29 October 2012

Using 'Hidden Influence Inequality' To Explain Quantum Nonlocality

In 1964, physicist John Stewart Bell published his paper, "On the Einstein Podolsky Rosen paradox". In the paper, he derived his theorem, Bells Theorem, that states that - No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. Local hidden variables refers to realism and the local causality theory where combined, it meant that distant events are assumed to have no instantaneous (or at least faster-than-light) effect on local ones.

This meant that classical mechanics cannot explain everything that is going on in quantum mechanics. Where classical mechanics would explain a set of physical laws describing the motion of bodies under the action of a system of forces in the real world, quantum mechanics deals with physical behavior at microscopic scales, where the action is on the order of the Planck constant (6.626068 × 10-34 m2 kg / s).

Albert Einstein felt that quantum mechanics was incomplete.

In his published series of lectures in 1921, "The Meaning of Relativity", he notes, "One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory and must lead to an attempt to find a purely algebraic theory for the representation of reality. But nobody knows how to find the basis for such a theory."

The EPR Paradox

Albert Einstein, Boris Podolsky and Nathan Rosen (collectively EPR) demonstrated this through a thought experiment known as the EPR Paradox.

They looked at quantum entanglement, a behavior where entangled particles behave as one even when separated by distance. With this, they came up with two explanations. Either the particles still have interaction or signal with each other despite being far away or that the outcome of all possible measurements has already been encoded (the effects are already prearranged) in both particles.

Since the first explanation goes against the theory of relativity (instantaneous interaction would need faster-than-light speeds), the second explanation would be logical. But since the variables for the information encoded in the particles are still 'hidden' and not yet known, quantum mechanics is incomplete.

It is this thought experiment that John Bell refuted with his theorem - No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Quantum Non-Locality

Quantum non-locality means that particles in quantum mechanics exhibit bizarre behavior, like what is observed in quantum entanglement. It meant that measurements in quantum levels does not necessarily follow behavior set forth in classical levels.

Video: Quantum Non-Locality

But trying to explain quantum behavior such as entanglement meant that if there was a signal between the two particles, it would have to travel faster than the speed of light. This would go against Einstein's theory of relativity.

Hidden Influence Inequality

An international team of physicists from Switzerland, Belgium, Spain and Singapore has proposed an experiment using 'hidden influence inequality' which challenges the understanding about the nature of space and time, and Einstein's theory of relativity.

They propose (using quantum entanglement) that the signals between the two particles can travel faster than the speed of light (around 10,000 times faster) but stays as 'hidden influences' – usable for nothing, and thus not violating relativity. Only if the signals can be harnessed for faster-than-light communication do they openly contradict relativity.

The new hidden influence inequality shows that this won't work when it comes to quantum predictions. To derive their inequality, which sets up a measurement of entanglement between four particles, the researchers considered what behaviours are possible for four particles that are connected by influences that stay hidden and that travel at some arbitrary finite speed.

Experimental Conundrums

Mathematically (and mind-bogglingly), these constraints define an 80-dimensional object. The testable hidden influence inequality is the boundary of the shadow this 80-dimensional shape casts in 44 dimensions. The researchers showed that quantum predictions can lie outside this boundary, which means they are going against one of the assumptions. Outside the boundary, either the influences can't stay hidden, or they must have infinite speed.

Experimental groups can already entangle four particles, so a test is feasible in the near future (though the precision of experiments will need to improve to make the difference measurable). Such a test will boil down to measuring a single number. In a Universe following the standard relativistic laws the limit is 7. If nature behaves as quantum physics predicts, the result can go up to 7.3.

So if the result is greater than 7 – in other words, if the quantum nature of the world is confirmed – what will it mean?

A Nonlocal Universe

Here, there are two choices. On the one hand, there is the option to defy relativity and 'unhide' the influences, which means accepting faster-than-light communication. Relativity is a successful theory that researchers would not call into question lightly, so for many physicists this is seen as the most extreme possibility.

The remaining option is to accept that influences must be infinitely fast – or that there exists some process that has an equivalent effect when viewed in our spacetime. The current test couldn't distinguish. Either way, it would mean that the Universe is fundamentally nonlocal, in the sense that every bit of the Universe can be connected to any other bit anywhere, instantly. That such connections are possible defies our everyday intuition and represents another extreme solution, but arguably preferable to faster-than-light communication.

"Our result gives weight to the idea that quantum correlations somehow arise from outside spacetime, in the sense that no story in space and time can describe them," says Nicolas Gisin, Professor at the University of Geneva, Switzerland, and member of the team.


Centre for Quantum Technologies at the National University of Singapore
Nature Physics
University of Geneva, Switzerland
ICFO-The Institute of Photonic Sciences, Spain
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EPR paradox
Bell's Theorem
Quantum Nonlocality