Werner Heisenberg is known for several groundbreaking discoveries in quantum physics. In 1925, he developed the precursor to quantum mechanics, a new type of mechanics based on matrices (matrix mechanics). Briefly explained, this theory is that physical properties evolve over time, in contrast to, for example, the classical "paths" of electrons in Bohr's well-known shell model. Heisenberg's introduction of matrices was at the time a truly radical departure from classical physics and laid the foundation for modern quantum mechanics. Two years later, in 1927, Heisenberg introduced the famous uncertainty principle, which states that it is impossible to measure both the position and the velocity of a particle with unlimited precision at the same time.
In perspective drawing, you do not draw the road and the houses on either side as they actually look. The classic mistake when drawing a hand is that you base your knowledge of the hand on what your eyes actually see from your own perspective. It is difficult for many to grasp that physics is also about perspective. Einstein’s special theory of relativity showed that distances in the universe and calculations of time depend on the position and speed of the person making the measurements. Thus, space and time were merged into a four-dimensional union known as space-time.
When Einstein developed the theory of relativity in the early 1920s, he worked from a fundamental assumption: The laws of physics should be the same for everyone. The problem was that the laws of electromagnetism require that light always travel at 299,792 kilometers per second, and Einstein realized that this created a problem. If you flew next to a beam of light in a spaceship at almost the speed of light, wouldn’t you expect to see the beam moving much more slowly than usual—just as neighboring cars don’t seem to be going as fast as you do when you’re speeding along the highway? But if you saw light slowly passing you, the laws of physics would be violated from your perspective. The law is the same for everyone.
Einstein was convinced that this could not happen, and was thus forced to propose that the speed of light is constant for everyone, regardless of how fast they are moving. To compensate, space and time themselves had to change from one perspective to the next. The equations of relativity allowed him to translate from one observer's perspective, or frame of reference, to another, and in so doing create an ideal whole world, based on everything seen and observed from all perspectives. But is this collective world real? Or was this like a dictionary that was still incomplete?
What was later discovered confused even Einstein. Quantum theory seemed to show that by measuring things, we play a role in determining their properties. Consider Schrödinger’s cat, the thought experiment in which an unfortunate cat is in a box with a radioactive particle. If the particle decays, it triggers a hammer that shatters a vial that releases a poison that kills the cat. If it doesn’t, the cat lives. You are outside the box. From your perspective, the contents are entangled and in a superposition. The particle both has and has not decayed, so the cat is both dead and alive at the same time. In line with the theory of relativity, shouldn’t it be possible to describe the situation from the cat’s perspective?
In the quantum world, unlike the theory of relativity, there has never been a direct goal of unifying different perspectives. In a sense, it has been accepted that there is no underlying, objective reality, at least not one that can be measured. A century later, many physicists, perhaps most, doubt whether there is even a single objective reality shared by all observers.
Quantum theory deals with matter and energy and is even more successful than the theory of relativity. But it paints a deeply unfamiliar picture of reality, one in which particles do not have definite properties until we measure them, but exist in a superposition of multiple states. It also shows that particles can become entangled, and that their properties are closely linked even over great distances. All of this puts the definition of a frame of reference on shaky ground.
And are the measurements of the observer objective? Imagine measuring time with a clock that is entangled, or distance with a ruler that is in several places at once? Časlav Brukner at the Institute for Quantum Optics and Quantum Information in Vienna, Austria, wanted to understand how one can see things from multiple perspectives in quantum theory. Following Einstein's lead, he started with the assumption that the laws of physics must be the same for everyone, and then developed a way to mathematically switch between quantum reference frames. If we could describe a situation from both sides of the Heisenberg kerf simultaneously, Brukner suspected that some truth about a common quantum world might emerge.
Now new ideas and new technology are emerging. For the first time, we can jump from one quantum perspective to another. This is already helping us solve difficult practical problems with high-speed communication. It also sheds light on whether there is any shared reality at the quantum level. Interestingly, the answer seems to be no – before we start talking to each other!
