumably) either happy or upset when he finds out what has happened. The key feature of this is that Schrodinger himself remains classical: he either is happy, or he is sad, but he is not both simultaneously. In contrast to the mouse, Schrodinger stays classical because he measures the state of the cat, collapsing the state of the cat and randomly updating his own knowledge in the process.

The key takeaway from this example is that classical systems can coexist with quantum systems when the classical parts act like they are measuring the quantum ones. Since measurements in quantum mechanics are fundamentally random, this means that any theory describing interacting classical and quantum systems must also be fundamentally random.

The fact that classical and quantum systems can coexist, contrary to early assumptions, implies an alternative to upgrading gravity to a quantum theory: keep gravity classical, but modify it to be random so that it can coexist with existing quantum theories.

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The exciting thing about a random classical theory of gravity coupled to quantum matter is that experimental answers may not be too far around the corner.

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The possibility of such an alternative lies in the fourth and final ground-breaking contribution of Einstein in 1905. The topic of this work was seemingly much more modest in scope compared to his other work that year – to explain the random motion of pollen particles suspended in water. Providing the first theoretical justification for the random, or “stochastic”, motion of these particles, this work came to be seen by modern physicists as evidencing the brilliance of Einstein, but ultimately independent of the fundamental questions posed by his other work of 1905.

However, it turns out that the kind of randomness inherent to the motion of particles in liquids is much tamer than the randomness of instant collapse in quantum mechanics. This means that as opposed to the classical system having to suddenly jump from one place to another, and the quantum system instantly collapse at the same time, the whole process can be slowed down. Rather than jumping, this alternate kind of randomness is more akin to a drunkard, taking steps in different directions at random, slowly moving further and further away from where they started. In this way, the random motion of the classical system coincides with a more gradual collapse of the quantum system.

Instead of needing to upgrade to a quantum theory of gravity, as is typically expected, Einstein’s work on the random motion of pollen in principle allows for a modification of classical gravity that is compatible with existing quantum theories. Whilst large jumps in the force of gravity, and instant collapse of quantum states would have already been observed, this more relaxed kind of randomness could still be an unobserved property of gravity, and thus allows for a random, classical theory of gravity that is compatible with our observations so far.

The exciting thing about a random classical theory of gravity coupled to quantum matter is that experimental answers may not be too far around the corner. An important feature of these theories is that they inherit the properties of measurement in quantum mechanics, namely that the classical part has random motion, while the quantum part collapses into a definite state, just as the Schrodinger’s cat becomes either alive or dead. It turns out that the rate of these two things are inversely related: the more random the classical motion is, the slower the cat becomes either alive or dead, while the more predictable the classical particle is, the faster the quantum system collapses into a definite state.

This provides a way of testing a stochastic classical theory of gravity. If we experimentally determine that the randomness in the gravitational field is very small, but that quantum systems don’t collapse as fast as expected, we can definitively rule out a classical theory of gravity. Although this may sound bad, ensuring that a theory can be easily falsified is an important feature of any good theory, and distinguishes this proposal for random classical gravity from some of its quantum gravity counterparts.

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Is it likely that gravity is fundamentally classical? Probably not. Then again, it would be extraordinary if it was fundamentally quantum either.

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Before getting too excited and making big claims, it is worth emphasising that there are many theoretical details still to be worked out. Although the framework of classical systems interacting with quantum ones has been well established, and certain experimental signatures of this in the case of gravity have been identified, applying this to a full theory of stochastic gravity coupled to quantum matter remains a difficult task. One notable reason is that remarkable symmetry of general relativity. Constructing and understanding theories that include randomness whilst still obeying these important symmetries seems to be a key theoretical challenge, which one may hope is easier than the problem of constructing a full quantum theory of gravity.

Is it likely that gravity is fundamentally classical? Probably not. Then again, it would be extraordinary if it was fundamentally quantum either. Throughout human history, we have continually come up with new theories of the world around us, and continually found at each point that some aspect wasn’t quite right, and needed fixing. A fundamentally classical and random theory of gravity may sound wrong, and may well be wrong too, but if it does the job even a little better than the previous theory then it’ll be the best we have. I hope you’ll agree it’s worthwhile spending the time to check.

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