View Full Version : Wikipedia & string theory
Lubos Motl
May9-04, 07:26 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, 9 May 2004, Daniel wrote:\n\n> by the way, have you heard of www.wikipedia.com?\n\nI really think that it is a very good idea. Everyone who has something to\nsay is invited to create an account there, and contibute and edit. Let me\nenumerate a couple of pages (this list is not complete) that I started\nthere:\n\nhttp://en.wikipedia.org/wiki/AdS/CFT\nhttp://en.wikipedia.org/wiki/Andrew_Strominger\nhttp://en.wikipedia.org/wiki/Cumrun_Vafa\nhttp://en.wikipedia.org/wiki/Ashoke_Sen\nhttp://en.wikipedia.org/wiki/Juan_Maldacena\nhttp://en.wikipedia.org/wiki/Mirror_symmetry\nhttp://en.wikipedia.org/wiki/String_field_theory\nhttp://en.wikipedia.org/wiki/Holonomy\nhttp://en.wikipedia.org/wiki/Heterotic_string\nhttp://en.wikipedia.org/wiki/Closed_string\nhttp://en.wikipedia.org/wiki/Open_string\nhttp://en.wikipedia.org/wiki/F-theory\nhttp://en.wikipedia.org/wiki/Background_independence\nhttp://en.wikipedia.org/wiki/Higgs_mechanism\nhttp://en.wikipedia.org/wiki/Conifold\nhttp://en.wikipedia.org/wiki/Tachyon_condensation\nhttp://en.wikipedia.org/wiki/Einsteinian_manifold\nhttp://en.wikipedia.org/wiki/Second_superstring_revolution\n\nAll the best,\nLubos\n____________________________________ __________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\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, 9 May 2004, Daniel wrote:
> by the way, have you heard of www.wikipedia.com?
I really think that it is a very good idea. Everyone who has something to
say is invited to create an account there, and contibute and edit. Let me
enumerate a couple of pages (this list is not complete) that I started
there:
http://en.wikipedia.org/wiki/AdS/CFT
http://en.wikipedia.org/wiki/Andrew_Strominger
http://en.wikipedia.org/wiki/Cumrun_Vafa
http://en.wikipedia.org/wiki/Ashoke_Sen
http://en.wikipedia.org/wiki/Juan_Maldacena
http://en.wikipedia.org/wiki/Mirror_symmetry
http://en.wikipedia.org/wiki/String_field_theory
http://en.wikipedia.org/wiki/Holonomy
http://en.wikipedia.org/wiki/Heterotic_string
http://en.wikipedia.org/wiki/Closed_string
http://en.wikipedia.org/wiki/Open_string
http://en.wikipedia.org/wiki/F-theory
http://en.wikipedia.org/wiki/Background_independence
http://en.wikipedia.org/wiki/Higgs_mechanism
http://en.wikipedia.org/wiki/Conifold
http://en.wikipedia.org/wiki/Tachyon_condensation
http://en.wikipedia.org/wiki/Einsteinian_manifold
http://en.wikipedia.org/wiki/Second_superstring_revolution
All the best,
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
<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 Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405091919020.9029-100000@feynman.harvard.edu>...\n\n> On Sun, 9 May 2004, Daniel wrote:\n>\n> > by the way, have you heard of www.wikipedia.com?\n>\n> I really think that it is a very good idea. Everyone who has something to\n> say is invited to create an account there, and contibute and edit. Let me\n> enumerate a couple of pages (this list is not complete) that I started\n> there:\n>\n> http://en.wikipedia.org/wiki/AdS/CFT\n> http://en.wikipedia.org/wiki/Andrew_Strominger\n> http://en.wikipedia.org/wiki/Cumrun_Vafa\n> http://en.wikipedia.org/wiki/Ashoke_Sen\n> http://en.wikipedia.org/wiki/Juan_Maldacena\n> http://en.wikipedia.org/wiki/Mirror_symmetry\n> http://en.wikipedia.org/wiki/String_field_theory\n> http://en.wikipedia.org/wiki/Holonomy\n> http://en.wikipedia.org/wiki/Heterotic_string\n> http://en.wikipedia.org/wiki/Closed_string\n> http://en.wikipedia.org/wiki/Open_string\n> http://en.wikipedia.org/wiki/F-theory\n> http://en.wikipedia.org/wiki/Background_independence\n> http://en.wikipedia.org/wiki/Higgs_mechanism\n> http://en.wikipedia.org/wiki/Conifold\n> http://en.wikipedia.org/wiki/Tachyon_condensation\n> http://en.wikipedia.org/wiki/Einsteinian_manifold\n> http://en.wikipedia.org/wiki/Second_superstring_revolution\n>\n> All the best,\n> Lubos\n\nYour links were posted at slashdot:\nhttp://science.slashdot.org/article.pl?sid=04/05/10/1048205&mode=thread&tid=134\nCongratulations :)\n\n[Moderator\'s note: Well, thank you. It seems that I should be\nhappy about that. Thanks to all the people who are contributing,\nand who are removing every incorrect occurence of "the" or any\nother error that I have made and will make. Lubos]\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 Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405091919020.9029-100000@feynman.harvard.edu>...
