View Full Version : What's so "beautiful" or "elegant" about string theory?
backdoorstudent
Jul22-04, 04:16 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>\nI ask this seriously and respectfully. And I apologize if it seems\nlike a troll. I always feel uncomfortable when I hear physicists make\nstatements about beauty. Who here thinks reality is ugly?\nInterestingly, I do not hear mathematicians speak like this as often\nas I do physicists. So what is it that string theorists find so\nbeautiful? Brian Greene did not convey it to me. Sorry and thanks.\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>I ask this seriously and respectfully. And I apologize if it seems
like a troll. I always feel uncomfortable when I hear physicists make
statements about beauty. Who here thinks reality is ugly?
Interestingly, I do not hear mathematicians speak like this as often
as I do physicists. So what is it that string theorists find so
beautiful? Brian Greene did not convey it to me. Sorry and thanks.
Peter Woit
Jul22-04, 09:40 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>backdoorstudent wrote:\n\n>I ask this seriously and respectfully. And I apologize if it seems\n>like a troll. I always feel uncomfortable when I hear physicists make\n>statements about beauty. Who here thinks reality is ugly?\n>Interestingly, I do not hear mathematicians speak like this as often\n>as I do physicists. So what is it that string theorists find so\n>beautiful? Brian Greene did not convey it to me. Sorry and thanks.\n\n\nI\'ve spent a lot of time thinking about this question, since the idea\nthat the universe can be described by a complicated 11 dimensional theory,\nwith 7 of them having a complicated structure which explains everything we\nsee, seems to be neither elegant nor beautiful.\n\nFor one thing, some string theorists (e.g. Susskind) are now explicitly\narguing that string theory is not an elegant theory, that its virtue is\nthat it can describe all sorts of complicated things, some of which are\ncomplicated enough to produce intelligent life. In his talks, Susskind\nexplicitly sneers at and criticizes the use of the term "elegant" to\nrefer to string theory.\n\nFirst of all, what does it mean to be "elegant"? Roughly what I\nthink this means is that a huge amoutnt of structure is packaged in\na small number of simple principles or equations. The Dirac\nequation is probably the best example: it is very simple, uses surprising\nideas from mathematics, and explains a huge range of complicated\nphenomena.\n\nWhy do string theorists call the theory elegant? The main thing to\nkeep in mind is that string theorists don\'t really know what string\ntheory is.\nAs a result, I think there are two reasons they call the theory elegant.\n\n1. What is known about string theory is that it is supposed to\nencompass a lot of different phenomena associated with 2d QFT,\nespecially conformal field theory.\n2d QFT is a fantastic subject, with a lot of examples of beauty and\nelegance. Often you can write down a very simple 2d QFT, and show\nthat it has a huge amount of very deep and surprising mathematical\nstrucure. Unfortunately these structures don\'t seem to have anything\nto do with the real world. None of the most beautiful aspects of\nCFT explain anything about the world, and if you want to make contact\nwith real physics, you need to bring in exceedingly complex and ugly\nCFTs.\n\n2. As long as you don\'t know what string theory really is, you can\nkeep hoping that it is something truly wonderful and beautiful. The\nbeautiful, elegant theory that string theorists often are referring to\nis the one they hope exists. Two of Witten\'s definitions of the "M"\nin M-theory are "Mystery" and "Magic". Much of the beauty of\nM-theory is the beauty of mystery, of something you don\'t understand\nthat you invest with your hopes and dreams. Other similar statements\nare characterizations of string theory as something magical that\ndropped in from the 21st century to the 20th, or as a spaceship we\ndon\'t have the instruction manual for. But maybe if one ever\nunderstands what M-theory is, it will turn out to be something\nhorribly complicated and ugly (see Susskind). Maybe the mysterious\nobject string theorists think is a space-ship is really a toaster.\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>backdoorstudent wrote:
>I ask this seriously and respectfully. And I apologize if it seems
>like a troll. I always feel uncomfortable when I hear physicists make
>statements about beauty. Who here thinks reality is ugly?
>Interestingly, I do not hear mathematicians speak like this as often
>as I do physicists. So what is it that string theorists find so
>beautiful? Brian Greene did not convey it to me. Sorry and thanks.
I've spent a lot of time thinking about this question, since the idea
that the universe can be described by a complicated 11 dimensional theory,
with 7 of them having a complicated structure which explains everything we
see, seems to be neither elegant nor beautiful.
For one thing, some string theorists (e.g. Susskind) are now explicitly
arguing that string theory is not an elegant theory, that its virtue is
that it can describe all sorts of complicated things, some of which are
complicated enough to produce intelligent life. In his talks, Susskind
explicitly sneers at and criticizes the use of the term "elegant" to
refer to string theory.
First of all, what does it mean to be "elegant"? Roughly what I
think this means is that a huge amoutnt of structure is packaged in
a small number of simple principles or equations. The Dirac
equation is probably the best example: it is very simple, uses surprising
ideas from mathematics, and explains a huge range of complicated
phenomena.
Why do string theorists call the theory elegant? The main thing to
keep in mind is that string theorists don't really know what string
theory is.
As a result, I think there are two reasons they call the theory elegant.
1. What is known about string theory is that it is supposed to
encompass a lot of different phenomena associated with 2d QFT,
especially conformal field theory.
2d QFT is a fantastic subject, with a lot of examples of beauty and
elegance. Often you can write down a very simple 2d QFT, and show
that it has a huge amount of very deep and surprising mathematical
strucure. Unfortunately these structures don't seem to have anything
to do with the real world. None of the most beautiful aspects of
CFT explain anything about the world, and if you want to make contact
with real physics, you need to bring in exceedingly complex and ugly
CFTs.
2. As long as you don't know what string theory really is, you can
keep hoping that it is something truly wonderful and beautiful. The
beautiful, elegant theory that string theorists often are referring to
is the one they hope exists. Two of Witten's definitions of the "M"
in M-theory are "Mystery" and "Magic". Much of the beauty of
M-theory is the beauty of mystery, of something you don't understand
that you invest with your hopes and dreams. Other similar statements
are characterizations of string theory as something magical that
dropped in from the 21st century to the 20th, or as a spaceship we
don't have the instruction manual for. But maybe if one ever
understands what M-theory is, it will turn out to be something
horribly complicated and ugly (see Susskind). Maybe the mysterious
object string theorists think is a space-ship is really a toaster.
Michael Varney
Jul22-04, 09:44 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>\n"backdoorstudent" <backdoorstudent@yahoo.com> wrote in message\nnews:750f5e99.0407211611.61f734a6@posting .google.com...\n>\n> I ask this seriously and respectfully. And I apologize if it seems\n> like a troll. I always feel uncomfortable when I hear physicists make\n> statements about beauty. Who here thinks reality is ugly?\n> Interestingly, I do not hear mathematicians speak like this as often\n> as I do physicists. So what is it that string theorists find so\n> beautiful? Brian Greene did not convey it to me. Sorry and thanks.\n\nBeauty is in the eye of the beholder... a truism that applies to physicists\nas well.\nReality is ugly in many cases.\n\nHowever, the mathematical description of reality is considered beautiful\nwhen it is concise, succinct, simple and encompassing.\n\nString theory is beautiful in its potential to unify physics... no\nadjustable parameters.\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>"backdoorstudent" <backdoorstudent@yahoo.com> wrote in message
news:750f5e99.0407211611.61f734a6@posting.google.c om...
>
> I ask this seriously and respectfully. And I apologize if it seems
> like a troll. I always feel uncomfortable when I hear physicists make
> statements about beauty. Who here thinks reality is ugly?
> Interestingly, I do not hear mathematicians speak like this as often
> as I do physicists. So what is it that string theorists find so
> beautiful? Brian Greene did not convey it to me. Sorry and thanks.
Beauty is in the eye of the beholder... a truism that applies to physicists
as well.
Reality is ugly in many cases.
However, the mathematical description of reality is considered beautiful
when it is concise, succinct, simple and encompassing.
String theory is beautiful in its potential to unify physics... no
adjustable parameters.
FrediFizzx
Jul23-04, 05:34 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>\n\n"backdoorstudent" <backdoorstudent@yahoo.com> wrote in message\nnews:750f5e99.0407211611.61f734a6@posting .google.com...\n|\n| I ask this seriously and respectfully. And I apologize if it seems\n| like a troll. I always feel uncomfortable when I hear physicists make\n| statements about beauty. Who here thinks reality is ugly?\n| Interestingly, I do not hear mathematicians speak like this as often\n| as I do physicists. So what is it that string theorists find so\n| beautiful? Brian Greene did not convey it to me. Sorry and thanks.\n\nErr... It is the Universe that is elegant and beautiful; not necessarily\nstring theory. Now, I happen to believe that this is a thing of freakin\'\nbeauty; vacuum charge = +,- sqrt(hbar*c). Quite possibly the simplest\nexpression of the marriage of QM + SR = QFT. The thing that I think is\nbeautiful about string theory is the concept of one thing being able to\nmaking it all. If you have massless point-like quantum entities traveling\nat c, they are going to be like strings. So strings make sense to me. Even\nif the point-like quantum entities are strings, you have strings making\nstrings. Fantastic!\n\nFrediFizzx\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>"backdoorstudent" <backdoorstudent@yahoo.com> wrote in message
news:750f5e99.0407211611.61f734a6@posting.google.c om...
|
| I ask this seriously and respectfully. And I apologize if it seems
| like a troll. I always feel uncomfortable when I hear physicists make
| statements about beauty. Who here thinks reality is ugly?
| Interestingly, I do not hear mathematicians speak like this as often
| as I do physicists. So what is it that string theorists find so
| beautiful? Brian Greene did not convey it to me. Sorry and thanks.
Err... It is the Universe that is elegant and beautiful; not necessarily
string theory. Now, I happen to believe that this is a thing of freakin'
beauty; vacuum charge = +,- \sqrt(\hbar*c). Quite possibly the simplest
expression of the marriage of QM + SR = QFT. The thing that I think is
beautiful about string theory is the concept of one thing being able to
making it all. If you have massless point-like quantum entities traveling
at c, they are going to be like strings. So strings make sense to me. Even
if the point-like quantum entities are strings, you have strings making
strings. Fantastic!
FrediFizzx
<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>\nbackdoorstudent@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.0407211611.61f734a6@posting.google. com>...\n> I ask this seriously and respectfully. And I apologize if it seems\n> like a troll. I always feel uncomfortable when I hear physicists make\n> statements about beauty. Who here thinks reality is ugly?\n> Interestingly, I do not hear mathematicians speak like this as often\n> as I do physicists. So what is it that string theorists find so\n> beautiful? Brian Greene did not convey it to me. Sorry and thanks.\n\nPhysicists usually use the word "elegant" and they use it to mean\nsomething that is predicted by the theory, or falls out naturally,\ninstead of being put in my hand in an ad hoc way, such as in gauge\ntheory, in the process of making it gauge invariant, you have to add\nvector term, which can then be identified with the gauge bosons that\nmediate the force.\n\nDavid\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>backdoorstudent@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.0407211611.61f734a6@posting.google.com>...
> I ask this seriously and respectfully. And I apologize if it seems
> like a troll. I always feel uncomfortable when I hear physicists make
> statements about beauty. Who here thinks reality is ugly?
> Interestingly, I do not hear mathematicians speak like this as often
> as I do physicists. So what is it that string theorists find so
> beautiful? Brian Greene did not convey it to me. Sorry and thanks.
Physicists usually use the word "elegant" and they use it to mean
something that is predicted by the theory, or falls out naturally,
instead of being put in my hand in an ad hoc way, such as in gauge
theory, in the process of making it gauge invariant, you have to add
vector term, which can then be identified with the gauge bosons that
mediate the force.
David
Doug Sweetser
Jul23-04, 07:25 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>\nHello "student":\n\n> So what is it that string theorists find so beautiful? Brian Greene\n> did not convey it to me. Sorry and thanks.\n\nI bought the 3 hour Nova documentary, not the book. Beauty,\nelegance, and mystery is all part of the way string theory is marketed\nto the general public which finances string theory. To "seriously and\nrespectively" challenge the beauty and elegance could be taken as a\nchallenge to financing. One needs to be careful.\n\nFor me, it is equations where one should look for beauty. In the TV\ndocumentary, only the second hour on the history of string theory had\nequations. Because I owned the DVD, I was able to stop and take a look\nat a few.\n\nThe first was the Euler Beta function. Gabriele Venezioano in 1968 used\nit to describe the strong force. The Beta function looks with obvious\nASCII limitations like so:\n\nB(p, q) = L(p) L(q)/L(p+q)\n\nThe L\'s are suppose to be capital gammas. Gammas are a continuous form\nof factorials, something that did strike me as really cool. Beta is\nfor a function with two variables. As for what beta does, here is one\ndescription:\n\n"The beta function comes into picture when calculating the total density\nby performing convolutions of classical state densities which have a\npower law form. An example is the situation of two subsystems composed\nof different sets of harmonic oscillators s1 and s2. Then the density\nis a function of B(s1, s2)."\n\n[from http://www.2dcurves.com/gamma/gammab.html]\n\nSuskind wrote the next equation from memory on a blackboard. It was an\nexample of beta in action:\n\nA(s, t) = L(1 - alpha(s)) L(1 - alpha(t)) / L(2 - alpha(s) - alpha(t))\n\nThey did not tell what alpha(s) or alpha(t) where. One of Suskind\'s\ncontributions was that this beta function could not only be stretched\nand compressed but also could vibrate at different frequencies. This\nfunction could thus represent a string of some sort in the strong\nforce. I could understand his words, but not see the string itself, so\nthat is frustrating.\n\nThis approach to the strong force had important technical problems, with\na massless particle and anomalies. It was John Schwartz in 1973 who\nfirst suggested a connection to gravity. The equation there was quite\ncomplicated:\n\nF_grav ~ i /2 g^2 (8 pi alpha\') g^4 [(P_1 - P_2)^2 - P_1^2 P_2^2/D-2]\ndelta phi_1 phi_2 delta phi_1 phi_2\n\nAlthough the massless particle now had the role of the graviton, there\nwere still anomalies. A calculation by Green and Schwartz in Aspen\n(1984?) during a thunderstorm showed that the number of gravitational\nanomalies, 496, exactly equaled the Yang Mills Anomalies at 496. That\nmeant that the theory was consistent. The calculation shown was far\ntoo complicated for anyone but an expert to follow. Still, it was\nperhaps the most satisfying because it looked like two very complicated\ncalculations were used to test the theory, and it passed a tough test.\n\nThe only partial equation to appear on the third episode was one of\nWitten\'s from String 95 where he unified the 5 string theories:\n\nG^10 = e^-gamma\nI = 1/2 Int d^10 x g^(1/2) e^-3 gamma R ...\n\nThe partial doodle had little impact on me, although it rocked the\nmeeting. That d^10 means the theory is in ten dimensions. To be\nbeautiful requires to be seen. String theorist try to sell the idea\nthat the six or seven hidden dimensions are part of a beautiful,\nmind-expanding concept. The compactification proposal is hollow for me\nbecause I will never be able to visit. Being there is a key to the\nappreciation of beauty.\n\nAt this time I do not find string theory beautiful or elegant. The\nequations look too complicated. That may be because Nature is that\nway, but I remain skeptical (in a positive sense of the word,\nrespecting this body of work while hoping for something better). I\nsupport the continued funding because the peer review process continues\nto find there are avenues worth exploring.\n\ndoug\nquaternions.com\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>Hello "student":
> So what is it that string theorists find so beautiful? Brian Greene
> did not convey it to me. Sorry and thanks.
