Don't symmetries need explaining?

Very cryptic

<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>Lately, it\'s become really common for high energy physicists to invoke\nsymmetry all the time, to the point that they prefer more symmetric\nmodels to less symmetric ones. And anytime they encounter a problem\nwith the unlikeliness of a model within parameter space (mostly of the\nform why a coefficient of a coupling is zero or many orders of\nmagnitude smaller than "typical"), they invoke a symmetry principle,\nbroken or unbroken. If we look at the parameter space all of possible\nmodels (OK, maybe that\'s too large and ill defined, but you get my\npoint), then it turns out our position within that space is rather\nunlikely, even in qualitative terms, because many orders of magnitude\nis qualitative, and not quantitative. Physicists, of course realize\nthat needs explaining. But their "solution" assumes a Bayesian\nviewpoint where somehow, the more symmetric a model is, the higher\nit\'s probability is of becoming true. But is that true and why should\nthat be the case? After all, the more symmetric a model is, the more\nthe parameters would have to conspire together to obey unlikely\nrelations. Wouldn\'t you expect the "most likely theory" to be one\nwhich is completely unsymmetric?\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>Lately, it's become really common for high energy physicists to invoke
symmetry all the time, to the point that they prefer more symmetric
models to less symmetric ones. And anytime they encounter a problem
with the unlikeliness of a model within parameter space (mostly of the
form why a coefficient of a coupling is zero or many orders of
magnitude smaller than "typical"), they invoke a symmetry principle,
broken or unbroken. If we look at the parameter space all of possible
models (OK, maybe that's too large and ill defined, but you get my
point), then it turns out our position within that space is rather
unlikely, even in qualitative terms, because many orders of magnitude
is qualitative, and not quantitative. Physicists, of course realize
that needs explaining. But their "solution" assumes a Bayesian
viewpoint where somehow, the more symmetric a model is, the higher
it's probability is of becoming true. But is that true and why should
that be the case? After all, the more symmetric a model is, the more
the parameters would have to conspire together to obey unlikely
relations. Wouldn't you expect the "most likely theory" to be one
which is completely unsymmetric?

alistair

<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>\nvery_cryptic@hotmail.com (Very cryptic) wrote in message news:<3cb3ea56.0408181857.53f4a1c9@posting.google.com>...\n\n> Wouldn\'t you expect the "most likely theory" to be one\n> which is completely unsymmetric?\n\nAlistair:\n\nNo because experiment shows that many physical quantities are conserved\nand that the associated conservation laws can be linked to symmetries.\nHowever it seems strange that general relativity is a theory built from\nprinciples of symmetry and yet energy might not be conserved in general relativity.\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>very_cryptic@hotmail.com (Very cryptic) wrote in message news:<3cb3ea56.0408181857.53f4a1c9@p...google.com>...

> Wouldn't you expect the "most likely theory" to be one
> which is completely unsymmetric?

Alistair:

No because experiment shows that many physical quantities are conserved
and that the associated conservation laws can be linked to symmetries.
However it seems strange that general relativity is a theory built from
principles of symmetry and yet energy might not be conserved in general relativity.

Charles Torre

<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> However it seems strange that general relativity is a theory built from\n> principles of symmetry and yet energy might not be conserved in general\n> relativity.\n\nIt is *not* correct to say energy is not conserved in\ngeneral relativity. Indeed, there *is* a sense in which the\nenergy of matter is locally conserved (the energy-momentum\ntensor is divergence-less in a freely falling reference\nframe). And where it can be defined (e.g., asymptotically\nflat spacetimes), the total energy of matter + gravity *is*\nconserved. The difficulty is that, in general (without\nadditional hypotheses), gravitational energy is not\neven *defined* in general relativity and in particular,\neven when the total energy can be defined, there is no good\nway to define gravitational energy density.\n\ncharlie\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>However it seems strange that general relativity is a theory built from
> principles of symmetry and yet energy might not be conserved in general
> relativity.

It is *not* correct to say energy is not conserved in
general relativity. Indeed, there [itex]*is* a[/itex] sense in which the
energy of matter is locally conserved (the energy-momentum
tensor is divergence-less in a freely falling reference
frame). And where it can be defined (e.g., asymptotically
flat spacetimes), the total energy of matter + gravity *is*
conserved. The difficulty is that, in general (without
additional hypotheses), gravitational energy is not
even *defined* in general relativity and in particular,
even when the total energy can be defined, there is no good
way to define gravitational energy density.

