The Meaning of the Einstein equation, redux [Archive]

Serenus Zeitblom

Aug19-04, 12:36 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 thought I would draw everyone\'s attention to the latest edition of\nthis paper, which is now better than ever:\n\nhttp://arxiv.org/abs/gr-qc/0103044\n\nWould I be correct in saying that the statement of the EFE in this\npaper is a sort of verbal version of the one in footnote 1 of\n\nhttp://arxiv.org/abs/gr-qc/0405072\n?\n\nI think that there is an interesting psychological point brought out\nby what Padmanabhan is saying: we all tend to discount anything that\n"depends on a choice of coordinates", but it is much more palatable to\nbe told that it "depends on a choice of observer field"! After all, we\nare all comfortable with the idea of isotropy in cosmology, which in\ngeneral only makes sense with respect to a particular family of\nobservers. Thus P. encourages us to think of energy density *not* as a\ncomponent of a tensor but rather as a *scalar* -- a scalar which,\nadmittedly, depends on a choice of observer field. So what? Well, for\nexample, I would feel more comfortable integrating a scalar over a\nlarge chunk of a spatial section --- I would not be plagued by guilt\nfeelings induced by worries over parallel transport and all that. So\nfor example it seems perfectly reasonable for a family of inertial\nobservers to talk about the *total energy* of deSitter spacetime at\nsome time --- just integrate the scalar energy density [coming from\nthe cosmological constant] over that 3-sphere.\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 thought I would draw everyone's attention to the latest edition of
this paper, which is now better than ever:

http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0103044

Would I be correct in saying that the statement of the EFE in this
paper is a sort of verbal version of the one in footnote 1 of

http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0405072
?

I think that there is an interesting psychological point brought out
by what Padmanabhan is saying: we all tend to discount anything that
"depends on a choice of coordinates", but it is much more palatable to
be told that it "depends on a choice of observer field"! After all, we
are all comfortable with the idea of isotropy in cosmology, which in
general only makes sense with respect to a particular family of
observers. Thus P. encourages us to think of energy density *not* as a
component of a tensor but rather as a *scalar* -- a scalar which,
admittedly, depends on a choice of observer field. So what? Well, for
example, I would feel more comfortable integrating a scalar over a
large chunk of a spatial section --- I would not be plagued by guilt
feelings induced by worries over parallel transport and all that. So
for example it seems perfectly reasonable for a family of inertial
observers to talk about the *total energy* of deSitter spacetime at
some time --- just integrate the scalar energy density [coming from
the cosmological constant] over that 3-sphere.

Danny Ross Lunsford

Aug20-04, 04:46 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>\nserenuszeitblomphd@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.0408182234.14f4204d@posting.google. com>...\n> I thought I would draw everyone\'s attention to the latest edition of\n> this paper, which is now better than ever:\n>\n> http://arxiv.org/abs/gr-qc/0103044\n\nThis paper starts with an enormous, fundamental error, setting G to 1.\nG is not a disposable parameter - Tmn and Gmn have differing conformal\nweight and so G is necessarily dimensionful.\n\nNote that setting G to 1 *afterwards* by a change of units is\nconceptually much different than eliminating it from the equation\naltogether. Also note that setting hbar = c = 1 is also a much\ndifferent animal - these represent a local choice of units independent\nof gravitation.\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>serenuszeitblomphd@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.0408182234.14f4204d@posting.google.com>...
> I thought I would draw everyone's attention to the latest edition of
> this paper, which is now better than ever:
>
> http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0103044

This paper starts with an enormous, fundamental error, setting G to 1.
G is not a disposable parameter - Tmn and Gmn have differing conformal
weight and so G is necessarily dimensionful.

Note that setting G to 1 *afterwards* by a change of units is
conceptually much different than eliminating it from the equation
altogether. Also note that setting \hbar = c = 1 is also a much
different animal - these represent a local choice of units independent
of gravitation.

