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Wed, Aug 18, 2010
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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


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gamma     Wed, Aug 25, 2010  Permanent link
Infinite doppelgängers may explain quantum probabilities

* 25 August 2010 by Rachel Courtland
* Magazine issue 2775. Subscribe and save

AN IDENTICAL copy of you is also reading this story. This twin is the same in every way, living on an Earth and in a universe that looks exactly like our own. And there may be an infinite number of them. Such doppelgängers could be a natural consequence of our present conception of the universe. Now, some physicists say they could pose a serious problem for quantum mechanics. But a possible fix may also be in sight, and it could help tie abstract quantum concepts to concrete physical causes.

In the uncertain, fuzzy world of quantum mechanics, particles do not have fixed properties until they are observed. Instead, objects that obey quantum rules exist in a "superposition" of all their possible states simultaneously. Schrödinger's famous cat, for example, is both alive and dead until we take a peek inside the booby-trapped box in which it has been placed.

Because the probability that the cat will be found alive is based on a quantum event - the decay of a radioactive substance within the box - it can be calculated using a principle called the Born rule. The rule is used to transform the vague "wave function" of a quantum state, which is essentially a mixture of all possible outcomes, into concrete probabilities of particular observations (in this case, the cat being alive or dead). But this staple of quantum mechanics fails when it is applied to the universe at large, says Don Page at the University of Alberta in Edmonton, Canada.

At issue is the possibility that there could be a multiplicity of copies of any particular experiment floating about the universe, just as there could be a multiplicity of yous. There could even be an infinite number of them if, as is thought, the early universe underwent a period of exponential growth, called inflation. Although this period ended very soon after the big bang in our observable region of space, inflation may have continued elsewhere, giving rise to a "multiverse", an infinite space containing infinite copies of our Earth. "In an infinite universe, every possible thing would happen, and it would happen an infinite number of times," says cosmologist Alex Vilenkin of Tufts University in Medford, Massachusetts.
Missing ingredient

Crucially, says Page, all of these copies pose a problem for the Born rule: it's unclear how to calculate the probability of different outcomes for a given experiment without first adding some extra ingredient that accounts for the multitude of copies (arxiv.org/abs/1003.2419). "You can't just plug in the Born rule and get answers that make sense," he says (see "Identity crisis").

Andreas Albrecht of the University of California, Davis, has dubbed the problem the "Born rule crisis". The shortcoming means we could not, in theory, calculate the probability of the outcome of any new measurement of the universe, such as the mass of the neutrino. "It's a deep failure of something, either of quantum theory or the multiverse," Albrecht says. "If you're a cosmologist, you should be worried," he adds.
It's a deep failure of something, either of quantum theory or the multiverse

Others, like physicist Mark Srednicki at the University of California, Santa Barbara, are not convinced there is a crisis. He says adjustments for missing information are fairly routine in quantum physics and should not require an overhaul of the theory.

A deeper problem, he says, is that we still don't understand what quantum probabilities really mean. "Quantum mechanics is now 100 or so years old, but it is still deeply mysterious," he says. "Because the concepts are so divorced from human experience, we're still not sure we're thinking of them in the right way."

Probability is treated differently in the two main interpretations of quantum mechanics. In the traditional view, observing a quantum system yields just one outcome. This view, called the Copenhagen interpretation, is a bit baffling. An initial superposition of states in a given system collapses into just one state upon being measured. Exactly why this change happens, or how the system "chooses" to be in one state or another, is unclear.

An alternative, proposed by physicist Hugh Everett in the 1950s, suggests the initial mix of states never collapses. Instead, making a measurement splits our universe into parallel versions that exist in an abstract quantum realm, and all possible outcomes occur somewhere. If a system is a mix of two equally probable states, the universe splits into two when the system is observed. But what if Schrödinger's cat is, say, 70 per cent more likely to be found alive? Does that mean the universe with the live cat would somehow be "more real" than the one in which the cat died?

Anthony Aguirre at the University of California, Santa Cruz, Max Tegmark of the Massachusetts Institute of Technology, and David Layzer of Harvard University, suspect the key to clearing this confusion could lie in the multiverse, and in tying quantum probabilities to real physical observers.

Without using the Born rule, they calculate the probabilities linked to an experiment with an infinite number of identical copies throughout the multiverse (arxiv.org/abs/1008.1066).

Imagine a quantum version of an experiment in which someone reaches into a bag containing 70 red balls and 30 blue balls. If there are an infinite number of such bags and ball-pickers, the probabilities associated with the experiment simply equate to the relative numbers of observers who find each kind of ball, says the team - in this case, 70 per cent red and 30 per cent blue. The situation is identical to one in which the same single experiment is repeated an infinite number of times. "Once you consider the combined system of all of these experiments, the probabilities come from counting up the observers and not from using the Born rule," Aguirre says.

Framed in this way, the Copenhagen and Everett interpretations look the same. The universe, filled with its infinite copies of ball-pickers, would still split into many different quantum versions in the Everett scheme. Each would have a different set of outcomes for the balls - in one version, person 1 might get a red ball and person 2 a blue, and so on up to 100 balls, for example, while in another quantum version, it might start with persons 1 and 2 both pulling out red balls. But if you counted all the balls in each quantum version, the final ratio between red and blue balls would be the same as that in every other quantum version.

That suggests that you only have to consider one quantum version of the universe, just as in the Copenhagen interpretation. Tegmark says this resolves the conundrum of how the many-worlds interpretation deals with probabilities - some do not have to be "less real" than others, as previously suggested. "All those many worlds that Everett invented are out there," he says.

"I think this is an important advance," says Vilenkin. "They showed that the mathematics really works out. It kind of clears up the foundations of quantum mechanics."
Identity crisis

Not knowing who you are is not just the cause of existential angst - it could also be the source of quantum uncertainty.

The outcomes of quantum experiments cannot be predicted exactly. Instead, a principle called the Born rule calculates the probability of each possible outcome.

The Born rule can't cope, however, if there are multiple doppelgängers running the same experiment elsewhere around the universe. It seems to need an extra ingredient, like a measure of the distribution of these doppelgängers, to work out the probability of outcomes in a given experiment.

A team led by Anthony Aguirre of the University of California, Santa Cruz, has tackled this problem without resorting to the Born rule (see main story).

They say an infinite number of doppelgängers, or copies, performing the experiment is equivalent to one observer doing the experiment an infinite number of times. This picture ties the abstract Born rule to something concrete - the existence of multiple, identical observers; a possibility that could arise if our universe is large.

In their scheme, some of these copies would get one outcome in a quantum experiment and others another outcome, with the relative numbers agreeing with the Born rule. So instead of a single observer who doesn't know the outcome of an experiment ahead of time, in this picture multiple observers get different outcomes, and quantum uncertainty "comes from the fact that you don't know which observer you are", Aguirre says.

But the probabilistic nature of quantum mechanics is still a mystery. "At this stage, I would say it is a matter of taste whether it's 'better' to have uncertainty from the existence of inaccessible copies or uncertainty that's intrinsic to quantum mechanics," says Mark Srednicki of the University of California, Santa Barbara.

 http://www.newscientist.com/article/mg20727753.600-infinite-doppelgangers-may-explain-quantum-probabilities.html?full=true