charlie

Rufus Anton

<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>\nOften times it is a useful step to trade a desciption of nature that\nis less symmetric for one that is more symmetric but redundant. Of\ncourse physics must not depend on how you choose to describe it. In\nthat sense the additional gauge symmetries you may have introduced in\norder to make the theory more tractable are completely fake in the\nsense that they can be eliminated without changing physics.\n\nA second point of view on this issue is that the gauge symmetries of\ntheories that describe nature are by no means unique. Nathan Seiberg\nkeeps stressing this point and the Seiberg dualities, named for him,\nare examples of this. Both the N=2 supersymmetric dualities as well as\nthe ones in noncommutative gauge theory, are examples how a single\ntheory can have equivalent descriptions with different gauge\nsymmetries. In string theory going from the Nambu-Goto action to the\nPolyakov action is an example of how you can usefully introduce an\nadditional symmetry at the expense of the redundancy coming with it.\n\nNotice that a few decades ago, when the gauge groups of the standard\nmodel where found, scientists didn\'t anticipate these recent\ndevelopments and tended to assign a more fundamental meaning to gauge\nsymmetries.\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>Often times it is a useful step to trade a desciption of nature that
is less symmetric for one that is more symmetric but redundant. Of
course physics must not depend on how you choose to describe it. In
that sense the additional gauge symmetries you may have introduced in
order to make the theory more tractable are completely fake in the
sense that they can be eliminated without changing physics.

A second point of view on this issue is that the gauge symmetries of
theories that describe nature are by no means unique. Nathan Seiberg
keeps stressing this point and the Seiberg dualities, named for him,
are examples of this. Both the N=2 supersymmetric dualities as well as
the ones in noncommutative gauge theory, are examples how a single
theory can have equivalent descriptions with different gauge
symmetries. In string theory going from the Nambu-Goto action to the
Polyakov action is an example of how you can usefully introduce an
additional symmetry at the expense of the redundancy coming with it.

Notice that a few decades ago, when the gauge groups of the standard
model where found, scientists didn't anticipate these recent
developments and tended to assign a more fundamental meaning to gauge
symmetries.

Thomas Larsson

<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>\nrufusanton@gmx.de (Rufus Anton) wrote in message news:<a1c70df8.0408201007.70ffdf77@posting.google.com>...\n>\n > A second point of view on this issue is that the gauge symmetries of\n> theories that describe nature are by no means unique. Nathan Seiberg\n> keeps stressing this point and the Seiberg dualities, named for him,\n> are examples of this. Both the N=2 supersymmetric dualities as well as\n> the ones in noncommutative gauge theory, are examples how a single\n> theory can have equivalent descriptions with different gauge\n> symmetries.\n\nI find it hard to understand the logic behind this argument.\nPeople have known for 30 years that the 3D Ising model is dual\nto 3D Ising gauge theory. The latter is a Z_2 gauge theory and\nthe former has no gauge symmetries at all, but this does not\nmake people posit that understanding gauge symmetry is\nirrelevant. Moreover, duality breaks down if you add matter\nfields on the gauge side or magnetic fields on the spin side.\n\nIsn\'t it true that Seiberg\'s dualites have only been proven (or\nmaybe just seriouly conjectured) in the presence of\nsupersymmetry? I thought that SUSY has many special properties\n(boson-fermion matching, non-renormalization theorems,\nanomaly-free conformal symmetry), which cannot be expected to\nhold in general? Besides, we all know that SUSY has serious\ntrouble with experiment.\n\n> In string theory going from the Nambu-Goto action to the\n> Polyakov action is an example of how you can usefully introduce an\n> additional symmetry at the expense of the redundancy coming with it.\n>\n> Notice that a few decades ago, when the gauge groups of the standard\n> model where found, scientists didn\'t anticipate these recent\n> developments and tended to assign a more fundamental meaning to gauge\n> symmetries.\n\nAs I pointed out, people did know about 3D Ising-Ising gauge duality\nthree decades ago.\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>rufusanton@gmx.de (Rufus Anton) wrote in message news:<a1c70df8.0408201007.70ffdf77@p...google.com>...
>
> A second point of view on this issue is that the gauge symmetries of
> theories that describe nature are by no means unique. Nathan Seiberg
> keeps stressing this point and the Seiberg dualities, named for him,
> are examples of this. Both the N=2 supersymmetric dualities as well as
> the ones in noncommutative gauge theory, are examples how a single
> theory can have equivalent descriptions with different gauge
> symmetries.

I find it hard to understand the logic behind this argument.
People have known for 30 years that the 3D Ising model is dual
to 3D Ising gauge theory. The latter is [itex]a Z_2[/itex] gauge theory and
the former has no gauge symmetries at all, but this does not
make people posit that understanding gauge symmetry is
irrelevant. Moreover, duality breaks down if you add matter
fields on the gauge side or magnetic fields on the spin side.

Isn't it true that Seiberg's dualites have only been proven (or
maybe just seriouly conjectured) in the presence of
supersymmetry? I thought that SUSY has many special properties
(boson-fermion matching, non-renormalization theorems,
anomaly-free conformal symmetry), which cannot be expected to
hold in general? Besides, we all know that SUSY has serious
trouble with experiment.

