Related papers: Logic and String Theory
This paper analyzes the effective field theory perspective on modern physics through the lens of the quantum theory of gravitational interaction. The historical part argues that the search for a theory of quantum gravity stimulated the…
We argue that string theory should have a formulation for which stability and causality are evident. Rather than regard strings as fundamental objects, we suggest they should be regarded as composite systems of more fundamental point-like…
String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string…
What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman…
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…
Extensions (modifications) of the Heisenberg Uncertainty principle are derived within the framework of the theory of Special Scale-Relativity proposed by Nottale. In particular, generalizations of the Stringy Uncertainty Principle are…
I present arguments to the affect that the topological phase of string theory must be event-symmetric. This motivates a search for a universal string group for discrete strings in event-symmetric space-time which unifies space-time symmetry…
We introduce and develop the theory of metaparticles. At the classical level, this is a world-line theory with the usual reparameterization invariance and two additional features. The theory is motivated by string theory on compact targets,…
There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…
Cosmic strings are linear concentrations of energy that form whenever phase transitions in the early universe break axial symmetries as originally shown by Kibble. They are the result of frustrated order in the quantum fields responsible…
Preliminary investigations of the topological phase of string theory along the lines of a (restricted) $\dot{w}_{\infty}$ non-linear sigma model are provided. Gauge fixing the w gravity gauge fields by preserving a geometric identity Lorenz…
Measures in the context of Category Theory lead to various relations, even differential relations, of categories that are independent of the mathematical structure forming objects of a category. Such relations, which are independent of…
We resolve the space-time canonical variables of the relativistic point particle into inner products of Weyl spinors with components in a Clifford algebra and find that these spinors themselves form a canonical system with generalized…
Some physicists hope to use string/M-theory to construct a comprehensive underlying theory of our physical world a "final theory". Can such a theory be tested? A quantum theory of gravity must be formulated in 10 dimensions, so obviously…
This is a broad-brush review of how string theory addresses several important questions of gravitational physics. The problem of non-renormalizability is first reviewed, followed by introduction of string theory as an ultraviolet-finite…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…
In these lectures I discuss various unsolved problems of string theory and their relations to quantum gravity, 3d Ising model, large N QCD, and quantum cosmology. No solutions are presented but some new and perhaps useful approaches are…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
If the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all non-gravitational physics: the Standard Model. But despite this monumental achievement…
It took two millennia after Euclid and until in the early 1880s, when we went beyond the ancient axiom of parallels, and inaugurated geometries of curved spaces. In less than one more century, General Relativity followed. At present,…