Related papers: Gods as Topological Invariants
Cosmology is operating now on a well established and tightly constraining empirical basis. The relativistic LambdaCDM hot big bang theory is consistent with all the present tests; it has become the benchmark. But the many open issues in…
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the…
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative…
The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this…
The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that…
A slight modification to one of Tarski's axioms of plane Euclidean geometry is proposed. This modification allows another of the axioms to be omitted from the set of axioms and proven as a theorem. This change to the system of axioms…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
Physical cosmology tries to understand the Universe at large with its origin and evolution. Observational and experimental situations in cosmology do not allow us to proceed purely based on the empirical means. We examine in which sense our…
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
In this paper we work out a multiverse scenario whose physical characteristics enable us to advance the following the conjecture that whereas the physics of particles and fields is confined to live in the realm of the whole multiverse…
Two people may claim both to be naturalists, but have divergent conceptions of basic elements of the natural world which lead them to mean different things when they talk about laws of nature, or states, or the role of mathematics in…
The boundary conditions to be imposed on the quantum state of the whole multiverse could be such that the universes would be created in entangled pairs. Then, inter-universal entanglement would provide us with a vacuum energy for each…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
A new cosmological theory is proposed in the theoretical framework of modified gravity theories which is based on a tachyonic field non-minimally coupled with a specific topological invariant constructed with third order contractions of the…
The idea of a multiverse -- an ensemble of universes -- has received increasing attention in cosmology, both as the outcome of the originating process that generated our own universe, and as an explanation for why our universe appears to be…
After a survey of the present state of cosmological theory and observations, this article discusses a series of major themes underlying the relation of philosophy to cosmology. These are: A: The uniqueness of the universe; B: The large…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…