> In string theory going from the Nambu-Goto action to the
> Polyakov action is an example of how you can usefully introduce an
> additional symmetry at the expense of the redundancy coming with it.
>
> Notice that a few decades ago, when the gauge groups of the standard
> model where found, scientists didn't anticipate these recent
> developments and tended to assign a more fundamental meaning to gauge
> symmetries.

As I pointed out, people did know about 3D Ising-Ising gauge duality
three decades ago.

ake

<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\ntorre@cc.usu.edu (Charles Torre) wrote in message news:<aaec8787.0408200906.c138f4b@posting.google.com>...\n> > However it seems strange that general relativity is a theory built from\n> > principles of symmetry and yet energy might not be conserved in general\n> > relativity.\n>\n> It is *not* correct to say energy is not conserved in\n> general relativity. Indeed, there *is* a sense in which the\n> energy of matter is locally conserved (the energy-momentum\n> tensor is divergence-less in a freely falling reference\n> frame). And where it can be defined (e.g., asymptotically\n> flat spacetimes), the total energy of matter + gravity *is*\n> conserved. The difficulty is that, in general (without\n> additional hypotheses), gravitational energy is not\n> even *defined* in general relativity and in particular,\n> even when the total energy can be defined, there is no good\n> way to define gravitational energy density.\n>\n> charlie\n\nIf the metric is time invariant i.e. there is a timelike Killing\nvector wouldn\'t energy be conserved then? This is the same definition\nas in Newtonian mechanics.\n\nÅke\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>torre@cc.usu.edu (Charles Torre) wrote in message news:<aaec8787.0408200906.c138f4b@po...google.com>...
> > However it seems strange that general relativity is a theory built from
> > principles of symmetry and yet energy might not be conserved in general
> > relativity.
>
> It is *not* correct to say energy is not conserved in
> general relativity. Indeed, there [itex]*is* a[/itex] sense in which the
> energy of matter is locally conserved (the energy-momentum
> tensor is divergence-less in a freely falling reference
> frame). And where it can be defined (e.g., asymptotically
> flat spacetimes), the total energy of matter + gravity *is*
> conserved. The difficulty is that, in general (without
> additional hypotheses), gravitational energy is not
> even *defined* in general relativity and in particular,
> even when the total energy can be defined, there is no good
> way to define gravitational energy density.
>
> charlie

If the metric is time invariant i.e. there is a timelike Killing
vector wouldn't energy be conserved then? This is the same definition
as in Newtonian mechanics.

Åke

Jeroen

<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>\nThomas Larsson wrote:\n\n>\n> rufusanton@gmx.de (Rufus Anton) wrote in message\n> news:<a1c70df8.0408201007.70ffdf77@posting.google.com>...\n>&g t;\n>> A second point of view on this issue is that the gauge symmetries of\n>> theories that describe nature are by no means unique. Nathan Seiberg\n>> keeps stressing this point and the Seiberg dualities, named for him,\n>> are examples of this. Both the N=2 supersymmetric dualities as well as\n>> the ones in noncommutative gauge theory, are examples how a single\n>> theory can have equivalent descriptions with different gauge\n>> symmetries.\n>\n> I find it hard to understand the logic behind this argument.\n> People have known for 30 years that the 3D Ising model is dual\n> to 3D Ising gauge theory. The latter is a Z_2 gauge theory and\n> the former has no gauge symmetries at all, but this does not\n> make people posit that understanding gauge symmetry is\n> irrelevant. Moreover, duality breaks down if you add matter\n> fields on the gauge side or magnetic fields on the spin side.\n>\n> Isn\'t it true that Seiberg\'s dualites have only been proven (or\n> maybe just seriouly conjectured) in the presence of\n> supersymmetry? I thought that SUSY has many special properties\n> (boson-fermion matching, non-renormalization theorems,\n> anomaly-free conformal symmetry), which cannot be expected to\n\nSo, what\'s your point? I think he just meant to say that there are different\nways to describe one system. Some ways are more symmetric than others.\nThere is no point in trying to "explain" the use of symmetry since many\ntimes you can find another way to describe the same system, yet using\nanother underlying symmetry (typically a gauge symmetry). In my opinion\nphysicists like to use symmetry, because it makes the problems _easier_ to\ndeal with.\n\n> hold in general? Besides, we all know that SUSY has serious\n> trouble with experiment.\n\nNo it doesn\'t, where did you get that idea?!? Wait for LHC, that will decide\nfor or against SUSY. Until now SUSY is the phenomenologists favorite toy.\n\n>> In string theory going from the Nambu-Goto action to the\n>> Polyakov action is an example of how you can usefully introduce an\n>> additional symmetry at the expense of the redundancy coming with it.\n>>\n>> Notice that a few decades ago, when the gauge groups of the standard\n>> model where found, scientists didn\'t anticipate these recent\n>> developments and tended to assign a more fundamental meaning to gauge\n>> symmetries.\n>\n> As I pointed out, people did know about 3D Ising-Ising gauge duality\n> three decades ago.\n\nWhich would be after the introduction of gauge symmetry in high-energy\nphysics if I\'m correct (not that it matters).\n\nbest,\nJeroen\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>Thomas Larsson wrote:

