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WE HAVE become accustomed to the universe blowing our minds 鈥� perhaps too accustomed. Quantum weirdness 鈥� things like particles being in two places at once, or appearing to share a telepathic link 鈥� 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鈥檛. So it is tempting to throw up our hands and say human brains can never grasp it.

But maybe we shouldn鈥檛 be so defeatist. Isn鈥檛 it just possible that we simply haven鈥檛 yet got to the bottom of how quantum mechanics really works? That鈥檚 what of the University of Pavia in Italy, and his colleagues Giulio Chiribella and Paolo Perinotti think 鈥� 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. 鈥淭heir work and their approach is extraordinary,鈥� says theorist of the Perimeter Institute in Waterloo, Canada. , a physicist at the University of Vienna, Austria, is equally impressed. There鈥檚 鈥渟omething deep about quantum mechanics鈥� here, he says.

For D鈥橝riano, 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. 鈥淚 was very embarrassed,鈥� he says.

His embarrassment wasn鈥檛 personal 鈥� 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鈥檚 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.

鈥淚f they can get this right, it might provide more than just a justification for quantum theory鈥�

In quantum theory, there are just the neat equations, developed not to encapsulate some universal principle, but in an ad hoc way to 鈥渆xplain鈥� 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 Schr枚dinger 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鈥檚 not quite clear why. 鈥淗e didn鈥檛 derive the equation from principles,鈥� says D鈥橝riano. 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鈥橝riano, Perinotti and Chiribella believe the answer to these questions is a resounding 鈥測es鈥�.

They are confident because the situation, though embarrassing, is hardly unprecedented. Newton鈥檚 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鈥檚 equations didn鈥檛 stem from any fundamental understanding of light, but they worked.

It took Einstein to propose some physical principles 鈥� that the speed of light in a vacuum is constant and independent of the motion of the source of light 鈥� from which he was able to derive Lorentz鈥檚 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鈥檚 and works over cosmological distances. 鈥淚t changed the way we are doing physics,鈥� says D鈥橝riano. 鈥淧rinciples are important.鈥�

Looking deeper

Can we pull off the same trick in the quantum world? 鈥淲hen I look at quantum theory, I see something that鈥檚 akin to the ad hoc nature of Kepler鈥檚 laws of planetary motion and of Lorentz transformations,鈥� says Hardy. 鈥淲hat we need is some deeper set of principles.鈥�

In the early 2000s, Hardy made his own attempt at coming up with some. It wasn鈥檛 a full solution, he admits, but it inspired D鈥橝riano, Perinotti and Chiribella to dig deeper. 鈥淭he idea was to somehow reprogram the genetic code of quantum mechanics, choose some physical properties and say, 鈥榯his is the fundamental thing鈥�, and re-derive the rest from it,鈥� says Chiribella, who is now at Tsinghua University in Beijing, China.

For both Hardy and D鈥橝riano鈥檚 team, the 鈥渇undamental thing鈥� 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鈥檚 logic gates. Rules governing information manipulation could ultimately determine what does and doesn鈥檛 happen in our universe.

鈥淲hat if all the messy uncertainty of the quantum world was due to lack of information?鈥�

D鈥橝riano鈥檚 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鈥檛 influence the past (see 鈥�The fivefold way鈥�). 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鈥檛 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鈥橝riano 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 鈥減ure鈥� 鈥� 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 鈥渕ixed鈥� states, for which our information is incomplete. One particle of an entangled pair is in a mixed state: you can鈥檛 know everything about one member of the pair without taking its counterpart into account.

But here鈥檚 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? 鈥淭he idea is not to get rid of the weirdness, but to explain it as a logical consequence of basic principles,鈥� 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 鈥� what Chiribella (who came up with the idea) calls the 鈥減urification principle鈥� 鈥� 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鈥檛 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. 鈥淭hanks to Einstein鈥檚 principles we know where it comes from and how to handle it,鈥� Chiribella says.

This in particular impresses Brukner. 鈥淚 think the purification postulate is a deep statement that ensures that these two descriptions are consistent with each other,鈥� he says. By assuming it is something that is true of nature, D鈥橝riano 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 Schr枚dinger equation, with no definitive success as yet 鈥� 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 鈥渉as been deeply rooted in the bones of physicists since the beginning of modern physics鈥�, says Chiribella.

Except thermodynamics doesn鈥檛 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鈥檚 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鈥� shorthand for this is the second law of thermodynamics, which states that entropy 鈥� the measure of a system鈥檚 disorder 鈥� 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鈥檙e 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. 鈥淚t is a basic fact about quantum theory: a noisy, irreversible evolution can be made reversible by including additional systems in the description,鈥� 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 鈥渕any worlds鈥� 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 鈥� and each happens in a different world, or universe. Take Schr枚dinger鈥檚 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. 鈥淚鈥檇 regard myself as an anti-advocate of the many worlds interpretation,鈥� he says. Even D鈥橝riano is wary of many worlds, although he agrees their work does seem to support it. It鈥檚 still just a piece of circumstantial evidence for, rather than a proof of, many worlds, he says.

In general, caution is still necessary. 鈥淚 don鈥檛 think that any of the sets of axioms that anyone has, including my own, are the final word,鈥� says Hardy. D鈥橝riano, 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鈥檚 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 鈥渢heory of everything鈥� 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.

This article appeared in print under the headline 鈥淧ath to enlightenment鈥�

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