WE HAVE become accustomed to the universe blowing our minds – perhaps too accustomed. Quantum weirdness – things like particles being in two places at once, or appearing to share a telepathic link – has been baffling us for more than a century now. The physicist Richard Feynman once said that nobody really understands the quantum world. Or as others have put it: if you think you understand it, then you definitely don’t. So it is tempting to throw up our hands and say human brains can never grasp it.
But maybe we shouldn’t be so defeatist. Isn’t it just possible that we simply haven’t yet got to the bottom of how quantum mechanics really works? That’s what of the University of Pavia in Italy, and his colleagues Giulio Chiribella and Paolo Perinotti think – and they have been doing something about it. They have come up with a non-weird foundation from which all quantum weirdness can arise. Although very much a work in progress, it has attracted some very positive attention. “Their work and their approach is extraordinary,” says theorist of the Perimeter Institute in Waterloo, Canada. , a physicist at the University of Vienna, Austria, is equally impressed. There’s “something deep about quantum mechanics” here, he says.
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For D’Ariano, it all started more than a decade ago, when students asked him to explain where the laws of quantum physics come from. It must have been tempting to dismiss it as a stupid question. Instead, he found himself at a loss for words. “I was very embarrassed,” he says.
His embarrassment wasn’t personal – it was for a whole field. Most physicists stand atop a firm foundation of physical principles: descriptions of how the physical world works. Take Newton’s law of gravitation, which states that two bodies attract each other according to the size of their masses and the inverse square of the distance between them. That physical principle, encapsulated in a neat equation, tells you everything about classical gravity.
“If they can get this right, it might provide more than just a justification for quantum theory”
In quantum theory, there are just the neat equations, developed not to encapsulate some universal principle, but in an ad hoc way to “explain” weird experimental results. Quantum objects are described by wave functions that might or might not correspond to anything physical, and which exist in an abstract, multidimensional domain called . What is more, they evolve according to abstruse rules laid down in the . Erwin Schrödinger came upon this formulation haphazardly in 1925 by studying the equations of classical optics, which dealt with waves rather than particles. It works well, but it’s not quite clear why. “He didn’t derive the equation from principles,” says D’Ariano. There seems to be precious little physics in quantum physics.
Can we change this? Can the basic laws of quantum theory be derived from physical principles, rather than mathematical conjuring? D’Ariano, Perinotti and Chiribella believe the answer to these questions is a resounding “yes”.
They are confident because the situation, though embarrassing, is hardly unprecedented. Newton’s universal law of gravity allowed physicists to derive from first principles a series of serviceable, purely mathematical laws of planetary motion formulated a century earlier by the astronomer Johannes Kepler. Also, towards the end of the 19th century, the physicist Hendrik Lorentz, trying to accommodate contradictory experimental observations about the speed of light, proposed a set of mathematical conversion rules for observers moving in different ways through the universe. Lorentz’s equations didn’t stem from any fundamental understanding of light, but they worked.
It took Einstein to propose some physical principles – that the speed of light in a vacuum is constant and independent of the motion of the source of light – from which he was able to derive Lorentz’s transformations. These became the principles of special relativity, which describes a universe where the laws of physics are consistent for all observers. Eventually, this led Einstein to the even more overarching theory of general relativity, a theory of gravity that betters Newton’s and works over cosmological distances. “It changed the way we are doing physics,” says D’Ariano. “Principles are important.”
Looking deeper
Can we pull off the same trick in the quantum world? “When I look at quantum theory, I see something that’s akin to the ad hoc nature of Kepler’s laws of planetary motion and of Lorentz transformations,” says Hardy. “What we need is some deeper set of principles.”
In the early 2000s, Hardy made his own attempt at coming up with some. It wasn’t a full solution, he admits, but it inspired D’Ariano, Perinotti and Chiribella to dig deeper. “The idea was to somehow reprogram the genetic code of quantum mechanics, choose some physical properties and say, ‘this is the fundamental thing’, and re-derive the rest from it,” says Chiribella, who is now at Tsinghua University in Beijing, China.
For both Hardy and D’Ariano’s team, the “fundamental thing” has to do with information. Many theorists are coming to the conclusion that physical interactions can all be described as a form of information processing. Atoms carry information in their momentum, for instance: when two atoms collide like balls on a billiard table, their momenta change in a way that is equivalent to the way binary digits change as they go through a computer’s logic gates. Rules governing information manipulation could ultimately determine what does and doesn’t happen in our universe.
“What if all the messy uncertainty of the quantum world was due to lack of information?”
D’Ariano’s quest started back in 2003 with an effort to understand what informational rules might be common to both the everyday world and the quantum realm. Eventually, they came up with five fairly common-sense ideas that worked: things like ensuring the future can’t influence the past (see “The fivefold way“). Then they looked for inspiration to help describe features unique to the quantum world.
Several phenomena distinguish quantum from everyday, classical physics. One is superposition, where particles seem to be in two places at once, or spin clockwise and anticlockwise at the same time. Another is entanglement: two particles are entangled when measuring the properties of one instantly influences the properties of the other, no matter how far apart they are. Then there is the apparently random outcome of any measurement on a quantum system. You can’t say what the result of any one measurement will be before you perform it; you can only calculate the probabilities of different outcomes.