I bought the 3 hour Nova documentary, not the book. Beauty,
elegance, and mystery is all part of the way string theory is marketed
to the general public which finances string theory. To "seriously and
respectively" challenge the beauty and elegance could be taken as a
challenge to financing. One needs to be careful.
For me, it is equations where one should look for beauty. In the TV
documentary, only the second hour on the history of string theory had
equations. Because I owned the DVD, I was able to stop and take a look
at a few.
The first was the Euler \Beta function. Gabriele Venezioano in 1968 used
it to describe the strong force. The \Beta function looks with obvious
ASCII limitations like so:
B(p, q) = L(p) L(q)/L(p+q)
The L's are suppose to be capital gammas. Gammas are a continuous form
of factorials, something that did strike me as really cool. \Beta is
for a function with two variables. As for what \beta does, here is one
description:
"The \beta function comes into picture when calculating the total density
by performing convolutions of classical state densities which have a
power law form. An example is the situation of two subsystems composed
of different sets of harmonic oscillators s1 and s2. Then the density
is a function of B(s1, s2)."
[from http://www.2dcurves.com/\gamma/gammab.html]
Suskind wrote the next equation from memory on a blackboard. It was an
example of \beta in action:
A(s, t) = L(1 - \alpha(s)) L(1 - \alpha(t)) / L(2 - \alpha(s) - \alpha(t))
They did not tell what \alpha(s) or \alpha(t) where. One of Suskind's
contributions was that this \beta function could not only be stretched
and compressed but also could vibrate at different frequencies. This
function could thus represent a string of some sort in the strong
force. I could understand his words, but not see the string itself, so
that is frustrating.
This approach to the strong force had important technical problems, with
a massless particle and anomalies. It was John Schwartz in 1973 who
first suggested a connection to gravity. The equation there was quite
complicated:
F_{grav} ~ i /2 g^2 (8 \pi \alpha') g^4 [(P_1 - P_2)^2 - P_1^2 P_2^2/D-2]\delta \phi_1 \phi_2 \delta \phi_1 \phi_2
Although the massless particle now had the role of the graviton, there
were still anomalies. A calculation by Green and Schwartz in Aspen
(1984?) during a thunderstorm showed that the number of gravitational
anomalies, 496, exactly equaled the Yang Mills Anomalies at 496. That
meant that the theory was consistent. The calculation shown was far
too complicated for anyone but an expert to follow. Still, it was
perhaps the most satisfying because it looked like two very complicated
calculations were used to test the theory, and it passed a tough test.
The only partial equation to appear on the third episode was one of
Witten's from String 95 where he unified the 5 string theories:
G^{10} = e^-\gammaI = 1/2 \Int d^{10} x g^(1/2) e^-3 \gamma R ...
The partial doodle had little impact on me, although it rocked the
meeting. That d^{10} means the theory is in ten dimensions. To be
beautiful requires to be seen. String theorist try to sell the idea
that the six or seven hidden dimensions are part of a beautiful,
mind-expanding concept. The compactification proposal is hollow for me
because I will never be able to visit. Being there is a key to the
appreciation of beauty.
At this time I do not find string theory beautiful or elegant. The
equations look too complicated. That may be because Nature is that
way, but I remain skeptical (in a positive sense of the word,
respecting this body of work while hoping for something better). I
support the continued funding because the peer review process continues
to find there are avenues worth exploring.
doug
quaternions.com
Franz Heymann
Jul25-04, 08:16 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>\n\n\n\n"Michael Varney" <varney@colorado_no_spam.edu> wrote in message\nnews:cmQLc.19\\$Xt6.5081@news.uswest.net. ..\n>\n> "backdoorstudent" <backdoorstudent@yahoo.com> wrote in message\n> news:750f5e99.0407211611.61f734a6@posting.google.c om...\n> >\n> > I ask this seriously and respectfully. And I apologize if it seems\n> > like a troll. I always feel uncomfortable when I hear physicists\nmake\n> > statements about beauty. Who here thinks reality is ugly?\n> > Interestingly, I do not hear mathematicians speak like this as\noften\n> > as I do physicists. So what is it that string theorists find so\n> > beautiful? Brian Greene did not convey it to me. Sorry and thanks.\n>\n> Beauty is in the eye of the beholder... a truism that applies to\nphysicists\n> as well.\n> Reality is ugly in many cases.\n>\n> However, the mathematical description of reality is considered\nbeautiful\n> when it is concise, succinct, simple and encompassing.\n>\n> String theory is beautiful in its potential to unify physics... no\n> adjustable parameters.\n\nAnd no testable predictions?\n\nFranz\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>"Michael Varney" <varney@colorado_no_spam.edu> wrote in message
news:cmQLc.19$Xt6.5081@news.uswest.net...
>
> "backdoorstudent" <backdoorstudent@yahoo.com> wrote in message
> news:750f5e99.0407211611.61f734a6@posting.google.c om...
> >
> > I ask this seriously and respectfully. And I apologize if it seems
> > like a troll. I always feel uncomfortable when I hear physicists
make
> > statements about beauty. Who here thinks reality is ugly?
> > Interestingly, I do not hear mathematicians speak like this as
often
> > as I do physicists. So what is it that string theorists find so
> > beautiful? Brian Greene did not convey it to me. Sorry and thanks.
>
> Beauty is in the eye of the beholder... a truism that applies to
physicists
> as well.
> Reality is ugly in many cases.
>
> However, the mathematical description of reality is considered
beautiful
> when it is concise, succinct, simple and encompassing.
>
> String theory is beautiful in its potential to unify physics... no
> adjustable parameters.
And no testable predictions?
Franz
Thomas Larsson
Jul27-04, 07:52 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nPeter Woit <woit@cpw.math.columbia.edu> wrote in message news:<cdohtu\\$siv\\$1@newsmaster.cc.columbia.edu> ...\n\n> 2d QFT is a fantastic subject, with a lot of examples of beauty and\n> elegance. Often you can write down a very simple 2d QFT, and show\n> that it has a huge amount of very deep and surprising mathematical\n> strucure. Unfortunately these structures don\'t seem to have anything\n> to do with the real world. None of the most beautiful aspects of\n> CFT explain anything about the world,\n\nActually, CFT explains just everything there is to know about phase\ntransitions in 2D. Soft condensed matter is not particle physics, but\nit is certainly part of the real world. Although people usually\ncompare CFT results to computer simulations or exact solutions,\nreal laboratory experiments have been done - a monolayer of argon\natoms on an inert graphite substrate seems to be a favorite system.\n\nSo even if string theory is wrong, the beauty of CFT is not wasted.\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>Peter Woit <woit@cpw.math.columbia.edu> wrote in message news:<cdohtu$siv$1@newsmaster.cc.columbia.edu>...
> 2d QFT is a fantastic subject, with a lot of examples of beauty and
> elegance. Often you can write down a very simple 2d QFT, and show
> that it has a huge amount of very deep and surprising mathematical
> strucure. Unfortunately these structures don't seem to have anything
> to do with the real world. None of the most beautiful aspects of
> CFT explain anything about the world,
Actually, CFT explains just everything there is to know about phase
transitions in 2D. Soft condensed matter is not particle physics, but
it is certainly part of the real world. Although people usually
compare CFT results to computer simulations or exact solutions,
real laboratory experiments have been done - a monolayer of argon
atoms on an inert graphite substrate seems to be a favorite system.
So even if string theory is wrong, the beauty of CFT is not wasted.
Esa A E Peuha
Jul28-04, 03:58 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>\n\nPeter Woit <woit@cpw.math.columbia.edu> writes:\n\n> 2. As long as you don\'t know what string theory really is, you can\n> keep hoping that it is something truly wonderful and beautiful. The\n> beautiful, elegant theory that string theorists often are referring to\n> is the one they hope exists. Two of Witten\'s definitions of the "M"\n> in M-theory are "Mystery" and "Magic". Much of the beauty of\n> M-theory is the beauty of mystery, of something you don\'t understand\n> that you invest with your hopes and dreams.\n\nThis reminds me a lot about how mathematicians couldn\'t find a way to do\nsome constructions with compass and ruler (trisecting an angle, squaring\na circle, halving a cube) but were convinced that those constructions\nwould turn out to be extremely beautiful and elegant once thay were\ndiscovered. The only problem was that those constructions are provably\nimpossible. I hope the obvious analogy to string theory isn\'t true...\n\n--\nEsa Peuha\nstudent of mathematics at the University of Helsinki\nhttp://www.helsinki.fi/~peuha/\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>Peter Woit <woit@cpw.math.columbia.edu> writes:
> 2. As long as you don't know what string theory really is, you can
> keep hoping that it is something truly wonderful and beautiful. The
> beautiful, elegant theory that string theorists often are referring to
> is the one they hope exists. Two of Witten's definitions of the "M"
> in M-theory are "Mystery" and "Magic". Much of the beauty of
> M-theory is the beauty of mystery, of something you don't understand
> that you invest with your hopes and dreams.
This reminds me a lot about how mathematicians couldn't find a way to do
some constructions with compass and ruler (trisecting an angle, squaring
a circle, halving a cube) but were convinced that those constructions
would turn out to be extremely beautiful and elegant once thay were
discovered. The only problem was that those constructions are provably
impossible. I hope the obvious analogy to string theory isn't true...
--
Esa Peuha
student of mathematics at the University of Helsinki
http://www.helsinki.fi/~peuha/
Danny Ross Lunsford
Jul29-04, 04:59 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>\n\n\nbackdoorstudent@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.0407211611.61f734a6@posting.google. com>...\n> I ask this seriously and respectfully. And I apologize if it seems\n> like a troll. I always feel uncomfortable when I hear physicists make\n> statements about beauty. Who here thinks reality is ugly?\n> Interestingly, I do not hear mathematicians speak like this as often\n> as I do physicists. So what is it that string theorists find so\n> beautiful? Brian Greene did not convey it to me. Sorry and thanks.\n\nThe beauty in physics is "operational" - by this I mean, the thing\nprogresses by stages, with an old theory settling into a new one in an\nextremely unexpected way that involves bringing in new mathematical\nideas. The end result is usually *simpler* on a conceptual level - and\nthe mathematical expression is usually "tighter", less dependent on\narbitrary assumptions, involving fewer ambiguous objects. The key\npoint is simplification. If we have a complex algebraic expression to\nsimplify, then there is a satisfaction in canceling this and that and\narriving at a simple expression. The same thing happens on a much more\nintense level in physics - to take the example of electrodynamics,\nhere were these two related but self-standing theories, one of magnets\nand the other of currents and charges - by introducing relativity they\nmagically coalesce into a single theory of a new thing, the EM field.\nThis in turn allows one to see the real physical principle in stark\nsimplicity - the conservation of charge. It\'s easy to imagine that the\nintroduction of spacetime and the seeming paradoxes of relativity make\nthings *more* complex, but that\'s not so at all - the final theory is\nfar simpler than the originals, and the apparent complexity is just an\nartifact of trying to interpret the new thing in the old context. The\nsimplification itself gives rise to a new context. It\'s the\nrecognition of the new context that is the "kicker", the "wow" factor\nthat impresses the mind.\n\nThe really huge advances are all like this. If something doesn\'t have\nan immediately perceptible new context along with some kind of\ndramatic simplication of a once thorny issue, then it is not likely to\nbe a fundamental advance.\n\nNote that math is not at all like this (IMO) - math gets more\nbeautiful with generalization, while physics gets more beautiful by\ngetting ever more specific and focused. That is why the exclusively\nmathematical approach to physics, that is, attempts at generalization\nof previous work, rarely succeed (Feynman) - to get to the\nsimplifications requires intuitive leaps that are, in hindsight,\nalmost obvious.\n\nAlso note that "revolutions" in physical thought are fictions. Physics\nis very "evolutionary" - the new develops gradually out of the old, in\nspite of the triumphalist titles given to popularizations. Again (IMO)\nthis is not at all like math - in math brand new things really are\nsometimes just invented on the spot and create a brand new context\nwithout an earlier referent.\n\n-drl\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>backdoorstudent@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.0407211611.61f734a6@posting.google.com>...
> I ask this seriously and respectfully. And I apologize if it seems
> like a troll. I always feel uncomfortable when I hear physicists make
> statements about beauty. Who here thinks reality is ugly?
> Interestingly, I do not hear mathematicians speak like this as often
> as I do physicists. So what is it that string theorists find so
> beautiful? Brian Greene did not convey it to me. Sorry and thanks.
The beauty in physics is "operational" - by this I mean, the thing
progresses by stages, with an old theory settling into a new one in an
extremely unexpected way that involves bringing in new mathematical
ideas. The end result is usually *simpler* on a conceptual level - and
the mathematical expression is usually "tighter", less dependent on
arbitrary assumptions, involving fewer ambiguous objects. The key
point is simplification. If we have a complex algebraic expression to
simplify, then there is a satisfaction in canceling this and that and
arriving at a simple expression. The same thing happens on a much more
intense level in physics - to take the example of electrodynamics,
here were these two related but self-standing theories, one of magnets
and the other of currents and charges - by introducing relativity they
magically coalesce into a single theory of a new thing, the EM field.
This in turn allows one to see the real physical principle in stark
simplicity - the conservation of charge. It's easy to imagine that the
introduction of spacetime and the seeming paradoxes of relativity make
things *more* complex, but that's not so at all - the final theory is
far simpler than the originals, and the apparent complexity is just an
artifact of trying to interpret the new thing in the old context. The
simplification itself gives rise to a new context. It's the
recognition of the new context that is the "kicker", the "wow" factor
that impresses the mind.
The really huge advances are all like this. If something doesn't have
an immediately perceptible new context along with some kind of
dramatic simplication of a once thorny issue, then it is not likely to
be a fundamental advance.
Note that math is not at all like this (IMO) - math gets more
beautiful with generalization, while physics gets more beautiful by
getting ever more specific and focused. That is why the exclusively
mathematical approach to physics, that is, attempts at generalization
of previous work, rarely succeed (Feynman) - to get to the
simplifications requires intuitive leaps that are, in hindsight,
almost obvious.
Also note that "revolutions" in physical thought are fictions. Physics
is very "evolutionary" - the new develops gradually out of the old, in
spite of the triumphalist titles given to popularizations. Again (IMO)
this is not at all like math - in math brand new things really are
sometimes just invented on the spot and create a brand new context
without an earlier referent.
