Planck scale

Gerald t Hooft, in a speculative 1988 paper [thooft88], suggests that a suitably defined deterministic, local reversible cellular automata might provide a viable formalism for constructing field theories at the Planck scale. 

R. M. Kiehn, paper presented at Gravitation and Cosmology From the Hubble Radius to the Planck Scale, Vigier 2000 Symp. Univ. of California, Berkeley, USA (Aug. 21-25, 2000) (to be published in Proceedings edited by R. L. Amoroso, G. Hunter, M. Kafatos, and J.-P. Vigier). 

It is clear from the preceding picture of statistical geometry that the geometry around the Planck scale is closely related to the geometry of hazy lumps. The... 

In fact, there exists a certain suspicion among the scientific community that nature may be discrete or rather that it behaves discretely on the Planck scale. But even if one is willing to agree with this working philosophy, it is far from evident what this vague metaphor actually means or how it should be implemented into a concrete and systematic inquiry concerning physics and mathematics in the Planck regime. 

There are basically two overall attitudes as to discreteness on the Planck scale one starts (to a greater or lesser degree) from continuum concepts (or more specifically, concepts that are more or less openly inspired by them) and then tries to detect or create modes of discrete behavior on very fine scales, typically by imposing quantum theory in full or in part on the model system or framework under discussion. We call this the top-down approach. ... 

This calculation is in principle valid till the breakdown of quantum held theory itself, i.e. till Planck scale, so that one can put an ultraviolet cutoff at kp 1/Lpi in the above equation and the result is... 

The notation is defined in ref. [2], where other, CPT even Lorentz-violating La-grangian terms are also given. High precision experiments on muonium (M) can measure or set limits on the parameters of these symmetry violating terms, which are sensitive at the Planck scale level [4]. 

V0I.669 G. Amelino-Camelia, J. Kowalski-Glikman (Eds.), Planck Scale Effects in Astrophysics and Cosmology... 

Note that different notations are used in the literature. Conversion factors between different definitions of the fundamental Planck scale can be found in Cavaglia 2003a. 

The first question reflects the fact that taking graviton energies up to the Planck scale, Mp, would produce a dark-energy density roughly of the order of... 

Does the renormalization mean that the Planck scale does not contribute to our experiments No, it does not mean that. The Planck scale indeed contributes, but it does not contribute to the constraint, because it only affects values of masses and charges, however, we do not calculate, but measure them. That makes the Planck-scale effects imobservable. To observe we should compare a measurement and a calculation, but we have only results of measurements. However, there is an option when we should be able to see some effects of the Planck scale [2]. That is a case when we have certain dynamic effects at the Planck scale (e.g., a variation of some constants) or some violation of symmetries which would make our low-energy picture wrong. 

That means that for a proper interpretation of a Michelson-Morley-like experiment with an interferometer built on an atomic bulk matter we need to consider a dynamic model of structure of this kind of matter with a possible violation of relativity. The latter may involve the Planck scale effects, where a certain relation on low-energy fundamental constants can be set. 

If for no other reasons, the mere fact that gravity is outside the SM tells us that new physics must emerge at some large energy scale A (i.e. equivalently at some small distance). The question (one of many questions, actually ) is what this scale A is, and how one can explain the huge value of Ep/Mw, i e. the ratio between the Planck scale and the electroweak scale. 

Foams are cellular materials made up of soft bubbles in which gas is dispersed in a continuous liquid or solid, when the volume fraction of the gas is larger than of the liquid or solid. Foam structures occur, or are conjectured to do so, on every length scale, from the Planck scale (10 meters) to that of the large-scale structure of the universe. On the everyday length scale of your favorite pub, foam is what we get when bubbles rise... 

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