Imagine a physicist observing a quantum system whose behavior is akin to a coin toss: it could come up heads or tails. They perform the quantum coin toss and see heads. Could they be certain that their result was an objective, absolute and indisputable fact about the world? If the coin was simply the kind we see in our everyday experience, then the outcome of the toss would be the same for everyone: heads all around! But as with most things in quantum physics, the result of a quantum coin toss would be a much more complicated “It depends.” There are theoretically plausible scenarios in which another observer might find that the result of our physicist’s coin toss was tails.
At the heart of this bizarreness is what’s called the measurement problem. Standard quantum mechanics accounts for what happens when you measure a quantum system: essentially, the measurement causes the system’s multiple possible states to randomly “collapse” into one definite state. But this accounting doesn’t define what constitutes a measurement—hence, the measurement problem.
Attempts to avoid the measurement problem—for example, by envisaging a reality in which quantum states don’t collapse at all—have led physicists into strange terrain where measurement outcomes can be subjective. “One major aspect of the measurement problem is this idea ... that observed events are not absolute,” says Nicholas Ormrod of the University of Oxford. This, in short, is why our imagined quantum coin toss could conceivably be heads from one perspective and tails from another.
But is such an apparently problematic scenario physically plausible or merely an artifact of our incomplete understanding of the quantum world? Grappling with such questions requires a better understanding of theories in which the measurement problem can arise—which is exactly what Ormrod, along with Vilasini Venkatesh of the Swiss Federal Institute of Technology in Zurich and Jonathan Barrett of Oxford, have now achieved. In a recent preprint, the trio proved a theorem that shows why certain theories—such as quantum mechanics—have a measurement problem in the first place and how one might develop alternative theories to sidestep it, thus preserving the “absoluteness” of any observed event. Such theories would, for instance, banish the possibility of a coin toss coming up heads to one observer and tails to another.
But their work also shows that preserving such absoluteness comes at a cost many physicists would deem prohibitive. “It’s a demonstration that there is no pain-free solution to this problem,” Ormrod says. “If we ever can recover absoluteness, then we’re going to have to give up on some physical principle that we really care about.”
Ormrod, Venkatesh and Barrett’s paper “addresses the question of which classes of theories are incompatible with absoluteness of observed events—and whether absoluteness can be maintained in some theories, together with other desirable properties,” says Eric Cavalcanti of Griffith University in Australia. (Cavalcanti, along with physicist Howard Wiseman and their colleagues, defined the term “absoluteness of observed events” in prior work that laid some of the foundations for Ormrod, Venkatesh and Barrett’s study.)
Holding on to absoluteness of observed events, it turns out, could mean that the quantum world is even weirder than we know it to be.
The Heart of the Problem
Gaining a sense of what exactly Ormrod, Venkatesh and Barrett have achieved requires a crash course in the basic arcana of quantum foundations. Let’s start by considering our hypothetical quantum system that can, when observed, come up either heads or tails.
In textbook quantum theory, before collapse, the system is said to be in a superposition of two states, and this quantum state is described by a mathematical construct called a wave function, which evolves in time and space. This evolution is both deterministic and reversible: given an initial wave function, one can predict what it’ll be at some future time, and one can in principle run the evolution backward to recover the prior state. Measuring the wave function, however, causes it to collapse, mathematically speaking, such that the system in our example shows up as either heads or tails.
This collapse-inducing process is the murky source of the measurement problem: it’s an irreversible, one-time-only affair—and no one even knows what defines the process or boundaries of measurement. What amounts to a “measurement” or, for that matter, an “observer”? Do either of these things have physical constraints, such as minimal or maximal sizes? And must they, too, be subject to various slippery quantum effects, or can they be somehow considered immune from such complications? None of these questions have easy, agreed-upon answers—but theorists have no shortage of proffered solutions.
Given the example system, one model that preserves the absoluteness of the observed event—meaning that it’s either heads or tails for all observers—is the Ghirardi-Rimini-Weber theory (GRW). In GRW, quantum systems can exist in a superposition of states until they reach some as-yet-underdetermined size, at which point the superposition spontaneously and randomly collapses, independent of an observer. Whatever the outcome—heads or tails in our example—it shall hold for all observers.
But GRW, which belongs to a broader class of “spontaneous collapse” theories, seemingly runs afoul of a long-cherished physical principle: the preservation of information. Just as a burned book could, in principle, be read by reassembling its pages from its ashes (ignoring the burning book’s initial emission of thermal radiation, for simplicity’s sake), preservation of information implies that a quantum system’s evolution through time should allow its antecedent states to be known. By postulating a random collapse, GRW theory destroys the possibility of knowing what led up to the collapsed state—which, by most accounts, means information about the system prior to its transformation becomes irrecoverably lost. “[GRW] would be a model that gives up information preservation, thereby preserving absoluteness of events,” Venkatesh says.