-drl
Lubos Motl
Oct24-04, 05:52 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>On Sun, 24 Oct 2004, backdoorstudent wrote:\n\n> What\'s so "beautiful" or "elegant" about string theory?\n>\n> I ask this seriously and respectfully. And I apologize if it seems\n> like a troll. I always feel uncomfortable when I hear physicists make\n> statements about beauty. Who here thinks reality is ugly?\n> Interestingly, I do not hear mathematicians speak like this as often\n> as I do physicists. So what is it that string theorists find so\n> beautiful? Brian Greene did not convey it to me. Sorry and thanks.\n\nOf course, I don\'t believe that if Brian failed, I can succeed. ;-) The\nfeeling of beauty in physics is something caused by very objective and\nrational properties of the physical theory, but finally it is an emotional\nfeeling, and if someone just does not have these emotions, it\'s hard to\nconvey them.\n\nBut let me try to answer it anyway.\n\nThe issue of beauty in theoretical physics is very subtle.\n\nFirst of all, the laws behind the Universe are not dumb. If a physicist\ntalks about beauty, she never thinks about "simplicity" of the kind that\nan average teenager who hates math classes at school might appreciate. The\nUniverse is not that simple, and its rules just can\'t be dumb.\n\nAs Einstein said, the laws of the Universe should be as simple as\npossible, but not more.\n\nIn physics, this naive notion of simplicity is often replaced by symmetry.\nSymmetry has something to do with beauty, and it is something that\nconstrains the physical system. If your face has a symmetry, you need to\nknow 1/2 of it only. If a theory respects some symmetries, it proves that\nit is special among other conceivable theories.\n\nIn older theories than string theory, some symmetries must be assumed, and\nthis reduces the number of free parameters and arbitrariness. For example,\nthe Standard Model has less than 30 parameters that describe the strength\nof various interactions (and masses) that are compatible with the given\nsymmetries. In this counting, string theory is maximally constrained - it\nhas no adjustable parameters. One of the first justifications of beauty.\n\nThere are many types of symmetries known in physics - rotational symmetry,\nU(1), SU(2), or SU(3) gauge symmetry, E_8 symmetry, supersymmetry,\nconformal symmetry, and so forth. All of them can be found in string\ntheory, but they always seem to be tiny reflections of something much more\nbeautiful. String theory is something that can start as a small package,\nhowever a package that contains so much good stuff. Moreover, the\nsymmetries can transmute into each other as you walk along the stringy\n"landscape" (I mean moduli space). They can be spontaneously broken,\nunbroken, enhanced, confined.\n\nSymmetric theories don\'t necessarily have to be simple, in the naive\nsense. Eleven-dimensional supergravity is, in some sense, the most\n(super)symmetric field theory, but its Lagrangian is pretty long. A real\nphysicist does not care whether it\'s long or not; a physicist is always\nready to spend an hour by writing a Lagrangian. That\'s not a big deal for\nher, and such superficial questions as time and money don\'t matter. The\nbeauty inside is more important, and eleven-dimensional supergravity has\n32 supersymmetries and other symmetries. There is no rule that beautiful\nobjects must fit one line.\n\nEleven-dimensional supergravity is a part of string theory, a low-energy\nlimit of M-theory in 11 dimensions. There are many potentially beautiful\ntheories in physics, and all of the good ones seem to be connected within\nstring theory. This union is not artificial, and it is another reason that\nmakes it beautiful. You usually find out that string theory can have\nmoduli (exactly massless scalar fields, some sort of dynamical\nparameters), and as you change them, the different theories with different\nsymmetries transform into one another in an exactly controllable and\nunique way.\n\nNevertheless, I don\'t really think that we view the symmetries as the most\nimportant reason why string theory is beautiful. Maybe string theory\'s\npower to naturally include all types of essential and "rigid" physical\nphenomena and derive them from a modest starting point may be a more\naccurate reason behind our claims about "beauty" in string theory. Of\ncourse, this point will not be appreciated by an enemy of reductionism. ;-)\n\nIf someone is not impressed by the fact that a formula (e.g. the\nLagrangian of QED) can explain a large number of physical situations,\nincluding chemistry and animals, as well as the sunset, she can never\nunderstand why the physicists think that string theory is beautiful. From\nthis perspective, string theory is the most advanced achievement of\nreductionism - everything is included in a theory that uniquely and\nnaturally follows from the assumption of a one-dimensional object with\nmeaningful interactions (or from other possible starting points, and\nstring theory now has many). The elementary particles and interactions of\nthe Standard Model are reduced to something even more fundamental -\nsomething that probably cannot be reduced further.\n\nBut I believe that one thing is perhaps even more important for the beauty\nof string theory: the way how it avoids all potential problems.\n\nIf you "glue" a random theory of some type and you try to quantize it, you\nwill be led to many different kinds of diseases that will make the quantum\ntheory unusable. Classical symmetries will be destroyed by quantum effects\n(anomalies). Physical quantities will be expressed by divergent integrals,\nand sometimes the divergences cannot be eliminated, even if you use the\nbest tricks (non-renormalizable theories).\n\nAll these problems always miraculously disappear in string theory. It\'s\nlike in a good movie that keeps you excited, nervous, but eventually leads\nto an unexpected (but reasonable) happy end. It\'s like the Superman who\ncan save the city in time by an unexpected move - except that in string\ntheory, you can prove that these unlikely events are *facts*. You may want\nto invent an "easier" approach than string theory to make the integrals\nconvergent, but such choices will always introduce new problems - such as\nanomalies (or more generally, some breaking of gauge symmetries). String\ntheory just seems to be the only framework where all these problems -\nanomalies and divergences - are avoided. It\'s the only movie with a real\nhappy end. Also, you must think for a while to see why the end is really\nhappy - string theory is not like the cheap movies. It requires you to\nthink, and the beauty can only be appreciated if it works through your\nmind for some time.\n\nPeter Woit finds it unacceptable to work with more than 4 coordinates, so\nhe will prefer movie directors that claim that a movie should only contain\n4 points. He may like these movies, but they are really cheap movies. You\nknow that good movies should really have several dimensions. The movie of\nstring theory is 10 or 11-dimensional, depending on the way how you look\nat it. ;-) Yes, the higher-dimensional geometry itself is beautiful, too.\nIt\'s what distinguishes a sophisticated 3D sculpture from a naive 2D\ncartoon.\n\nBut let me return to the miraculous power of string/M-theory to eliminate\ninconsistencies.\n\nWhat we\'re thinking about is the infinite ocean of "ugly" theories. Each\nof them suffers from a problem. And string/M-theory marches on an\ninfinitely thin road (or string) stretched above this ocean, and its\ncalculations always miraculously combine in such a way that the\npredictions are unique, and they fit together. The detailed features are\nalways "right" so that the result makes sense, even though a single\n"error" would make the theory meaningless.\n\nFinally, string theory is beautiful because of dualities. Take five things\nthat you like - for example, your girlfriend, your favorite bird, a\nphotograph with a sunset above the ocean, your favorite food in a French\nrestaurant, and your new car. ;-) Now imagine an object ST that can be\nobserved from five different directions, or in five different ways of\nthinking. From one vantage point, it will look like your girlfriend, and\nso forth.\n\nYou may think that it is impossible - if something looks like your\ngirlfriend from the left, it can\'t look like a car from another direction.\nSomeone may come with a similar argument in string theory. Nevertheless\nstring theory always brings a set of miracles that make these different\npictures compatible, and therefore it can look like five (or more)\ndifferent beautiful things simultaneously.\n\nString theory is able to change an object to a different object or\nphenomenon smoothly; it is free of any unpredictable singularities. Every\ntime something becomes too singular or sharp and one starts to be afraid\nthat a disaster is looming, string theory always predicts some new objects\nand phenomena that regularize physics and make it as smooth as before.\n\nOK, the beauty is a combination of symmetries and their interplays\n(something that Einstein knows well from his theories of relativity, and\nsomething that underlies the Standard Model too); inevitability and\nuniqueness of the predictions; cancellation of divergences and anomalies\nand the unexpected character of these cancelations; equivalences between\ndifferent ways to look at the theory that eventually turn out to be\ntotally compatible; its natural unification of virtually all other\nimportant phenomena and concepts in quantum field theory and general\nrelativity; its connections to structures in mathematics that are also\ncalled "beautiful" - for example those associated with higher-dimensional\ngeometry (mirror symmetry).\n\nYes, some mathematicians do not talk about "beauty" as often - many of\nthem, in fact, really enjoy if their research is really dry. ;-)\n_______________________________________________ _______________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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>On Sun, 24 Oct 2004, backdoorstudent wrote:
> What's so "beautiful" or "elegant" about string theory?
>
> I ask this seriously and respectfully. And I apologize if it seems
> like a troll. I always feel uncomfortable when I hear physicists make
> statements about beauty. Who here thinks reality is ugly?
> Interestingly, I do not hear mathematicians speak like this as often
> as I do physicists. So what is it that string theorists find so
> beautiful? Brian Greene did not convey it to me. Sorry and thanks.
Of course, I don't believe that if Brian failed, I can succeed. ;-) The
feeling of beauty in physics is something caused by very objective and
rational properties of the physical theory, but finally it is an emotional
feeling, and if someone just does not have these emotions, it's hard to
convey them.
But let me try to answer it anyway.
The issue of beauty in theoretical physics is very subtle.
First of all, the laws behind the Universe are not dumb. If a physicist
talks about beauty, she never thinks about "simplicity" of the kind that
an average teenager who hates math classes at school might appreciate. The
Universe is not that simple, and its rules just can't be dumb.
As Einstein said, the laws of the Universe should be as simple as
possible, but not more.
In physics, this naive notion of simplicity is often replaced by symmetry.
Symmetry has something to do with beauty, and it is something that
constrains the physical system. If your face has a symmetry, you need to
know 1/2 of it only. If a theory respects some symmetries, it proves that
it is special among other conceivable theories.
In older theories than string theory, some symmetries must be assumed, and
this reduces the number of free parameters and arbitrariness. For example,
the Standard Model has less than 30 parameters that describe the strength
of various interactions (and masses) that are compatible with the given
symmetries. In this counting, string theory is maximally constrained - it
has no adjustable parameters. One of the first justifications of beauty.
There are many types of symmetries known in physics - rotational symmetry,
U(1), SU(2), or SU(3) gauge symmetry, E_8 symmetry, supersymmetry,
conformal symmetry, and so forth. All of them can be found in string
theory, but they always seem to be tiny reflections of something much more
beautiful. String theory is something that can start as a small package,
however a package that contains so much good stuff. Moreover, the
symmetries can transmute into each other as you walk along the stringy
"landscape" (I mean moduli space). They can be spontaneously broken,
unbroken, enhanced, confined.
Symmetric theories don't necessarily have to be simple, in the naive
sense. Eleven-dimensional supergravity is, in some sense, the most
(super)symmetric field theory, but its Lagrangian is pretty long. A real
physicist does not care whether it's long or not; a physicist is always
ready to spend an hour by writing a Lagrangian. That's not a big deal for
her, and such superficial questions as time and money don't matter. The
beauty inside is more important, and eleven-dimensional supergravity has
32 supersymmetries and other symmetries. There is no rule that beautiful
objects must fit one line.
Eleven-dimensional supergravity is a part of string theory, a low-energy
limit of M-theory in 11 dimensions. There are many potentially beautiful
theories in physics, and all of the good ones seem to be connected within
string theory. This union is not artificial, and it is another reason that
makes it beautiful. You usually find out that string theory can have
moduli (exactly massless scalar fields, some sort of dynamical
parameters), and as you change them, the different theories with different
symmetries transform into one another in an exactly controllable and
unique way.
Nevertheless, I don't really think that we view the symmetries as the most
important reason why string theory is beautiful. Maybe string theory's
power to naturally include all types of essential and "rigid" physical
phenomena and derive them from a modest starting point may be a more
accurate reason behind our claims about "beauty" in string theory. Of
course, this point will not be appreciated by an enemy of reductionism. ;-)
If someone is not impressed by the fact that a formula (e.g. the
Lagrangian of QED) can explain a large number of physical situations,
including chemistry and animals, as well as the sunset, she can never
understand why the physicists think that string theory is beautiful. From
this perspective, string theory is the most advanced achievement of
reductionism - everything is included in a theory that uniquely and
naturally follows from the assumption of a one-dimensional object with
meaningful interactions (or from other possible starting points, and
string theory now has many). The elementary particles and interactions of
the Standard Model are reduced to something even more fundamental -
something that probably cannot be reduced further.
But I believe that one thing is perhaps even more important for the beauty
of string theory: the way how it avoids all potential problems.
If you "glue" a random theory of some type and you try to quantize it, you
will be led to many different kinds of diseases that will make the quantum
theory unusable. Classical symmetries will be destroyed by quantum effects
(anomalies). Physical quantities will be expressed by divergent integrals,
and sometimes the divergences cannot be eliminated, even if you use the
best tricks (non-renormalizable theories).
All these problems always miraculously disappear in string theory. It's
like in a good movie that keeps you excited, nervous, but eventually leads
to an unexpected (but reasonable) happy end. It's like the Superman who
can save the city in time by an unexpected move - except that in string
theory, you can prove that these unlikely events are *facts*. You may want
to invent an "easier" approach than string theory to make the integrals
convergent, but such choices will always introduce new problems - such as
anomalies (or more generally, some breaking of gauge symmetries). String
theory just seems to be the only framework where all these problems -
anomalies and divergences - are avoided. It's the only movie with a real
happy end. Also, you must think for a while to see why the end is really
happy - string theory is not like the cheap movies. It requires you to
think, and the beauty can only be appreciated if it works through your
mind for some time.
Peter Woit finds it unacceptable to work with more than 4 coordinates, so
he will prefer movie directors that claim that a movie should only contain
4 points. He may like these movies, but they are really cheap movies. You
know that good movies should really have several dimensions. The movie of
string theory is 10 or 11-dimensional, depending on the way how you look
at it. ;-) Yes, the higher-dimensional geometry itself is beautiful, too.
It's what distinguishes a sophisticated 3D sculpture from a naive 2D
cartoon.
But let me return to the miraculous power of string/M-theory to eliminate
inconsistencies.
What we're thinking about is the infinite ocean of "ugly" theories. Each
of them suffers from a problem. And string/M-theory marches on an
infinitely thin road (or string) stretched above this ocean, and its
calculations always miraculously combine in such a way that the
predictions are unique, and they fit together. The detailed features are
always "right" so that the result makes sense, even though a single
"error" would make the theory meaningless.
Finally, string theory is beautiful because of dualities. Take five things
that you like - for example, your girlfriend, your favorite bird, a
photograph with a sunset above the ocean, your favorite food in a French
restaurant, and your new car. ;-) Now imagine an object ST that can be
observed from five different directions, or in five different ways of
thinking. From one vantage point, it will look like your girlfriend, and
so forth.
You may think that it is impossible - if something looks like your
girlfriend from the left, it can't look like a car from another direction.
Someone may come with a similar argument in string theory. Nevertheless
string theory always brings a set of miracles that make these different
pictures compatible, and therefore it can look like five (or more)
different beautiful things simultaneously.
String theory is able to change an object to a different object or
phenomenon smoothly; it is free of any unpredictable singularities. Every
time something becomes too singular or sharp and one starts to be afraid
that a disaster is looming, string theory always predicts some new objects
and phenomena that regularize physics and make it as smooth as before.
OK, the beauty is a combination of symmetries and their interplays
(something that Einstein knows well from his theories of relativity, and
something that underlies the Standard Model too); inevitability and
uniqueness of the predictions; cancellation of divergences and anomalies
and the unexpected character of these cancelations; equivalences between
different ways to look at the theory that eventually turn out to be
totally compatible; its natural unification of virtually all other
important phenomena and concepts in quantum field theory and general
relativity; its connections to structures in mathematics that are also
called "beautiful" - for example those associated with higher-dimensional
geometry (mirror symmetry).