>
> rufusanton@gmx.de (Rufus Anton) wrote in message
> news:<a1c70df8.0408201007.70ffdf77@p...google.com>...
>>
>> A second point of view on this issue is that the gauge symmetries of
>> theories that describe nature are by no means unique. Nathan Seiberg
>> keeps stressing this point and the Seiberg dualities, named for him,
>> are examples of this. Both the N=2 supersymmetric dualities as well as
>> the ones in noncommutative gauge theory, are examples how a single
>> theory can have equivalent descriptions with different gauge
>> symmetries.
>
> I find it hard to understand the logic behind this argument.
> People have known for 30 years that the 3D Ising model is dual
> to 3D Ising gauge theory. The latter is [itex]a Z_2[/itex] gauge theory and
> the former has no gauge symmetries at all, but this does not
> make people posit that understanding gauge symmetry is
> irrelevant. Moreover, duality breaks down if you add matter
> fields on the gauge side or magnetic fields on the spin side.
>
> Isn't it true that Seiberg's dualites have only been proven (or
> maybe just seriouly conjectured) in the presence of
> supersymmetry? I thought that SUSY has many special properties
> (boson-fermion matching, non-renormalization theorems,
> anomaly-free conformal symmetry), which cannot be expected to

So, what's your point? I think he just meant to say that there are different
ways to describe one system. Some ways are more symmetric than others.
There is no point in trying to "explain" the use of symmetry since many
times you can find another way to describe the same system, yet using
another underlying symmetry (typically a gauge symmetry). In my opinion
physicists like to use symmetry, because it makes the problems _easier_ to
deal with.

> hold in general? Besides, we all know that SUSY has serious
> trouble with experiment.

No it doesn't, where did you get that idea?!? Wait for LHC, that will decide
for or against SUSY. Until now SUSY is the phenomenologists favorite toy.

>> In string theory going from the Nambu-Goto action to the
>> Polyakov action is an example of how you can usefully introduce an
>> additional symmetry at the expense of the redundancy coming with it.
>>
>> Notice that a few decades ago, when the gauge groups of the standard
>> model where found, scientists didn't anticipate these recent
>> developments and tended to assign a more fundamental meaning to gauge
>> symmetries.
>
> As I pointed out, people did know about 3D Ising-Ising gauge duality
> three decades ago.

Which would be after the introduction of gauge symmetry in high-energy
physics if I'm correct (not that it matters).

best,
Jeroen

Jeroen

<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>\nake wrote:\n\n>\n>\n> torre@cc.usu.edu (Charles Torre) wrote in message\n> news:<aaec8787.0408200906.c138f4b@posting.google.com>...\n>&gt ; > However it seems strange that general relativity is a theory built from\n>> > principles of symmetry and yet energy might not be conserved in general\n>> > relativity.\n>>\n>> It is *not* correct to say energy is not conserved in\n>> general relativity. Indeed, there *is* a sense in which the\n>> energy of matter is locally conserved (the energy-momentum\n>> tensor is divergence-less in a freely falling reference\n>> frame). And where it can be defined (e.g., asymptotically\n>> flat spacetimes), the total energy of matter + gravity *is*\n>> conserved. The difficulty is that, in general (without\n>> additional hypotheses), gravitational energy is not\n>> even *defined* in general relativity and in particular,\n>> even when the total energy can be defined, there is no good\n>> way to define gravitational energy density.\n>>\n>> charlie\n>\n> If the metric is time invariant i.e. there is a timelike Killing\n> vector wouldn\'t energy be conserved then? This is the same definition\n> as in Newtonian mechanics.\n\nThe problem is usually to define a _global_ time-like Killing vector. For\nsome space-times it is easy, for some impossible.\n\nbest,\nJeroen\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>ake wrote:

>
>
> torre@cc.usu.edu (Charles Torre) wrote in message
> news:<aaec8787.0408200906.c138f4b@po...google.com>...
>> > However it seems strange that general relativity is a theory built from
>> > principles of symmetry and yet energy might not be conserved in general
>> > relativity.
>>
>> It is *not* correct to say energy is not conserved in
>> general relativity. Indeed, there [itex]*is* a[/itex] sense in which the
>> energy of matter is locally conserved (the energy-momentum
>> tensor is divergence-less in a freely falling reference
>> frame). And where it can be defined (e.g., asymptotically
>> flat spacetimes), the total energy of matter + gravity *is*
>> conserved. The difficulty is that, in general (without
>> additional hypotheses), gravitational energy is not
>> even *defined* in general relativity and in particular,
>> even when the total energy can be defined, there is no good
>> way to define gravitational energy density.
>>
>> charlie
>
> If the metric is time invariant i.e. there is a timelike Killing
> vector wouldn't energy be conserved then? This is the same definition
> as in Newtonian mechanics.

