View Full Version : compactified dimensions
alistair
Jul16-04, 02:34 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>What would happen if a compactified dimension unfolded now?\nAnd would this process require energy?\n\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>What would happen if a compactified dimension unfolded now?
And would this process require energy?
Urs Schreiber
Jul16-04, 07:34 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>"alistair" <alistair@goforit64.fsnet.co.uk> schrieb im Newsbeitrag\nnews:861c1b21.0407151158.6c993070-100000@posting.google.com...\n\n> What would happen if a compactified dimension unfolded now?\n\nThe size and shape of compactified dimensions would control all kinds of\naspects of the 4-d world, like particle content, particle masses, coupling\nconstants, etc. All these might change. Robert Helling has recently\nmentioned the idea of observing such changes in this message:\n\nhttp://groups.google.de/groups?selm=2jg1veF11m4t6U1-100000%40uni-berlin.de\n\n> And would this process require energy?\n\nThe moduli (i.e. the parameters that determine the size and shape of the\nextra dimensions) will be fields that have in general (nonperturbatively\ncalculable) potentials. So changing them would "require energy" in some\ngeneral sense.\n\nThink of the size and shape of the extra dimensions as a piece of the\ngeometry of spacetime. You can change that geometry, according to Einstein\'s\nequations, by turning on energy-momentum densities.\n\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>"alistair" <alistair@goforit64.fsnet.co.uk> schrieb im Newsbeitrag
news:861c1b21.0407151158.6c993070-100000@posting.google.com...
> What would happen if a compactified dimension unfolded now?
The size and shape of compactified dimensions would control all kinds of
aspects of the 4-d world, like particle content, particle masses, coupling
constants, etc. All these might change. Robert Helling has recently
mentioned the idea of observing such changes in this message:
http://groups.google.de/groups?selm=2jg1veF11m4t6U1-100000%40uni-berlin.de
> And would this process require energy?
The moduli (i.e. the parameters that determine the size and shape of the
extra dimensions) will be fields that have in general (nonperturbatively
calculable) potentials. So changing them would "require energy" in some
general sense.
Think of the size and shape of the extra dimensions as a piece of the
geometry of spacetime. You can change that geometry, according to Einstein's
equations, by turning on energy-momentum densities.
agnostikos
Dec31-09, 07:12 PM
String theory, lesson 1: there are no points in space--- Planck lengths/areas/volumes only. ST, lesson 2: there is a calabicle (as I like to call them) at every point in space. Am I alone in sensing a contradiction here?
Jimmy Snyder
Jan1-10, 06:59 AM
String theory, lesson 1: there are no points in space--- Planck lengths/areas/volumes only. ST, lesson 2: there is a calabicle (as I like to call them) at every point in space. Am I alone in sensing a contradiction here?
I am aware that string theory assumes that particles are not points, but I was unaware that it also assumes there are no points in space. Where did you read that there are no points in space?
agnostikos
Jan4-10, 08:10 PM
Where did I read there are no points in space? On reflection, can't recall. The idea is certainly not original to me---. Points are useful in mathematics; but infinities and infinitesimals (including points) are poison in physics. Remember, Newton's gadfly Berkeley, himself an idealist, mocked fluxions: "ghostes of depart'd Quantityes." QT, Uncertainty Principle, standard model, Non-Commutative Geometry are all tasked with getting rid of infinities/infinitesimals. UP and NGC (the former a class of theorems of the latter) tell us that the smallest accessible region of space is what I want to call the planckon. Furthermore, the planckon is a collection of points which are indistinguishable and thereby fail the definition of 'point'. I am not saying there are no points because there are no point-particles; quite the reverse: there are no point particles because there are no points. To speak of a piece (or part, or constituent) of a planckon is like (or, importantly, the same as) to speak of a part of a bit of information: meaningless. "Worauf man kann nicht sprechen, darauf muss man schweigen." Like an atom of mayonnaise. So, I see Euclidean 3-space, the mathematical construct, points and all, revised by Quantum Geometry to model real space, slicendiced into a collection of planckons. And I suspect the 6-D Calabi-Yau spaces undergo something similar. Thanks, jimmysnyder, for your attention. Sincerely, Agnostikos.
Agnostikos, I like the quotes from Wittgenstein and Berkeley. The Wittgen. one sounds especially good in German---Worauf stronger than English "Whereof"
I like the posting style too.
You might be interested in something by Princeton's Paul Steinhardt (who has contributed both to string, back in its boom years, and to inflation, and to the ekpyrotic alternative.
He concluded that inflation wasn't really very compatible with compactified extra dimensions and has started proving a kind of "no-go". Either inflation is no-go, or else rolled up extra dimensions are a no-go.
http://arxiv.org/abs/0811.1614
Dark Energy, Inflation and Extra Dimensions
Paul J. Steinhardt, Daniel Wesley
26 pages, Physical Review D
(Submitted on 11 Nov 2008 )
"We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in the compact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications."
He works both in the NEC case and in the NEC-violating case. Gets interesting results either way.
ensabah6
Jan5-10, 12:11 AM
Agnostikos, I like the quotes from Wittgenstein and Berkeley. The Wittgen. one sounds especially good in German---Worauf stronger than English "Whereof"
I like the posting style too.