Yes, some mathematicians do not talk about "beauty" as often - many of
them, in fact, really enjoy if their research is really dry. ;-)
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Doug Sweetser
Oct28-04, 01:29 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>\n\n\nHello Lubos:\n\n> On Sun, 24 Oct 2004, backdoorstudent wrote:\n>\n>> What\'s so "beautiful" or "elegant" about string theory?\n\nI bought the DVD and looked for the elegant equations. The few I found\ndid not make a strong case for the thesis.\n\n\n> First of all, the laws behind the Universe are not dumb.\n\nPerhaps instead of "dumb", backdoorstudent should have said something\nabout "no thought involved" or "necessarily automatic". Fundamental\nparticles are labeled that due to their simplicity. We don\'t understand\nall the rules or logic, but no particles are making tricky calculations\nvery rapidly.\n\n\n> If someone is not impressed by the fact that a formula (e.g. the\n> Lagrangian of QED) can explain a large number of physical situations,\n> including chemistry and animals, as well as the sunset, she can never\n> understand why the physicists think that string theory is beautiful.\n\nFor me, the focus should be on Lagrange densities, so lets write out\nexplicitly some that are gorgeous. Here is the Lagrange density for\ngeneral relativity in a vacuum:\n\nL = (-g)^(1/2) R\n\nwhere\ng is the determinant of the metric tensor\nR is the Ricci scalar\n\nVary the action with respect to the metric tensor, and Einstein\'s field\nequations results. It is all about the how the connection varies,\nthere is nothing else. There is a problem of completeness, or\nconnections to other aspects of physics, because this metric is only\nabout how spacetime geometry changes.\n\nCase two, already cited, EM, but I\'ll do the classical form in a vacuum:\n\nL = -(d^u A^v - d^v A^u)(d_u A_v - d_v A_u)\n\nVary the action with respect to the potential and you get the Maxwell\nequations in a vacuum. It is all about the potential. Because this\ntensor uses the exterior derivative, it is silent on the connection,\nhow the metric changes. This is why the metric and connection must be\nsupplied to solve any problems in EM, although a flat metric and a\nconnection that is torsion-free and metric compatible is usually\nassumed (nothing dictates this must be so).\n\nI am one of the few people posting to the newsgroup to write out the\nstandard model Lagrange density explicitly. Here it is again:\n\nL = g_mu_nu phi* gamma^mu D^nu phi\n\nwhere D^nu = d^nu - i k_EM Y/2 A^nu - i k_weak tau^i/2 W^i^nu\n- i k_strong lambda^j/2 G^j^nu\ni goes from 1-3, j from 1-8\nk_EM, k_weak, and k_strong are coupling constants.\nY, tau^i, and lambda^j generate U(1), SU(2), and SU(3).\nA^nu, W^i^nu, and G^j^nu are potentials.\n\nDifferent symmetries are brought in in similar fashion. The aspect that\nfeels incomplete is why Nature decided to use U(1), SU(2), and SU(3)\nbut not some other combination. Still, who can argue with success?\n\nSo Lubos, that brings me to a question for you. I would like to see one\nof these "pretty long" Lagrangians in 11 dimensions. Please try to\nlabel all the parts that go into it as I did for the standard model\nLagrangian. I realize this is an ongoing area of research, so there is\nno consensus on which particular one to write out, I just would like to\nsee one of the 11D Lagrange densities as part of my continuing\neducation in string theory.\n\n\ndoug\nquaternions.com\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>Hello Lubos:
> On Sun, 24 Oct 2004, backdoorstudent wrote:
>
>> What's so "beautiful" or "elegant" about string theory?
I bought the DVD and looked for the elegant equations. The few I found
did not make a strong case for the thesis.
> First of all, the laws behind the Universe are not dumb.
Perhaps instead of "dumb", backdoorstudent should have said something
about "no thought involved" or "necessarily automatic". Fundamental
particles are labeled that due to their simplicity. We don't understand
all the rules or logic, but no particles are making tricky calculations
very rapidly.
> If someone is not impressed by the fact that a formula (e.g. the
> Lagrangian of QED) can explain a large number of physical situations,
> including chemistry and animals, as well as the sunset, she can never
> understand why the physicists think that string theory is beautiful.
For me, the focus should be on Lagrange densities, so lets write out
explicitly some that are gorgeous. Here is the Lagrange density for
general relativity in a vacuum:
L = (-g)^(1/2) R
where
g is the determinant of the metric tensor
R is the Ricci scalar
Vary the action with respect to the metric tensor, and Einstein's field
equations results. It is all about the how the connection varies,
there is nothing else. There is a problem of completeness, or
connections to other aspects of physics, because this metric is only
about how spacetime geometry changes.
Case two, already cited, EM, but I'll do the classical form in a vacuum:
L = -(d^u A^v - d^v A^u)(d_u A_v - d_v A_u)
Vary the action with respect to the potential and you get the Maxwell
equations in a vacuum. It is all about the potential. Because this
tensor uses the exterior derivative, it is silent on the connection,
how the metric changes. This is why the metric and connection must be
supplied to solve any problems in EM, although a flat metric and a
connection that is torsion-free and metric compatible is usually
assumed (nothing dictates this must be so).
I am one of the few people posting to the newsgroup to write out the
standard model Lagrange density explicitly. Here it is again:
L = g_{mu_nu} \phi* \gamma^\mu D^\nu \phi
where D^\nu = d^\nu - i k_{EM} Y/2 A^\nu - i k_{weak} \tau^i/2 W^i^\nu- i k_{strong} \lambda^j/2 G^j^\nu
i goes from 1-3, j from 1-8
k_{EM}, k_{weak}, and k_{strong} are coupling constants.
Y, \tau^i, and \lambda^j generate U(1), SU(2), and SU(3).
A^\nu, W^i^\nu, and G^j^\nu are potentials.
Different symmetries are brought in in similar fashion. The aspect that
feels incomplete is why Nature decided to use U(1), SU(2), and SU(3)
but not some other combination. Still, who can argue with success?
So Lubos, that brings me to a question for you. I would like to see one
of these "pretty long" Lagrangians in 11 dimensions. Please try to
label all the parts that go into it as I did for the standard model
Lagrangian. I realize this is an ongoing area of research, so there is
no consensus on which particular one to write out, I just would like to
see one of the 11D Lagrange densities as part of my continuing
education in string theory.
doug
quaternions.com
backdoorstudent
Oct29-04, 02:07 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>\n\n\n\nDoug Sweetser <sweetser@alum.mit.edu> wrote in message news:<clqlfl\\$7a1\\$1@pcls4.std.com>...\n> Hello Lubos:\n>\n> > On Sun, 24 Oct 2004, backdoorstudent wrote:\n> >\n> >> What\'s so "beautiful" or "elegant" about string theory?\n>\n> I bought the DVD and looked for the elegant equations. The few I found\n> did not make a strong case for the thesis.\n>\n>\n> > First of all, the laws behind the Universe are not dumb.\n>\n> Perhaps instead of "dumb", backdoorstudent should have said something\n> about "no thought involved" or "necessarily automatic".\n\nI never said any such thing; that was Lubos putting words in my mouth.\nNevertheless, I would say that it\'s dumb to call the laws of nature\ndumb (or smart).\n\nIf my opinion matters, -it doesn\'t, yet I cannot resist sharing it:)-\nit is that the laws of the universe are completely indifferent to our\npresumptions of beauty. Physicists love to romanticize about their\nsense of beauty leading the way and repeatedly quote and make\nreference to Einstein and his intellectual methods to support this\nthesis. But the history of science reflects a much more mundane and\ntortured endeavor based mostly on curiosity and common sense rather\nthan aesthetics. This is what leads me to feel that all this blather\nabout beauty and elegance is nothing more than pontification.\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>Doug Sweetser <sweetser@alum.mit.edu> wrote in message news:<clqlfl$7a1$1@pcls4.std.com>...
> Hello Lubos:
>
> > On Sun, 24 Oct 2004, backdoorstudent wrote:
> >
> >> What's so "beautiful" or "elegant" about string theory?
>
> I bought the DVD and looked for the elegant equations. The few I found
> did not make a strong case for the thesis.
>
>
> > First of all, the laws behind the Universe are not dumb.
>
> Perhaps instead of "dumb", backdoorstudent should have said something
> about "no thought involved" or "necessarily automatic".
I never said any such thing; that was Lubos putting words in my mouth.
Nevertheless, I would say that it's dumb to call the laws of nature
dumb (or smart).
If my opinion matters, -it doesn't, yet I cannot resist sharing it:)-
it is that the laws of the universe are completely indifferent to our
presumptions of beauty. Physicists love to romanticize about their
sense of beauty leading the way and repeatedly quote and make
reference to Einstein and his intellectual methods to support this
thesis. But the history of science reflects a much more mundane and
tortured endeavor based mostly on curiosity and common sense rather
than aesthetics. This is what leads me to feel that all this blather
about beauty and elegance is nothing more than pontification.
Lubos Motl
Oct30-04, 05:16 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>On Fri, 29 Oct 2004, backdoorstudent wrote:\n\n> backdoorstudent: What\'s so "beautiful" or "elegant" about string theory?\n>\n> > Lubos Motl: First of all, the laws behind the Universe are not dumb.\n>\n> backdoorstudent: I never said any such thing; that was Lubos putting\n> words in my mouth. Nevertheless, I would say that it\'s dumb to call the\n> laws of nature dumb (or smart).\n\nI was also surprised when someone confiscated my quote. ;-) Incidentally,\nthe laws of Nature are pretty smart, and it\'s dumb if someone does not see\nit, and even more dumb if someone says that they are *not* smart. They are\nsmarter than we are, and string theory seems to be smarter yet.\n\nI was not putting anything in your mouth. Instead, I was seriously writing\nan important fact about the physical laws - and the only relation to you\nis that I was trying to answer your question "What\'s beauty in physics and\nstring theory". Sorry for any potential contributions of mine to the\nmisunderstanding.\n\nThe context of my sentence was that the laws of physics are not "simple"\nin the naive sense - i.e. simple from the viewpoint of a teenager who\nhates math. The beauty of the laws of Nature requires some intelligence\nand research to be appreciated.\n\n> If my opinion matters, -it doesn\'t, yet I cannot resist sharing it:)-\n> it is that the laws of the universe are completely indifferent to our\n> presumptions of beauty.\n\nI agree with that. They are indifferent - and they are beautiful. ;-)\n\n> Physicists love to romanticize about their\n> sense of beauty leading the way and repeatedly quote and make\n> reference to Einstein and his intellectual methods to support this\n> thesis.\n\nRight. Einstein, Dirac, and others were the people who started to\nemphasize beauty of the physical laws, and all of us are just followers,\nin a sense. But of course, it\'s not quite the same type of beauty that\nartists appreciate and create - or the beauty of women that attracts men.\n\nThe beauty of the laws of Nature is a very rational thing - at the very\nend, XY\'s statement that the laws are beautiful really means that the laws\nmake sense to XY, and they fit together, and XY sort of understands them\nand can remember them - much like a smooth shape of a beautiful object (or\nsubject). The other people, those who do *not* understand the laws of\nNature, also don\'t appreciate their beauty. As long as something looks\nconvoluted and unnatural to me, I won\'t say that it\'s beautiful.\n\n> But the history of science reflects a much more mundane and\n> tortured endeavor based mostly on curiosity and common sense rather\n> than aesthetics. This is what leads me to feel that all this blather\n> about beauty and elegance is nothing more than pontification.\n\nYou don\'t seem to appreciate how amazing it is that the world satisfies\nsome simple enough comprehensible laws at all. Einstein said that the most\nincomprehensible thing about the world is that it is comprehensible. If\nthe laws of Nature were something that a theoretical physicist would call\n"ugly", it would be pretty difficult to find out how they exactly work -\nbecause this "ugliness" really means that the theories would not be\nrobust, and there would be too many arbitrary components in them.\n___________________________________________ ___________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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>On Fri, 29 Oct 2004, backdoorstudent wrote:
> backdoorstudent: What's so "beautiful" or "elegant" about string theory?
>
> > Lubos Motl: First of all, the laws behind the Universe are not dumb.
>
> backdoorstudent: I never said any such thing; that was Lubos putting
> words in my mouth. Nevertheless, I would say that it's dumb to call the
> laws of nature dumb (or smart).
I was also surprised when someone confiscated my quote. ;-) Incidentally,
the laws of Nature are pretty smart, and it's dumb if someone does not see
it, and even more dumb if someone says that they are *not* smart. They are
smarter than we are, and string theory seems to be smarter yet.
I was not putting anything in your mouth. Instead, I was seriously writing
an important fact about the physical laws - and the only relation to you
is that I was trying to answer your question "What's beauty in physics and
string theory". Sorry for any potential contributions of mine to the
misunderstanding.
The context of my sentence was that the laws of physics are not "simple"
in the naive sense - i.e. simple from the viewpoint of a teenager who
hates math. The beauty of the laws of Nature requires some intelligence
and research to be appreciated.
> If my opinion matters, -it doesn't, yet I cannot resist sharing it:)-
> it is that the laws of the universe are completely indifferent to our
> presumptions of beauty.
I agree with that. They are indifferent - and they are beautiful. ;-)
> Physicists love to romanticize about their
> sense of beauty leading the way and repeatedly quote and make
> reference to Einstein and his intellectual methods to support this
> thesis.
Right. Einstein, Dirac, and others were the people who started to
emphasize beauty of the physical laws, and all of us are just followers,
in a sense. But of course, it's not quite the same type of beauty that
artists appreciate and create - or the beauty of women that attracts men.
The beauty of the laws of Nature is a very rational thing - at the very
end, XY's statement that the laws are beautiful really means that the laws
make sense to XY, and they fit together, and XY sort of understands them
and can remember them - much like a smooth shape of a beautiful object (or
subject). The other people, those who do *not* understand the laws of
Nature, also don't appreciate their beauty. As long as something looks
convoluted and unnatural to me, I won't say that it's beautiful.
> But the history of science reflects a much more mundane and
> tortured endeavor based mostly on curiosity and common sense rather
> than aesthetics. This is what leads me to feel that all this blather
> about beauty and elegance is nothing more than pontification.