-drl

Ken S. Tucker

Aug24-04, 04:56 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>antimatter33@yahoo.com (Danny Ross Lunsford) wrote in message news:<2b93dd16.0408191500.53cb4f09@posting.google. com>...\n> serenuszeitblomphd@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.0408182234.14f4204d@posting.google. com>...\n> > I thought I would draw everyone\'s attention to the latest edition of\n> > this paper, which is now better than ever:\n> >\n> > http://arxiv.org/abs/gr-qc/0103044\n>\n> This paper starts with an enormous, fundamental error, setting G to 1.\n\nI posted a crude, rudimentary analysis of that apprehension\nin sp relativity, thread "The meaning of the Einstein Equation",\nbased on applying SR to Newtons Theory.\n\n> G is not a disposable parameter - Tmn and Gmn have differing conformal\n> weight and so G is necessarily dimensionful.\n\nDo you mean the tensor weight, whereby the Jacobian\ndeterminant is part of the transformation, and also\nwould you briefly advise why you think that is true or\nprovide a ref? (not arguing, just wish to understand more).\n\nI\'m guessing the tensor weights of the determinants,\n|Tmn| and |Gmn| differ?\n\n> Note that setting G to 1 *afterwards* by a change of units is\n> conceptually much different than eliminating it from the equation\n> altogether. Also note that setting hbar = c = 1 is also a much\n> different animal - these represent a local choice of units independent\n> of gravitation.\n> -drl\n\nRegards\nKen S. Tucker\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>antimatter33@yahoo.com (Danny Ross Lunsford) wrote in message news:<2b93dd16.0408191500.53cb4f09@posting.google.com>...
> serenuszeitblomphd@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.0408182234.14f4204d@posting.google.com>...
> > I thought I would draw everyone's attention to the latest edition of
> > this paper, which is now better than ever:
> >
> > http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0103044
>
> This paper starts with an enormous, fundamental error, setting G to 1.

I posted a crude, rudimentary analysis of that apprehension
in sp relativity, thread "The meaning of the Einstein Equation",
based on applying SR to Newtons Theory.

> G is not a disposable parameter - Tmn and Gmn have differing conformal
> weight and so G is necessarily dimensionful.

Do you mean the tensor weight, whereby the Jacobian
determinant is part of the transformation, and also
would you briefly advise why you think that is true or
provide a ref? (not arguing, just wish to understand more).

I'm guessing the tensor weights of the determinants,
|Tmn| and |Gmn| differ?

> Note that setting G to 1 *afterwards* by a change of units is
> conceptually much different than eliminating it from the equation
> altogether. Also note that setting \hbar = c = 1 is also a much
> different animal - these represent a local choice of units independent
> of gravitation.
> -drl

Regards
Ken S. Tucker

FrediFizzx

Aug24-04, 04:56 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>"Danny Ross Lunsford" <antimatter33@yahoo.com> wrote in message\nnews:2b93dd16.0408191500.53cb4f09@posting .google.com...\n|\n| serenuszeitblomphd@yahoo.com (Serenus Zeitblom) wrote in message\nnews:<c7fd6c7a.0408182234.14f4204d@postin g.google.com>...\n| > I thought I would draw everyone\'s attention to the latest edition of\n| > this paper, which is now better than ever:\n| >\n| > http://arxiv.org/abs/gr-qc/0103044\n|\n| This paper starts with an enormous, fundamental error, setting G to 1.\n| G is not a disposable parameter - Tmn and Gmn have differing conformal\n| weight and so G is necessarily dimensionful.\n|\n| Note that setting G to 1 *afterwards* by a change of units is\n| conceptually much different than eliminating it from the equation\n| altogether. Also note that setting hbar = c = 1 is also a much\n| different animal - these represent a local choice of units independent\n| of gravitation.\n\nI suspect that you are very correct about this. It seems to me that G is\ninvolved as part of a coupling "constant" which is easy to see in the\nexpression G*mass^2/hbar*c = dimensionless number. This seems to imply to\nme that there might be a mass quantum that is not the Planck mass but\nsomething really small and less than 1 eV/c^2. Maybe much less. Is this\nsmall mass quantum a fourth unknown limit for the Universe? The Planck mass\nsimply makes the above expression equal to 1. Why should this have any\nsignificance?\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>"Danny Ross Lunsford" <antimatter33@yahoo.com> wrote in message
news:2b93dd16.0408191500.53cb4f09@posting.google.c om...
|
| serenuszeitblomphd@yahoo.com (Serenus Zeitblom) wrote in message
news:<c7fd6c7a.0408182234.14f4204d@posting.google.com>...
| > I thought I would draw everyone's attention to the latest edition of
| > this paper, which is now better than ever:
| >
| > http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0103044
|
| This paper starts with an enormous, fundamental error, setting G to 1.
| G is not a disposable parameter - Tmn and Gmn have differing conformal
| weight and so G is necessarily dimensionful.
|
| Note that setting G to 1 *afterwards* by a change of units is
| conceptually much different than eliminating it from the equation
| altogether. Also note that setting \hbar = c = 1 is also a much
| different animal - these represent a local choice of units independent
| of gravitation.

