910 research outputs found
Review of Hyperspace by Michio Kaku (1994)
"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact" Mark Twain-Life on the Mississippi
This is a lovely book full of fascinating info on the evolution of physics and cosmology. Its main theme is how the idea of higher dimensional geometry created by Riemann, recently extended to 24 dimensions by string theory, has revolutionized our understanding of the universe. Everyone knows that Riemann created multidimensional geometry in 1854 but it is amazing to learn that he also was a physicist who believed that it held the key to explaining the fundamental laws of physics. Maxwell´s equations did not exist then and Riemann´s untimely death at age 39 prevented his pursuit of these ideas. Both he and his British translator Clifford believed that magnetic and electric fields resulted from the bending of space in the 4th dimension-more than 50 years before Einstein! The fourth dimension became a standard subject in the popular media for the next 50 years with several stories by HG Wells using it and even Lenin wrote about it. The American mathematician Hinton had widely publicized his idea that light is a vibration in the 4th spatial dimension. Amazingly, physicists and most mathematicians forgot about it and when Einstein was looking for the math needed to encompass general relativity 60 years later, he had never heard of Riemannian geometry. He spent 3 years trying to find the equations for general relativity and only after a math friend told him about Riemann was he able to complete his work. Riemann´s equations with four dimensional metric tensors describing every point in space were incorporated almost unchanged into relativity. And on and on it goes. Since this review I have written a great deal on the language games of math and science, uncertainty, incompleteness, the limits of computation etc., so those interested should find them useful since this volume like most science frequently wanders across the line into philosophy (scientism).
Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019
Matrix Model Approach to Non-critical Superstrings
We apply light-cone quantization to a dimensional supersymmetric field
theory of large N matrices. We provide some preliminary numerical evidence that
when the coupling constant is tuned to a critical value, this model describes a
2+1 dimensional non-critical superstring.Comment: 11 pages, 3 Encapsulated Postscript figures. uses psfig.sty
(available from http://xxx.lanl.gov/ftp/hep-th/papers/macros
String Theory - From Physics to Metaphysics
Currently, string theory represents the only advanced approach to a
unification of all interactions, including gravity. In spite of the more than
thirty years of its existence it did not make any empirically testable
predictions. And it is completely unknown which physically interpretable
principles could form the basis of string theory. At the moment, "string
theory" is no theory at all, but rather a labyrinthic structure of mathematical
procedures and intuitions which get their justification from the fact that
they, at least formally, reproduce general relativity and the standard model of
elementary particle physics as low energy approximations. However, there are
now strong indications that string theory does not only reproduce the dynamics
and symmetries of our standard model, but a plethora of different scenarios
with different low energy nomologies and symmetries. String theory seems to
describe not only our world, but an immense landscape of possible worlds. So
far, all attempts to find a selection principle which could be motivated
intratheoretically remained without success. So, recently the idea that the low
energy nomology of our world, and therefore also the observable phenomenology,
could be the result of an anthropic selection from a vast arena of
nomologically different scenarios entered string theory. Although multiverse
scenarios and anthropic selection are not only motivated by string theory, but
lead also to a possible explanation for the fine tuning of the universe, they
are concepts which transcend the framework defined by the epistemological and
methodological rules which conventionally form the basis of physics as an
empirical science.Comment: 30 pages, submitted to "Physics and Philosophy" (Online-Journal
Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
We give an AdS/CFT interpretation to homogeneous Yang-Baxter deformations of
the AdS_5 x S^5 superstring as noncommutative deformations of the dual gauge
theory, going well beyond the canonical noncommutative case. These homogeneous
Yang-Baxter deformations can be of so-called abelian or jordanian type. While
abelian deformations have a clear interpretation in string theory and many
already had well understood gauge theory duals, jordanian deformations appear
novel on both counts. We discuss the symmetry structure of the deformed string
from the uniformizing perspective of Drinfeld twists and indicate that this
structure can be realized on the gauge theory side by considering theories on
various noncommutative spaces. We then conjecture that these are the gauge
theory duals of our strings, modulo subtleties involving singularities. We
support this conjecture by a brane construction for two jordanian examples,
corresponding to noncommutative spaces with [x^-,x^i] ~ x^i (i=1,2). We also
discuss kappa-Minkowski type deformations of AdS_5 x S^5, one of which may be
the gravity dual of gauge theory on spacelike kappa-Minkowski space.Comment: v5, published version up to formatting, 32 page
The numerical approach to quantum field theory in a non-commutative space
Numerical simulation is an important non-perturbative tool to study quantum
field theories defined in non-commutative spaces. In this contribution, a
selection of results from Monte Carlo calculations for non-commutative models
is presented, and their implications are reviewed. In addition, we also discuss
how related numerical techniques have been recently applied in computer
simulations of dimensionally reduced supersymmetric theories.Comment: 15 pages, 6 figures, invited talk presented at the Humboldt Kolleg
"Open Problems in Theoretical Physics: the Issue of Quantum Space-Time", to
appear in the proceedings of the Corfu Summer Institute 2015 "School and
Workshops on Elementary Particle Physics and Gravity" (Corfu, Greece, 1-27
September 2015
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N)
Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling
constant by applying a simple Monte Carlo method to the matrix model that can
be derived from the theory by using the localization technique. This opens up
the possibility of probing the quantum aspects of M-theory and testing the
AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy,
and confirm the N^{3/2} scaling in the M-theory limit predicted from the
gravity side. We also find that our results nicely interpolate the analytical
formulae proposed previously in the M-theory and type IIA regimes. Furthermore,
we show that some results obtained by the Fermi gas approach can be clearly
understood from the constant map contribution obtained by the genus expansion.
The method can be easily generalized to the calculations of BPS operators and
to other theories that reduce to matrix models.Comment: 35 pages, 20 figures; reference added. The simulation code is
available upon request to [email protected]
- …