Charles J. Quarra
Aug19-04, 04:51 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nHi,\n\nThis question its really more suited for sci.physics.strings, but i\nhavent received a response; besides this question is probably of\ngeneral relevance to understanding what to expect from quantum\ntheories of geometry\n\n\nI have a couple of semi-technical questions from the point of view of\none that has not studied this subject (my current knowledge stops at\nquantum mechanics and some of second quantization) but anyway i think\nmy questions are whatsoever well formulated (i gladly accept any\ndisproval)\n\nafaik, string theory enhances GR in the sense that space-time can\nsuffer transitions between inequivalent homeomorphic classes. My\nquestion is, what do we know of the dependence of the transition\nprobabilities? do they depend on global, invariant quantities on the\nmanifold, or they may depend on local densities of the fields on the\nmanifold?\n\none can easily find homeotopic deformations of different topologies\n(e.g. a torus on a sphere) but then one finds that at the transition\nsingular points on the manifold must occur. in a "intuitive" sense one\nwould expect that a sphere with two antipodal increasingly singular\npoints its "more like" to become a torus than a sphere with, say, one\nsingle increasingly singular point. Anyhow, this "intuition" is a\ncheat of the senses because its based on the pictorial usage of the\nmetric of the embedding space of the sphere (R^3 for example) to apply\na correspondence between such a metric and the probabilities. Which\nbrings me to another question\n\nAs far as my understand goes Riemannian (and pseudo-Riemannian)\ndynamical geometries are well defined in the absence of an embedding\nspace, leaving all the observables as combinations of surface\nintrinsics quantities (covariants). But i wonder, does string theories\nhave something to say about spacetime embeddings? i understand that\nthe unseen extra-dimensions needed for standard model fields are\nviewed as the kaluza-klein compactifications of higher dimensional\nspacetimes, but im sure i heard/read somewhere that some models try a\ndifferent approach: Thinking in the space-time as a 3+1-dimensional\nmembrane onto a flat embedding manifold, but where the\nextra-dimensions of the physical embedding are used to reproduce the\nneeded standard model fields (as YangMills), with the (unexplained)\nfact that usual fields are constrained to propagate only (or mostly)\nonto the 3+1-brane,\nis there a common name for those theories?\n\n\ngreetings\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi,
This question its really more suited for sci.physics.strings, but i
havent received a response; besides this question is probably of
general relevance to understanding what to expect from quantum
theories of geometry
I have a couple of semi-technical questions from the point of view of
one that has not studied this subject (my current knowledge stops at
quantum mechanics and some of second quantization) but anyway i think
my questions are whatsoever well formulated (i gladly accept any
disproval)
afaik, string theory enhances GR in the sense that space-time can
suffer transitions between inequivalent homeomorphic classes. My
question is, what do we know of the dependence of the transition
probabilities? do they depend on global, invariant quantities on the
manifold, or they may depend on local densities of the fields on the
manifold?
one can easily find homeotopic deformations of different topologies
(e.g. a torus on a sphere) but then one finds that at the transition
singular points on the manifold must occur. in a "intuitive" sense one
would expect that a sphere with two antipodal increasingly singular
points its "more like" to become a torus than a sphere with, say, one
single increasingly singular point. Anyhow, this "intuition" is a
cheat of the senses because its based on the pictorial usage of the
metric of the embedding space of the sphere (R^3 for example) to apply
a correspondence between such a metric and the probabilities. Which
brings me to another question
As far as my understand goes Riemannian (and pseudo-Riemannian)
dynamical geometries are well defined in the absence of an embedding
space, leaving all the observables as combinations of surface
intrinsics quantities (covariants). But i wonder, does string theories
have something to say about spacetime embeddings? i understand that
the unseen extra-dimensions needed for standard model fields are
viewed as the kaluza-klein compactifications of higher dimensional
spacetimes, but im sure i heard/read somewhere that some models try a
different approach: Thinking in the space-time as a 3+1-dimensional
membrane onto a flat embedding manifold, but where the
extra-dimensions of the physical embedding are used to reproduce the
needed standard model fields (as YangMills), with the (unexplained)
fact that usual fields are constrained to propagate only (or mostly)
onto the 3+1-brane,
is there a common name for those theories?
greetings
This question its really more suited for sci.physics.strings, but i
havent received a response; besides this question is probably of
general relevance to understanding what to expect from quantum
theories of geometry
I have a couple of semi-technical questions from the point of view of
one that has not studied this subject (my current knowledge stops at
quantum mechanics and some of second quantization) but anyway i think
my questions are whatsoever well formulated (i gladly accept any
disproval)
afaik, string theory enhances GR in the sense that space-time can
suffer transitions between inequivalent homeomorphic classes. My
question is, what do we know of the dependence of the transition
probabilities? do they depend on global, invariant quantities on the
manifold, or they may depend on local densities of the fields on the
manifold?
one can easily find homeotopic deformations of different topologies
(e.g. a torus on a sphere) but then one finds that at the transition
singular points on the manifold must occur. in a "intuitive" sense one
would expect that a sphere with two antipodal increasingly singular
points its "more like" to become a torus than a sphere with, say, one
single increasingly singular point. Anyhow, this "intuition" is a
cheat of the senses because its based on the pictorial usage of the
metric of the embedding space of the sphere (R^3 for example) to apply
a correspondence between such a metric and the probabilities. Which
brings me to another question
As far as my understand goes Riemannian (and pseudo-Riemannian)
dynamical geometries are well defined in the absence of an embedding
space, leaving all the observables as combinations of surface
intrinsics quantities (covariants). But i wonder, does string theories
have something to say about spacetime embeddings? i understand that
the unseen extra-dimensions needed for standard model fields are
viewed as the kaluza-klein compactifications of higher dimensional
spacetimes, but im sure i heard/read somewhere that some models try a
different approach: Thinking in the space-time as a 3+1-dimensional
membrane onto a flat embedding manifold, but where the
extra-dimensions of the physical embedding are used to reproduce the
needed standard model fields (as YangMills), with the (unexplained)
fact that usual fields are constrained to propagate only (or mostly)
onto the 3+1-brane,
is there a common name for those theories?
greetings