Convention of n_(i,j) [Archive]

Andy Y

Jun30-04, 05:39 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi Physicists,\nI\'m a chemist studying relativity. I have two references that use\nopposite conventions for Eta n_(i,j):\n\n| 1 0 0 0 |\n| 0 -1 0 0 |\nn = | 0 0 -1 0 |\n| 0 0 0 -1 |\n\n| -1 0 0 0 |\n| 0 1 0 0 |\nn = | 0 0 1 0 |\n| 0 0 0 1 |\n\nThree questions:\n1. Does that reverse the convention of which vectors are time like and\nwhich vectors are space like?\n2. Which convention is the modern one (i.e. which one is found in\ncurrent literature)?\n3. Why didn\'t you folks "standardize" this?\n\nI am aware that the results will be the same either way, but it seems\nto be something that might cause continual annoyance.\n\nYour buddy,\nAndy\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi Physicists,
I'm a chemist studying relativity. I have two references that use
opposite conventions for \Eta n_(i,j):

| 1 |
| -1 |
n = |-1 |
| -1 || -1 |
| 1 |
n = | 1 |
| 1 |

Three questions:
1. Does that reverse the convention of which vectors are time like and
which vectors are space like?
2. Which convention is the modern one (i.e. which one is found in
current literature)?
3. Why didn't you folks "standardize" this?

I am aware that the results will be the same either way, but it seems
to be something that might cause continual annoyance.

Your buddy,
Andy

Aaron Bergman

Jul2-04, 04:31 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>\nIn article <c3214d0d.0406291214.25f36f71@posting.google.com>, \nandy314159pi@yahoo.com (Andy Y) wrote:\n\n(Mostly plus versus mostly minus)\n\n> 1. Does that reverse the convention of which vectors are time like and\n> which vectors are space like?\n\nNope. The classification of vectors is the same; it\'s just their norms\nthat get switched.\n\n> 2. Which convention is the modern one (i.e. which one is found in\n> current literature)?\n\nBoth. Particle physicists tend to like mostly minus.\n\n> 3. Why didn\'t you folks "standardize" this?\n\nObstinacy.\n\nAaron\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 <c3214d0d.0406291214.25f36f71@posting.google.com>,
andy314159pi@yahoo.com (Andy Y) wrote:

(Mostly plus versus mostly minus)

> 1. Does that reverse the convention of which vectors are time like and
> which vectors are space like?

Nope. The classification of vectors is the same; it's just their norms
that get switched.

> 2. Which convention is the modern one (i.e. which one is found in
> current literature)?

Both. Particle physicists tend to like mostly minus.

> 3. Why didn't you folks "standardize" this?

Obstinacy.

Aaron

carlip@no-physics-spam.ucdavis.edu

Jul2-04, 04:32 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>\nAndy Y <andy314159pi@yahoo.com> wrote:\n> Hi Physicists,\n> I\'m a chemist studying relativity. I have two references that use\n> opposite conventions for Eta n_(i,j):\n[...]\n\nThe ``mostly minuses\'\' metric is sometimes called the ``west coast\'\'\nmetric; the ``mostly pluses\'\' is te ``east coast\'\' metric.\n\n> Three questions:\n> 1. Does that reverse the convention of which vectors are time like and\n> which vectors are space like?\n\nNo. The definition of timelike depends on the signature of the metric;\nit\'s defined so that the vector (1,0,0,0), which has only a time\ncomponent, is timelikew.\n\n> 2. Which convention is the modern one (i.e. which one is found in\n> current literature)?\n\nBoth appear in the literature, about equally often. Which one is\nused depends largely on which one an author learned in school, but\neach has its advantages. If you\'re looking at a canonical (Hamiltonian)\nformulation of gravity, for example, in which a spacelike hypersurface\nevolves in time, it\'s natural to want the induced spatial metric to\nbe positive, so you are likely to prefer the east coast convention.\nIf you\'re working on Euclidean quantum gravity, it\'s easiest to have\nthe ``imaginary time\'\' metric positive definite rather than negative\ndefinite, so you\'re again likely to prefer the east coast convention.\nOn the other hand, if you\'re looking at motion of observers in a\nspacetime, it\'s easiest to have the interval ds be proper time, which\nmeans you\'ll use the west coast convention. And particle physicists\nusually, though not always, use the west coast metric, in part because\nit means that physical (timelike) four-momenta have positive squares.\n\nIn the end it\'s an arbitrary choice, and the textbooks are split\nalmost evenly. The only place it makes a difference is if you aren\'t\ncareful about matching your definition of spinors to your choice\nof metric signature; then the sign of the metric can matter. (See\nS. Carlip and C. DeWitt-Morette, ``Where the Sign of the Metric\nMakes a Difference,\'\' Phys. Rev. Lett.60 (1988) 1599.)\n\n> 3. Why didn\'t you folks "standardize" this?\n\nHistory. The usage is too evenly split; standardizing would require\nthat some very large group of people change their convention, and\nno one will agree to that.\n\n> I am aware that the results will be the same either way, but it seems\n> to be something that might cause continual annoyance.\n\nAfter a while, you get used to it, and it becomes less annoying (though\nI\'ve actually seen published papers that were wrong because their\nauthors accidentally mixed two conventions).\n\nSteve Carlip\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>Andy Y <andy314159pi@yahoo.com> wrote:
> Hi Physicists,
> I'm a chemist studying relativity. I have two references that use
> opposite conventions for \Eta n_(i,j):
[...]