A counterexample that allows for nonabsoluteness of observed events is the “many worlds” interpretation of quantum mechanics. In this view, our example wave function will branch into multiple contemporaneous realities, such that in one “world,” the system will come up heads, while in another, it’ll be tails. In this conception, there is no collapse. “So the question of what happens is not absolute; it’s relative to a world,” Ormrod says. Of course, in trying to avoid the collapse-induced measurement problem, the many worlds interpretation introduces the mind-numbing branching of wave functions and runaway proliferation of worlds at each and every fork in the quantum road—an unpalatable scenario for many.
Nevertheless, the many worlds interpretation is an example of what are called perspectival theories, wherein the outcome of a measurement depends on the observer’s perspective.
Crucial Aspects of Reality
To prove their theorem without getting mired in any particular theory or interpretation, quantum mechanical or otherwise, Ormrod, Venkatesh and Barrett focused on perspectival theories that obey three important properties. Again, we need some fortitude to grasp the import of these properties and to appreciate the rather profound outcome of the researchers’ proof.
The first property is called Bell nonlocality (B). It was first identified in 1964 by physicist John Bell in an eponymous theorem and has been shown to be an undisputed empirical fact about our physical reality. Let’s say that Alice and Bob each have access to one of a pair of particles, which are described by a single state. Alice and Bob make individual measurements of their respective particles and do this for a number of similarly prepared pairs of particles. Alice chooses her type of measurement freely and independently of Bob, and vice versa. That Alice and Bob choose their measurement settings of their own free will is an important assumption. Then, when they eventually compare notes, the duo will find that their measurement outcomes are correlated in a manner that implies the states of the two particles are inseparable: knowing the state of one tells you about the state of the other. Theories that can explain such correlations are said to be Bell nonlocal.
The second property is the preservation of information (I). Quantum systems that show deterministic and reversible evolution satisfy this condition. But the requirement is more general. Imagine that you are wearing a green sweater today. In an information-preserving theory, it should still be possible, in principle, 10 years hence to retrieve the color of your sweater even if no one saw you wearing it. But “if the world is not information-preserving, then it might be that in 10 years’ time, there’s simply no way to find out what color jumper I was wearing,” Ormrod says.
The third is a property called local dynamics (L). Consider two events in two regions of spacetime. If there exists a frame of reference in which the two events appear simultaneous, then the regions of space are said to be “spacelike separated.” Local dynamics implies that the transformation of a system in one of these regions cannot causally affect the transformation of a system in the other region any faster than the speed of light, and vice versa, where a transformation is any operation that takes a set of input states and produces a set of output states. Each subsystem undergoes its own transformation, and so does the entire system as a whole. If the dynamics are local, the transformation of the full system can be decomposed into transformations of its individual parts: the dynamics are said to be separable. “The local dynamics [constraint] ensures that you are not somehow faking Bell [nonlocality],” Venkatesh says.
In quantum theory, transformations can be decomposed into their constituent parts. “So quantum theory is dynamically separable,” Ormrod says. In contrast, when two particles share a state that’s Bell nonlocal (that is, when two particles are entangled, per quantum theory), the state is said to be inseparable into the individual states of the two particles. If transformations behaved similarly, in that the global transformation could not be described in terms of the transformations of individual subsystems, then the whole system would be dynamically inseparable.
All the pieces are in place to understand the trio’s result. Ormrod, Venkatesh and Barrett’s work comes down to a sophisticated analysis of how such “BIL” theories (those satisfying all three aforementioned properties) handle a deceptively simple thought experiment. Imagine that Alice and Bob, each in their own lab, make a measurement on one of a pair of particles. Both Alice and Bob make one measurement each, and both do the exact same measurement. For example, they might both measure the spin of their particle in the up-down direction.
Viewing Alice and Bob and their labs from the outside are Charlie and Daniela, respectively. In principle, Charlie and Daniela should be able to measure the spin of the same particles, say, in the left-right direction. In an information-preserving theory, this should be possible.
Let’s take the specific example of what might happen in standard quantum theory. Charlie, for example, treats Alice, her lab and the measurement she makes as one system that is subject to deterministic, reversible evolution. Assuming that he has complete control of the overall system, Charlie can reverse the process such that the particle comes back to its original state (like a burned book being reconstituted from its ashes). Daniela does the same with Bob and his lab. Now Charlie and Daniela each make a different measurement on their respective particles in the left-right direction.
Using this scenario, the team proved that the predictions of any BIL theory for the measurement outcomes of the four observers contradict the absoluteness of observed events. In other words, “all BIL theories have a measurement problem,” Ormrod says.