> On Sun, 9 May 2004, Daniel wrote:
>
> > by the way, have you heard of www.wikipedia.com?
>
> I really think that it is a very good idea. Everyone who has something to
> say is invited to create an account there, and contibute and edit. Let me
> enumerate a couple of pages (this list is not complete) that I started
> there:
>
> http://en.wikipedia.org/wiki/AdS/CFT
> http://en.wikipedia.org/wiki/Andrew_Strominger
> http://en.wikipedia.org/wiki/Cumrun_Vafa
> http://en.wikipedia.org/wiki/Ashoke_Sen
> http://en.wikipedia.org/wiki/Juan_Maldacena
> http://en.wikipedia.org/wiki/Mirror_symmetry
> http://en.wikipedia.org/wiki/String_field_theory
> http://en.wikipedia.org/wiki/Holonomy
> http://en.wikipedia.org/wiki/Heterotic_string
> http://en.wikipedia.org/wiki/Closed_string
> http://en.wikipedia.org/wiki/Open_string
> http://en.wikipedia.org/wiki/F-theory
> http://en.wikipedia.org/wiki/Background_independence
> http://en.wikipedia.org/wiki/Higgs_mechanism
> http://en.wikipedia.org/wiki/Conifold
> http://en.wikipedia.org/wiki/Tachyon_condensation
> http://en.wikipedia.org/wiki/Einsteinian_manifold
> http://en.wikipedia.org/wiki/Second_superstring_revolution
>
> All the best,
> Lubos
Your links were posted at slashdot:
http://science.slashdot.org/article.pl?sid=04/05/10/1048205&mode=thread&tid=134
Congratulations :)
[Moderator's note: Well, thank you. It seems that I should be
happy about that. Thanks to all the people who are contributing,
and who are removing every incorrect occurence of "the" or any
other error that I have made and will make. Lubos]
Serenus Zeitblom
May10-04, 11:32 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 Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405091919020.9029-100000@feynman.harvard.edu>...\n\n> On Sun, 9 May 2004, Daniel wrote:\n>\n> > by the way, have you heard of www.wikipedia.com?\n>\n> I really think that it is a very good idea. Everyone who has something to\n> say is invited to create an account there, and contibute and edit.\n\nYeah, it\'s cool, but there are lots of mistakes. For example the\nwrong symmetry group is given for deSitter space, it is claimed\nthat AdS is a cosmological model [which is true I suppose if you allow\nspacetimes that aren\'t expanding!] and worst of all the article\non GR claims\n"The theory of special relativity concerns itself with inertial\n(non-accelerating) frames while general relativity deals with all\nframes of reference."\n\nwhich is the oldest mistake in the book.\n\n\n[Moderator\'s note: Why is the last statement a mistake,\nas opposed to a definition of special and general\ntheories of relativity? LM]\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 Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0405091919020.9029-100000@feynman.harvard.edu>...