The ``mostly minuses'' metric is sometimes called the ``west coast''
metric; the ``mostly pluses'' is te ``east coast'' metric.

> Three questions:
> 1. Does that reverse the convention of which vectors are time like and
> which vectors are space like?

No. The definition of timelike depends on the signature of the metric;
it's defined so that the vector (1,0,0,0), which has only a time
component, is timelikew.

> 2. Which convention is the modern one (i.e. which one is found in
> current literature)?

Both appear in the literature, about equally often. Which one is
used depends largely on which one an author learned in school, but
each has its advantages. If you're looking at a canonical (Hamiltonian)
formulation of gravity, for example, in which a spacelike hypersurface
evolves in time, it's natural to want the induced spatial metric to
be positive, so you are likely to prefer the east coast convention.
If you're working on Euclidean quantum gravity, it's easiest to have
the ``imaginary time'' metric positive definite rather than negative
definite, so you're again likely to prefer the east coast convention.
On the other hand, if you're looking at motion of observers in a
spacetime, it's easiest to have the interval ds be proper time, which
means you'll use the west coast convention. And particle physicists
usually, though not always, use the west coast metric, in part because
it means that physical (timelike) four-momenta have positive squares.

In the end it's an arbitrary choice, and the textbooks are split
almost evenly. The only place it makes a difference is if you aren't
careful about matching your definition of spinors to your choice
of metric signature; then the sign of the metric can matter. (See
S. Carlip and C. DeWitt-Morette, ``Where the Sign of the Metric
Makes a Difference,'' Phys. Rev. Lett.60 (1988) 1599.)

> 3. Why didn't you folks "standardize" this?

History. The usage is too evenly split; standardizing would require
that some very large group of people change their convention, and
no one will agree to that.

> I am aware that the results will be the same either way, but it seems
> to be something that might cause continual annoyance.

After a while, you get used to it, and it becomes less annoying (though
I've actually seen published papers that were wrong because their
authors accidentally mixed two conventions).

Steve Carlip

ebunn@lfa221051.richmond.edu

Jul2-04, 04:32 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>\n\nIn article <c3214d0d.0406291214.25f36f71@posting.google.com>, \nAndy Y <andy314159pi@yahoo.com> wrote:\n>Hi Physicists,\n>I\'m a chemist studying relativity. I have two references that use\n>opposite conventions for Eta n_(i,j):\n\n>Three questions:\n>1. Does that reverse the convention of which vectors are time like and\n>which vectors are space like?\n\nWith one convention, timelike vectors are those with positive squared\nnorm, and spacelike vectors are those with negative squared norm.\n(That is, sum over i,j of eta_{ij} v_i v_j is positive if v is\ntimelike and negative if v is spacelike.) With the opposite\nconvention, timelike vectors are those with negative squared norm and\nspacelike vectors are those with positive squared norm.\n\nBut the choice of convention doesn\'t change which vectors are timelike\nand which vectors are spacelike. For instance, everyone agrees\nthat the vector with components (t,x,y,z) = (0,1,0,0) is spacelike,\nalthough people who adopt different sign conventions will\ndisagree over whether its squared norm is positive or negative.\n\n>2. Which convention is the modern one (i.e. which one is found in\n>current literature)?\n\nI think both are still common. In general, people who do\nparticle physics are most likely to use the time-is-positive\nconvention, whereas people who do general relativity are somewhat\nmore likely to use the space-is-positive convention.\n\nThere\'s a pretty good reason for particle physicists to adopt the\ntime-is-positive convention. The most common 4-vector that particle\nphysicists deal with is the energy-momentum 4-vector. That\'s\na timelike vector. With the time-is-positive convention, its\nnorm is just the particle\'s rest mass. With the opposite\nconvention.\n\n>3. Why didn\'t you folks "standardize" this?\n\nI don\'t know. We\'re all used to it, so it doesn\'t bother us,\nand it gives us a way to appear more obscure to outsiders!\n\n-Ted\n\n--\n[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]\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 <c3214d0d.0406291214.25f36f71@posting.google.com>,
Andy Y <andy314159pi@yahoo.com> wrote:
>Hi Physicists,
>I'm a chemist studying relativity. I have two references that use
>opposite conventions for \Eta n_(i,j):

>Three questions:
>1. Does that reverse the convention of which vectors are time like and
>which vectors are space like?

With one convention, timelike vectors are those with positive squared
norm, and spacelike vectors are those with negative squared norm.
(That is, sum over i,j of \eta_{ij} v_i v_j is positive if v is
timelike and negative if v is spacelike.) With the opposite
convention, timelike vectors are those with negative squared norm and
spacelike vectors are those with positive squared norm.

But the choice of convention doesn't change which vectors are timelike
and which vectors are spacelike. For instance, everyone agrees
that the vector with components (t,x,y,z) = (0,1,0,0) is spacelike,
although people who adopt different sign conventions will
disagree over whether its squared norm is positive or negative.

>2. Which convention is the modern one (i.e. which one is found in
>current literature)?

I think both are still common. In general, people who do
particle physics are most likely to use the time-is-positive
convention, whereas people who do general relativity are somewhat
more likely to use the space-is-positive convention.

There's a pretty good reason for particle physicists to adopt the
time-is-positive convention. The most common 4-vector that particle
physicists deal with is the energy-momentum 4-vector. That's
a timelike vector. With the time-is-positive convention, its
norm is just the particle's rest mass. With the opposite
convention.

>3. Why didn't you folks "standardize" this?

I don't know. We're all used to it, so it doesn't bother us,
and it gives us a way to appear more obscure to outsiders!

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]