The problem is usually to define a _global_ time-like Killing vector. For
some space-times it is easy, for some impossible.

best,
Jeroen

very_cryptic@hotmail.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>alistair wrote:\n\n> No because experiment shows that many physical quantities are\nconserved\n> and that the associated conservation laws can be linked to\nsymmetries.\n\nBut this is completely circular. Conservation laws need explaining as\nwell and explaining symmetries in terms of conservation laws and\nconservation laws in terms of symmetries doesn\'t get us anywhere.\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>alistair wrote:

> No because experiment shows that many physical quantities are
conserved
> and that the associated conservation laws can be linked to
symmetries.

But this is completely circular. Conservation laws need explaining as
well and explaining symmetries in terms of conservation laws and
conservation laws in terms of symmetries doesn't get us anywhere.

Thomas Larsson

<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>Jeroen <wijnhout@science.uva.nl> wrote in message news:<cgcgfu\\$re1\\$1@info.science.uva.nl>...\n>\n> > hold in general? Besides, we all know that SUSY has serious\n> > trouble with experiment.\n>\n> No it doesn\'t, where did you get that idea?!? Wait for LHC, that will decide\n> for or against SUSY. Until now SUSY is the phenomenologists favorite toy.\n\nThere are a variety of experiments where SUSY signatures could\nhave been seen but there is no clearcut signal: sparticles,\nlight Higgs, muon g-2, permanent electric dipole moments,\nproton decay, WIMPs, etc. Consensus now seems to be that SUSY\nrequires fine-tuning at the 1% level, which in some sense must\nmean that 99% of the available parameter space has already been\nruled out by experiments. Moreover, I have heard rumors that the\nunification of couplings at the GUT scale, which was the only\nevidence in favor of SUSY at the first place, was a first-order\nresult which breaks down at second order.\n\nAs a consequence, string theory is now (perhaps) starting to predict\nno low-energy SUSY, see e.g.\n\nhttp://www.arxiv.org/abs/hep-th/0405159\nhttp://www.arxiv.org/abs/hep-th/0405189\nhttp://www.arxiv.org/abs/hep-th/0405279\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>Jeroen <wijnhout@science.uva.nl> wrote in message news:<cgcgfu$re1$1@info.science.uva.nl>...
>
> > hold in general? Besides, we all know that SUSY has serious
> > trouble with experiment.
>
> No it doesn't, where did you get that idea?!? Wait for LHC, that will decide
> for or against SUSY. Until now SUSY is the phenomenologists favorite toy.

There are a variety of experiments where SUSY signatures could
have been seen but there is no clearcut signal: sparticles,
light Higgs, muon [itex]g-2,[/itex] permanent electric dipole moments,
proton decay, WIMPs, etc. Consensus now seems to be that SUSY
requires fine-tuning at the 1% level, which in some sense must
mean that 99% of the available parameter space has already been
ruled out by experiments. Moreover, I have heard rumors that the
unification of couplings at the GUT scale, which was the only
evidence in favor of SUSY at the first place, was a first-order
result which breaks down at second order.

As a consequence, string theory is now (perhaps) starting to predict
no low-energy SUSY, see e.g.

http://www.arxiv.org/abs/http://www....hep-th/0405159
http://www.arxiv.org/abs/http://www....hep-th/0405189
http://www.arxiv.org/abs/http://www....hep-th/0405279

Jeroen

<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>\nThomas Larsson wrote:\n\n> Jeroen <wijnhout@science.uva.nl> wrote in message\n> news:<cgcgfu\\$re1\\$1@info.science.uva.nl>...\n>>\n>&gt ; > hold in general? Besides, we all know that SUSY has serious\n>> > trouble with experiment.\n>>\n>> No it doesn\'t, where did you get that idea?!? Wait for LHC, that will\n>> decide for or against SUSY. Until now SUSY is the phenomenologists\n>> favorite toy.\n>\n> There are a variety of experiments where SUSY signatures could\n> have been seen but there is no clearcut signal: sparticles,\n> light Higgs, muon g-2, permanent electric dipole moments,\n> proton decay, WIMPs, etc. Consensus now seems to be that SUSY\n> requires fine-tuning at the 1% level, which in some sense must\n> mean that 99% of the available parameter space has already been\n> ruled out by experiments. Moreover, I have heard rumors that the\n> unification of couplings at the GUT scale, which was the only\n> evidence in favor of SUSY at the first place, was a first-order\n> result which breaks down at second order.\n\nSo where is the problem with experiment? Some SUSY models _could_ have\npredicted something, but they didn\'t find it? Again, where is the problem\nwith experiment?\n\n> As a consequence, string theory is now (perhaps) starting to predict\n> no low-energy SUSY, see e.g.\n>\n> http://www.arxiv.org/abs/hep-th/0405159\n> http://www.arxiv.org/abs/hep-th/0405189\n> http://www.arxiv.org/abs/hep-th/0405279\n\nYeah, this is interesting stuff indeed. However I am not suprised by this.\nThere are many models in string theory that "predict" some aspects of the\nstandard model, it is explaining all aspects of the standard model that is\nthe problem :-) Nature doesn\'t respond to the latests trends in theoretical\nphysics, does it? Let experiment decide, LHC is our best bet so far.\n\nbest,\nJeroen\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>Thomas Larsson wrote:

