Quantum is general, world is not

Is quantum theory weird enough for the real world?

Our most successful theory of nature is bewilderingly remote from reality. But fixing that may require a weirder theory still

PHYSICS, its practitioners will proudly tell you, is the most fundamental of sciences. Its theories and laws distil the workings of the real world - of particles and planets, heat and light - into stark, sweeping statements of universal validity. Think Newton's law of gravity, which describes with equal assurance how an apple falls and Earth orbits the sun, or the laws of thermodynamics that govern how energy flows. These physical laws are generally couched in the language of mathematics, to be sure. But this is merely a convenient shorthand. The mathematical quantities are ciphers, proxies for the tangible objects of the real, physical world and their measurable properties.

That was all true until quantum theory arrived on the scene. Quantum theory is odd, not just because its weird predictions are a source of consternation for physicists and philosophers, but because its mathematical structures bear no obvious connection to the real world, as far as we can see. "We do not have a source for the mathematical formalism of quantum mechanics," says Caslav Brukner of the University of Vienna in Austria. "We do not have a nice physically plausible set of principles from which to derive it." Quantum physics might be quantum - but as far as we can tell it isn't physics.

We don't have a physically plausible set of principles from which to derive quantum theory

Now Brukner and a small band of physicists want to change that. Their efforts may lead to a better understanding of quantum reality, or expose weaknesses in the theory that will teach us a new and potentially weirder language with which to describe the world. Either way, it is an ambitious quest.

If you want to devise a physical theory, there is a traditional recipe to follow. First, you make observations about how the world works. Next you sieve the data to pick out any patterns. If anything catches your eye, you dress it up in mathematical language. The proof of the theory is in its predictions. If it can tell us further details of how the world works, you have a winning formula.

Newton's theory of gravity is a classic example. It is embodied in one simple equation, which says that two bodies will experience a mutual attraction that increases with their masses and decreases as the square of the distance between them. It was the centrepiece of his monumental work Principia, published in 1687. Its origins, though, reach back almost a century earlier, to the first truly precise observations of the motions of celestial bodies, made by the Danish astronomer Tycho Brahe.

After Brahe's death, his one-time assistant Johannes Kepler spent years poring over the data. Eventually he was able to show that the motions could be described by three "laws" governing the nature and geometry of planetary orbits. It was Newton's mathematical genius that extracted from these the single equation from which almost all facets of planetary motion can be derived.

Here, as in the other laws of classical mechanics derived in the Principia, mathematics and physics work in perfect tandem. Physical quantities such as force, mass or acceleration are expressed as numbers that can be measured, and the correspondence between the real and the abstract is obvious, seamless and intuitive.

Not so with quantum theory. Although it was initially inspired by an idea rooted in the real world - that energy came in small packets called quanta - by the time luminaries such as Erwin Schrödinger and Werner Heisenberg had finished its mathematical formulation, the theory had acquired a life of its own (see chart).

Quantum links

Gone was any certain correspondence between mathematical variables and physical properties. In their place were abstruse objects such as wave functions, state vectors and matrices, all acting in an unreal mathematical environment called Hilbert space - a higher-dimensional, complex version of normal three-dimensional space.

Bizarrely, though, these abstractions work. Follow a set of mathematical rules laid down by the founders of quantum theory and you can make physical predictions that are confirmed time and time again by experiment. Particles that pop up out of nothingness only to disappear again, objects whose physical states can become "entangled" and can influence each other instantaneously over vast distances, cats that remain suspended between life and death as long as we don't look at them: all of these flow from the mathematical formulation of quantum theory, and all seem to be true reflections of how the world works.

Does it matter that we don't know why? Surrounded by lasers, microchips and other trappings of quantum technology, we might be tempted to say if the theory ain't broke, don't fix it.

That is true up to a point, says Martin Plenio of the University of Ulm in Germany. "Quantum mechanics is, in our range of experience, a correct theory. It is sort of fine and we don't know what is better." But there are niggles that make him and others itch for something new. One is the great unfinished business of unifying quantum theory with general relativity, Einstein's resolutely classical theory of gravity. "Quantum mechanics and general relativity don't like each other," says Plenio.

Many physicists see that as the fault of gravity, and have expended vast energies on untested constructions such as string theory that try to dress up gravity in a quantum costume. An alternative view is that, for all its successes, quantum theory might actually be the problem. As long as we do not know what the physical basis of quantum theory is, that possibility remains both real and hard to test.

So how do we set about finding what makes quantum theory tick? Most of the recent work has homed in on one central yet unexplained feature of quantum physics- the degree of "correlation" between the states of unconnected bodies that the theory does, or does not, allow.

