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In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is particularly interesting because topological structures are at the foundation of geometrical structures, which play a fundamental role within modern mathematical physics. In this paper we will show a set of necessary and sufficient conditions under which those topological structures lead to real quantities and manifolds, which are a typical requirement for geometry. These conditions will provide a physically meaningful procedure that is the physical counter-part of the use of Dedekind cuts in mathematics. We then show that those conditions are unlikely to be met at Planck scale, leading to a breakdown of the concept of ordering. This would indicate that the mathematical structures required to describe space-time at that scale, while still topological, may not be geometrical.
It is often said that asymmetric dark matter is light compared to typical weakly interacting massive particles. Here we point out a simple scheme with a neutrino portal and $mathcal{O}(60 text{ GeV})$ asymmetric dark matter which may be added to any
We suggest the possibility that the mysterious dark energy component driving the acceleration of the Universe is the leading term, in the de Sitter temperature, of the free energy density of space-time seen as a quantum gravity coherent state of the
This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to generalize th
We analyze the X-ray spectrum of the quasar PG1211+143 observed with the CCD and grating spectrometers on board XMM-Newton. Using an ion by ion fitting model we find an outflow component of about 3000 km/s that includes absorption lines of K-shell an
We construct an idealized universe for didactic purposes. This universe is assumed to consist of absolute Euclidean space and to be filled with a classical medium which allows for sound waves. A known solution to the wave equation describing the dyna