Generic arguments lead to the idea that quantum gravity has a minimal length scale. A possible observational signal of such scale is photons should exhibit dispersion. In 2009, observation short gamma ray burst seemed push distances smaller than Planck length. This poses challenge for distance models. Here we propose modification position and momentum operators, xˆ pˆ, which scale, but preserve...

Minkowski’s second theorem can be stated as an inequality for n-dimensional flat Finsler tori relating the volume and minimal product of lengths closed geodesics which form a homology basis. In this paper we show how fundamental result promoted to principle holding larger class manifolds. This includes manifolds first Betti number dimension do no necessarily coincide, prime example being case s...

On large scales, a chaotic deterministic signal is indistinguishable from a random process. Determinism becomes visible only below a critical length scale. We analyse the dependence of this scale on the entropy of the signal and the minimal embedding dimension for state space reconstruction. Also the problem of the optimal choice of the delay time for ow data can be discussed in this framework.