Skolem's paradox

So far I never mentioned how I understand
the famous Löwenheim-Skolem result (*):

"no matter how fancy your axiomatic system, which seems to talk about real numbers, complex numbers, geometries, fields etc.,

in the end, all it really does is talk about the countable natural numbers, nothing more and nothing less."



In my opinion it is the most shocking result of the Grundlagenstreit.

But does this tell us something about the true nature of physical reality?



(*) and let me be very clear that I am a layman who read exactly one book about number theory (and I understood perhaps half of it).

down to earth

I assume you will be relieved that
this blog post for once is not some crazy speculation about our universe and it does not contain empty pseudo-philosophical thoughts. It does not even count espressos.

Instead, it is about the down-to-earth topic of quantum gravity. Actually it is just a collection of links to pre-prints; In other words I am cleaning out my to-do list.



B.F.L. Ward: ".. by using recently developed exact resummation techniques ... we get quantum field theoretic descriptions for the UV fixed-point behaviors of the dimensionless gravitational and cosmological constants postulated by Weinberg. Connecting our work to the attendant phenomenological asymptotic safety analysis of Planck scale cosmology by Bonanno and Reuter, we predict the value of the cosmological constant ..."



U. Gursoy: "We propose a general correspondence between gravity and spin models, inspired by the well-known IR equivalence between lattice gauge theories and the spin models. This suggests a connection between continuous type Hawking-phase transitions in gravity and the continuous order-disorder transitions in ferromagnets. ..."



N. J. Poplawski: "The Einstein-Cartan-Kibble-Sciama theory of gravity provides a simple scenario in early cosmology which is alternative to standard cosmic inflation and does not require scalar fields. The torsion of spacetime prevents the appearance of the cosmological singularity in the early Universe filled with Dirac particles averaged as a spin fluid. Instead, its expansion starts from a state at which the Universe has a minimum but finite radius. ..."



A. Strominger et al.: "The problem of gravitational fluctuations confined inside a finite cutoff at radius r=r_c outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff r_c the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. ..."



If this would be a better blog, each one would have its own blog post with interesting explanations etc. - some value added.

But by now you should know that with this blog you will have to make up your own mind about all this ...