> Jeroen <wijnhout@science.uva.nl> wrote in message
> news:<cgcgfu$re1$1@info.science.uva.nl>...
>>
>> > hold in general? Besides, we all know that SUSY has serious
>> > trouble with experiment.
>>
>> No it doesn't, where did you get that idea?!? Wait for LHC, that will
>> decide for or against SUSY. Until now SUSY is the phenomenologists
>> favorite toy.
>
> There are a variety of experiments where SUSY signatures could
> have been seen but there is no clearcut signal: sparticles,
> light Higgs, muon [itex]g-2,[/itex] permanent electric dipole moments,
> proton decay, WIMPs, etc. Consensus now seems to be that SUSY
> requires fine-tuning at the 1% level, which in some sense must
> mean that 99% of the available parameter space has already been
> ruled out by experiments. Moreover, I have heard rumors that the
> unification of couplings at the GUT scale, which was the only
> evidence in favor of SUSY at the first place, was a first-order
> result which breaks down at second order.

So where is the problem with experiment? Some SUSY models _could_ have
predicted something, but they didn't find it? Again, where is the problem
with experiment?

> As a consequence, string theory is now (perhaps) starting to predict
> no low-energy SUSY, see e.g.
>
> http://www.arxiv.org/abs/http://www....hep-th/0405159
> http://www.arxiv.org/abs/http://www....hep-th/0405189
> http://www.arxiv.org/abs/http://www....hep-th/0405279

Yeah, this is interesting stuff indeed. However I am not suprised by this.
There are many models in string theory that "predict" some aspects of the
standard model, it is explaining all aspects of the standard model that is
the problem :-) Nature doesn't respond to the latests trends in theoretical
physics, does it? Let experiment decide, LHC is our best bet so far.

best,
Jeroen

ake

<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>Jeroen <wijnhout@science.uva.nl> wrote in message news:<cgcgi9\\$re1\\$2@info.science.uva.nl>...\n> ake wrote:\n>\n> >\n> >\n> > torre@cc.usu.edu (Charles Torre) wrote in message\n> > news:<aaec8787.0408200906.c138f4b@posting.google.com>...\n> >> > However it seems strange that general relativity is a theory built from\n> >> > principles of symmetry and yet energy might not be conserved in general\n> >> > relativity.\n> >>\n> >> It is *not* correct to say energy is not conserved in\n> >> general relativity. Indeed, there *is* a sense in which the\n> >> energy of matter is locally conserved (the energy-momentum\n> >> tensor is divergence-less in a freely falling reference\n> >> frame). And where it can be defined (e.g., asymptotically\n> >> flat spacetimes), the total energy of matter + gravity *is*\n> >> conserved. The difficulty is that, in general (without\n> >> additional hypotheses), gravitational energy is not\n> >> even *defined* in general relativity and in particular,\n> >> even when the total energy can be defined, there is no good\n> >> way to define gravitational energy density.\n> >>\n> >> charlie\n> >\n> > If the metric is time invariant i.e. there is a timelike Killing\n> > vector wouldn\'t energy be conserved then? This is the same definition\n> > as in Newtonian mechanics.\n>\n> The problem is usually to define a _global_ time-like Killing vector. For\n> some space-times it is easy, for some impossible.\n>\n> best,\n> Jeroen\n\nOk I can understand this as a mathematical fact, but if the global\ntopology has singularities which makes it impossible to define a\nglobal vector there should be a physicial explanation for this\n(sources sinks or whatever but you should understand what I mean)\n\nÅke\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>Jeroen <wijnhout@science.uva.nl> wrote in message news:<cgcgi9$re1$2@info.science.uva.nl>...
> ake wrote:
>
> >
> >
> > torre@cc.usu.edu (Charles Torre) wrote in message
> > news:<aaec8787.0408200906.c138f4b@po...google.com>...
> >> > However it seems strange that general relativity is a theory built from
> >> > principles of symmetry and yet energy might not be conserved in general
> >> > relativity.
> >>
> >> It is *not* correct to say energy is not conserved in
> >> general relativity. Indeed, there [itex]*is* a[/itex] sense in which the
> >> energy of matter is locally conserved (the energy-momentum
> >> tensor is divergence-less in a freely falling reference
> >> frame). And where it can be defined (e.g., asymptotically
> >> flat spacetimes), the total energy of matter + gravity *is*
> >> conserved. The difficulty is that, in general (without
> >> additional hypotheses), gravitational energy is not
> >> even *defined* in general relativity and in particular,
> >> even when the total energy can be defined, there is no good
> >> way to define gravitational energy density.
> >>
> >> charlie
> >
> > If the metric is time invariant i.e. there is a timelike Killing
> > vector wouldn't energy be conserved then? This is the same definition
> > as in Newtonian mechanics.
>
> The problem is usually to define a _global_ time-like Killing vector. For
> some space-times it is easy, for some impossible.
>
> best,
> Jeroen