In our day-to-day world, we are accustomed to the idea that two events are unlikely to be correlated unless there is a clear connection of cause and effect. Pulling a red sock onto my right foot in no way ensures that my left foot will also be clad in red - unless I purposely reach into the drawer for another red sock. In 1964, John Bell of the CERN particle physics laboratory near Geneva, Switzerland, described the degree of correlation that classical theories allow. Bell's result relied on two concepts: realism and locality.

Realism amounts to saying that the properties of an object exist prior to, and independent of, measurement. In the classical world, that second sock in my drawer is red regardless of whether or not I "measure" its state by looking at it. Locality is the assumption that these properties are independent of any remote influence.

In the quantum world, these are dangerous assumptions. "It turns out that either one or both of Bell's principles must be wrong," says Brukner. If quantum effects were visible in our everyday world, I might well find that my pulling on a red sock leads to the colour of the sock left in my drawer automatically changing to red.

The mathematical framework developed by Bell and others allows us to quantify how correlated quantum theory allows seemingly unrelated objects to be. Considerably more than in classical physics, it seems - yet not half as correlated as they could be. In 1994, Sandu Popescu, now at the University of Bristol, UK, and Daniel Rohrlich, now at Ben Gurion University of the Negev in Beersheba, Israel, considered a hypothetical theory that obeyed just one rule - that cause and effect cannot propagate faster than the speed of light. Intriguingly, they found that any such theory would permit even greater correlation than even quantum theory allows (Foundations of Physics, vol 24, p 379).

Hypothetical theories that obey only the cosmic speed limit turn out to be weirder than quantum mechanics

A world with this degree of interconnection would be weird indeed. I might find that by selecting a red sock from my drawer in the morning, I had predetermined the colour not just of my other sock, but that of my shirt, underpants and of the bus I ride to work. As Gilles Brassard of the University of Montreal, Canada, and his colleagues showed in 2006, in such a maximally correlated world certain problems in communication and computation reduce to implausible trivialities (Physical Review Letters, vol 96, p 250401).

What lies beneath?

That might not be a good thing. David Gross of the Leibniz University of Hannover, Germany, and colleagues have demonstrated that everything in this world would be so correlated that nothing could evolve, which raises the paradoxical question of how the correlations themselves could have developed (Physical Review Letters, vol 104, p 080402).

How is this relevant? If we could only understand why quantum theory allows precisely the degree of correlation it does, we would have a much better grasp of the underlying physics. "We know that quantum correlations can be stronger than classical," says Plenio. "But then there is the question, why aren't quantum correlations even stronger? Is there any physical principle that says quantum correlations must have the upper bound they do?"

Popescu and Rohrlich had shown that the principle of "relativistic causality" alone was not the answer: the cosmic speed limit set in Einstein's relativity can produce theories that allow greater correlation than quantum mechanics. That prompted Marek Zukowski of the University of Gdansk, Poland, and colleagues to suggest last year that a tighter variant of the principle might do the trick.

They call their idea "causality of information access". It states that if you send me a certain number of bits of information, the maximum amount of information I can access is that number of bits - a truism in both the classical and the quantum worlds. "Say I want to send you a part of my nine-digit home phone number in an encoded form," says Zukowski. "If I send you information about the first three digits, you can only decode the first three digits."

In a world where information causality does not apply, the correlations between the digits would be so strong that if you knew the first three bits, you could deduce any three digits of the original number (Nature, vol 461, p 1101).

It is an intriguing idea, and it narrows down considerably the maximum level of correlations that a theory can sustain, but not all the way down to the quantum limit. To define quantum theory uniquely would seem to require some other principle, too.

In 2001, Lucien Hardy, then at the University of Oxford, took a subtly different, more laborious tack. Rather than trying to pick out a single principle that reduces correlations between remote particles to the levels of quantum mechanics, he aimed to develop from scratch a full set of physically plausible axioms that defined quantum theory alone.

What he came up with was a series of five rules, some physical and some more mathematical in nature, which together defined quantum theory.

Unfortunately, though, Hardy's axioms are also compatible with systems of mathematical constructs other than quantum theory. "That suggests one of two things," says Brukner. "Either we are missing something very significant to define quantum theory, or these other theories are all around us too."

Either we are missing something very significant or other theories are around us too

Together with his colleague Borivoje Daki, Brukner has explored the first of these options further. They formulated their own three rules that describe how, according to experiments, quantum theory works in the case of the simplest possible quantum system - a quantum bit or "qubit" that is in a mixture, or superposition, of two possible states. If any of the rules applied to quantum theory alone, it would rule out other theories that happen to be consistent with Hardy's axioms.

