Charles J. Quarra
Aug4-04, 12:22 PM
<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>Hi,\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 are viewed as the kaluza-klein\ncompactifications, but im not sure how you call it when you think in\nspace-time as a membrane onto a flat manifold, where the\nextra-dimensions belong to the physical embedding, but where normal\nfields are constrained to propagate only (or mostly) onto the brane,\nis there a name for that?\n\n\ngreetings\n\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,
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 are viewed as the kaluza-klein
compactifications, but im not sure how you call it when you think in
space-time as a membrane onto a flat manifold, where the
extra-dimensions belong to the physical embedding, but where normal
fields are constrained to propagate only (or mostly) onto the brane,
is there a name for that?
greetings
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 are viewed as the kaluza-klein
compactifications, but im not sure how you call it when you think in
space-time as a membrane onto a flat manifold, where the
extra-dimensions belong to the physical embedding, but where normal
fields are constrained to propagate only (or mostly) onto the brane,
is there a name for that?
greetings