Ok I can understand this as a mathematical fact, but if the global
topology has singularities which makes it impossible to define a
global vector there should be a physicial explanation for this
(sources sinks or whatever but you should understand what I mean)

Åke

Jeroen

<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>\nake wrote:\n> Ok I can understand this as a mathematical fact, but if the global\n> topology has singularities which makes it impossible to define a\n> global vector there should be a physicial explanation for this\n> (sources sinks or whatever but you should understand what I mean)\n>=20\n> =C5ke\n\nWell, de Sitter space is one of those spaces without a global time-like\nKilling vector. Some people say de Sitter space is quite relevant for\nphysics ;-)\n\nbest,\nJeroen\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>ake wrote:
> Ok I can understand this as a mathematical fact, but if the global
> topology has singularities which makes it impossible to define a
> global vector there should be a physicial explanation for this
> (sources sinks or whatever but you should understand what I mean)
[itex]>=20[/itex]
> [itex]=C5ke[/itex]

Well, de Sitter space is one of those spaces without a global time-like
Killing vector. Some people say de Sitter space is quite relevant for
physics ;-)

best,
Jeroen

Mark Palenik

<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><very_cryptic@hotmail.com> wrote in message\nnews:cg61bu\\$p2c@odah37.prod.google.com...\n> alistair wrote:\n>\n> > No because experiment shows that many physical quantities are\n> conserved\n> > and that the associated conservation laws can be linked to\n> symmetries.\n>\n> But this is completely circular. Conservation laws need explaining as\n> well and explaining symmetries in terms of conservation laws and\n> conservation laws in terms of symmetries doesn\'t get us anywhere.\n>\n\nIt almost sounds to me like you\'re asking "why is there stuff?", which is a\nquestion that physics doesn\'t really address. No matter how many big bangs,\nor imaginary dimensions of time, or spin foams you use to explain the\norigins of the universe, we can\'t really address the questions of why any of\nthe stuff the may have created the universe exists, or why logic exists, or\nwhy certain axioms that seem fundimental to existence, like mathematics,\nexist.\n\nSometimes I think we just have to say that certain base rules exist, like 1\n+ 1 = 2 (does that need explaining as well?) and work from there.\n\nOf course, maybe physics will eventually have something more to say about\nwhy conservation laws exist, since in the very early universe, things like\nCPT symmetry and various conservation laws (baryon numer, I believe is one,\nprobably others, too) had to have been violated.\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><very_cryptic@hotmail.com> wrote in message
news:cg61bu$p2c@odah37.prod.google.com...
> alistair wrote:
>
> > No because experiment shows that many physical quantities are
> conserved
> > and that the associated conservation laws can be linked to
> symmetries.
>
> But this is completely circular. Conservation laws need explaining as
> well and explaining symmetries in terms of conservation laws and
> conservation laws in terms of symmetries doesn't get us anywhere.
>

It almost sounds to me like you're asking "why is there stuff?", which is a
question that physics doesn't really address. No matter how many big bangs,
or imaginary dimensions of time, or spin foams you use to explain the
origins of the universe, we can't really address the questions of why any of
the stuff the may have created the universe exists, or why logic exists, or
why certain axioms that seem fundimental to existence, like mathematics,
exist.

Sometimes I think we just have to say that certain base rules exist, like 1
[itex]+ 1 = 2[/itex] (does that need explaining as well?) and work from there.

