Curves in spacetime violate Heisenberg’s uncertainty principle

By | February 20, 2013

20130219-214708.jpgIf an object traveling through spacetime can loop back in time in a certain way, then its trajectory can allow a pair of its components to be measured with perfect accuracy, violating Heisenberg’s uncertainty principle. This new finding involves a particular trajectory called an open timelike curve (OTC), which is a special case of a closed timelike curve (CTC), a theoretical concept that has previously provoked controversy because it raises the possibility of traveling backwards in time.According to Heisenberg’s uncertainty principle, measurements of any pair of variables must have at least a minimum amount of error. The most well-known example of the pair of variables is position and momentum, but the principle applies to any two variables that have a mathematical relationship which makes them conjugate variables. The uncertainty principle is thought to be an inherent property of quantum systems due to their wave-particle duality, rather than any observational limitations. Although previous studies have found that CTC models can theoretically violate the uncertainty principle, nobody knew that this could happen for the special case of an OTC.

Now, physicists Jacques Pienaar, Tim Ralph, and Casey Myers at The University of Queensland in Australia have theoretically shown that OTCs can allow scientists to measure a pair of conjugate variables of a quantum state to an arbitrary degree of accuracy forbidden by the uncertainty principle. The finding could have implications for quantum gravity and change the way that scientists view quantum uncertainty.

“There is some speculation that the Heisenberg uncertainty principle might be different in a future theory of quantum gravity,” Pienaar told “However, most of these studies suggest that quantum gravity will introduce more uncertainty. Our model suggests the complete opposite: that a theory of quantum gravity might actually remove the uncertainty of quantum mechanics.”

This perfect measurement ability arises from the nature of OTC trajectories. As the physicists explain, OTCs are the simplest and most normal type of CTCs. Whereas CTCs form closed loops in time that allow systems to affect events in their own past, OTCs form open loops in time and do not allow systems to interact with previous versions of themselves. These interaction-free OTCs overcome some of the paradoxes associated with time travel, such as the grandfather paradox in which a time traveler kills their own grandfather, preventing their own existence.

Despite such paradoxes, CTCs in general are compatible with general relativity; however, they are not compatible with quantum mechanics. One way to make them compatible is to extend quantum mechanics in a way that resolves the paradoxical aspects of CTCs. An example of such an extension is the Deutsch model, which makes the mathematics of quantum mechanics nonlinear, allowing for CTCs. Previously, scientists have shown that this nonlinearity leads to some unusual properties, such as the possibility to build a super quantum computer that can quickly solve some complex problems called NP-complete problems, a task that would take trillions of years using today’s computers. …

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