<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\nDavid Park wrote:\n>\n> "Alex Green" <dralexgreen@yahoo.co.uk> wrote in message\n> news:42c8441.0407220559.6ad09eb2@posting.google.com...\n> >\n> >\n> > The \'flat metric\' (*) of modern Special Relativity is conventionally\n> > described by a metric tensor that has a principle diagonal given by\n> > (-1,1,1,1) or equivalently (1,-1,-1,-1).\n> >\n> > I have always been troubled by the change of sign in the principle\n> > diagonal of the metric tensor, not because it is mathematically\n> > suspect but because it seems to have a physical significance that is\n> > dynamical rather than geometrical. The negative coefficient in the\n> > metric tensor implies that -(ct)^2 in the metric ( ds^2 = dx^2 + dy^2\n> > + dz^2 - (cdt)^2 ) originates in multiplying -dt by +dt rather than\n> > squaring (sqrt -1)*dt. This use of -dt*+dt seems to imply a movement\n> > through time and back again rather than a simple geometric phenomenon\n> > such as occurs in Pythagoras\' Theorem (which expresses the spherical\n> > symmetry of space).\n> >\n> > Can anyone tell me about the true physical significance of the\n> > negative coefficient in the metric tensor of \'flat\' space-time?\n> >\n> >\n> > * See for instance "An Introduction to General Relativity" by Hughston\n> > & Todd.p7.\n>\n> There is a very good recent pedagogical paper on this topic, "Spacetime and\n> Euclidean Geometry" by Dieter Brill and Ted Jacobson, arXiv:gr-qc/0407044.\n> Using the invariance of the speed of light and the equivalence of inertial\n> frames, they derive the analog of the Pythagorean theorem in Minkowskian\n> space, T^2 = t^2 - x^2. This is an elegant and geometrical presentation.\n\nhttp://arXiv.org/abs/gr-qc/0407022\n\n"8^>)\n\n--\nUncle Al\nhttp://www.mazepath.com/uncleal/\n(Toxic URL! Unsafe for children and most mammals)\nhttp://www.mazepath.com/uncleal/qz.pdf\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>David Park wrote:
>
> "Alex Green" <dralexgreen@yahoo.co.uk> wrote in message
> news:42c8441.0407220559.6ad09eb2@posting.google.com...
> >
> >
> > The 'flat metric' (*) of modern Special Relativity is conventionally
> > described by a metric tensor that has a principle diagonal given by
> > (-1,1,1,1) or equivalently (1,-1,-1,-1).
> >
> > I have always been troubled by the change of sign in the principle
> > diagonal of the metric tensor, not because it is mathematically
> > suspect but because it seems to have a physical significance that is
> > dynamical rather than geometrical. The negative coefficient in the
> > metric tensor implies that -(ct)^2 in the metric ( ds^2 = dx^2 + dy^2
> > + dz^2 - (cdt)^2 ) originates in multiplying -dt by +dt rather than
> > squaring (\sqrt -1)*dt. This use of -dt*+dt seems to imply a movement
> > through time and back again rather than a simple geometric phenomenon
> > such as occurs in Pythagoras' Theorem (which expresses the spherical
> > symmetry of space).
> >
> > Can anyone tell me about the true physical significance of the
> > negative coefficient in the metric tensor of 'flat' space-time?
> >
> >
> > * See for instance "An Introduction to General Relativity" by Hughston
> > & Todd.p7.
>
> There is a very good recent pedagogical paper on this topic, "Spacetime and
> Euclidean Geometry" by Dieter Brill and Ted Jacobson, arXiv:http://www.arxiv.org/abs/gr-qc/0407044.
> Using the invariance of the speed of light and the equivalence of inertial
> frames, they derive the analog of the Pythagorean theorem in Minkowskian
> space, T^2 = t^2 - x^2. This is an elegant and geometrical presentation.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Peter
Jul31-04, 10:15 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>It\'s actually arXiv:gr-qc/0407044, I believe.\n\nPeter\n\n> There is a very good recent pedagogical paper on this topic, "Spacetime and\n> Euclidean Geometry" by Dieter Brill and Ted Jacobson, arXiv:gr-qc/0407044.\n> Using the invariance of the speed of light and the equivalence of inertial\n> frames, they derive the analog of the Pythagorean theorem in Minkowskian\n> space, T^2 = t^2 - x^2. This is an elegant and geometrical presentation.\n>\n> David Park\n> djmp@earthlink.net\n> http://home.earthlink.net/~djmp/\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>It's actually arXiv:http://www.arxiv.org/abs/gr-qc/0407044, I believe.
Peter
> There is a very good recent pedagogical paper on this topic, "Spacetime and
> Euclidean Geometry" by Dieter Brill and Ted Jacobson, arXiv:http://www.arxiv.org/abs/gr-qc/0407044.
> Using the invariance of the speed of light and the equivalence of inertial
> frames, they derive the analog of the Pythagorean theorem in Minkowskian
> space, T^2 = t^2 - x^2. This is an elegant and geometrical presentation.