Of course, maybe physics will eventually have something more to say about
why conservation laws exist, since in the very early universe, things like
CPT symmetry and various conservation laws (baryon numer, I believe is one,
probably others, too) had to have been violated.

ake

<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\nJeroen <wijnhout@science.uva.nl> wrote in message news:<cghm0m\\$994\\$1@info.science.uva.nl>...\n> ake wrote:\n> > Ok I can understand this as a mathematical fact, but if the global\n> > topology has singularities which makes it impossible to define a\n> > global vector there should be a physicial explanation for this\n> > (sources sinks or whatever but you should understand what I mean)\n> >=20\n> > =C5ke\n>\n> Well, de Sitter space is one of those spaces without a global time-like\n> Killing vector. Some people say de Sitter space is quite relevant for\n> physics ;-)\n>\n> best,\n> Jeroen\n\nYes but it describes an expanding universe so its not really static.\nThere might be strict destinctions between static,stationary and time\ninvariant, which I don\'t really know, but I have no problem to\nunderstand why energy is not conserved in this case. What I mean is\nthat I like physical _explanations_ not just mathematical curiosities.\n\nÅke\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>Jeroen <wijnhout@science.uva.nl> wrote in message news:<cghm0m$994$1@info.science.uva.nl>...
> ake wrote:
> > Ok I can understand this as a mathematical fact, but if the global
> > topology has singularities which makes it impossible to define a
> > global vector there should be a physicial explanation for this
> > (sources sinks or whatever but you should understand what I mean)
> [itex]>=20[/itex]
> > [itex]=C5ke[/itex]
>
> Well, de Sitter space is one of those spaces without a global time-like
> Killing vector. Some people say de Sitter space is quite relevant for
> physics ;-)
>
> best,
> Jeroen

Yes but it describes an expanding universe so its not really static.
There might be strict destinctions between static,stationary and time
invariant, which I don't really know, but I have no problem to
understand why energy is not conserved in this case. What I mean is
that I like physical _explanations_ not just mathematical curiosities.

Åke

Jeroen

<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>ake wrote:\n\n>\n>\n> Jeroen <wijnhout@science.uva.nl> wrote in message\n> news:<cghm0m\\$994\\$1@info.science.uva.nl>...\n>> ake wrote:\n>> > Ok I can understand this as a mathematical fact, but if the global\n>> > topology has singularities which makes it impossible to define a\n>> > global vector there should be a physicial explanation for this\n>> > (sources sinks or whatever but you should understand what I mean)\n>> >=20\n>> > =C5ke\n>>\n>> Well, de Sitter space is one of those spaces without a global time-like\n>> Killing vector. Some people say de Sitter space is quite relevant for\n>> physics ;-)\n>>\n>> best,\n>> Jeroen\n>\n> Yes but it describes an expanding universe so its not really static.\n\nSo? Our universe is _not_ static.\n\n> There might be strict destinctions between static,stationary and time\n> invariant, which I don\'t really know, but I have no problem to\n> understand why energy is not conserved in this case. What I mean is\n\nWho says energy is not conserved? It is difficult (impossible?) to define\nthe notion of global energy in de Sitter. First you define energy, then we\nstart talking about whether or not it is conserved.\n\n> that I like physical _explanations_ not just mathematical curiosities.\n\nde Sitter is a mathematical curiosity? Man, from which universe are you?\nSurely not this one, because I\'m in a de Sitter universe! The notion of\nglobal energy is a fundamental problem if we want to describe our universe.\n\nbest,\nJeroen\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>ake wrote:

>
>
> Jeroen <wijnhout@science.uva.nl> wrote in message
> news:<cghm0m$994$1@info.science.uva.nl>...
>> ake wrote:
>> > Ok I can understand this as a mathematical fact, but if the global
>> > topology has singularities which makes it impossible to define a
>> > global vector there should be a physicial explanation for this
>> > (sources sinks or whatever but you should understand what I mean)
[itex]>> >=20>> > =C5ke[/itex]
>>
>> Well, de Sitter space is one of those spaces without a global time-like
>> Killing vector. Some people say de Sitter space is quite relevant for
>> physics ;-)
>>
>> best,
>> Jeroen
>
> Yes but it describes an expanding universe so its not really static.

So? Our universe is _not_ static.

> There might be strict destinctions between static,stationary and time
> invariant, which I don't really know, but I have no problem to
> understand why energy is not conserved in this case. What I mean is

Who says energy is not conserved? It is difficult (impossible?) to define
the notion of global energy in de Sitter. First you define energy, then we
start talking about whether or not it is conserved.

> that I like physical _explanations_ not just mathematical curiosities.

de Sitter is a mathematical curiosity? Man, from which universe are you?
Surely not this one, because I'm in a de Sitter universe! The notion of
global energy is a fundamental problem if we want to describe our universe.

best,
Jeroen

Charles Torre

<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>> The notion of\n> global energy is a fundamental problem if we want to describe our universe.\n>\n\nWhy?\n\nThere is no such thing in Einstein\'s theory of gravity and it gets along\nwithout it just fine.\n\ncharlie\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>> The notion of
> global energy is a fundamental problem if we want to describe our universe.
>

Why?

There is no such thing in Einstein's theory of gravity and it gets along
without it just fine.

charlie

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