Related papers: Living with Infinities
In this work we argue against the interpretation that underlies the "Standard" account of Quantum Mechanics (SQM) that was established during the 1930s by Niels Bohr and Paul Dirac. Ever since, following this orthodox narrative, physicists…
This paper collects into one place my replies to the questions posed by Maximilian Schlosshauer in his interview volume about the foundations of quantum mechanics, "Elegance and Enigma: The Quantum Interviews" (Springer, 2011).
The N_c to infinity limit of a matrix quantum field theory is equivalent to summing only planar Feynman diagrams. The possibility of interpreting this sum as some kind world-sheet theory has been in the air ever since 't Hooft's original…
We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena - a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. I summarize a number of fascinating recent developments that grew out of Bekenstein's pioneering…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the…
In this presentation, I will summarize the present status of the developments with a Universal Theory of Relativity \cite{smw-utr}. Some general challenges to be overcome will also be discussed.
Invited contribution to "Quantum Aspects of Life", D. Abbott Ed. (World Scientific, Singapore, 2007).
This is a chapter surveying the current state of our understanding of tilings with infinite local complexity. It is intended to appear in the volume {\em Directions in Aperiodic Order}, D. Lenz, J. Kellendonk, and J. Savienen, eds.
This is an essay sketching the line of thinking which has led the present author to propose the constituent or atomic model of gravitation more than a decade ago. It turns out that viewing the problem of gravitation as a quantum many body…
It is shown that observed peculiarities of the Universe expansion are an inevitable consequence of the gravitational force properties following from gauge-invariant gravitation equations considered in detail in an author's paper in Annalen…
This is the first paper by Gunnar Nordstr{\"o}m (1881--1923) on his five dimensional theory. In his summary he states: ''It is shown, that a unifying treatment of the electromagnetic and gravitational fields is possible, if one considers…
This paper analyzes two different proposals, one by Ellis and Brundrit, based on classical relativistic cosmology, the other by Garriga and Vilenkin, based on the DH interpretation of quantum mechanics, both of which conclude that, in an…
The purpose of these lectures is to discuss in some detail a new, non-perturbative approach to quantum gravity. I would like to present the basic ideas, outline the key results that have been obtained so far and indicate where we are headed…
We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)
The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schr\"odinger on foundational issues in quantum mechanics into a quantitative prediction of a new…
In this contribution to the conference "Beyond Einstein: Historical Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century", we give a critical status report of attempts to explain the late accelerated expansion of the…