I suspect that you are very correct about this. It seems to me that G is
involved as part of a coupling "constant" which is easy to see in the
expression G*mass^2/\hbar*c = dimensionless number. This seems to imply to
me that there might be a mass quantum that is not the Planck mass but
something really small and less than 1 eV/c^2. Maybe much less. Is this
small mass quantum a fourth unknown limit for the Universe? The Planck mass
simply makes the above expression equal to 1. Why should this have any
significance?

FrediFizzx

ebunn@lfa221051.richmond.edu

Sep1-04, 03:21 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>In article <c7fd6c7a.0408182234.14f4204d@posting.google.com>, \nSerenus Zeitblom <serenuszeitblomphd@yahoo.com> wrote:\n>I thought I would draw everyone\'s attention to the latest edition of\n>this paper, which is now better than ever:\n>\n>http://arxiv.org/abs/gr-qc/0103044\n\nThanks for the kind words!\n\n>Would I be correct in saying that the statement of the EFE in this\n>paper is a sort of verbal version of the one in footnote 1 of\n>\n>http://arxiv.org/abs/gr-qc/0405072\n>?\n\nThe two statements don\'t look transparently equivalent to me. Of\ncourse, they are equivalent to each other because they\'re both\nequivalent to Einstein\'s equation. But in this context to say that\none is a version of the other seems to mean that the equivalence is\nimmediately obvious, which doesn\'t seem true to me. If other people\n(e.g., my coauthor) think the correspondence is transparent, I\'d be\ninterested to hear it.\n\nIncidentally, I don\'t understand Danny Ross Lunsford\'s objection to\nour setting 8 pi G = 1 in this paper. Anyone who\'s bothered by that\nis cordially invited to get out their Dixon Ticonderoga Number 2\npencil and fill in all the missing 8 pi G\'s. It doesn\'t make a bit of\ndifference to the substance of the paper.\n\n-Ted\n\n--\n[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]\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 <c7fd6c7a.0408182234.14f4204d@posting.google.com>,
Serenus Zeitblom <serenuszeitblomphd@yahoo.com> wrote:
>I thought I would draw everyone's attention to the latest edition of
>this paper, which is now better than ever:
>
>http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0103044

Thanks for the kind words!

>Would I be correct in saying that the statement of the EFE in this
>paper is a sort of verbal version of the one in footnote 1 of
>
>http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0405072
>?

The two statements don't look transparently equivalent to me. Of
course, they are equivalent to each other because they're both
equivalent to Einstein's equation. But in this context to say that
one is a version of the other seems to mean that the equivalence is
immediately obvious, which doesn't seem true to me. If other people
(e.g., my coauthor) think the correspondence is transparent, I'd be
interested to hear it.

Incidentally, I don't understand Danny Ross Lunsford's objection to
our setting 8 \pi G = 1 in this paper. Anyone who's bothered by that
is cordially invited to get out their Dixon Ticonderoga Number 2
pencil and fill in all the missing 8 \pi G's. It doesn't make a bit of
difference to the substance of the paper.