You don't seem to appreciate how amazing it is that the world satisfies
some simple enough comprehensible laws at all. Einstein said that the most
incomprehensible thing about the world is that it is comprehensible. If
the laws of Nature were something that a theoretical physicist would call
"ugly", it would be pretty difficult to find out how they exactly work -
because this "ugliness" really means that the theories would not be
robust, and there would be too many arbitrary components in them.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Lubos Motl
Oct30-04, 05:42 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>On Thu, 28 Oct 2004, Doug Sweetser wrote:\n\n> I bought the DVD and looked for the elegant equations. The few I found\n> did not make a strong case for the thesis.\n\nThe document on PBS has been created for regular viewers, so it does not\ncover any math - except for potential anomalies in 1+1=2 and 31x16=496,\nand except for Einstein\'s equations and the Euler beta function (Veneziano\namplitude) which are not really explained. ;-) I thought it was\ncomprehensible that the document was not created for physics PhD students\nor professionals. :-)\n\n> > L.M.: First of all, the laws behind the Universe are not dumb.\n>\n> Perhaps instead of "dumb", backdoorstudent should have said something\n> about "no thought involved" or "necessarily automatic".\n\nIt was my statement, not backdoorstudent\'s statement, as we now explain in\ntwo other postings.\n\n> Fundamental particles are labeled that due to their simplicity.\n\nElementary particles are called elementary because according to the most\ncurrent theory that describes them (and their interactions), namely the\nStandard Model, they have no internal structure. In string theory, they\nwould not be quite elementary, but we tolerate the term anyway. ;-)\n\n> ... We don\'t understand all the rules or logic, ...\n\nWhich rules of logic do you precisely misunderstand? We may be able to\nhelp you. ;-)\n\n> but no particles are making tricky calculations very rapidly.\n\nApologies for I don\'t quite understand this sentence.\n\n> For me, the focus should be on Lagrange densities, ...\n\nThe whole of string theory probably cannot be written as a simple\nLagrangian density in spacetime.\n\n> L = (-g)^(1/2) R\n\nThis is the 1915 type of beauty, but in 2004 we\'re a bit further.\n\n> L = -(d^u A^v - d^v A^u)(d_u A_v - d_v A_u)\n\nThat\'s a 1864-style beauty.\n\n> Different symmetries are brought in in similar fashion. The aspect that\n> feels incomplete is why Nature decided to use U(1), SU(2), ...\n\n1969.\n\n> and SU(3) ...\n\n1974.\n\n> ... but not some other combination.\n\nWe can eliminate many other combinations because they would be anomalous,\nbut something is missing. String theory is the only framework with the\ncapacity to answer such questions about the gauge groups, but it has not\ndone it yet.\n\n> So Lubos, that brings me to a question for you. I would like to see one\n> of these "pretty long" Lagrangians in 11 dimensions.\n\nOnce again, local field theories with Lagrangians for a finite number of\nfields in spacetime are just approximations of string theory at long\ndistances. At general distances, string theory predicts an infinite number\nof new fields, phenomena, and their precise structure.\n\nThe only Lagrangian in large 11 dimensions worth your time is the\nLagrangian of 11-dimensional supergravity - which is more beautiful, in a\nphysics counting, than just general relativity - because it has not only\ngeneral covariance, but also local supersymmetry. But in a sense, it is\njust some Lagrangian - a generalization of your GR and Maxwell\'s system,\nplus some fermions. See e.g. the original paper by Cremmer+Julia+Scherk\n\nhttp://ccdb3fs.kek.jp/cgi-bin/img_index?7805106\n\nor one of its citations or the textbooks on SUGRA or string theory - for\nexample volumes II of Polchinski\'s "String Theory" (page 85) or\nGreen+Schwarz+Witten "Superstring theory".\n\nThe bosonic part of the Lagrangian has 11D version of \\sqrt(g).R, as in\nGeneral Relativity, plus |F(4)|^2, where F(4) is the completely\nantisymmetric tensor with 4 indices (4-form), plus C(3) /\\ F(4) /\\ F(4) / 6,\nwhere C(3) is the 3-form potential for the 4-form F(4). The last term is\ncalled the Chern-Simons term, and it is required by supersymmetry. There\nare also the fermionic terms for the gravitino - psi^a_\\mu with one spinor\nindex and one vector index (gravitino is spin 3/2, in the 4-dimensional\nlanguage). The gravitino psi also couples to the field strength F(4), and\nthere is also a quartic term of the form psi^4, with some contractions.\nAll this structure is completely determined by supersymmetry.\n\nThe exact physics of M-theory at all energies can also be described by a\nLagrangian - of the large N BFSS matrix model\n\nhttp://arxiv.org/abs/hep-th/9610043\n\n> Please try to label all the parts that go into it as I did for the\n> standard model Lagrangian. I realize this is an ongoing area of\n> research, so there is no consensus on which particular one to write\n> out, I just would like to see one of the 11D Lagrange densities as\n> part of my continuing education in string theory.\n\nThere is only one meaningful SUSY Lagrangian in 11 dimensions, and it is\njust too long to write it again, and therefore I referred to literature.\nRealistic models based on 11-dimensional M-theory are obtained by\ncompactifying the M-theory on a singular 7-dimensional manifold of G2\nholonomy.\n___________________________________ ___________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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>On Thu, 28 Oct 2004, Doug Sweetser wrote:
> I bought the DVD and looked for the elegant equations. The few I found
> did not make a strong case for the thesis.
The document on PBS has been created for regular viewers, so it does not
cover any math - except for potential anomalies in 1+1=2 and 31x16=496,
and except for Einstein's equations and the Euler \beta function (Veneziano
amplitude) which are not really explained. ;-) I thought it was
comprehensible that the document was not created for physics PhD students
or professionals. :-)
> > L.M.: First of all, the laws behind the Universe are not dumb.
>
> Perhaps instead of "dumb", backdoorstudent should have said something
> about "no thought involved" or "necessarily automatic".
It was my statement, not backdoorstudent's statement, as we now explain in
two other postings.
> Fundamental particles are labeled that due to their simplicity.
Elementary particles are called elementary because according to the most
current theory that describes them (and their interactions), namely the
Standard Model, they have no internal structure. In string theory, they
would not be quite elementary, but we tolerate the term anyway. ;-)
> ... We don't understand all the rules or logic, ...
Which rules of logic do you precisely misunderstand? We may be able to
help you. ;-)
> but no particles are making tricky calculations very rapidly.
Apologies for I don't quite understand this sentence.
> For me, the focus should be on Lagrange densities, ...
The whole of string theory probably cannot be written as a simple
Lagrangian density in spacetime.
> L = (-g)^(1/2) R
This is the 1915 type of beauty, but in 2004 we're a bit further.
> L = -(d^u A^v - d^v A^u)(d_u A_v - d_v A_u)
That's a 1864-style beauty.
> Different symmetries are brought in in similar fashion. The aspect that
> feels incomplete is why Nature decided to use U(1), SU(2), ...
1969.
> and SU(3) ...
1974.
> ... but not some other combination.
We can eliminate many other combinations because they would be anomalous,
but something is missing. String theory is the only framework with the
capacity to answer such questions about the gauge groups, but it has not
done it yet.
> So Lubos, that brings me to a question for you. I would like to see one
> of these "pretty long" Lagrangians in 11 dimensions.
Once again, local field theories with Lagrangians for a finite number of
fields in spacetime are just approximations of string theory at long
distances. At general distances, string theory predicts an infinite number
of new fields, phenomena, and their precise structure.
The only Lagrangian in large 11 dimensions worth your time is the
Lagrangian of 11-dimensional supergravity - which is more beautiful, in a
physics counting, than just general relativity - because it has not only
general covariance, but also local supersymmetry. But in a sense, it is
just some Lagrangian - a generalization of your GR and Maxwell's system,
plus some fermions. See e.g. the original paper by Cremmer+Julia+Scherk
http://ccdb3fs.kek.jp/cgi-bin/img_index?7805106
or one of its citations or the textbooks on SUGRA or string theory - for
example volumes II of Polchinski's "String Theory" (page 85) or
Green+Schwarz+Witten "Superstring theory".
The bosonic part of the Lagrangian has 11D version of \sqrt(g).R, as in
General Relativity, plus |F(4)|^2, where F(4) is the completely
antisymmetric tensor with 4 indices (4-form), plus C(3) /\ F(4) /\ F(4) / 6,
where C(3) is the 3-form potential for the 4-form F(4). The last term is
called the Chern-Simons term, and it is required by supersymmetry. There
are also the fermionic terms for the gravitino - \psi^a_\mu with one spinor
index and one vector index (gravitino is spin 3/2, in the 4-dimensional
language). The gravitino \psi also couples to the field strength F(4), and
there is also a quartic term of the form \psi^4, with some contractions.
All this structure is completely determined by supersymmetry.
The exact physics of M-theory at all energies can also be described by a
Lagrangian - of the large N BFSS matrix model
http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9610043
> Please try to label all the parts that go into it as I did for the
> standard model Lagrangian. I realize this is an ongoing area of
> research, so there is no consensus on which particular one to write
> out, I just would like to see one of the 11D Lagrange densities as
> part of my continuing education in string theory.
There is only one meaningful SUSY Lagrangian in 11 dimensions, and it is
just too long to write it again, and therefore I referred to literature.
Realistic models based on 11-dimensional M-theory are obtained by
compactifying the M-theory on a singular 7-dimensional manifold of G2
holonomy.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
backdoorstudent
Nov2-04, 12:38 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>\n\n\n\nLubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0410301801160.20931-100000@feynman.harvard.edu>...\n> You don\'t seem to appreciate how amazing it is that the world satisfies\n> some simple enough comprehensible laws at all.\n\nOf course I do. I think almost everybody reading this newsgroup does.\n\n> Einstein said that the most incomprehensible thing about the world is that it is comprehensible.\n\nI know. And I\'m getting sick of hearing everybody parrot it around as\ntheir mantra. And if you insist on presuming that it must be that way\nyou may miss out on finding out something more accurate about the\nworld. Because our experience of the world being this way is a very\nshort one so far, and it is an idealist extrapolation to think it will\ncontinue forever. I am not saying I believe it won\'t. I\'m just saying\nkeep your mind open to other possibilties.\n\nWould you really be surprised if the world was ultimately\nincomprehensible?\n\n> If the laws of Nature were something that a theoretical physicist would call\n> "ugly", it would be pretty difficult to find out how they exactly work -\n> because this "ugliness" really means that the theories would not be\n> robust, and there would be too many arbitrary components in them.\n\nIf this is really what you mean by "ugliness" then it looks to me as\nthough we have indeed reached that place of being not robust with too\nmany arbitrary components. Am I wrong?\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>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0410301801160.20931-100000@feynman.harvard.edu>...
> You don't seem to appreciate how amazing it is that the world satisfies
> some simple enough comprehensible laws at all.
Of course I do. I think almost everybody reading this newsgroup does.
> Einstein said that the most incomprehensible thing about the world is that it is comprehensible.
I know. And I'm getting sick of hearing everybody parrot it around as
their mantra. And if you insist on presuming that it must be that way
you may miss out on finding out something more accurate about the
world. Because our experience of the world being this way is a very
short one so far, and it is an idealist extrapolation to think it will
continue forever. I am not saying I believe it won't. I'm just saying
keep your mind open to other possibilties.
Would you really be surprised if the world was ultimately
incomprehensible?
> If the laws of Nature were something that a theoretical physicist would call
> "ugly", it would be pretty difficult to find out how they exactly work -
> because this "ugliness" really means that the theories would not be
> robust, and there would be too many arbitrary components in them.
If this is really what you mean by "ugliness" then it looks to me as
though we have indeed reached that place of being not robust with too
many arbitrary components. Am I wrong?
John Gonsowski
Nov3-04, 09:59 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>Doug Sweetser <sweetser@alum.mit.edu> wrote in message news:<clqlfl\\$7a1\\$1@pcls4.std.com>...\n> So Lubos, that brings me to a question for you. I would like to see one\n> of these "pretty long" Lagrangians in 11 dimensions. Please try to\n> label all the parts that go into it as I did for the standard model\n> Lagrangian. I realize this is an ongoing area of research, so there is\n> no consensus on which particular one to write out, I just would like to\n> see one of the 11D Lagrange densities as part of my continuing\n> education in string theory.\n>\n>\n> doug\n> quaternions.com\n\nHere is Tony Smith\'s very well labeled Lagrangian for bosonic string\ntheory, I\'m curious as to what you think of it:\n\nthe Integral over the Cl(1,7) vector 1+7=8-dimensional SpaceTime of\n\ndd P\' /\\ * dd P + F /\\ *F + S\' D S + GF + GG\nwhere\n\nd is the 8-dim covariant derivative\nP is the scalar field\nF is the adjoint Spin(8) curvature\nS\' and S are half-spinor fermion spaces\nD is the 8-dim Dirac operator\nGF is the gauge-fixing term\nGG is the ghost term,\nplus a topological Pontrjagin term.\n\nThe Pontrjagin term represents Instantons in 8-dimensional spacetime\nthat is locally RP1 x S7. Since, after dimensional reduction of\nspacetime from 8 to 4 dimensions, the Pontrjagin term goes into the\nSpin(6) conformal gravity sector of the D4-D5-E6-E7-E8 VoDou physics\nmodel, it does not go to the SU(3) color force sector. Therefore, the\nSU(3) color force Sector has no THETA-term and the D4-D5-E6-E7-E8\nVodou Physics model has no theoretical THETA-CP problem.\n\nAfter dimensional reduction to 4-dimensional spacetime, the S7 of RP1\nx S7 is factored by the Hopf fibration S3 -> S7 -> S4 into\n4-dimensional spacetime that is locally RP1 x S3, plus a CP2 part\nrelated to 4-dimensional Internal Symmetry Space.\n\nReduction also produces, for each World of the Many-Worlds, a\n4-dimensional lattice Spacetime with MacDowell-Mansouri Gravity, a\nHiggs Mechanism, and a Complex Propagator Phase;\n\na 4-dimensional lattice Internal Symmetry Space with 8 Color Force\nGluons, 3 Weak Force Bosons, and a Photon that live on the links of\nthe lattice Spacetime; and 3 generations of 8 Fermion Particles and 8\nFermion AntiParticles that live on the vertices of the lattice\nSpacetime.\n\nIn terms of a 5-level grading of the E6 Lie algebra, that is, the\nGraded Lie Alagebra of type e7, we have\n\nE6(-14) =\n8-dim\n+ 16-dim\n+ R + so(1,7) + iR\n+ 16-dim\n+ 8-dim\nwith physical interpretation in the Lagrangian of the D4-D5-E6-E7-E8\nVoDou Physics Model as:\n\n8-dim of g(-2) plus R of g(0) plus 8-dim of g(2), an\n8-Complex-dimensional domain plus an R generator of Complex U(1)\nsymmetry, with an 8-real-dimensional Shilov boundary of the form S1 x\nS7, corresponds to an 8-dimensional spacetime base manifold over which\nthe Lagrangian integral is integrated;\nso(1,7) of g(0), the double cover of the Lorentz group over the\nOctonions, corresponds to the 28 generators of gauge bosons in the\ncurvature term of the Lagrangian integrand; and\n16-dim of g(-1) plus iR of g(0) plus 16-dim of g(1), a\n16-Complex-dimensional domain, the Complexified Octonion Plane\n(CxO)P2, plus an iR generator of Complex U(1) symmetry, with a Shilov\nboundary ( not entirely real, as the 16-Complex-dimensional domain is\nnot of tube type ) that may be regarded as being a bundle made up of a\nreal fibre S1 x S7 over a base space made up of S1 and CP4 ( note that\nthe CP4 has embedded S7 structure ), so that the real fibre S1 x S7\nrepresents 8 first-generation fermion particles in the Dirac spinor\nterm of the Lagrangian integrand, and an S1 x S7 in the base space\nrepresents 8 corresponding antiparticles.\n\n\nRelated Graded Lie Algebra structures give:\n\na Bohm Quantum Potential from 26-dimensional String Theory;\na 27-dimensional M-theory of timelike branes in the MacroSpace of the\nMany-Worlds; and\na 28-dimensional F-theory of spacelike branes in the MacroSpace of the\nMany-Worlds.\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>Doug Sweetser <sweetser@alum.mit.edu> wrote in message news:<clqlfl$7a1$1@pcls4.std.com>...
> So Lubos, that brings me to a question for you. I would like to see one
> of these "pretty long" Lagrangians in 11 dimensions. Please try to
> label all the parts that go into it as I did for the standard model
> Lagrangian. I realize this is an ongoing area of research, so there is
> no consensus on which particular one to write out, I just would like to
> see one of the 11D Lagrange densities as part of my continuing
> education in string theory.