> On Sun, 9 May 2004, Daniel wrote:
>
> > by the way, have you heard of www.wikipedia.com?
>
> I really think that it is a very good idea. Everyone who has something to
> say is invited to create an account there, and contibute and edit.
Yeah, it's cool, but there are lots of mistakes. For example the
wrong symmetry group is given for deSitter space, it is claimed
that AdS is a cosmological model [which is true I suppose if you allow
spacetimes that aren't expanding!] and worst of all the article
on GR claims
"The theory of special relativity concerns itself with inertial
(non-accelerating) frames while general relativity deals with all
frames of reference."
which is the oldest mistake in the book.
[Moderator's note: Why is the last statement a mistake,
as opposed to a definition of special and general
theories of relativity? LM]
Serenus Zeitblom
May11-04, 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>> [Moderator\'s note: Why is the last statement a mistake,\n> as opposed to a definition of special and general\n> theories of relativity? LM]\n\nSerenus Zeitblom:\n\nCan you cite an example of a problem which involves things accelerating\nin flat spacetime and which special relativity is not able to handle?\nThe definition of special relativity is that it is what you get\nwhen you take GR but force the curvature tensor to be zero under\nall circumstances.\n\n=====\n[Moderator\'s note: Nope, special relativity is able to handle any\naccelerating motion in flat spacetime, but what is important is that the\nform of the laws of physics changes if one transforms the coordinates\nby any transformation that is not a Poincare transformation. In other\nwords, the accelerating observers must use different (transformed)\nequations.\n\nOn the other hand, the defining equations of general relativity are\ninvariant under *any* coordinate transformations. In other words,\ngeneral relativity treats *all* observers as equal. It is true that\nGR describes spacetime that can be curved, but the nice fact is that\nthe spacetime curvature is a *derived* insight. It has been derived by\nEinstein from two principles - the principle of equivalence, and the\nprinciple of general covariance. What you say is a description of the\noutcome, not a description of the fundamental defining properties of\nthese theories. While it is true that special relativity is the limit\nof GR in which the space becomes flat - or I would rather say the limit\nin which the gravity is turned off (G_{newton}=0), the starting points\nare the postulates based on the symmetries.\n\nThe postulates of special relativity are:\n\n* the invariance of the laws of physics under Lorentz/Poincare\ntransformations, i.e. the equivalence of all inertial observers\n* constancy of the speed of light; its independence on the speed of\nthe source as well as the observer\n\nNote that these two postulates are related, and the second one\nessentially says that even the speed of light is a universal quantity,\nindependent of the speed of the observer.\n\nThe postulates of general relativity are\n\n* the invariance of the laws of physics under any coordinate\ntransformations, i.e. the equivalence of all observers\n* the principle of equivalence, i.e. the impossibility to locally\ndistinguish gravity from acceleration.\n\nNote that the second postulate is again reducing the number of\nindependent fundamental mechanisms in Nature. If we allow all\n(accelerating) observers, it is clear that our equations will have to\nallow inertial forces - and the principle says that the objects (metric)\nthat are necessary to describe the inertial forces are already sufficient\nto describe another force, namely gravity. LM]\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>> [Moderator's note: Why is the last statement a mistake,
> as opposed to a definition of special and general
> theories of relativity? LM]
Serenus Zeitblom:
Can you cite an example of a problem which involves things accelerating
in flat spacetime and which special relativity is not able to handle?
The definition of special relativity is that it is what you get
when you take GR but force the curvature tensor to be zero under
all circumstances.
=====
[Moderator's note: Nope, special relativity is able to handle any
accelerating motion in flat spacetime, but what is important is that the
form of the laws of physics changes if one transforms the coordinates
by any transformation that is not a Poincare transformation. In other
words, the accelerating observers must use different (transformed)
equations.
On the other hand, the defining equations of general relativity are
invariant under *any* coordinate transformations. In other words,
general relativity treats *all* observers as equal. It is true that
GR describes spacetime that can be curved, but the nice fact is that
the spacetime curvature is a *derived* insight. It has been derived by
Einstein from two principles - the principle of equivalence, and the
principle of general covariance. What you say is a description of the
outcome, not a description of the fundamental defining properties of
these theories. While it is true that special relativity is the limit
of GR in which the space becomes flat - or I would rather say the limit
in which the gravity is turned off (G_{newton}=0), the starting points
are the postulates based on the symmetries.