>
> David Park
> djmp@earthlink.net
> http://home.earthlink.net/~djmp/
Alex Green
Aug2-04, 07:11 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>Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<40FFDFA8.80B797A6@hate.spam.net>...\n> David Park wrote:\n> >\n> > "Alex Green" <dralexgreen@yahoo.co.uk> wrote in message\n> > news:42c8441.0407220559.6ad09eb2@posting.google.com...\n> > >\n> > >\n> > > The \'flat metric\' (*) of modern Special Relativity is conventionally\n> > > described by a metric tensor that has a principle diagonal given by\n> > > (-1,1,1,1) or equivalently (1,-1,-1,-1).\n> > >\n> > > I have always been troubled by the change of sign in the principle\n> > > diagonal of the metric tensor, not because it is mathematically\n> > > suspect but because it seems to have a physical significance that is\n> > > dynamical rather than geometrical. The negative coefficient in the\n> > > metric tensor implies that -(ct)^2 in the metric ( ds^2 = dx^2 + dy^2\n> > > + dz^2 - (cdt)^2 ) originates in multiplying -dt by +dt rather than\n> > > squaring (sqrt -1)*dt. This use of -dt*+dt seems to imply a movement\n> > > through time and back again rather than a simple geometric phenomenon\n> > > such as occurs in Pythagoras\' Theorem (which expresses the spherical\n> > > symmetry of space).\n> > >\n> > > Can anyone tell me about the true physical significance of the\n> > > negative coefficient in the metric tensor of \'flat\' space-time?\n> > >\n> > >\n> > > * See for instance "An Introduction to General Relativity" by Hughston\n> > > & Todd.p7.\n> >\n>\n\nThis is a rather original approach to the metric of space-time:\n\nAugust 1992. J. Greensite\nDYNAMICAL ORIGIN OF THE LORENTZIAN SIGNATURE OF SPACETIME\nhttp://ernie.ecs.soton.ac.uk/opcit/cgi-bin/pdf?id=oai%3AarXiv.org%3Agr-qc%2F9210008\n\nThe use of the Feynman Path Integral is interesting, is the author\nsuggesting that the Lorentzian metric tensor is due to movement back\nand forth in time as well as the raising the possibility that the\nmetric tensor itself is dynamical?\n\nBest Wishes\n\nAlex Green\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>Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<40FFDFA8.80B797A6@hate.spam.net>...
> David Park wrote:
> >
> > "Alex Green" <dralexgreen@yahoo.co.uk> wrote in message
> > news:42c8441.0407220559.6ad09eb2@posting.google.com...
> > >
> > >
> > > The 'flat metric' (*) of modern Special Relativity is conventionally
> > > described by a metric tensor that has a principle diagonal given by
> > > (-1,1,1,1) or equivalently (1,-1,-1,-1).
> > >
> > > I have always been troubled by the change of sign in the principle
> > > diagonal of the metric tensor, not because it is mathematically
> > > suspect but because it seems to have a physical significance that is
> > > dynamical rather than geometrical. The negative coefficient in the
> > > metric tensor implies that -(ct)^2 in the metric ( ds^2 = dx^2 + dy^2
> > > + dz^2 - (cdt)^2 ) originates in multiplying -dt by +dt rather than
> > > squaring (\sqrt -1)*dt. This use of -dt*+dt seems to imply a movement
> > > through time and back again rather than a simple geometric phenomenon
> > > such as occurs in Pythagoras' Theorem (which expresses the spherical
> > > symmetry of space).
> > >
> > > Can anyone tell me about the true physical significance of the
> > > negative coefficient in the metric tensor of 'flat' space-time?
> > >
> > >
> > > * See for instance "An Introduction to General Relativity" by Hughston
> > > & Todd.p7.
> >
>
This is a rather original approach to the metric of space-time:
August 1992. J. Greensite
DYNAMICAL ORIGIN OF THE LORENTZIAN SIGNATURE OF SPACETIME
http://ernie.ecs.soton.ac.uk/opcit/cgi-bin/pdf?id=oai%3AarXiv.org%3Agr-qc%2F9210008
The use of the Feynman Path Integral is interesting, is the author
suggesting that the Lorentzian metric tensor is due to movement back
and forth in time as well as the raising the possibility that the
metric tensor itself is dynamical?
Best Wishes
Alex Green
Danny Ross Lunsford
Aug12-04, 09:30 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\nUncle Al <UncleAl0@hate.spam.net> wrote in message news:<40FFDFA8.80B797A6@hate.spam.net>...\n\n> "8^>)\n\nI assume this is a happy face, so perhaps you\'ll like the algebraic\nargument, given here with student commentary :)\n\nhttp://membrane.com/sidd/wundrelat.txt\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>Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<40FFDFA8.80B797A6@hate.spam.net>...
> "8^>)
I assume this is a happy face, so perhaps you'll like the algebraic
argument, given here with student commentary :)
http://membrane.com/sidd/wundrelat.txt
-drl
Norm Dresner
Aug12-04, 09:31 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"Peter" <peterbat@gmail.com> wrote in message\nnews:410ba988@news.sentex.net...\n> It\'s actually arXiv:gr-qc/0407044, I believe.\n\nActually it\'s gr-qc/0407022\n\nNorm\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" <peterbat@gmail.com> wrote in message
news:410ba988@news.sentex.net...
> It's actually arXiv:http://www.arxiv.org/abs/gr-qc/0407044, I believe.