>
>
> doug
> quaternions.com
Here is Tony Smith's very well labeled Lagrangian for bosonic string
theory, I'm curious as to what you think of it:
the Integral over the Cl(1,7) vector 1+7=8-dimensional SpaceTime of
dd P' /\ * dd P + F /\ *F + S' D S + GF + GG
where
d is the 8-dim covariant derivative
P is the scalar field
F is the adjoint Spin(8) curvature
S' and S are half-spinor fermion spaces
D is the 8-dim Dirac operator
GF is the gauge-fixing term
GG is the ghost term,
plus a topological Pontrjagin term.
The Pontrjagin term represents Instantons in 8-dimensional spacetime
that is locally RP1 x S7. Since, after dimensional reduction of
spacetime from 8 to 4 dimensions, the Pontrjagin term goes into the
Spin(6) conformal gravity sector of the D4-D5-E6-E7-E8 VoDou physics
model, it does not go to the SU(3) color force sector. Therefore, the
SU(3) color force Sector has no \THETA-term and the D4-D5-E6-E7-E8
Vodou Physics model has no theoretical \THETA-CP problem.
After dimensional reduction to 4-dimensional spacetime, the S7 of RP1
x S7 is factored by the Hopf fibration S3 -> S7 -> S4 into
4-dimensional spacetime that is locally RP1 x S3, plus a CP2 part
related to 4-dimensional Internal Symmetry Space.
Reduction also produces, for each World of the Many-Worlds, a
4-dimensional lattice Spacetime with MacDowell-Mansouri Gravity, a
Higgs Mechanism, and a Complex Propagator Phase;
a 4-dimensional lattice Internal Symmetry Space with 8 Color Force
Gluons, 3 Weak Force Bosons, and a Photon that live on the links of
the lattice Spacetime; and 3 generations of 8 Fermion Particles and 8
Fermion AntiParticles that live on the vertices of the lattice
Spacetime.
In terms of a 5-level grading of the E6 Lie algebra, that is, the
Graded Lie Alagebra of type e7, we have
E6(-14) =8-dim+ 16-dim
+ R + so(1,7) + iR+ 16-dim+ 8-dim
with physical interpretation in the Lagrangian of the D4-D5-E6-E7-E8
VoDou Physics Model as:
8-dim of g(-2) plus R of g(0) plus 8-dim of g(2), an
8-Complex-dimensional domain plus an R generator of Complex U(1)
symmetry, with an 8-real-dimensional Shilov boundary of the form S1 x
S7, corresponds to an 8-dimensional spacetime base manifold over which
the Lagrangian integral is integrated;
so(1,7) of g(0), the double cover of the Lorentz group over the
Octonions, corresponds to the 28 generators of gauge bosons in the
curvature term of the Lagrangian integrand; and
16-dim of g(-1) plus iR of g(0) plus 16-dim of g(1), a
16-Complex-dimensional domain, the Complexified Octonion Plane
(CxO)P2, plus an iR generator of Complex U(1) symmetry, with a Shilov
boundary ( not entirely real, as the 16-Complex-dimensional domain is
not of tube type ) that may be regarded as being a bundle made up of a
real fibre S1 x S7 over a base space made up of S1 and CP4 ( note that
the CP4 has embedded S7 structure ), so that the real fibre S1 x S7
represents 8 first-generation fermion particles in the Dirac spinor
term of the Lagrangian integrand, and an S1 x S7 in the base space
represents 8 corresponding antiparticles.
Related Graded Lie Algebra structures give:
a Bohm Quantum Potential from 26-dimensional String Theory;
a 27-dimensional M-theory of timelike branes in the MacroSpace of the
Many-Worlds; and
a 28-dimensional F-theory of spacelike branes in the MacroSpace of the
Many-Worlds.
Doug Sweetser
Nov3-04, 09:59 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>Hello backdoorstudent:\n\nSorry if I misquoted you.\n\nNature was using all the same laws of physics two billion years ago when\nonly single-celled organisms lived here, so she has historically been\nindifferent to us beings that did not exist :-) No matter our fate,\nshe will continue to work on grand scales.\n\nIt is common to quote Einstein, he is the Jimi Hendricks of physics :-)\nI tried to stay focused on equations and how they work. Do you know\nhow to:\n\n1. Derive the Maxwell equations from the classical Lagrange density?\n2. Derive Einstein\'s field equations from the Hilbert action?\n3. Derive the field equation of the standard model from its\nLagrangian?\n\nNo one was born knowing how to do these three. I learned how to do the\nfirst one in ~2001. I learned how to do the second one a few months\nago. The third one should be similar to the first, but I have not done\nit yet. If you have learned enough physics to do the calculation\nyourself, these are some of the most elegant uses of paper you will\nexperience in your life. The equations govern the behavior of photons,\nelectrons, and gravity throughout the entire Universe. Yes, much of\nphysics can and should be mundane, but the specific Lagrange densities\ncited reach across the Universe.\n\nI suspect the long, complicated Lagrange densities of string theory will\nnot have that same feel. Yet the pitch to the public does try to make\na connection. I want to see at least one example, kind of like calling\nthe bluff of a string theorist.\n\ndoug\nquaternions.com\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>Hello backdoorstudent:
Sorry if I misquoted you.
Nature was using all the same laws of physics two billion years ago when
only single-celled organisms lived here, so she has historically been
indifferent to us beings that did not exist :-) No matter our fate,
she will continue to work on grand scales.
It is common to quote Einstein, he is the Jimi Hendricks of physics :-)
I tried to stay focused on equations and how they work. Do you know
how to:
1. Derive the Maxwell equations from the classical Lagrange density?
2. Derive Einstein's field equations from the Hilbert action?
3. Derive the field equation of the standard model from its
Lagrangian?
No one was born knowing how to do these three. I learned how to do the
first one in ~2001. I learned how to do the second one a few months
ago. The third one should be similar to the first, but I have not done
it yet. If you have learned enough physics to do the calculation
yourself, these are some of the most elegant uses of paper you will
experience in your life. The equations govern the behavior of photons,
electrons, and gravity throughout the entire Universe. Yes, much of
physics can and should be mundane, but the specific Lagrange densities
cited reach across the Universe.
I suspect the long, complicated Lagrange densities of string theory will
not have that same feel. Yet the pitch to the public does try to make
a connection. I want to see at least one example, kind of like calling
the bluff of a string theorist.
doug
quaternions.com
<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>backdoorstudent@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.0410281615.67aeff9a@posting.google. com>...\n<snip>\n> > >> What\'s so "beautiful" or "elegant" about string theory?\n<snip>\n\n> If my opinion matters, -it doesn\'t, yet I cannot resist sharing it:)-\n> it is that the laws of the universe are completely indifferent to our\n> presumptions of beauty. Physicists love to romanticize about their\n> sense of beauty leading the way and repeatedly quote and make\n> reference to Einstein and his intellectual methods to support this\n> thesis. But the history of science reflects a much more mundane and\n> tortured endeavor based mostly on curiosity and common sense rather\n> than aesthetics. This is what leads me to feel that all this blather\n> about beauty and elegance is nothing more than pontification.\n\nRelevant:\nI have heard a Freemason use the word "Masonic" in relation to the\ndevelopment of the sciences and Brians book on string theory/s.\n\nSpud\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>backdoorstudent@yahoo.com (backdoorstudent) wrote in message news:<750f5e99.0410281615.67aeff9a@posting.google.com>...
<snip>
> > >> What's so "beautiful" or "elegant" about string theory?
<snip>
> If my opinion matters, -it doesn't, yet I cannot resist sharing it:)-
> it is that the laws of the universe are completely indifferent to our
> presumptions of beauty. Physicists love to romanticize about their
> sense of beauty leading the way and repeatedly quote and make
> reference to Einstein and his intellectual methods to support this
> thesis. But the history of science reflects a much more mundane and
> tortured endeavor based mostly on curiosity and common sense rather
> than aesthetics. This is what leads me to feel that all this blather
> about beauty and elegance is nothing more than pontification.
Relevant:
I have heard a Freemason use the word "Masonic" in relation to the
development of the sciences and Brians book on string theory/s.
Spud
Rahul Jain
Nov3-04, 10:03 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>backdoorstudent@yahoo.com (backdoorstudent) writes:\n\n> If my opinion matters, -it doesn\'t, yet I cannot resist sharing it:)-\n> it is that the laws of the universe are completely indifferent to our\n> presumptions of beauty.\n\nIt has been proposed that we have evolved a sense of aesthetics that\nmakes us appreciate ideas that resonate well with the laws of the\nuniverse. Probably something to do with innately applying the idea and\nseeing if it works well with the phenomena we\'ve observed or know about.\n\n--\nRahul Jain\nrjain@nyct.net\nProfessional Software Developer, Amateur Quantum Mechanicist\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>backdoorstudent@yahoo.com (backdoorstudent) writes:
> If my opinion matters, -it doesn't, yet I cannot resist sharing it:)-
> it is that the laws of the universe are completely indifferent to our
> presumptions of beauty.
It has been proposed that we have evolved a sense of aesthetics that
makes us appreciate ideas that resonate well with the laws of the
universe. Probably something to do with innately applying the idea and
seeing if it works well with the phenomena we've observed or know about.
--
Rahul Jain
rjain@nyct.net
Professional Software Developer, Amateur Quantum Mechanicist
Gerard Westendorp
Nov3-04, 10:05 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>>\n>>On Sun, 24 Oct 2004, backdoorstudent wrote:\n>>\n>>\n>>>What\'s so "beautiful" or "elegant" about string theory?\n>>>\n\nThe problem we humans have is that we have only limited\ntime, data and imagination. So we need theories that\nallow our brains to very efficiently process reality.\n\nWhen we find a theory that allows us to do this,\nwe like it, and the theory will seem beautiful and\nelegant to us.\n\nQuantum mechanics helps us to understand particles,\nand general relativity helps us to understand gravity.\nGeneral relativity is beautiful because it starts with\nonly very few basic assumptions, and from there it\nderives how gravity behaves, and redefines our concepts\nof space and time. Quantum mechanics is a lot more messy,\nbut it is so successful that only Einstein could afford\nto say it might be wrong.\n\nThe ultimate theory would have to unify general relativity\nand quantum mechanics. But to be a worthy ultimate theory,\nit would have to start from some very basic principles.\n\nThe basic principles of string theory are not clear yet,\nwhich is an ugly aspect. At the same time, it probably\ncontains lots of nice maths, which is beautiful. Maths\nis beautiful because it shows us how all kinds of\nthings are deeply interrelated.\n\nGerard\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>>
>>On Sun, 24 Oct 2004, backdoorstudent wrote:
>>
>>
>>>What's so "beautiful" or "elegant" about string theory?
>>>
The problem we humans have is that we have only limited
time, data and imagination. So we need theories that
allow our brains to very efficiently process reality.
When we find a theory that allows us to do this,
we like it, and the theory will seem beautiful and
elegant to us.
Quantum mechanics helps us to understand particles,
and general relativity helps us to understand gravity.
General relativity is beautiful because it starts with
only very few basic assumptions, and from there it
derives how gravity behaves, and redefines our concepts
of space and time. Quantum mechanics is a lot more messy,
but it is so successful that only Einstein could afford
to say it might be wrong.
The ultimate theory would have to unify general relativity
and quantum mechanics. But to be a worthy ultimate theory,
it would have to start from some very basic principles.
The basic principles of string theory are not clear yet,
which is an ugly aspect. At the same time, it probably
contains lots of nice maths, which is beautiful. Maths
is beautiful because it shows us how all kinds of
things are deeply interrelated.
Gerard
Doug Sweetser
Nov3-04, 10:05 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>Hello Lubos:\n\n> The document on PBS has been created for regular viewers, so it does\n> not cover any math\n\nFor the pure fun of it, I am making my own physics videos. This is the\nstandard practice, don\'t show the math, or if it does, make it slide\naway quickly. In my own productions, the equations I reference are\nalways on the screen. Why? Because that is what I am talking about,\nhow a small set of symbols are relevant to how our Universe works. If\none talks about Beethoven, one should also hear his tunes. It\nis a fun challenge to come up with graphics good enough that my\ngirlfirend wants them on the walls of our apartment :-)\n\n\n> Elementary particles are called elementary because according to the\n> most current theory that describes them (and their interactions),\n> namely the Standard Model, they have no internal structure. In string\n> theory, they would not be quite elementary, but we tolerate the term\n> anyway. ;-)\n\nAgreed, my language was imprecise.\n\n\n> Which rules of logic do you precisely misunderstand? We may be able to\n> help you. ;-)\n\nTake for example the two slit experiment. We completely understand the\nmath (it is easy). Feynman gets the math. Yet he said in his New\nZealand he does not understand why it works that way. There have\ncertainly been quite a few threads in SPR on the topic.\n\n\n>> but no particles are making tricky calculations very rapidly.\n>\n> Apologies for I don\'t quite understand this sentence.\n\nThere are limits to how many Feynman diagrams we can include in a\nperturbation series expansion, say of an electron being scattered by a\nphoton. I don\'t know what the current record is, perhaps 8. That is a\n"tricky calculation". I know I cannot do it, getting hung up at 2.\nYet electrons interact with photons all the time, and apparently to the\ncomplete perturbation series expansion.\n\n....\n> This is the 1915 type of beauty, but in 2004 we\'re a bit further.\n....\n> That\'s a 1864-style beauty.\n(question: I know that Maxwell wrote up his field equations in that\nyear, but did he also wrote down the Lagrangian then too, or if someone\nelse gets the credit for that?)\n....\n> 1969.\n....\n> 1974.\n\nFor me, this is too focused on the humans who have achieved great\ninsights. To a flaw, I am equation-centric, not physicist-centric.\nThese equations will last, no matter when they were discovered.\nImagine changing the order of their discovery, and that has no effect\non the beauty of the Lagrangians.\n\n\n> The only Lagrangian in large 11 dimensions worth your time is the\n> Lagrangian of 11-dimensional supergravity - which is more beautiful,\n> in a physics counting, than just general relativity - because it has\n> not only general covariance, but also local supersymmetry. But in a\n> sense, it is just some Lagrangian - a generalization of your GR and\n> Maxwell\'s system, plus some fermions. See e.g. the original paper by\n> Cremmer+Julia+Scherk\n>\n> http://ccdb3fs.kek.jp/cgi-bin/img_index?7805106\n\nOK, I did print this one out with some difficulty (odd page length). So\nI can try to write this one out, at least for the record. To quote the\nentire abstract:\n\n"We present the action and transformation laws of supergravity in 11\ndimensions which is expected to be closely related to the O(8) theory\nin 4 dimensions after dimensional reduction."\n\nThis must be a classic paper since it dates to 1978. Here is the\nLagrangian:\n\nL = 1. Bosonic part like GR,\n2. Fermionic terms for the gravitino,\n3. Antisymmetric gauge field strength F(4) contraction,\n4. Gravitino coupling to the F(4),\n5. Chern-Simons term required by super symmetry.\n\n1. = - V/(4 k^2) R(omega)\n2. - iV/2 phibar_mu Gamma^mu nu rho D_nu (omega + omegahat)/2 phi_rho\n3. - V/48 F_mu nu rho sigma F^mu nu rho sigma\n4. + KV/192 (phibar_mu Gamma^mu nu alpha beta gamma sigma phi_nu +\n12 phibar^alpha Gamma^gamma sigma phi^beta)\n(F_alpha beta gamma sigma + Fhat_alpha beta gamma sigma)\n5. + 2K/(144)^2 Eta^alpha1 alpha2 alpha3 alpha4 beta1 beta2 beta3\nbeta4 mu nu rho\nF_alpha1 alpha2 alpha3 alpha4\nF_beta1 beta2 beta3 beta4 A_mu nu rho\n\nwhere\nV^alpha_mu is the vierbein (graviton field?)\nphi^mu is a Majorana spin 3/2\nA_mu nu rho is an antisymmetric gauge tensor\nF_mu nu rho sigma is the field strength tensor\nassociated with A_mu nu rho (4 d[_mu A_nu rho sigma])\nD_nu omega phi_mu is the covariant derivative of phi_mu\n(= d_nu phi_mu + 1/4 omega_nu alpha beta Gamma^alpha beta phi_mu)\n\nAt this point in my intellectual development, I don\'t understand this\nLagrange density, although if I wrote it down correctly, it is in a\nrare class of "meaningful SUSY Lagrangian in 11 dimensions". As Bob\nDylan once penned in a very different context, "Don\'t criticize what\nyou can\'t understand." So I will comment that the SUSY 11D Lagrange\ndensity looks difficult even for bright folks to fully comprehend.\n\ndoug\nquaternions.com\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>Hello Lubos:
> The document on PBS has been created for regular viewers, so it does
> not cover any math
For the pure fun of it, I am making my own physics videos. This is the
standard practice, don't show the math, or if it does, make it slide
away quickly. In my own productions, the equations I reference are
always on the screen. Why? Because that is what I am talking about,
how a small set of symbols are relevant to how our Universe works. If
one talks about Beethoven, one should also hear his tunes. It
is a fun challenge to come up with graphics good enough that my
girlfirend wants them on the walls of our apartment :-)
> Elementary particles are called elementary because according to the
> most current theory that describes them (and their interactions),
> namely the Standard Model, they have no internal structure. In string
> theory, they would not be quite elementary, but we tolerate the term
> anyway. ;-)
Agreed, my language was imprecise.