“What is quantum and what is classical depends on the choice of quantum reference frames,” says Brukner. When you jump into the cat’s point of view, it turns out that – just like in the theory of relativity – things have to be distorted in order to preserve the laws of physics. The quantumness previously attributed to the cat is shuffled across the Heisenberg cut. From this perspective, the cat is in a specific state – it is the observer outside the box who is in a superposition, entangled in the laboratory outside. Entanglement was long thought to be an absolute property of reality. But in this new picture, it is all a matter of perspective.
Then take the famous double-slit experiment, which showed that a quantum particle can move through two slits in a lattice at the same time. “We see that, relative to the electron, the slits themselves are in a superposition,” says Pienaar at the University of Massachusetts. “To me, this is amazing.” While all this may sound like pure theorizing, one thing that gives Brukner’s ideas credibility is that they have already helped solve an intractable problem related to qubits in quantum communication.
Quantum frames of reference, however, have an Achilles’ heel, albeit one that may eventually point us to a deeper understanding of reality. It comes in the form of “Wigner’s friend,” a thought experiment dreamed up in the 1950s by physicist Eugene Wigner. It offers a thought-provoking twist on Schrödinger’s puzzle: Let’s say Wigner has a friend who opens the box and discovers whether the cat is alive or not. But suppose Wigner himself is standing outside the lab door? Within his frame of reference, the cat is still in a superposition of alive and dead, but now it is entangled in the friend, who is in a superposition of having-seen-a-live-cat and having-seen-a-dead-cat. Wigner's description of the cat and the friend's description of it are mutually exclusive, but according to quantum theory they are both right. It is a profound paradox that seems to reveal a split reality.
You can’t jump from one side of the Heisenberg cut to the other, because the two people are using different cuts. The friend has the cut between herself and the box; Wigner has it between himself and the lab. They’re not staring at each other from across the classical quantum divide. They’re not looking at each other at all. “My colleagues and I hoped that Wigner’s friend situation could be reformulated in quantum frames of reference,” Brukner says. But so far, that hasn’t been possible. “I don’t know,” he sighs. “There’s an element missing.”
Hints about what that might be come from work by Flavio Mercati at the University of Burgos in Spain and Giovanni Amelino-Camelia at the University of Naples Federico II in Italy. Their research seems to suggest that by exchanging quantum information, observers can create a shared reality, even if it’s not there to begin with.
The duo was inspired by research conducted in 2016 by Markus Müller and Philipp Höhn, both then at the Perimeter Institute in Waterloo, Canada, who imagined a scenario in which two people, Alice and Bob, send each other quantum particles in a specific state of “spin.” Spin is a quantum property that can be compared to an arrow that can point up or down along any of the three spatial axes. Alice sends Bob a particle and Bob has to figure out the spin; then Bob prepares a new particle with the same spin and sends it back to Alice, who confirms that he got it right. The trick is that Alice and Bob don’t know the relative orientation of their frames of reference: one’s x-axis could be the other’s y-axis.
If Alice sends Bob just one particle, he will never be able to decode the spin. Sometimes in physics, two variables are linked in such a way that if you measure one precisely, the other no longer exists in a specific state. This tricky problem, known as the Heisenberg Uncertainty Principle, concerns the spin of particles along different axes. So if Bob wants to measure the spin along what he thinks is Alice’s x-axis, he has to guess which axis it really is—if he’s wrong, he’ll erase all the information. However, the pair can get around this by exchanging lots of particles. Alice can tell Bob, “I’m sending you 100 particles that are all spinning ‘up’ along the x-axis.” As Bob measures more and more of them, he can start to work out the relative orientation of their frames of reference.
Here’s where it gets interesting. Müller and Höhn realized that by doing all this, Alice and Bob automatically derive the equations that allow you to translate the view from one perspective to another in Einstein’s special theory of relativity. We tend to think of space-time as the existing structure through which observers communicate. But Müller and Höhn turned the story around. Start with observers sending messages, and you can derive space-time.
For Mercati and Amelino-Camelia, who first came across the work a few years ago, that turn was a light-bulb moment. It raised a key question that turns out to have crucial implications for Brukner’s work: Are Alice and Bob learning about a pre-existing space-time, or are space-time emerging as they communicate?