The postulates of special relativity are:
* the invariance of the laws of physics under Lorentz/Poincare
transformations, i.e. the equivalence of all inertial observers
* constancy of the speed of light; its independence on the speed of
the source as well as the observer
Note that these two postulates are related, and the second one
essentially says that even the speed of light is a universal quantity,
independent of the speed of the observer.
The postulates of general relativity are
* the invariance of the laws of physics under any coordinate
transformations, i.e. the equivalence of all observers
* the principle of equivalence, i.e. the impossibility to locally
distinguish gravity from acceleration.
Note that the second postulate is again reducing the number of
independent fundamental mechanisms in Nature. If we allow all
(accelerating) observers, it is clear that our equations will have to
allow inertial forces - and the principle says that the objects (metric)
that are necessary to describe the inertial forces are already sufficient
to describe another force, namely gravity. LM]
Tuukka Toivonen
May11-04, 10:11 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>> [Moderator\'s note: Nope, special relativity is able to handle any\n> ...\n> invariant under *any* coordinate transformations. In other words,\n> general relativity treats *all* observers as equal. It is true that\n\nDoes this hold also in rotating frames of reference, ie.\nif there is just a single object in the whole universe, can it\ndetect whether it is rotating or not?\n\n[Moderator\'s note: In general relativity, it is possible\nto distinguish a rotating object from a non-rotating object\n- they have a different metric around. The proposal that\nrotating and non-rotating objects would be indistinguishable\nin a completely empty Universe, because the rotation and\nacceleration only makes sense in comparison with other objects,\nis known as Mach\'s principle. Although this principle inspired\nEinstein tremendously, it has not become a part of the final\nform of Einstein\'s general relativity. LM]\n\n(Speculation: if it can detect, could the dark energy be due\nto rotation of the universe as a whole?)\n\n[Moderator\'s note: it could not. The local geometry in the\npresence of the dark energy is curved - and this curvature\ncan be measured independently of any observers. Rotation\ncannot induce any (Riemann\'s) curvature locally.\nI encourage all participants to focus on string theory. LM]\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>> [Moderator's note: Nope, special relativity is able to handle any
> ...
> invariant under *any* coordinate transformations. In other words,
> general relativity treats *all* observers as equal. It is true that
Does this hold also in rotating frames of reference, ie.
if there is just a single object in the whole universe, can it
detect whether it is rotating or not?
[Moderator's note: In general relativity, it is possible
to distinguish a rotating object from a non-rotating object
- they have a different metric around. The proposal that
rotating and non-rotating objects would be indistinguishable
in a completely empty Universe, because the rotation and
acceleration only makes sense in comparison with other objects,
is known as Mach's principle. Although this principle inspired
Einstein tremendously, it has not become a part of the final
form of Einstein's general relativity. LM]
(Speculation: if it can detect, could the dark energy be due
to rotation of the universe as a whole?)
[Moderator's note: it could not. The local geometry in the
presence of the dark energy is curved - and this curvature
can be measured independently of any observers. Rotation
cannot induce any (Riemann's) curvature locally.