The defining feature

The first rule is that this qubit can slide smoothly and continuously between the two states in its superposition. This is sufficient to distinguish quantum theory from classical physics, where such effortless reversible transitions are not possible, but does not rule out a weirder theory.

The second rule is that whatever superposition state the qubit is in, you can only ever extract one bit of information from it- you can only measure it in one state at once.

The third rule applies only to composite systems of two or more qubits. Knowing the probabilities that the individual qubits are in a particular state plus the probabilities of correlations between them tells you the state of the whole system. This encapsulates the property of entanglement between remote quantum states that experiments show holds in the real world.

And it turns out that this last feature- entanglement- might hold the key. Only a theory precisely as correlated as quantum theory can obey all the axioms and produce the kind of entanglement observed in nature. Less correlated theories don't create entanglement at all, while weirder theories produce a situation where, for example, you might measure the state of all the qubits in a system, know the correlations between them, and still not be able to say what state the whole system is in. "Entanglement is the unique feature, and it comes out of the three axioms," says Brukner.

If true, that is at best half an answer. Why is entanglement the defining feature? Brukner hazards a guess. "In many materials around us, the ground states are entangled with each other. Perhaps matter would not be stable without entanglement," he says.

Others are less convinced, and see the physics behind quantum theory as far from solved. Brukner's scheme takes the traditional route in which observations determine axioms determine theory, but that assumes our observations represent a complete and true picture of how the world works.

There is another possibility: observation might actually be leading us astray. Miguel Navascues of Imperial College London is trying to find out what maximum level of correlation a reasonable physical theory can sustain if a different constraint is imposed - the requirement that quantum physics reduces to classical physics at macroscopic scales, say. He, too, is finding a maximum well above the quantum bound. That leads him to speculate that lurking somewhere, unprobed by experiment, is evidence that a theory weirder than quantum mechanics is the "right" answer- a theory that might even be capable of incorporating gravity into its framework. "That is what I think," he says. "But we are a long way away from proving that."

As long as niggling doubts about quantum theory's status remain, such an outcome is not unthinkable. A century ago, a few loose ends in classical physics eventually caused the whole tapestry to unravel. Betting the same thing might happen to quantum physics - now is that so weird?

Richard Webb is a features editor for New Scientist

Our most successful theory of nature is bewilderingly remote from reality. But fixing that may require a weirder theory still

PHYSICS, its practitioners will proudly tell you, is the most fundamental of sciences. Its theories and laws distil the workings of the real world - of particles and planets, heat and light - into stark, sweeping statements of universal validity. Think Newton's law of gravity, which describes with equal assurance how an apple falls and Earth orbits the sun, or the laws of thermodynamics that govern how energy flows. These physical laws are generally couched in the language of mathematics, to be sure. But this is merely a convenient shorthand. The mathematical quantities are ciphers, proxies for the tangible objects of the real, physical world and their measurable properties.

That was all true until quantum theory arrived on the scene. Quantum theory is odd, not just because its weird predictions are a source of consternation for physicists and philosophers, but because its mathematical structures bear no obvious connection to the real world, as far as we can see. "We do not have a source for the mathematical formalism of quantum mechanics," says Caslav Brukner of the University of Vienna in Austria. "We do not have a nice physically plausible set of principles from which to derive it." Quantum physics might be quantum - but as far as we can tell it isn't physics.

We don't have a physically plausible set of principles from which to derive quantum theory

Now Brukner and a small band of physicists want to change that. Their efforts may lead to a better understanding of quantum reality, or expose weaknesses in the theory that will teach us a new and potentially weirder language with which to describe the world. Either way, it is an ambitious quest.

If you want to devise a physical theory, there is a traditional recipe to follow. First, you make observations about how the world works. Next you sieve the data to pick out any patterns. If anything catches your eye, you dress it up in mathematical language. The proof of the theory is in its predictions. If it can tell us further details of how the world works, you have a winning formula.

Newton's theory of gravity is a classic example. It is embodied in one simple equation, which says that two bodies will experience a mutual attraction that increases with their masses and decreases as the square of the distance between them. It was the centrepiece of his monumental work Principia, published in 1687. Its origins, though, reach back almost a century earlier, to the first truly precise observations of the motions of celestial bodies, made by the Danish astronomer Tycho Brahe.

After Brahe's death, his one-time assistant Johannes Kepler spent years poring over the data. Eventually he was able to show that the motions could be described by three "laws" governing the nature and geometry of planetary orbits. It was Newton's mathematical genius that extracted from these the single equation from which almost all facets of planetary motion can be derived.