There are two ways the latter could play out. The first has to do with the trade-off in quantum mechanics between information and energy. “To get information about a quantum system, you have to pay energy,” Mercati says. Every time Bob chooses the right axis, he loses some energy; when he chooses the wrong one and erases Alice’s information, he gains some. Because the curvature of space-time depends on the energy present, when Bob measures his relative orientation, he also ends up changing his orientation slightly.
There may be a deeper meaning in which quantum communication creates space-time. This comes into play if space is what is called “noncommutative.” If you want to get to a point on a regular map, it doesn’t matter in which order you enter the coordinates. You can go over five and up two; or up two and over five—either way, you’ll end up in the same place. But if the laws of quantum mechanics apply to space-time itself, this might not be true. Just as knowing a particle’s position prevents you from measuring its momentum, going over five might prevent you from going up two.
Mercati and Amelino-Camelia say that if space-time works this way, Alice and Bob’s attempts to figure out their relative orientation would not only reveal the structure of space-time, they would actively falsify it. The choices they make about which axes to measure would change the very thing their communication was intended to reveal. The pair have also developed a way to test whether this is indeed the case (see “Does Space-Time Commute?”).
All of this work points to a startling conclusion: that when people exchange quantum information, they are collaborating to construct their mutual reality. This means that if we only look at space and time from one perspective, we are not only missing its full beauty, but there may not be a deeper shared reality. For Mercati and Amelino-Camelia, one observer does not make a space-time.
This brings us back to Wigner’s friend paradox that troubled Brukner. In his work, observers can be treated as having perspectives on the same reality only when they are staring at each other from the other side of the Heisenberg cut. Or, put another way, only when it is possible for them to communicate, which is precisely what Wigner and his friend cannot do. Perhaps this tells us that until two people interact, they do not share the same reality - because it is the communication itself that creates it.
Networks of cables carrying quantum information are already being set up around the world as a prototype for a coming quantum internet. These networks transport information in the form of qubits, or quantum bits, which can be encoded in the properties of particles - typically in a quantum property called spin. One person sends a stream of particles to another, who then measures the spin to decode the message.
Except, not so fast. To be a useful means of communication, these particles must travel close to the speed of light. At such speeds, a particle's spin becomes "quantum entangled" with its momentum in such a way that if the receiver were to measure only the spin, information would be lost. "This is serious," says Flaminia Giacomini of the Perimeter Institute in Canada. "The qubit is the basis of quantum information, but for a particle moving at very high speeds, we can no longer identify a qubit." As if that weren't enough of a problem, each qubit doesn't move at a specific speed: thanks to quantum mechanics, it's in what's known as a superposition of speeds.
The rules for quantum reference frames developed by Časlav Brukner (see main story) may be the answer. Giacomini has shown how the rules can be used to jump into the particle’s frame of reference, even when the particle is in a superposition. From that perspective, the rest of reality is whizzing by in a blurry superposition. Armed with knowledge of how the qubit sees the world, you can then determine the mathematical transformation to perform on the particle to recover the information in the original qubit.
In space, the route of travel doesn’t matter as much as the destination. If you’re trying to get to a given location, it doesn’t matter whether you go 5 kilometers south and then 3 kilometers west, or vice versa. That’s because the coordinates “commutate”; they get you to the same place regardless of the order.
At very small scales, which is what quantum theory is all about, this may not be true. In quantum theory, measuring a particle’s position erases information about its momentum. Similarly, the order in which the movements are made could affect the structure of space. If this is the case, it makes no sense to talk about spacetime as a fixed arena.
Physicists Flavio Mercati and Giovanni Amelino-Camelia think they have a way to find out whether spacetime “commutes.” They were inspired by research that imagined two people exchanging quantum particles and measuring their properties to infer their relative orientation (see main story). What would happen, Mercati and Amelino-Camelia asked, if this game were played for real?
As people exchange more and more particles, their uncertainty about their orientation should decrease. But does it ever go to zero? In ordinary spacetime, it will. But if spacetime is noncommutative, there will always be some uncertainty, since their orientation is ever so slightly rewritten with each measurement. The pair will probably have to exchange trillions of particles before we get an answer—but Mercati thinks it’s worth a try...!
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