To make sense of these quantum quirks, D’Ariano joined forces with Perinotto and Chiribella. Together, they saw a glimmer of an opening in the field of quantum information theory, and in particular a distinction that people who study this field make between different types of quantum state. For applications such as cryptography, they designate some states as “pure” – meaning that we know everything we can about such states. It is fairly straightforward, for example, to know everything about a single isolated hydrogen atom in its lowest energy state: this is a pure state. Then there are “mixed” states, for which our information is incomplete. One particle of an entangled pair is in a mixed state: you can’t know everything about one member of the pair without taking its counterpart into account.
But here’s the intriguing point: both entangled particles together form a pure state. The two particles embody all the information there is to know about the quantum system.
Could it be that all the messy uncertainty of the quantum world simply stems from lack of information: making a measurement of a mixed state without having access to the larger pure state of which it is part? “The idea is not to get rid of the weirdness, but to explain it as a logical consequence of basic principles,” Chiribella says.
If every mixed state were part of a pure state, it would be possible to describe each physical process with maximum information. Take the existence of such a perspective as a principle – what Chiribella (who came up with the idea) calls the “purification principle” – and then it is always possible for someone with access to the pure state to make measurements consistent with those of less well-positioned observers who are dealing with mixed states (see diagram). It doesn’t make the weirdness go away, but it does make it explicable. It is like time dilation in special relativity, Chiribella points out. It is undeniably strange to us that time flows differently for people moving in different ways through the universe, but it still sort of makes sense. “Thanks to Einstein’s principles we know where it comes from and how to handle it,” Chiribella says.
This in particular impresses Brukner. “I think the purification postulate is a deep statement that ensures that these two descriptions are consistent with each other,” he says. By assuming it is something that is true of nature, D’Ariano and his colleagues were also able to derive much of the mathematics describing quantum oddities: things such as superposition and the Born rule, a mathematical trick used to calculate the probability of any particular outcome in a quantum measurement. They are working now on the Schrödinger equation, with no definitive success as yet – although they are encouraged by early results in which an equation of the right form pops out.
More tentatively, they also think the purification principle might illuminate another perennial mystery: the strange irreversibility of thermodynamics. All the basic equations of physics, whether quantum or classical, are reversible; you can run them from the past to the future or vice versa. The notion of reversibility “has been deeply rooted in the bones of physicists since the beginning of modern physics”, says Chiribella.
Except thermodynamics doesn’t work that way. It is the study of energy transfer, and its effects on the arrangement of something like molecules in a gas. They can, for instance, be neatly ordered within a container, but you are much more likely to find them spread around haphazardly. That’s because there are many more possible haphazard arrangements of the molecules than neat ones, and so the chances of the gas moving to a more ordered state are extremely low.
One-way street
Physicists’ shorthand for this is the second law of thermodynamics, which states that entropy – the measure of a system’s disorder – will always increase over time. For Chiribella, that might be an artefact of perspective. because measurements made in thermodynamics always look at a subsystem in a mixed state, where we’re not in possession of all the information. In other words, the laws of thermodynamics are what they are because we apply them to parts of a larger composite system. “It is a basic fact about quantum theory: a noisy, irreversible evolution can be made reversible by including additional systems in the description,” says Chiribella. So, on paper at least, irreversibility can be reduced to a reversible evolution. Whether this is the case in the real world is another question, but we do know that the fundamental laws of physics governing the microscopic world are reversible.
Not only are such connections still highly speculative, but the purification principle holds a sting in the tail, too, at least for quantum purists: it seems to side with the controversial “many worlds” interpretation of quantum mechanics. One of very many interpretations of the random outcome of quantum measurements, this argues that every possible outcome of a measurement does happen – and each happens in a different world, or universe. Take Schrödinger’s cat, for instance, which notoriously can be simultaneously dead and alive unless someone looks to see what state it is in. In the many worlds scenario, the cat is dead in one world and alive in another. That fits in with the purification principle: these different worlds are mixed states of an underlying reality that can be described by a pure state.
Hardy is reluctant to embrace these implications, though. “I’d regard myself as an anti-advocate of the many worlds interpretation,” he says. Even D’Ariano is wary of many worlds, although he agrees their work does seem to support it. It’s still just a piece of circumstantial evidence for, rather than a proof of, many worlds, he says.
In general, caution is still necessary. “I don’t think that any of the sets of axioms that anyone has, including my own, are the final word,” says Hardy. D’Ariano, Chiribella and Perinotti are trying to move forward by developing a way to track the evolution of a quantum system. For that they need to work out where specific properties such as a particle’s mass fit into their framework. If they can get that right, it might provide more than just a justification for quantum theory: it might be another route to combining general relativity with quantum mechanics. That could lead us to a description of quantum gravity, a “theory of everything” researchers have long been keen to create. Whatever the eventual outcome, at least we now have proof that, when it comes to quantum theory, there is no such thing as a stupid question.
The fivefold way
What are the basic rules about how the world works? Giacomo Mauro D’Ariano of the University of Pavia in Italy and his colleagues Giulio Chiribella and Paolo Perinotti have come up with five fundamental principles that must apply to any physical system to make a sensible measurement of it – as well as a sixth that they claim explains the weirdness of quantum measurements (see main story).
Causality
Stuff in the future cannot affect a measurement you’re making right now.
Distinguishability
If a state is not too noisy, then there exists another state that can be distinguished from it.
Composition
If you know everything it is possible to know about all the stages of a process, then you know everything you can about the whole process.
Compression
There are ways to efficiently transmit all the information relevant to a measurement of a physical system without having to transmit the system itself.
Tomography
When you have a system with several parts, the statistics of measurements carried out on the parts is enough to identify the state of the whole system.
This article appeared in print under the headline “Path to enlightenment”
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