Choose Your Poison
This leaves physicists at an unpalatable impasse: either accept the nonabsoluteness of observed events or give up one of the assumptions of a BIL theory.
Venkatesh thinks that there’s something compelling about giving up absoluteness of observed events. After all, she says, physics successfully transitioned from a rigid Newtonian framework to a more nuanced and fluid Einsteinian description of reality. “We had to adjust some notions of what we thought was absolute. There was absolute space and time for Newton,” Venkatesh says. But in Albert Einstein’s conception of the universe, space and time are one, and this single spacetime isn’t something absolute but can warp in ways that don’t fit with Newtonian ways of thinking.
On the other hand, a perspectival theory that depends on observers creates its own problems. Most prominently, how can one do science within the confines of a theory where two observers cannot agree on the outcomes of measurements? “It’s not clear that science can work in the way [it’s] supposed to work if we’re not coming up with predictions for observed events that we take to be absolute,” Ormrod says.
So if one were to insist on absoluteness of observed events, then something has to give. It’s not going to be Bell nonlocality or preservation of information: the former is on solid empirical footing, and the latter is considered an important aspect of any theory of reality. The focus shifts to local dynamics—in particular, to dynamical separability.
Dynamical separability is “kind of an assumption of reductionism,” Ormrod says. “You can explain the big stuff in terms of these little pieces.”
Preserving the absoluteness of observed events could imply that such reductionism doesn’t hold: just like a Bell nonlocal state cannot be reduced to some constituent states, it may be that the dynamics of a system are similarly holistic, adding another kind of nonlocality to the universe. Importantly, giving it up doesn’t cause a theory to fall afoul of Einstein’s theories of relativity, much like physicists have argued that Bell nonlocality doesn’t require superluminal or nonlocal causal influences but merely nonseparable states.
“Perhaps the lesson of Bell is that the states of distant particles are inextricably linked, and the lesson of the new ... theorems is that their dynamics are, too,” Ormrod, Venkatesh and Barrett wrote in their paper.
“I like the idea of rejecting dynamical separability a lot, because if it works, then ... we get to have our cake and eat it, [too],” Ormrod says. “We get to continue to believe what we take to be the most fundamental things about the world: the fact that relativity theory is true, and information is preserved, and this kind of thing. But we also get to believe in absoluteness of observed events.”
Jeffrey Bub, a philosopher of physics and a professor emeritus at the University of Maryland, College Park, is willing to swallow some bitter pills if that means living in an objective universe. “I would want to hold on to the absoluteness of observed events,” he says. “It seems, to me, absurd to give this up just because of the measurement problem in quantum mechanics.” To that end, Bub thinks a universe in which dynamics are not separable is not such a bad idea. “I guess I would agree, tentatively, with the authors that [dynamical] nonseparability is the least unpalatable option,” he says.
The problem is that no one yet knows how to construct a theory that rejects dynamical separability—assuming it’s even possible to construct—while holding on to the other properties such as preservation of information and Bell nonlocality.
A More Profound Nonlocality
Griffith University’s Howard Wiseman, who is seen as a founding figure for such theoretical musings, appreciates Ormrod, Venkatesh and Barrett’s effort to prove a theorem that is applicable but not specific to quantum mechanics. “It’s nice that they are pushing in that direction,” he says. “We can say things more generally without referring to quantum mechanics at all.”
He points out that the thought experiment used in the analysis doesn’t require Alice, Bob, Charlie and Daniela to make any choices—they always make the same measurements. As a result, the assumptions used to prove the theorem don’t explicitly include an assumption about freedom of choice because no one is exercising such a choice. Normally, the fewer the assumptions, the stronger the proof, but that might not be the case here, Wiseman says. That’s because the first assumption—that the theory must accommodate Bell nonlocality—requires agents to have free will. Any empirical test of Bell nonlocality involves Alice and Bob choosing of their own free will the types of measurements they make. So if a theory is Bell nonlocal, it implicitly acknowledges the free will of the experimenters. “What I suspect is that they are sneaking in a free choice assumption,” Wiseman says.
This is not to say that the proof is weaker. Rather it would have been stronger if it had not required an assumption of free will. As it happens, free will remains a requirement. Given that, the most profound import of this theorem could be that the universe is nonlocal in an entirely new way. If so, such nonlocality would equal or rival Bell nonlocality, an understanding of which has paved the way for quantum communications and quantum cryptography. It’s anybody’s guess what a new kind of nonlocality—hinted at by dynamical nonseparability—would mean for our understanding of the universe.
In the end, only experiments will point the way toward the correct theory, and quantum physicists can only prepare themselves for any eventuality. “Irrespective of one’s personal view on which [theory] is a better one, all of them have to be explored,” Venkatesh says. “Ultimately, we’ll have to look at the experiments we can perform. It could be one way or the other, and it’s good to be prepared.”