I WOULD like to take you with me, just for a minute or two, on a journey through space and time. We are minding our own business, watching the stars and galaxies zip by, when, suddenly, an invisible force draws us in. The closer we get to its source, the faster we move. Eventually, we are moving so quickly that time slows. We become extremely heavy and nothing can stop us – we are hurtling towards a black hole.
On our approach, we start to see streaks of light curving around a dark centre. This is the event horizon, the point beyond which gravity is so great that nothing, not even light, can escape.
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But our journey must end here. Putting aside the torture it would place on our bodies to go further, we can’t even imagine what lies beyond this point. At the centre of a black hole, our best description of gravity, the general theory of relativity, breaks down and our other great theory of nature, quantum mechanics, must kick in. We have reached a place where our two best ways to describe the universe – relativity on the larger scale, quantum mechanics on the very small – come together in some way we don’t yet understand. Trying to unify these remains one of our greatest challenges.
However, there are now glimmers of hope. Recently, I have been developing an idea that might get us somewhere by making quantum mechanics more like general relativity. With the help of some experiments, it could lead us to the centre of our black hole, and to a unified theory at last.
In physics today, we have two pictures that don’t match up. First is general relativity, Albert Einstein’s set of equations that describe the way classical objects are affected by gravity. It sets out the three dimensions of space and the fourth dimension of time as part of the same entity, woven together in the fabric of space-time. That works extremely well, to a point. It is excellent at describing the way space-time bends around large masses, the way time slows down when objects move close to the speed of light, and anything that concerns the dynamics of things larger than an individual particle.
But the fundamental force of gravity doesn’t fit into quantum mechanics, our best description of the very small. Atoms and subatomic particles seem to follow a totally different rule book. They are governed by the other three fundamental forces of nature, the electromagnetic force and the strong and weak nuclear forces. Particles can appear to be in two places at once. They can be entangled, with information seemingly passing between them instantaneously, even when they are far away from each other. The quantum world is also characterised by a strange fuzziness – the uncertainty principle that says the more we know about a particle’s position, the less we can be sure of its momentum. If this were the case in general relativity, then you would only be able to know where your car is or how fast it is going, never both.
Both theories have been remarkably successful in their own domains. But the problems occur when they are applied, at the same time, to a situation where both should matter, like the centre of a black hole. We know black holes, which were predicted by general relativity, exist. But since they involve a humongous gravitational field packed into a quantum-sized region of space, we have no way of describing what happens in their centres.
This leaves a huge question: how to marry the physics of the very big and the very small into one coherent theory of everything? This question is at the heart of the search for a single mathematical framework that describes the whole universe, and there is no shortage of people trying to find an answer.
It would be impossible to mention every individual idea that attempts to unite physics, but I like to consider them in groups. The first I think of as theories of quantum gravity. These take ideas from general relativity – like space-time, for example – and tweak them to fit quantum mechanics. Among the most popular of these is an idea that treats gravity like any other field, such as the electromagnetic field. In this theory, gravity is thought to be mediated by a hypothetical particle called a graviton, similar to the photons that mediate electromagnetic interactions. Gravitons, however, would interact so weakly that directly detecting one is nigh-on impossible.
In other approaches, space and time become discrete, meaning they can only exist in finite chunks – the same way that the energy levels in an atom are discrete, or quantised. An example of these is loop quantum gravity, in which these quantised chunks of space-time are tiny loops.
Then there are approaches that favour gravity over quantum physics. In the 1970s and 80s, for instance, and Roger Penrose speculated that quantum physics won’t endure beyond some basic strength of gravity, at which point the so-called quantum wave function that encapsulates quantum properties collapses. Classical gravity, according to this view, ultimately wins. Other such approaches are keen to understand quantum physics geometrically, to cast it in a form that is mathematically closer to general relativity, like thinking of quantum superpositions as analogous to the curvature of space-time in relativity.
Finally, there are advocates for a more fundamental theory from which general relativity and quantum mechanics both evolve. String theory, which seeks to rewrite our understanding of what everything is made of, is the most prominent of these. Instead of electrons and quarks being fundamental, string theory claims everything is made of unbelievably tiny, vibrating “strings”, and that those vibrations produce effects that we interpret as the particles we see. Unfortunately, string theory also requires a host of other entities – such as multiple extra dimensions – that are well beyond our experimental reach.
It is fair to say that all of our approaches to unify quantum physics and gravity have failed so far, due to both the lack of mathematically consistent descriptions and the absence of experimental tests. This is a problem.
But what if we look at things another way? Instead of taking ideas from general relativity and moulding them to fit into quantum mechanics, I think we need to change the way we think of time in quantum mechanics. What if, to make quantum mechanics more compatible with general relativity, we treat space and time in the quantum world as we do in space-time – namely, on an equal footing?
In relativity, time is interwoven with space. It can bend and stretch, depending on the speed or the gravity involved. This is a far cry from the way most physicists talk about time in quantum mechanics, where it is a fixed, separate entity, a series of steps through which interactions evolve and nothing more. In traditional quantum mechanics, time is only inferred from looking at other observable quantities, such as the hands of a clock.