-Ted

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

Danny Ross Lunsford

Sep2-04, 03:44 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\nebunn@lfa221051.richmond.edu wrote in message news:<ch2m58\\$1jo\\$1@lfa222122.richmond.edu>...\ n> In article <c7fd6c7a.0408182234.14f4204d@posting.google.com>, \n> Serenus Zeitblom <serenuszeitblomphd@yahoo.com> wrote:\n> >I thought I would draw everyone\'s attention to the latest edition of\n> >this paper, which is now better than ever:\n> >\n> >http://arxiv.org/abs/gr-qc/0103044\n>\n> Thanks for the kind words!\n>\n> >Would I be correct in saying that the statement of the EFE in this\n> >paper is a sort of verbal version of the one in footnote 1 of\n> >\n> >http://arxiv.org/abs/gr-qc/0405072\n> >?\n>\n> The two statements don\'t look transparently equivalent to me. Of\n> course, they are equivalent to each other because they\'re both\n> equivalent to Einstein\'s equation. But in this context to say that\n> one is a version of the other seems to mean that the equivalence is\n> immediately obvious, which doesn\'t seem true to me. If other people\n> (e.g., my coauthor) think the correspondence is transparent, I\'d be\n> interested to hear it.\n>\n> Incidentally, I don\'t understand Danny Ross Lunsford\'s objection to\n> our setting 8 pi G = 1 in this paper. Anyone who\'s bothered by that\n> is cordially invited to get out their Dixon Ticonderoga Number 2\n> pencil and fill in all the missing 8 pi G\'s. It doesn\'t make a bit of\n> difference to the substance of the paper.\n>\n> -Ted\n\nAs I pointed out, it makes no difference at all AFTER the theory is\nwritten down. The role of G in its context however is VASTLY different\nthan the role of say the speed of light in SR or hbar in QM. This\nultimately comes from the fact that in GR, the metaphysical ground\namounts to the idea that space itself is a dynamical thing, but this\ngets compromised by the fact that matter is POSITED on the right side\nas in a background theory. GR is only a background-free theory in the\nabsence of matter! This contradiction in spirit has two bad\nconsequences: 1) The definition of energy in GR gets all balled up,\nforcing elaborate workaround arguments 2) you can\'t naively quantize\nthe theory because G is dimensionful, with dimensions (angular\nmomentum/mass^2), so an amplitude of order G^n diverges like a\nmomentum space integral p^(2n-1) dp. This clearly shows the\n*phenomenological* character of positing Tmn on the right side. Thus G\nis a kind of phenomenological parameter showing how space is related\nto matter in some kind of weak limit, *not* a fundamental constant\nlike c that can be used to scale the theory.\n\nOn a closer look, the problem is easy to identify - GR is only\npartially local in that, under parallel transport, length is assumed\nto be integrable. In a purely *local* theory, Rmn and Tmn are *not the\nsame class of object* and so cannot be equated.\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>ebunn@lfa221051.richmond.edu wrote in message news:<ch2m58$1jo$1@lfa222122.richmond.edu>...
> In article <c7fd6c7a.0408182234.14f4204d@posting.google.com>,
> Serenus Zeitblom <serenuszeitblomphd@yahoo.com> wrote:
> >I thought I would draw everyone's attention to the latest edition of
> >this paper, which is now better than ever:
> >
> >http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0103044
>
> Thanks for the kind words!
>
> >Would I be correct in saying that the statement of the EFE in this
> >paper is a sort of verbal version of the one in footnote 1 of
> >
> >http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0405072
> >?
>
> The two statements don't look transparently equivalent to me. Of
> course, they are equivalent to each other because they're both
> equivalent to Einstein's equation. But in this context to say that
> one is a version of the other seems to mean that the equivalence is
> immediately obvious, which doesn't seem true to me. If other people
> (e.g., my coauthor) think the correspondence is transparent, I'd be
> interested to hear it.
>
> Incidentally, I don't understand Danny Ross Lunsford's objection to
> our setting 8 \pi G = 1 in this paper. Anyone who's bothered by that
> is cordially invited to get out their Dixon Ticonderoga Number 2
> pencil and fill in all the missing 8 \pi G's. It doesn't make a bit of
> difference to the substance of the paper.
>
> -Ted

As I pointed out, it makes no difference at all AFTER the theory is
written down. The role of G in its context however is VASTLY different
than the role of say the speed of light in SR or \hbar in QM. This
ultimately comes from the fact that in GR, the metaphysical ground
amounts to the idea that space itself is a dynamical thing, but this
gets compromised by the fact that matter is POSITED on the right side
as in a background theory. GR is only a background-free theory in the
absence of matter! This contradiction in spirit has two bad
consequences: 1) The definition of energy in GR gets all balled up,
forcing elaborate workaround arguments 2) you can't naively quantize
the theory because G is dimensionful, with dimensions (angular
momentum/mass^2), so an amplitude of order G^n diverges like a
momentum space integral p^(2n-1) dp. This clearly shows the
*phenomenological* character of positing Tmn on the right side. Thus G
is a kind of phenomenological parameter showing how space is related
to matter in some kind of weak limit, *not* a fundamental constant
like c that can be used to scale the theory.