Here, as in the other laws of classical mechanics derived in the Principia, mathematics and physics work in perfect tandem. Physical quantities such as force, mass or acceleration are expressed as numbers that can be measured, and the correspondence between the real and the abstract is obvious, seamless and intuitive.

Not so with quantum theory. Although it was initially inspired by an idea rooted in the real world - that energy came in small packets called quanta - by the time luminaries such as Erwin Schrödinger and Werner Heisenberg had finished its mathematical formulation, the theory had acquired a life of its own (see chart).

Quantum links

Gone was any certain correspondence between mathematical variables and physical properties. In their place were abstruse objects such as wave functions, state vectors and matrices, all acting in an unreal mathematical environment called Hilbert space - a higher-dimensional, complex version of normal three-dimensional space.

Bizarrely, though, these abstractions work. Follow a set of mathematical rules laid down by the founders of quantum theory and you can make physical predictions that are confirmed time and time again by experiment. Particles that pop up out of nothingness only to disappear again, objects whose physical states can become "entangled" and can influence each other instantaneously over vast distances, cats that remain suspended between life and death as long as we don't look at them: all of these flow from the mathematical formulation of quantum theory, and all seem to be true reflections of how the world works.

Does it matter that we don't know why? Surrounded by lasers, microchips and other trappings of quantum technology, we might be tempted to say if the theory ain't broke, don't fix it.

That is true up to a point, says Martin Plenio of the University of Ulm in Germany. "Quantum mechanics is, in our range of experience, a correct theory. It is sort of fine and we don't know what is better." But there are niggles that make him and others itch for something new. One is the great unfinished business of unifying quantum theory with general relativity, Einstein's resolutely classical theory of gravity. "Quantum mechanics and general relativity don't like each other," says Plenio.

Many physicists see that as the fault of gravity, and have expended vast energies on untested constructions such as string theory that try to dress up gravity in a quantum costume. An alternative view is that, for all its successes, quantum theory might actually be the problem. As long as we do not know what the physical basis of quantum theory is, that possibility remains both real and hard to test.

So how do we set about finding what makes quantum theory tick? Most of the recent work has homed in on one central yet unexplained feature of quantum physics- the degree of "correlation" between the states of unconnected bodies that the theory does, or does not, allow.

In our day-to-day world, we are accustomed to the idea that two events are unlikely to be correlated unless there is a clear connection of cause and effect. Pulling a red sock onto my right foot in no way ensures that my left foot will also be clad in red - unless I purposely reach into the drawer for another red sock. In 1964, John Bell of the CERN particle physics laboratory near Geneva, Switzerland, described the degree of correlation that classical theories allow. Bell's result relied on two concepts: realism and locality.

Realism amounts to saying that the properties of an object exist prior to, and independent of, measurement. In the classical world, that second sock in my drawer is red regardless of whether or not I "measure" its state by looking at it. Locality is the assumption that these properties are independent of any remote influence.

In the quantum world, these are dangerous assumptions. "It turns out that either one or both of Bell's principles must be wrong," says Brukner. If quantum effects were visible in our everyday world, I might well find that my pulling on a red sock leads to the colour of the sock left in my drawer automatically changing to red.

The mathematical framework developed by Bell and others allows us to quantify how correlated quantum theory allows seemingly unrelated objects to be. Considerably more than in classical physics, it seems - yet not half as correlated as they could be. In 1994, Sandu Popescu, now at the University of Bristol, UK, and Daniel Rohrlich, now at Ben Gurion University of the Negev in Beersheba, Israel, considered a hypothetical theory that obeyed just one rule - that cause and effect cannot propagate faster than the speed of light. Intriguingly, they found that any such theory would permit even greater correlation than even quantum theory allows (Foundations of Physics, vol 24, p 379).

Hypothetical theories that obey only the cosmic speed limit turn out to be weirder than quantum mechanics

A world with this degree of interconnection would be weird indeed. I might find that by selecting a red sock from my drawer in the morning, I had predetermined the colour not just of my other sock, but that of my shirt, underpants and of the bus I ride to work. As Gilles Brassard of the University of Montreal, Canada, and his colleagues showed in 2006, in such a maximally correlated world certain problems in communication and computation reduce to implausible trivialities (Physical Review Letters, vol 96, p 250401).

What lies beneath?

That might not be a good thing. David Gross of the Leibniz University of Hannover, Germany, and colleagues have demonstrated that everything in this world would be so correlated that nothing could evolve, which raises the paradoxical question of how the correlations themselves could have developed (Physical Review Letters, vol 104, p 080402).

