Can Choices Curve Spacetime?

Our view of space and time has changed dramatically over the past century. We’ve gone from a rigid coordinate grid inspired by Newton, to Einstein’s view of spacetime as a stretchable fabric that flexes under the influence of mass. But it might be time for another revolution. There are hints that observers may be able to act on spacetime, not only by their physical properties, but also by their choices.

As bizarre as this sounds, the idea stems from frameworks that bring quantum mechanics—the physics governing the microscopic realm—into the spacetime picture. These are being given a fresh spin by two independent groups of physicists. Giovanni Amelino-Camelia, of the University of Naples Federico II, in Italy, is leading one approach to examine whether quantum-gravitational effects might one day be detectable, manifesting in the way that different observers, Alice and Bob, disagree about their measurements of the same events. Meanwhile Caslav Brukner, of the Institute for Quantum Optics and Quantum Information in Vienna, Austria, and colleagues are calculating what would happen if Alice and Bob’s laboratories are themselves put into a quantum ’superposition’—in which the labs are in more than one physical state at the same time.

Amelino-Camelia’s project, which was awarded over $50,000 by FQXi, was inspired when he and his Naples colleague, Flavio Mercati, met physicists from a very different community at an FQXi workshop in Rome, in January 2018. On the one side Amelino-Camelia and Mercati have been working on the decades’ long pursuit of theories of quantum gravity. On the other side, Philipp Höhn of the Okinawa Institute of Science and Technology Graduate University, in Japan, and Markus Müller, of the Perimeter Institute in Vienna, Austria, are quantum information theorists investigating phenomena such as quantum communication, which is routinely demonstrated in the lab. "It looked to us that our different research programs were pointing in a common direction," says Amelino-Camelia. "But these sides of theoretical physics never talk to one another."

Ironically, their new project stems from a criticism Amelino-Camelia has of a program that he himself pioneered, and still contributes toward. Physicists have struggled for decades to unite Einstein’s theory of gravity, general relativity, with the physical theory governing the microscopic realm, quantum mechanics. One major issue has been that the arenas in which quantum-gravitational effects are predicted to come into play—in the very early universe or in the center of a black hole—seemed forever inaccessible to observations or experiments. But Amelino-Camelia’s research program initiated interest in examining whether it is feasible to detect the effects of quantum gravity today. For instance, he suggested that the tiny influence of quantum gravity could accumulate over vast distances and be detected in the arrival times of highly energetic photons from distant stars (Nature Astronomy 1, 0139 (2017)). (See "Journeying Through the Quantum Froth.")

For the past 20 years, the program has spawned a great deal of effort and investment. NASA’s Fermi gamma-ray space telescope has been collecting light from cosmic explosions since it launched in 2008 to hunt for possible quantum-gravitational effects. None have yet been found—a null result that is still useful for ruling out certain types of quantum-gravity theories. But Amelino-Camelia remains unsatisfied with the lack of progress, arguing that the approach would be sharpened by a deeper, quantum analysis. "We are still giving crude guidance," he says. He notes that the models used for calculating quantum-gravitational effects neglect to account for the quantum nature of the emission of particles from distant stars. Similarly, they treat the way that these particles are detected by telescopes on Earth as a ’classical’—non-quantum—event. "Our ambition is to understand how that picture arises as a fully quantum process," he explains.

This is where Höhn and Müller, who are experts on quantum information, come in. Quantum information theorists investigate protocols for sending and receiving particles in quantum communication experiments. For instance, physicists often use ’quantum teleportation,’ to transmit information from one quantum particle to another. At the workshop, Amelino-Camelia was struck by research presented by Höhn and Müller in which two observers—they are always called Alice and Bob—who are distant to one another, try to establish a common reference frame to compare their measurements (New J. Phys. 18 063026 (2016)). For example, if I tell you that I see a planet spinning upwards, to my left, and you tell me that you see the planet spinning upwards to your right, we can orient ourselves and establish a framework for understanding the information we share.

But Höhn and Müller noticed a curious thing. They were not interested in investigating gravity, so they had not considered the spacetime that Alice and Bob were living in—be it flat or curved. Yet when they developed their simple picture of observers establishing a shared reference frame, they found the mathematics arising for a flat, classical spacetime, without having made any assumptions of having a spacetime in the first place. The quantum relativists, Amelino Camelia and Mercati, found this fascinating. "It was a lot of fun to talk to Giovanni (Amelino-Camelia) about this, because he was so excited and full of ideas," says Müller.