On a closer look, the problem is easy to identify - GR is only
partially local in that, under parallel transport, length is assumed
to be integrable. In a purely *local* theory, Rmn and Tmn are *not the
same class of object* and so cannot be equated.

-drl

ebunn@lfa221051.richmond.edu

Sep6-04, 01:16 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>\n\nIn article <2b93dd16.0409012001.262ad4ae@posting.google.com>, \nDanny Ross Lunsford <antimatter33@yahoo.com> wrote:\n>\n>\n>ebunn@lfa221051.richmond.edu wrote in message news:<ch2m58\\$1jo\\$1@lfa222122.richmond.edu>...\ n\n>> Incidentally, I don\'t understand Danny Ross Lunsford\'s objection to\n>> our setting 8 pi G = 1 in this paper.\n>\n>As I pointed out, it makes no difference at all AFTER the theory is\n>written down.\n\nI\'m still not sure I understand you. If instead of saying\n\n| The basic equation of general relativity is called Einstein\'s\n| equation. In units where c = 8 pi G = 1, it says\n|\n| G_{\\alpha \\beta} = T_{\\alpha \\beta} .\n\nwe had written\n\n| The basic equation of general relativity is called Einstein\'s\n| equation. It says\n|\n| G_{\\alpha \\beta} = 8 pi G T_{\\alpha \\beta} .\n|\n| From now on, we will work in units where c = 8 pi G = 1.\n\nwould that be OK with you?\n\nIf so, I have trouble elevating that difference to the status of an\n"enormous, fundamental error." (But then I had similar problems with\nthe phrase "high crimes and misdemeanors" a while back, so maybe my\nthreshold for outrage is set too high.)\n\nI guess my point is this: we don\'t derive Einstein\'s equation in this\npaper, nor do we intend to do anything so fundamental. As far as\nwe\'re concerned, the theory has already been "written down," and we\'re\njust trying to express it in a different way. In other words, our\npaper *starts* "after the theory is written down."\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 <2b93dd16.0409012001.262ad4ae@posting.google.com>,
Danny Ross Lunsford <antimatter33@yahoo.com> wrote:
>
>
>ebunn@lfa221051.richmond.edu wrote in message news:<ch2m58$1jo$1@lfa222122.richmond.edu>...

>> Incidentally, I don't understand Danny Ross Lunsford's objection to
>> our setting 8 \pi G = 1 in this paper.
>
>As I pointed out, it makes no difference at all AFTER the theory is
>written down.

I'm still not sure I understand you. If instead of saying

| The basic equation of general relativity is called Einstein's
| equation. In units where c = 8 \pi G = 1, it says
|
| G_{\alpha \beta} = T_{\alpha \beta} .

we had written

| The basic equation of general relativity is called Einstein's
| equation. It says
|
| G_{\alpha \beta} = 8 \pi G T_{\alpha \beta} .
|
| From now on, we will work in units where c = 8 \pi G = 1.

would that be OK with you?

If so, I have trouble elevating that difference to the status of an
"enormous, fundamental error." (But then I had similar problems with
the phrase "high crimes and misdemeanors" a while back, so maybe my
threshold for outrage is set too high.)

I guess my point is this: we don't derive Einstein's equation in this
paper, nor do we intend to do anything so fundamental. As far as
we're concerned, the theory has already been "written down," and we're
just trying to express it in a different way. In other words, our
paper *starts* "after the theory is written down."