> Which rules of logic do you precisely misunderstand? We may be able to
> help you. ;-)
Take for example the two slit experiment. We completely understand the
math (it is easy). Feynman gets the math. Yet he said in his New
Zealand he does not understand why it works that way. There have
certainly been quite a few threads in SPR on the topic.
>> but no particles are making tricky calculations very rapidly.
>
> Apologies for I don't quite understand this sentence.
There are limits to how many Feynman diagrams we can include in a
perturbation series expansion, say of an electron being scattered by a
photon. I don't know what the current record is, perhaps 8. That is a
"tricky calculation". I know I cannot do it, getting hung up at 2.
Yet electrons interact with photons all the time, and apparently to the
complete perturbation series expansion.
....
> This is the 1915 type of beauty, but in 2004 we're a bit further.
....
> That's a 1864-style beauty.
(question: I know that Maxwell wrote up his field equations in that
year, but did he also wrote down the Lagrangian then too, or if someone
else gets the credit for that?)
....
> 1969.
....
> 1974.
For me, this is too focused on the humans who have achieved great
insights. To a flaw, I am equation-centric, not physicist-centric.
These equations will last, no matter when they were discovered.
Imagine changing the order of their discovery, and that has no effect
on the beauty of the Lagrangians.
> The only Lagrangian in large 11 dimensions worth your time is the
> Lagrangian of 11-dimensional supergravity - which is more beautiful,
> in a physics counting, than just general relativity - because it has
> not only general covariance, but also local supersymmetry. But in a
> sense, it is just some Lagrangian - a generalization of your GR and
> Maxwell's system, plus some fermions. See e.g. the original paper by
> Cremmer+Julia+Scherk
>
> http://ccdb3fs.kek.jp/cgi-bin/img_index?7805106
OK, I did print this one out with some difficulty (odd page length). So
I can try to write this one out, at least for the record. To quote the
entire abstract:
"We present the action and transformation laws of supergravity in 11
dimensions which is expected to be closely related to the O(8) theory
in 4 dimensions after dimensional reduction."
This must be a classic paper since it dates to 1978. Here is the
Lagrangian:
L = 1[/itex]. Bosonic part like GR,
2. Fermionic terms for the gravitino,
3. Antisymmetric gauge field strength F(4) contraction,
4. Gravitino coupling to the F(4),
5. Chern-Simons term required by super symmetry.
1. = - V/(4 k^2) R(\omega)
2. - iV/2 phibar_mu \Gamma^\mu \nu \rho D_{nu} (\omega + omegahat)/2 \phi_rho
3. - V/48 F_{mu} \nu \rho \sigma F^\mu \nu \rho \sigma
4. + KV/192 (phibar_mu \Gamma^\mu \nu \alpha \beta \gamma \sigma \phi_nu +12 phibar^\alpha \Gamma^\gamma \sigma \phi^\beta)(F_{alpha} \beta \gamma \sigma + Fhat_alpha \beta \gamma \sigma)
5. + 2K/(144)^2 \Eta^alpha1 alpha2 alpha3 alpha4 beta1 beta2 beta3
beta4 \mu \nu \rhoF_{alpha1} alpha2 alpha3 alpha4
F_{beta1} beta2 beta3 beta4 [itex]A_{mu} \nu \rho
where
V^\alpha_mu is the vierbein (graviton field?)
\phi^\mu is a Majorana spin 3/2
A_{mu} \nu \rho is an antisymmetric gauge tensor
F_{mu} \nu \rho \sigma is the field strength tensor
associated with A_{mu} \nu \rho (4 d[_mu A_{nu} \rho \sigma])D_{nu} \omega \phi_mu is the covariant derivative of \phi_mu(= d_{nu} \phi_mu + 1/4 \omega_nu \alpha \beta \Gamma^\alpha \beta \phi_mu)
At this point in my intellectual development, I don't understand this
Lagrange density, although if I wrote it down correctly, it is in a
rare class of "meaningful SUSY Lagrangian in 11 dimensions". As Bob
Dylan once penned in a very different context, "Don't criticize what
you can't understand." So I will comment that the SUSY 11D Lagrange
density looks difficult even for bright folks to fully comprehend.
doug
quaternions.com
Lubos Motl
Nov6-04, 12:54 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>On Tue, 2 Nov 2004, backdoorstudent wrote:\n\n>> LM: You don\'t seem to appreciate how amazing it is that the world\n>> satisfies some simple enough comprehensible laws at all.\n>\n> Of course I do. I think almost everybody reading this newsgroup does.\n\nI\'ve quoted this sentence of yours in order to highlight that you\ncontradict yourself below.\n\n> ... I\'m just saying keep your mind open to other possibilties.\n\nI cannot really keep open mind about this question whether science should\neventually declare the world incomprehensible. Of course that science\ncannot declare the world incomprehensible - simply because its purpose is\njust the opposite. If science ever does so and declares the world (or a\npiece of it) permanently incomprehensible, it would mean that science\nceases to exist. What you say is a logical oxymoron, as I describe below\nin more detail.\n\n> Would you really be surprised if the world was ultimately\n> incomprehensible?\n\nFirst of all, the world is definitely not *completely* incomprehensible.\nIt\'s not only largely comprehensible, but we have already understood\nquite a lot.\n\nYour question contradicts reality, as well as Einstein\'s quote that you\nagreed with at the very beginning. So I suppose you wanted to ask whether\nI would have been surprised if *some* features of the world would remain\nincomprehensible.\n\nBut even this restricted question is actually nonsensical.\n\nThe essential point is that science can *never* lead to the conclusion\nthat something is incomprehensible. It\'s just an oxymoron. Science can\nreveal that some aspects of the Universe are probabilistic; or they are\nenvironmental details that are hardly predictable because they depend on\ntoo many things.\n\nBut even in these two cases, the insight that implies these statements\nbrings us a better *understanding* of reality, and it must be so,\notherwise the argument would have no scientific value. The only real\nreason why we believe the statement of quantum mechanics that only\nprobabilities can be predicted is the highly quantitatively successful\nagreement of quantum mechanics with experiments.\n\nIn science, something\'s being "incomprehensible" is always a temporary\nstate of the affairs.\n\nOne can never prove, in science, that something is "incomprehensible",\nsimply because the very meaning of science is to understand things better.\nThings may *look* incomprehensible to us until we comprehend them. But\nit\'s just logically impossible to imagine that someone proves that\nsomething is inherently and permanently "incomprehensible".\n\nTherefore your question whether I would be surprised, if you ask it as a\nserious scientific question, does not really make sense - the answer can\nbe both "yes" and "no" because the assumption of your sentence can never\noccur. There will never be a moment in which something in the Universe\nwill be scientifically identified as "permanently incomprehensible", and\ntherefore I will never have the opportunity to be surprised by this\nimpossible insight.\n\nThe idea that someone will make a discovery that something is\nincomprehensible and science will be limited is just a totally\nnon-scientific, medieval idea. No doubt, many powerful people in religion,\nphilosophy, social sciences and humanities - both left-wing and right-wing\npeople - would love to prove that science will never understand something\nabout the material world around - but such an "insight" is simply\nimpossible in science.\n\n> If this is really what you mean by "ugliness" then it looks to me as\n> though we have indeed reached that place of being not robust with too\n> many arbitrary components. Am I wrong?\n\nBy "too many arbitrary components", you mean the field contents of the\nnu-Standard Model and its 30 parameters? Do you realize that these\ncomponents explain all of the billions of observations we have ever made?\nIt\'s amazing, and it\'s not the end of science yet. This is why we\'re\nworking to understand even the last "incomprehensible" components of our\ntheories of reality.\n________________________________________ ______________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\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>On Tue, 2 Nov 2004, backdoorstudent wrote:
>> LM: You don't seem to appreciate how amazing it is that the world
>> satisfies some simple enough comprehensible laws at all.
>
> Of course I do. I think almost everybody reading this newsgroup does.
I've quoted this sentence of yours in order to highlight that you
contradict yourself below.
> ... I'm just saying keep your mind open to other possibilties.
I cannot really keep open mind about this question whether science should
eventually declare the world incomprehensible. Of course that science
cannot declare the world incomprehensible - simply because its purpose is
just the opposite. If science ever does so and declares the world (or a
piece of it) permanently incomprehensible, it would mean that science
ceases to exist. What you say is a logical oxymoron, as I describe below
in more detail.
> Would you really be surprised if the world was ultimately
> incomprehensible?
First of all, the world is definitely not *completely* incomprehensible.
It's not only largely comprehensible, but we have already understood
quite a lot.
Your question contradicts reality, as well as Einstein's quote that you
agreed with at the very beginning. So I suppose you wanted to ask whether
I would have been surprised if *some* features of the world would remain
incomprehensible.
But even this restricted question is actually nonsensical.
The essential point is that science can *never* lead to the conclusion
that something is incomprehensible. It's just an oxymoron. Science can
reveal that some aspects of the Universe are probabilistic; or they are
environmental details that are hardly predictable because they depend on
too many things.
But even in these two cases, the insight that implies these statements
brings us a better *understanding* of reality, and it must be so,
otherwise the argument would have no scientific value. The only real
reason why we believe the statement of quantum mechanics that only
probabilities can be predicted is the highly quantitatively successful
agreement of quantum mechanics with experiments.
In science, something's being "incomprehensible" is always a temporary
state of the affairs.
One can never prove, in science, that something is "incomprehensible",
simply because the very meaning of science is to understand things better.
Things may *look* incomprehensible to us until we comprehend them. But
it's just logically impossible to imagine that someone proves that
something is inherently and permanently "incomprehensible".
Therefore your question whether I would be surprised, if you ask it as a
serious scientific question, does not really make sense - the answer can
be both "yes" and "no" because the assumption of your sentence can never
occur. There will never be a moment in which something in the Universe
will be scientifically identified as "permanently incomprehensible", and
therefore I will never have the opportunity to be surprised by this
impossible insight.
The idea that someone will make a discovery that something is
incomprehensible and science will be limited is just a totally
non-scientific, medieval idea. No doubt, many powerful people in religion,
philosophy, social sciences and humanities - both left-wing and right-wing
people - would love to prove that science will never understand something
about the material world around - but such an "insight" is simply
impossible in science.
> If this is really what you mean by "ugliness" then it looks to me as
> though we have indeed reached that place of being not robust with too
> many arbitrary components. Am I wrong?
By "too many arbitrary components", you mean the field contents of the
\nu-Standard Model and its 30 parameters? Do you realize that these
components explain all of the billions of observations we have ever made?
It's amazing, and it's not the end of science yet. This is why we're
working to understand even the last "incomprehensible" components of our
theories of reality.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
<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>Doug Sweetser <sweetser@alum.mit.edu> wrote in message news:<cluf7f\\$v1\\$1@pcls4.std.com>...\n> Hello backdoorstudent:\n\n>\n> I suspect the long, complicated Lagrange densities of string theory will\n> not have that same feel.\n\nActually, for me they do have a feel of beauty. Because these "long,\ncomplicated Lagrange densities of string theory" are derived\nquantities that follow from little input.\n\nFor example, starting from just a simple two-dimensional conformal\nfield theory (even a bunch of free 2d fields would do), you can\nturn the crank and _systematically compute_ these complicated\nLagrange densities, including Einstein\'s lagrangian coupled to gauge\nfields, out of almost nothing.\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>Doug Sweetser <sweetser@alum.mit.edu> wrote in message news:<cluf7f$v1$1@pcls4.std.com>...
> Hello backdoorstudent:
>
> I suspect the long, complicated Lagrange densities of string theory will
> not have that same feel.
Actually, for me they do have a feel of beauty. Because these "long,
complicated Lagrange densities of string theory" are derived
quantities that follow from little input.
For example, starting from just a simple two-dimensional conformal
field theory (even a bunch of free 2d fields would do), you can
turn the crank and _systematically compute_ these complicated
Lagrange densities, including Einstein's lagrangian coupled to gauge
fields, out of almost nothing.
Patrick G
Nov7-04, 04:06 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>I am inclined to agree with backdoorstudent\'s sentiment about\nEinstein\'s remark. In my view, the words of successful scientists are\ntaken as dogma all too often -- recall that Einstein is equally famous\nfor the quip that God does not play dice. In the end, it is very easy\nto both appreciate what Einstein said and also think that, when\ncarried to its logical conclusion, the statement could be wrong.\n\nIt seems that you are stuck in a mode of discovery and proof with\nregard to the limitation of science. I doubt very seriously that\nanyone who thinks science might ultimately be unable to explain the\nuniverse envisions that one day some researcher will present this at a\nconference as the result of his work. You talk about "science"\ndeclaring things incomprehensible as if science is something other\nthan a human activity and a nice method we have for understanding\nthings. It\'s not. You are either confusing or obfuscating the very\nreal differences between human limitations, methodological\nlimitations, and natural limitations.\n\nMost likely no one will ever know for sure where the limit of science\nis in terms of our highest order of natural understanding. If it\nturns out that we reach a point where we cannot possibly learn\nanything deeper about nature we won\'t know it. We are a stubborn\nbunch and we will just keep banging away at the problems until we die.\nTo invoke Feynman, if it turns out that nature is like an onion and\nthere are millions and millions of layers we might get sick of peeling\nthem. If there are an infinite number of layers we can never finish.\n\nFinally, I don\'t think science ceases to exist when it turns out that\npart of the world is incomprehensible to it. Science has been wildly\nsuccessful in explaining some aspects of nature as manifested in\nphysics and chemistry. However, the social sciences have been far\nless groundbreaking and very little in the way of deep understanding\nhas come from them even though questions in that field have been\npursued scientifically. In this regard, science fails every day.\nThus, although we have reason to believe that physics will march on\nbecause of past experience, we also have reason to believe that there\nare domains inaccessible to science. Nonetheless, I won\'t stop being\ncurious and trying to find out more about the universe.\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>I am inclined to agree with backdoorstudent's sentiment about
Einstein's remark. In my view, the words of successful scientists are
taken as dogma all too often -- recall that Einstein is equally famous
for the quip that God does not play dice. In the end, it is very easy
to both appreciate what Einstein said and also think that, when
carried to its logical conclusion, the statement could be wrong.
