Wednesday, 11 July 2012

Information Theory "proves" the uncertainty principle

Or rather, it helps with an intuitive justification of the uncertainty principle, which is what the authors were seeking, and, maybe, suggests the search for 'hidden variables' explanations of the uncertainty principle are unlikely to succeed.

From the New Scientist 23rd June 2012:
Stephanie Wehner and Esther Hänggi at the National University of Singapore's Centre for Quantum Technology have taken a new tack, recasting the uncertainty principle in the language of information theory.

First, they suggest that the two properties of a single object that cannot be known simultaneously can be thought of as two streams of information encoded in the same particle. In the same way that you can't know a particle's momentum and location to an arbitrarily high level of accuracy, you also can't completely decode both of these messages. If you figure out how to read message 1 more accurately, then your ability to decrypt message 2 becomes more limited.

Next the pair calculate what happens if they loosen the limits of the uncertainty principle in this scenario, allowing the messages to be better decoded and letting you access information that you wouldn't have had when the uncertainty principle was in force.

Wehner and Hänggi conclude that this is the same as getting more useful energy, or work, out of a system than is put in, which is forbidden by the second law of thermodynamics. That is because both energy and information are needed to extract work from a system.

To understand why, imagine trying to drive a piston using a container full of heated gas. If you don't know in which direction the gas particles are moving, you may angle the piston wrongly and get no useful work out of the system. But if you do know which way they are moving, you will be able to angle the piston so that the moving particles drive it. You will have converted the heat into useful work in the second scenario, even though the same amount of energy is available as in the first scenario.

Being able to decode both of the messages in Wehner and Hänggi's imaginary particle suddenly gives you more information. As demonstrated by the piston, this means you have the potential to do more work. But this extra work comes for free so is the same as creating a perpetual motion machine, which is forbidden by thermodynamics (

"The second law of thermodynamics is something which we see everywhere and basically no one is questioning," says Mario Berta, a theoretical physicist from the Swiss Federal Institute of Technology in Zurich, who was not involved in the work. "Now we know that without an uncertainty principle we could break the second law."

Jessica Giggs "To be quantum is to be uncertain", New Scientist v214 n2870 (online here)

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