-Ted

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

Ken S. Tucker

Sep9-04, 02:55 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>antimatter33@yahoo.com (Danny Ross Lunsford) wrote in message news:<2b93dd16.0409012001.262ad4ae@posting.google. com>...\n> ebunn@lfa221051.richmond.edu wrote in message news:<ch2m58\\$1jo\\$1@lfa222122.richmond.edu>...\ n[...]\n> > Incidentally, I don\'t understand Danny Ross Lunsford\'s objection to\n> > our setting 8 pi G = 1 in this paper. Anyone who\'s bothered by that\n> > is cordially invited to get out their Dixon Ticonderoga Number 2\n> > pencil and fill in all the missing 8 pi G\'s. It doesn\'t make a bit of\n> > difference to the substance of the paper.\n> > -Ted\n\n> As I pointed out, it makes no difference at all AFTER the theory is\n> written down. The role of G in its context however is VASTLY different\n> than the role of say the speed of light in SR or hbar in QM.\n[...]\n> -drl\n\nWhat puzzles me are the invariants in GR, apart\nfrom the invariant q in EM theory, h in QT and c\nis SR, all of course invariant in GR, specifically,\nit appears GR and the Schwarzschild solution assume\nthe Newtonian gravitational potential Phi = GM/r is\ninvariant, and that seems to hold true in many\nexperimental tests of GR at various speeds, from\nMercury to Light, is that reasonable?\n\nThe invariants q,h,c are constants, Phi isn\'t,\nso it\'s circumstances are more difficult to relate\nto. I\'m supposing the simplest way is to set some\npoint fixed relative to Mass M at a distance r,\nthen set Phi\' = Phi invariantly at that point.\n\nExamining that from the point of view of SR using\na frame K\' moving along r, with K at rest relative\nto M then requires,\n\nPhi\'= G\'M\'/r\' = GM/r = Phi .\n\nSR provides M\'= M*gamma and r\'= r/gamma so\n\nPhi\'= G\'(M/r)*gamma^2 = GM/r or\n\nG\' = G/gamma^2 .\n\nSuppose instead John Baez and Ted Bunn are correct\nin assuming G is invariant, then Phi transforms as,\n\nPhi\' = Phi*gamma^2\n\nand that has implications for a metric\ncomponent like g_00 = 1 - 2*Phi.\n\nWho is right and can that be determined?\n\nTIA\nKen S. Tucker\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>antimatter33@yahoo.com (Danny Ross Lunsford) wrote in message news:<2b93dd16.0409012001.262ad4ae@posting.google.com>...
> ebunn@lfa221051.richmond.edu wrote in message news:<ch2m58$1jo$1@lfa222122.richmond.edu>...
[...]
> > Incidentally, I don't understand Danny Ross Lunsford's objection to
> > our setting 8 \pi G = 1 in this paper. Anyone who's bothered by that
> > is cordially invited to get out their Dixon Ticonderoga Number 2
> > pencil and fill in all the missing 8 \pi G's. It doesn't make a bit of
> > difference to the substance of the paper.
> > -Ted

> As I pointed out, it makes no difference at all AFTER the theory is
> written down. The role of G in its context however is VASTLY different
> than the role of say the speed of light in SR or \hbar in QM.
[...]
> -drl

What puzzles me are the invariants in GR, apart
from the invariant q in EM theory, h in QT and c
is SR, all of course invariant in GR, specifically,
it appears GR and the Schwarzschild solution assume
the Newtonian gravitational potential \Phi = GM/r is
invariant, and that seems to hold true in many
experimental tests of GR at various speeds, from
Mercury to Light, is that reasonable?

The invariants q,h,c are constants, \Phi isn't,
so it's circumstances are more difficult to relate
to. I'm supposing the simplest way is to set some
point fixed relative to Mass M at a distance r,
then set \Phi' = \Phi invariantly at that point.

Examining that from the point of view of SR using
a frame K' moving along r, with K at rest relative
to M then requires,

\Phi'= G'M'/r' = GM/r = \Phi .

SR provides M'= M*\gamma and r'= r/\gamma so

\Phi'= G'(M/r)*\gamma^2 = GM/r[/itex] or

[itex]G' = G/\gamma^2 .

Suppose instead John Baez and Ted Bunn are correct
in assuming G is invariant, then \Phi transforms as,

\Phi' = \Phi*\gamma^2

and that has implications for a metric
component like g_{00} = 1 - 2*\Phi.

Who is right and can that be determined?

TIA
Ken S. Tucker