Xavier Calmet | PubMed Health

PubMed2005

Dynamics of the Fisher information metric.

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional J [g(mu nu) (theta(i)) ] , where g(mu nu) (theta(i)) is the Fisher metric. We postulate that this functional of the dynamical variable g(mu nu) (theta(i)) is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to the Fisher information metric. It allows one to impose symmetries on a statistical system in a systematic way.

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PubMed2004

Minimum length from quantum mechanics and classical general relativity.

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements.

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