How is this relevant? If we could only understand why quantum theory allows precisely the degree of correlation it does, we would have a much better grasp of the underlying physics. "We know that quantum correlations can be stronger than classical," says Plenio. "But then there is the question, why aren't quantum correlations even stronger? Is there any physical principle that says quantum correlations must have the upper bound they do?"

Popescu and Rohrlich had shown that the principle of "relativistic causality" alone was not the answer: the cosmic speed limit set in Einstein's relativity can produce theories that allow greater correlation than quantum mechanics. That prompted Marek Zukowski of the University of Gdansk, Poland, and colleagues to suggest last year that a tighter variant of the principle might do the trick.

They call their idea "causality of information access". It states that if you send me a certain number of bits of information, the maximum amount of information I can access is that number of bits - a truism in both the classical and the quantum worlds. "Say I want to send you a part of my nine-digit home phone number in an encoded form," says Zukowski. "If I send you information about the first three digits, you can only decode the first three digits."

In a world where information causality does not apply, the correlations between the digits would be so strong that if you knew the first three bits, you could deduce any three digits of the original number (Nature, vol 461, p 1101).

It is an intriguing idea, and it narrows down considerably the maximum level of correlations that a theory can sustain, but not all the way down to the quantum limit. To define quantum theory uniquely would seem to require some other principle, too.

In 2001, Lucien Hardy, then at the University of Oxford, took a subtly different, more laborious tack. Rather than trying to pick out a single principle that reduces correlations between remote particles to the levels of quantum mechanics, he aimed to develop from scratch a full set of physically plausible axioms that defined quantum theory alone.

What he came up with was a series of five rules, some physical and some more mathematical in nature, which together defined quantum theory.

Unfortunately, though, Hardy's axioms are also compatible with systems of mathematical constructs other than quantum theory. "That suggests one of two things," says Brukner. "Either we are missing something very significant to define quantum theory, or these other theories are all around us too."

Either we are missing something very significant or other theories are around us too

Together with his colleague Borivoje Daki, Brukner has explored the first of these options further. They formulated their own three rules that describe how, according to experiments, quantum theory works in the case of the simplest possible quantum system - a quantum bit or "qubit" that is in a mixture, or superposition, of two possible states. If any of the rules applied to quantum theory alone, it would rule out other theories that happen to be consistent with Hardy's axioms.

The defining feature

The first rule is that this qubit can slide smoothly and continuously between the two states in its superposition. This is sufficient to distinguish quantum theory from classical physics, where such effortless reversible transitions are not possible, but does not rule out a weirder theory.

The second rule is that whatever superposition state the qubit is in, you can only ever extract one bit of information from it- you can only measure it in one state at once.

The third rule applies only to composite systems of two or more qubits. Knowing the probabilities that the individual qubits are in a particular state plus the probabilities of correlations between them tells you the state of the whole system. This encapsulates the property of entanglement between remote quantum states that experiments show holds in the real world.

And it turns out that this last feature- entanglement- might hold the key. Only a theory precisely as correlated as quantum theory can obey all the axioms and produce the kind of entanglement observed in nature. Less correlated theories don't create entanglement at all, while weirder theories produce a situation where, for example, you might measure the state of all the qubits in a system, know the correlations between them, and still not be able to say what state the whole system is in. "Entanglement is the unique feature, and it comes out of the three axioms," says Brukner.

If true, that is at best half an answer. Why is entanglement the defining feature? Brukner hazards a guess. "In many materials around us, the ground states are entangled with each other. Perhaps matter would not be stable without entanglement," he says.

Others are less convinced, and see the physics behind quantum theory as far from solved. Brukner's scheme takes the traditional route in which observations determine axioms determine theory, but that assumes our observations represent a complete and true picture of how the world works.

There is another possibility: observation might actually be leading us astray. Miguel Navascues of Imperial College London is trying to find out what maximum level of correlation a reasonable physical theory can sustain if a different constraint is imposed - the requirement that quantum physics reduces to classical physics at macroscopic scales, say. He, too, is finding a maximum well above the quantum bound. That leads him to speculate that lurking somewhere, unprobed by experiment, is evidence that a theory weirder than quantum mechanics is the "right" answer- a theory that might even be capable of incorporating gravity into its framework. "That is what I think," he says. "But we are a long way away from proving that."

As long as niggling doubts about quantum theory's status remain, such an outcome is not unthinkable. A century ago, a few loose ends in classical physics eventually caused the whole tapestry to unravel. Betting the same thing might happen to quantum physics - now is that so weird?

Richard Webb is a features editor for New Scientist