Momentum Space

To make sense of what was happening, Amelino-Camelia invokes an abstract four-dimensional ’space’ that describes energy on one axis and the components of the momentum (in the x, y, and z directions) on the other three axes, and thus is dubbed "momentum space" by physicists. Any object can be located on this four-dimensional grid based on its energy and momentum.

Just like spacetime, momentum space can be flat or curved. The key point is that in a curved momentum space, Amelino-Camelia and colleagues realized, observers will no longer agree on measurements made in a unified spacetime. The upshot is the way an event appears to an observer will strongly depend on the energy of the probes they use to observe it: on their choices. "We are betting that the first manifestation of quantum gravity will be that spacetime looks different when you combine different ways to observe it—that the picture should seem strange," say Amelino-Camelia. "You will not be observing the same set of stars in the same places."

Putting these two perspectives together, the teams wondered: what if the communications between Alice and Bob take into account this curvature of momentum space? Could this have some detectable consequences, such as ’fuzziness’ in their reference frame relations? The fuzziness would be minute, as it is related to quantum events on a tiny scale, says Höhn. "But the fascinating question that arises is whether it would have any physical consequences," he says.

The teams are now exploring whether fuzzy reference-frame transformations could have measurable effects in the lab, using quantum bits, or ’qubits.’ They are looking for operations that allow different observers to synchronize their description of qubits. "The fuzzy reference frame relations imply that different observers cannot sharply synchronize their reference frames as a fundamental principle," says Höhn.

Labs in Superposition

But there are other attempts to investigate how an observer’s reference frame can smear their perceptions of events in spacetime—by putting the observer’s labs into superposition. Superposition is a feature of quantum mechanics in which the physical aspects of quantum experiments, such as a particle’s position or momentum, are not well defined before they are measured. This is the quantum effect that allows an object to be in two places at the same time, before it is measured, or to exist in two different states simultaneously. Brukner and his colleagues have already outlined how atomic-scale clocks could be put into superposition, while exerting a gravitational influence on each other Nature Communications 11, 2672 (2020)). This work already showed that in such circumstances, where both quantum and gravitational effects are at work, the notion of a ’well-defined’ event can become blurred. (See "Blurring Causal Lines.")

In the current project—awarded over $100,000 by FQXi—Brukner and his team take things a step further, by considering what would happen if Alice and Bob perform quantum experiments in different laboratories that are in superposition. It would be pretty impractical to literally put a whole laboratory into a quantum superposition. (Although experimentalists keep pushing up the mass of molecules that can be put into superposition—Markus Arndt of the University of Vienna in Austria and colleagues have achieved superposition for molecules of 2,000 atoms—physicists are nowhere close to achieving this feat with humans or buildings). "We could not dream of creating a large superposition of labs—but we can still think about this idea and proof-of-principle experiments," says Brukner.

But just imagining the possibility allows the team to pose the question: Are physical laws independent of where and when an experiment is performed in Bob’s laboratory—even though we cannot say definitely where and when it is located in spacetime? The independence of physical laws is one of the cornerstone principles of physics—"one of the most beautiful ideas in theoretical physics," in Brukner’s words. But does it always hold true?

A key part of the investigation is to find the right transformations between the different laboratory reference frames—what you would see if you jumped from one reference frame to another. "It turns out that when we jump into Bob’s reference frame, then Alice’s reference frame becomes smeared from Bob’s perspective, and vice versa," says Brukner. So what is quantum or not depends very much on the reference frame you are looking from.

The work is theoretical, but signs are good that the transformations predict what would be seen in the lab. "The most convincing part of the story, which tells us we are on the right track with our transformation, is that we can obtain or determine certain phenomena that we know or would observe in a real experiment, and we get that," says Brukner.

Others are impressed and keen to see how the project pans out. "I see Caslav (Brukner) as a pioneer and visionary of quantum physics," says Müller. "He has a feeling for the really important fundamental questions, and for how to address them in fruitful ways." The work partly motivated Müller to work on the topic himself and separately inspired physicist Lee Smolin of the Perimeter Institute in Waterloo, Ontario, to draft a paper (arXiv:2007.05957 (2020)). "By studying simple examples where the reference frame is described by a quantum state, they have discovered interesting new potential quantum phenomena which result from the states of the observers being superposed," says Smolin. "This is very interesting and suggests there may be an extension of the formalism of special relativity which incorporates them elegantly."

"Caslav (Brukner) is showing us doors," agrees Amelino-Camelia. "His work is now taking a very radical and exciting direction."