You might be interested in something by Princeton's Paul Steinhardt (who has contributed both to string, back in its boom years, and to inflation, and to the ekpyrotic alternative.
He concluded that inflation wasn't really very compatible with compactified extra dimensions and has started proving a kind of "no-go". Either inflation is no-go, or else rolled up extra dimensions are a no-go.
http://arxiv.org/abs/0811.1614
Dark Energy, Inflation and Extra Dimensions
Paul J. Steinhardt, Daniel Wesley
26 pages, Physical Review D
(Submitted on 11 Nov 2008 )
"We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in the compact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications."
He works both in the NEC case and in the NEC-violating case. Gets interesting results either way.
This sounds bad for string theory -- what do string theorists say? Has this been cited in other papers and either supported or clarified or refuted?
To my knowledge there is nothing wrong with Steinhardt's proofs. He's tops, Princeton Institute for Advanced Studies.
His longtime co-author Neil Turok is now director of Perimeter BTW.
One way out for string is to figure out how NOT TO NEED inflation. Steinhardt, as someone very friendly to string back in the 1990s, got together with Turok and invented the clashing branes (ekpyrotic) cosmology, primarily just so inflation would not be needed. Steinhardt suspected for a long time that string extra dimensions don't mix well with inflation, and he wanted to see if the puzzles like flatness, isotropy etc could be addressed without inflation.
But clashing branes cosmology has never really caught on. It seems a bit contrived, I guess.
Inflation continues to be preferred, as a scenario.
So another way out for string is to accommodate inflation by some sort of fine adjustment or special arrangement. Steinhardt's theorems don't absolutely rule out everything you can think of. They have assumptions, which are stated in the paper. You can always say "well suppose those assumptions don't apply!"
Another thing the paper deals with is dark energy. Accelerated expansion. It shows there is a tendency for string extra dimension to be incompatible with that too. Under assumptions which the authors argue are fairly reasonable natural ones.
Different opinions are possible about this. Basically it looks to me like just one more thing for string theorists to go into intricate contortions trying to accommodate. In that sense, similar to the 10500 vacuums "Landscape" problem. There will always be people who deny the encumbrances, ignore whatever awkwardness, and just go on doing stringy math.
Jimmy Snyder
Jan5-10, 04:51 AM
Where did I read there are no points in space? On reflection, can't recall.
Perhaps you never read it?
So, I see Euclidean 3-space, the mathematical construct, points and all, revised by Quantum Geometry to model real space, slicendiced into a collection of planckons.
There is a version of QM called Lattice QM that treats space as a collection of lattice points. But string theory is not built on it. Have you read Zwiebach's "A First Course in String Theory"? He treats space as a continuum of points.
ensabah6
Jan5-10, 11:14 AM
To my knowledge there is nothing wrong with Steinhardt's proofs. He's tops, Princeton Institute for Advanced Studies.
His longtime co-author Neil Turok is now director of Perimeter BTW.
One way out for string is to figure out how NOT TO NEED inflation. Steinhardt, as someone very friendly to string back in the 1990s, got together with Turok and invented the clashing branes (ekpyrotic) cosmology, primarily just so inflation would not be needed. Steinhardt suspected for a long time that string extra dimensions don't mix well with inflation, and he wanted to see if the puzzles like flatness, isotropy etc could be addressed without inflation.
But clashing branes cosmology has never really caught on. It seems a bit contrived, I guess.
Inflation continues to be preferred, as a scenario.
So another way out for string is to accommodate inflation by some sort of fine adjustment or special arrangement. Steinhardt's theorems don't absolutely rule out everything you can think of. They have assumptions, which are stated in the paper. You can always say "well suppose those assumptions don't apply!"
Another thing the paper deals with is dark energy. Accelerated expansion. It shows there is a tendency for string extra dimension to be incompatible with that too. Under assumptions which the authors argue are fairly reasonable natural ones.
Different opinions are possible about this. Basically it looks to me like just one more thing for string theorists to go into intricate contortions trying to accommodate. In that sense, similar to the 10500 vacuums "Landscape" problem. There will always be people who deny the encumbrances, ignore whatever awkwardness, and just go on doing stringy math.
It does sound that way to me. Perhaps 10^500 has to be multiplied by the probability of an inflationary scenario and fine-tuning in string theory initial conditions to produce our universe, while avoiding those no-go theorems. Epicycles upon epicycles. I will suspend judgment until LHC starts pouring in data on SUSY.
agnostikos
Jan5-10, 06:18 PM
Marcus, this is a bogglesome ST factoid: the (visible) universe has dimensions of circa ((10exp27)mexp3)((10exp-35)mexp6) for a 9-volume of ((10exp-129)mexp9) and a diameter of (10exp-14.33)m, about the size of a proton. Why hasn't the popsci press been all over this? Concerning inflation in a ST context: I want to visualize(metaphorically!) a little piece of 9-space expanding evenly,then for some reason 6 Ds contract at a rate #; the remaining 3 Ds now expand at #exp2, making this 'inflation' a (nearly) volume-conserving process. Does this seem any less ad-hoc, less deus-ex-machina than currently-accepted scenarios? jimmysnyde, re:quantization of space: no, I don't think I made it up, or imagined it, as I am neither that crazy nor that smart. In all probability I have misunderstood it. Google it, though, and see: I am not alone.
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