This is reflected in the way we tackle equations in quantum mechanics – how we, for example, describe the position in space of a qubit, a quantum mechanical alternative to the classical bit in computing, which can exist in superpositions of several states at once. We describe the qubit over time using a bit of mathematics called the Schrödinger equation, which describes the strange and equivocal behaviour of quantum objects and allows you to reliably calculate the odds of which of that object’s properties, such as its location, you will see when we take a measurement of it.
Entangled in time
About 10 years ago, I began to consider an alternative to the Schrödinger equation. I read about some experiments showing that quantum entanglement – the superstrong link between the states of two quantum particles after they have interacted – , but also between the states of the same object . This means that, in some cases, particles seem to be affected by events that happen in their future. This is a strange idea to get your head around, undoubtedly. But it got me thinking, if particles can be entangled over time, then perhaps in quantum mechanics, time isn’t the steady, outside ticking clock we think it is.
After this realisation, I wasn’t entirely clear how to proceed. But, for the past decade, along with my colleagues and , I have developed an alternative mathematical approach, one with profound implications.
Instead of describing the behaviour of a quantum object in space at one specific time, we describe the behaviour of quantum objects across all space-time at once. When making calculations about how a particle should interact, for example, we write down all the possible outcomes at all the possible points in space and every instance of time, instead of just at one instance of time as is normally done with the Schrödinger equation. The fundamental dynamics are the same – particles are still governed by the three fundamental forces. But instead of, for instance, describing a particle’s position over space at one point in time, we describe it over space-time.
Just as time is relative in general relativity, meaning it depends on the observer, time becomes relative in this description of quantum mechanics, too. It is no longer a fixed, separate entity. It depends on the observer. What this means is that when you are looking at two descriptions of a position in space-time, for example, it isn’t always possible to say whether one happened before the other. This ambiguity doesn’t exist in standard quantum mechanics, where each of two events are in a clear relationship with one another as far as any observer is concerned.
In our description, which we , space-time is an entangled web of quantum-correlated events all given in advance. This is important because this new way of thinking about quantum mechanics lends itself to unifying quantum theory with general relativity, in the sense that both now have a way of describing time that matches up.
Now, 10 years since I began working on this idea, my colleagues and I have started to test it. We have performed experiments with two types of qubits to illustrate that our approach works.
In one experiment, in Turin, Italy, and his group looked at photons and their polarisation, which is the way that the electric field oscillates as a photon moves through space. In another experiment, published in February 2021, Jones used – which is driven by an external magnetic field – to illustrate the same idea. The crux of both experiments is to measure the qubits at multiple times and calculate the quantum state we are probing, be it nuclear spin or polarisation, across both space and time, then test this against our predictions.
What these experiments have demonstrated is that anything that can be calculated using the standard approach to quantum physics can also be calculated – just as easily – using our space-time version. Our description of quantum states is a perfectly valid alternative to that of standard quantum mechanics. But because it shares a description of time with general relativity, it is a step towards a unifying theory.
What we haven’t shown yet is that our approach has advantages over the standard one. To do this, we need to zoom in to the very smallest of scales. Let us go back to our journey towards the singularity at the centre of a black hole, where general relativity breaks down. The breakdown is intimately related to the fact that general relativity equations blow up when we allow space and time to be arbitrarily small around the black hole centre, leading to an infinite quantity called a singularity. But when we apply our new way of thinking about space-time in quantum mechanics, we can incorporate an extra degree of fuzziness that will save us from these singularities.
Quantum time travel
Just like the uncertainty that exists in quantum theory between a particle’s position and momentum, there may also be an uncertainty between space and time. If this is true, it means that at the centre of a black hole, the regions of space-time would be so small that space and time can no longer be discriminated from one another.
We can – in principle – probe that experimentally, too. The test would be similar to how we check the uncertainty relations between the position and momentum of a single particle, but we would now be testing the uncertainty between space and time. If we measure a distance between two events in space more precisely, their temporal separation becomes more uncertain. We don’t know if this is the way nature is, but our approach can certainly handle it in case it turns out to be true. Current experiments don’t seem to have enough resolution to test space and time at these minute scales. However, the technology required to do so is progressing rapidly.
If we turn out to be right, then the centre of a black hole would be one place in which space and time could no longer be discriminated from one another. A singularity occurs at the point where both space and time contract to zero. But a quantum uncertainty in space-time would prevent something like this from happening, since both space and time couldn’t have the precise value of zero at the same time. Getting over this stumbling block would be a breakthrough towards being able to unite general relativity and quantum mechanics.
As if that isn’t mind-boggling enough, there is an unexpected implication of all of this, too: quantum time travel. Closed time-like loops are theoretical loops created when space-time curves so much that it closes in on itself – a route, it might seem, to the past. But until now, although they appear to make sense in relativity, physicists have dismissed time-like loops, because they are prohibited by quantum mechanics.
Think about an entangled pair of particles, connected through some interaction so that a measurement on one immediately affects the other. If one of the two particles goes through a time-like loop, this trip back in time creates two copies of that particle, one younger and one older. Each of the two copies ought to be maximally entangled to the other particle, the one that didn’t go through the time loop, which isn’t allowed in conventional quantum physics. But if we use our method to describe the situation, then the younger and older versions of the particle are simply entangled in time, something that is perfectly possible in our quantum space-time.
All of which means that, with our new theory of everything, not only could we finally finish our imaginary journey into a black hole, we might just find a route back in time as well.