I encourage all participants to focus on string theory. LM]
Serenus Zeitblom
May12-04, 10:27 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 Motl wrote:\n\n> [Moderator\'s note: Nope, special relativity is able to handle any\n> accelerating motion in flat spacetime, ...\n\nSZ: So you agree that the original wikipedia entry, stating\n"The theory of special relativity concerns itself with inertial\n(non-accelerating) frames while general relativity deals with all\nframes of reference." is seriously misleading?\n\n[Moderator\'s note - answer. The verb "deals with" is awkward and\nsimplified, but otheriwse the links between SR and GR and the\ncorresponding symmetries between a class of frames are correct. LM]\n\nL.M. wrote:\n\n> but what is important is that the\n> form of the laws of physics changes if one transforms the coordinates\n> by any transformation that is not a Poincare transformation. In other\n> words, the accelerating observers must use different (transformed)\n> equations.\n\nSZ: Not true, if the laws are formulated --- as they should be ---\nin a geometric way. After all, as you know, Minkowski\nspacetime does have a linear [Riemannian] connection, and if\neverything is formulated using that connection then all of your\nequations will of course be form-invariant under *all*\nchanges of coordinates.\n\n[Moderator\'s note: that\'s correct, but one must insist on some\ncommonsense, otherwise we could say that an apple has an E_8 symmetry\nas long as the E_8 group acts trivially. The connection in your case\nis clearly an auxilliary, unphysical, derived, non-dynamical object.\nOne does not gain any physics by adding such a connection, and therefore\nthis "enhanced" symmetry of all diffeomorphisms is unphysical in flat\nspace. As long as commonsense is preserved, the symmetry of SR is\nthe Poincare symmetry, and the symmetry of GR are all diffeomorphisms.\nI don\'t necessarily claim that these are rigorous statements, but I\nbelieve that every physicist must know why we say that SR only puts\nthe inertial frames on equal footing, while GR puts all frames on equal\nfooting, and why your examples are misleading. If you disagree, please\nlet us agree to disagree, and stop these off-topic discussions. LM]\n\nSZ: For example, one set of Maxwell\'s equations can be written as\n[covariant divergence operator]F = J,\nwhere J is the current one-form; here the covariant divergence is\ndefined using the Minkowski connection. All this is in special\nrelativity and the form of this equation does not change under\n*any* coordinate transformation.\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 Motl wrote:
> [Moderator's note: Nope, special relativity is able to handle any
> accelerating motion in flat spacetime, ...
SZ: So you agree that the original wikipedia entry, stating
"The theory of special relativity concerns itself with inertial
(non-accelerating) frames while general relativity deals with all
frames of reference." is seriously misleading?
[Moderator's note - answer. The verb "deals with" is awkward and
simplified, but otheriwse the links between SR and GR and the
corresponding symmetries between a class of frames are correct. LM]
L.M. wrote:
> but what is important is that the
> form of the laws of physics changes if one transforms the coordinates
> by any transformation that is not a Poincare transformation. In other
> words, the accelerating observers must use different (transformed)
> equations.
SZ: Not true, if the laws are formulated --- as they should be ---
in a geometric way. After all, as you know, Minkowski
spacetime does have a linear [Riemannian] connection, and if
everything is formulated using that connection then all of your
equations will of course be form-invariant under *all*
changes of coordinates.
[Moderator's note: that's correct, but one must insist on some
commonsense, otherwise we could say that an apple has an E_8 symmetry
as long as the E_8 group acts trivially. The connection in your case
is clearly an auxilliary, unphysical, derived, non-dynamical object.
One does not gain any physics by adding such a connection, and therefore
this "enhanced" symmetry of all diffeomorphisms is unphysical in flat
space. As long as commonsense is preserved, the symmetry of SR is
the Poincare symmetry, and the symmetry of GR are all diffeomorphisms.
I don't necessarily claim that these are rigorous statements, but I
believe that every physicist must know why we say that SR only puts
the inertial frames on equal footing, while GR puts all frames on equal
footing, and why your examples are misleading. If you disagree, please
let us agree to disagree, and stop these off-topic discussions. LM]
SZ: For example, one set of Maxwell's equations can be written as
[covariant divergence operator]F = J,
where J is the current one-form; here the covariant divergence is
defined using the Minkowski connection. All this is in special
relativity and the form of this equation does not change under
*any* coordinate transformation.
Haelfix
May15-04, 08:15 AM
'Although this principle inspired
Einstein tremendously, it has not become a part of the final
form of Einstein's general relativity'
Yea, its a bit of a dilemma in GR.. Mach's principle really only makes sense mathematically in a decelerating FRW universe... One wants finite boundary conditions. Alas, experiment seems to say otherwise.. Chalk another minus for 'the universe we live in is beautiful' argument.
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