It seems that you are stuck in a mode of discovery and proof with
regard to the limitation of science. I doubt very seriously that
anyone who thinks science might ultimately be unable to explain the
universe envisions that one day some researcher will present this at a
conference as the result of his work. You talk about "science"
declaring things incomprehensible as if science is something other
than a human activity and a nice method we have for understanding
things. It's not. You are either confusing or obfuscating the very
real differences between human limitations, methodological
limitations, and natural limitations.
Most likely no one will ever know for sure where the limit of science
is in terms of our highest order of natural understanding. If it
turns out that we reach a point where we cannot possibly learn
anything deeper about nature we won't know it. We are a stubborn
bunch and we will just keep banging away at the problems until we die.
To invoke Feynman, if it turns out that nature is like an onion and
there are millions and millions of layers we might get sick of peeling
them. If there are an infinite number of layers we can never finish.
Finally, I don't think science ceases to exist when it turns out that
part of the world is incomprehensible to it. Science has been wildly
successful in explaining some aspects of nature as manifested in
physics and chemistry. However, the social sciences have been far
less groundbreaking and very little in the way of deep understanding
has come from them even though questions in that field have been
pursued scientifically. In this regard, science fails every day.
Thus, although we have reason to believe that physics will march on
because of past experience, we also have reason to believe that there
are domains inaccessible to science. Nonetheless, I won't stop being
curious and trying to find out more about the universe.
Lubos Motl
Nov8-04, 12:33 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>On Sun, 7 Nov 2004, Patrick G wrote:\n\n> I am inclined to agree with backdoorstudent\'s sentiment about\n> Einstein\'s remark. In my view, the words of successful scientists are\n> taken as dogma all too often -- recall that Einstein is equally famous\n> for the quip that God does not play dice.\n\nThat\'s right. There is no ultimate God in science and Einstein\'s\nstatements can turn out to be correct as well as wrong. His statement\nabout the amazing fact that the world is comprehensible seems to be one of\nthe "correct" statements even though it is more poetry than a statement. ;-)\n\n> It seems that you are stuck in a mode of discovery and proof with\n> regard to the limitation of science. I doubt very seriously that\n> anyone who thinks science might ultimately be unable to explain the\n> universe envisions that one day some researcher will present this at a\n> conference as the result of his work.\n\nBut if there\'s no result, there is nothing to talk about. If we admit\nthat there can be no result, the only reason why science could eventually\nbe unable to explain something in the Universe is that the scientists will\ngive up. In some sense, that would be the end the end of science, and\npartly the end of the modern civilization.\n\nIf the scientists give up, it won\'t mean that the world is\nincomprehensible. It will just mean that they are defeatists.\n\nIf the scientists don\'t give up, and there will be no no-go results, then\nthey will always believe that an explanation exists.\n\n> You talk about "science" declaring things incomprehensible as if\n> science is something other than a human activity and a nice method we\n> have for understanding things. It\'s not.\n\nOf course that science is something much more than "a human activity" or\n"a nice method". Science is the strategy to reveal the objective features\nof this whole world.\n\n> You are either confusing or obfuscating the very real differences\n> between human limitations, methodological limitations, and natural\n> limitations.\n\nNeither of these limitations can lead to an *insight* that the world is\n*incomprehensible*. There can be psychological feelings that something is\ntoo hard for us to understand, but these are just feelings and feelings\nare not the primary facts that influence scientists.\n\nThere are *principles* of Nature, such as the uncertainty principle, that\nare universally valid and confirmed by the physical laws as we know them.\nThey\'re the only real constraints, but they can never be viewed as\nlimitations of our "understanding". The uncertainty principle restricts\nthe actual information that objectively *exists* in the world: it says\nthat the question "what is exactly the position and the momentum" is\nmeaningless if you want a too high accuracy.\n\nBut the uncertainty principle does not limit our understanding. On the\ncontrary, it improves our understanding and leads to a more exact theory\n(quantum theory) that reduces to the previous theory (classical theory) in\nthe appropriate limit.\n\nConcerning "human limitations" and "methodological limitations": they\'re\nmuch less relevant for this debate. Of course that if we use a bad method,\nwe may have problems to learn something. And if we employ wrong people,\nthe same thing holds. But the conclusion is not that the world is\nincomprehensible: the conclusion is that we should probably try a\ndifferent method (or different people?) to learn.\n\n> Most likely no one will ever know for sure where the limit of science\n> is in terms of our highest order of natural understanding.\n\nThat\'s a rather convoluted sentence. I believe that we will eventually\nfind the theory of everything that will provide us with the framework to\nunderstand everything from the first principles, and these questions\nabout the limits of science will be eliminated entirely.\n\nSo far they\'re eliminated partially, and it will be so until the situation\nin the previous paragraph will become true.\n\n> If it turns out that we reach a point where we cannot possibly learn\n> anything deeper about nature we won\'t know it.\n\nThat\'s right. But the assumption of a scientist, of course, must be that\nfurther progress is possible - otherwise this scientist should not really\nbe employed by anyone. The ideas that our progress in understanding of the\nworld will stop is not too deep; it\'s very easy to stop progress, and all\nlazy people know very well how to do it. The nontrivial and interesting\noption is to keep on going.\n\n> We are a stubborn bunch and we will just keep banging away at the\n> problems until we die.\n\nWe may also realize that something was a wrong problem. We may realize\nthat the previous questions were not well-posed, and they must be replaced\nby refined questions. Well, this is what a scientific revolution means, it\nhas occured many times, and it always led to better understanding.\n\nThinking about the possibility that no further progress is possible is\nentirely unconstructive and useless.\n\n> To invoke Feynman, if it turns out that nature is like an onion and\n> there are millions and millions of layers we might get sick of peeling\n> them. If there are an infinite number of layers we can never finish.\n\nThere is a cutoff at the Planck scale or earlier. At super-Planckian\nenergies you produce the black holes, and we already know them. The onion\nmetaphor is just a metaphor for a very unlikely scenario.\n\n> Finally, I don\'t think science ceases to exist when it turns out that\n> part of the world is incomprehensible to it.\n\nIf it gives up a part of the world only, then - of course - it is only a\npiece of science that dies.\n\n> Science has been wildly successful in explaining some aspects of\n> nature as manifested in physics and chemistry. However, the social\n> sciences have been far less groundbreaking and very little in the way\n> of deep understanding has come from them even though questions in that\n> field have been pursued scientifically. In this regard, science fails\n> every day.\n\nWell, there is science and there is "science". The questions in social\nsciences are not incomprehensible; they\'re just complex and rather random,\nwhich makes the scientific method in this context less effective.\n\n> Thus, although we have reason to believe that physics will march on\n> because of past experience, we also have reason to believe that there\n> are domains inaccessible to science.\n\nI did not quite get the latter point.\n\n> Nonetheless, I won\'t stop being curious and trying to find out more\n> about the universe.\n\nRight.\n_____________________________ _________________________________________________\ nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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>On Sun, 7 Nov 2004, Patrick G wrote:
> I am inclined to agree with backdoorstudent's sentiment about
> Einstein's remark. In my view, the words of successful scientists are
> taken as dogma all too often -- recall that Einstein is equally famous
> for the quip that God does not play dice.
That's right. There is no ultimate God in science and Einstein's
statements can turn out to be correct as well as wrong. His statement
about the amazing fact that the world is comprehensible seems to be one of
the "correct" statements even though it is more poetry than a statement. ;-)
> It seems that you are stuck in a mode of discovery and proof with
> regard to the limitation of science. I doubt very seriously that
> anyone who thinks science might ultimately be unable to explain the
> universe envisions that one day some researcher will present this at a
> conference as the result of his work.
But if there's no result, there is nothing to talk about. If we admit
that there can be no result, the only reason why science could eventually
be unable to explain something in the Universe is that the scientists will
give up. In some sense, that would be the end the end of science, and
partly the end of the modern civilization.
If the scientists give up, it won't mean that the world is
incomprehensible. It will just mean that they are defeatists.
If the scientists don't give up, and there will be no no-go results, then
they will always believe that an explanation exists.
> You talk about "science" declaring things incomprehensible as if
> science is something other than a human activity and a nice method we
> have for understanding things. It's not.
Of course that science is something much more than "a human activity" or
"a nice method". Science is the strategy to reveal the objective features
of this whole world.
> You are either confusing or obfuscating the very real differences
> between human limitations, methodological limitations, and natural
> limitations.
Neither of these limitations can lead to an *insight* that the world is
*incomprehensible*. There can be psychological feelings that something is
too hard for us to understand, but these are just feelings and feelings
are not the primary facts that influence scientists.
There are *principles* of Nature, such as the uncertainty principle, that
are universally valid and confirmed by the physical laws as we know them.
They're the only real constraints, but they can never be viewed as
limitations of our "understanding". The uncertainty principle restricts
the actual information that objectively *exists* in the world: it says
that the question "what is exactly the position and the momentum" is
meaningless if you want a too high accuracy.
But the uncertainty principle does not limit our understanding. On the
contrary, it improves our understanding and leads to a more exact theory
(quantum theory) that reduces to the previous theory (classical theory) in
the appropriate limit.
Concerning "human limitations" and "methodological limitations": they're
much less relevant for this debate. Of course that if we use a bad method,
we may have problems to learn something. And if we employ wrong people,
the same thing holds. But the conclusion is not that the world is
incomprehensible: the conclusion is that we should probably try a
different method (or different people?) to learn.
> Most likely no one will ever know for sure where the limit of science
> is in terms of our highest order of natural understanding.
That's a rather convoluted sentence. I believe that we will eventually
find the theory of everything that will provide us with the framework to
understand everything from the first principles, and these questions
about the limits of science will be eliminated entirely.
So far they're eliminated partially, and it will be so until the situation
in the previous paragraph will become true.
> If it turns out that we reach a point where we cannot possibly learn
> anything deeper about nature we won't know it.
That's right. But the assumption of a scientist, of course, must be that
further progress is possible - otherwise this scientist should not really
be employed by anyone. The ideas that our progress in understanding of the
world will stop is not too deep; it's very easy to stop progress, and all
lazy people know very well how to do it. The nontrivial and interesting
option is to keep on going.
> We are a stubborn bunch and we will just keep banging away at the
> problems until we die.
We may also realize that something was a wrong problem. We may realize
that the previous questions were not well-posed, and they must be replaced
by refined questions. Well, this is what a scientific revolution means, it
has occured many times, and it always led to better understanding.
Thinking about the possibility that no further progress is possible is
entirely unconstructive and useless.
> To invoke Feynman, if it turns out that nature is like an onion and
> there are millions and millions of layers we might get sick of peeling
> them. If there are an infinite number of layers we can never finish.
There is a cutoff at the Planck scale or earlier. At super-Planckian
energies you produce the black holes, and we already know them. The onion
metaphor is just a metaphor for a very unlikely scenario.
> Finally, I don't think science ceases to exist when it turns out that
> part of the world is incomprehensible to it.
If it gives up a part of the world only, then - of course - it is only a
piece of science that dies.
> Science has been wildly successful in explaining some aspects of
> nature as manifested in physics and chemistry. However, the social
> sciences have been far less groundbreaking and very little in the way
> of deep understanding has come from them even though questions in that
> field have been pursued scientifically. In this regard, science fails
> every day.
Well, there is science and there is "science". The questions in social
sciences are not incomprehensible; they're just complex and rather random,
which makes the scientific method in this context less effective.
> Thus, although we have reason to believe that physics will march on
> because of past experience, we also have reason to believe that there
> are domains inaccessible to science.
I did not quite get the latter point.
> Nonetheless, I won't stop being curious and trying to find out more
> about the universe.
Right.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
jgraber
Nov25-04, 03:42 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>Lubos wrote:\n>Realistic models based on 11-dimensional M-theory are obtained by\n>compactifying the M-theory on a singular 7-dimensional manifold of G2\n>holonomy.\n\nCool. What is (are) the clearest ref(s) for these realistic models,\nnot necessarily the original(s)? TIA. Jim Graber\n\n------------------------------------------------------------------------\nThis post submitted through the LaTeX-enabled physicsforums.com\nTo view this post with LaTeX images:\nhttp://www.physicsforums.com/showthread.php?t=36198#post358343\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>Lubos wrote:
>Realistic models based on 11-dimensional M-theory are obtained by
>compactifying the M-theory on a singular 7-dimensional manifold of G2
>holonomy.
Cool. What is (are) the clearest ref(s) for these realistic models,
not necessarily the original(s)? TIA. Jim Graber
------------------------------------------------------------------------
This post submitted through the LaTeX-enabled physicsforums.com
To view this post with LaTeX images:
http://www.physicsforums.com/showthread.php?t=36198#post358343
John Baez
Feb1-05, 01:31 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>\n\nIn article <jgraber.1g91hh@physicsforums.com>, jgraber <jgra@loc.gov> wrote:\n\n>Lubos wrote:\n\n>>Realistic models based on 11-dimensional M-theory are obtained by\n>>compactifying the M-theory on a singular 7-dimensional manifold of G2\n>>holonomy.\n\n>Cool. What is (are) the clearest ref(s) for these realistic models,\n>not necessarily the original(s)? TIA. Jim Graber\n\nI found this one to be pretty clear and helpful:\n\nB. S. Acharya, M theory, G2 manifolds and four-dimensional physics,\nClass. Quant. Grav. 19 (2002), 5619-5653.\n\nIf you don\'t know what G2 manifolds are, or how they\'re related\nto 6-dimensional Calabi-Yau manifolds, you may find this helpful:\n\nhttp://math.ucr.edu/home/baez/week195.html\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>In article <jgraber.1g91hh@physicsforums.com>, jgraber <jgra@loc.gov> wrote:
>Lubos wrote:
>>Realistic models based on 11-dimensional M-theory are obtained by
>>compactifying the M-theory on a singular 7-dimensional manifold of G2
>>holonomy.
>Cool. What is (are) the clearest ref(s) for these realistic models,
>not necessarily the original(s)? TIA. Jim Graber
I found this one to be pretty clear and helpful:
B. S. Acharya, M theory, G2 manifolds and four-dimensional physics,
Class. Quant. Grav. 19 (2002), 5619-5653.
If you don't know what G2 manifolds are, or how they're related
to 6-dimensional Calabi-Yau manifolds, you may find this helpful:
http://math.ucr.edu/home/baez/week195.html
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