View Full Version : quantizing gravity
alistair
May25-04, 01:29 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>If a graviton has energy presumably it curves space-time.A virtual\nphoton has energy and presumably it curves space-time.So can a\ngraviton affect the motion of a virtual photon through space-time and\nvice-versa? If so, can the gravitational field be quantized\nindependently of the electric field?\nDoes there have to be a field operator that gives two probabilities\nfor each point in space: one probability for creating particles for\nthe gravitational field and another probability for creating particles\nfor the electric field ?\nThe electric field has been quantized independently of the\ngravitational field but was this just the inevitability of "adjusting"\nequations in QED?\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>If a graviton has energy presumably it curves space-time.A virtual
photon has energy and presumably it curves space-time.So can a
graviton affect the motion of a virtual photon through space-time and
vice-versa? If so, can the gravitational field be quantized
independently of the electric field?
Does there have to be a field operator that gives two probabilities
for each point in space: one probability for creating particles for
the gravitational field and another probability for creating particles
for the electric field ?
The electric field has been quantized independently of the
gravitational field but was this just the inevitability of "adjusting"
equations in QED?
Martin Lohmann
May26-04, 05:12 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>\nalistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0405230924.72e700b8@posting.google. com>...\n> If a graviton has energy presumably it curves space-time.A virtual\n> photon has energy and presumably it curves space-time.So can a\n> graviton affect the motion of a virtual photon through space-time and\n> vice-versa?\n\nI am not actually sure if a virtual photon would also do it. After\nall, there might be problems with relativistics off the mass shell.\n\n\n\n> If so, can the gravitational field be quantized\n> independently of the electric field?\n\nMathematically, yes, but it would not match experiment. Notice that\nquantization of gravity is actually a mathematical problem.\n\n\n\n> The electric field has been quantized independently of the\n> gravitational field but was this just the inevitability of "adjusting"\n> equations in QED?\n\nWell, the effects of gravity are so strong that you can really neglect\nit at the QED scale. An electron-graviton vertex would have no effect\non your result because the coupling constant is much too small. You\nhave to keep in mind that quantization is a rule in nature that holds\nwhatever forces there are actually present: You can quantize all\nforces seperately. But if the theory so obtained will match experiment\nis another question. In the case of QED being quantized and gravity\nnot being quantized, it does match.\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@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0405230924.72e700b8@posting.google.com>...
> If a graviton has energy presumably it curves space-time.A virtual
> photon has energy and presumably it curves space-time.So can a
> graviton affect the motion of a virtual photon through space-time and
> vice-versa?
I am not actually sure if a virtual photon would also do it. After
all, there might be problems with relativistics off the mass shell.
> If so, can the gravitational field be quantized
> independently of the electric field?
Mathematically, yes, but it would not match experiment. Notice that
quantization of gravity is actually a mathematical problem.
> The electric field has been quantized independently of the
> gravitational field but was this just the inevitability of "adjusting"
> equations in QED?
Well, the effects of gravity are so strong that you can really neglect
it at the QED scale. An electron-graviton vertex would have no effect
on your result because the coupling constant is much too small. You
have to keep in mind that quantization is a rule in nature that holds
whatever forces there are actually present: You can quantize all
forces seperately. But if the theory so obtained will match experiment
is another question. In the case of QED being quantized and gravity
not being quantized, it does match.
Urs Schreiber
May26-04, 05:51 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"Martin Lohmann" <martin_lohmann@t-online.de> schrieb im Newsbeitrag\nnews:f38a1178.0405251009.373793ee@pos ting.google.com...\n>\n> alistair@goforit64.fsnet.co.uk (alistair) wrote in message\nnews:<861c1b21.0405230924.72e700b8@postin g.google.com>...\n\n> > If so, can the gravitational field be quantized\n> > independently of the electric field?\n>\n> Mathematically, yes, but it would not match experiment. Notice that\n> quantization of gravity is actually a mathematical problem.\n\nThis statement seems to assume that we know in principle what we\'d have to\ndo, in order to "quantize gravity", i.e. that some general prescription is\nknown, that there is a generally accepted well-posed problem which could be\nsubmitted to the math department for them to figure out how to do it in\ndetail.\n\nBut I think this is not quite what is going on. There is indeed one naive\ngeneral prescription, based on ordinary QFT - but this one is well known to\nfail!\n\nSo now the problem is to change the rules of the game somehow, in order to\nfind a new general prescription which should approximate the naive one to\nsome degree but without inheriting its inconistencies.\n\nThis is genuinely a question of physics: "Find a new theory with more\ndesireable features." And that\'s also the reason why it is not easily\npossible to rule out (or to confirm!) proposals for quantum gravity.\n\nActually, when it comes to quantum gravity there is apparently not only no\ngeneral agreement on what it means to "quantize gravity" but even on what it\nmeans to "quantize anything". For some recent discussion on this point see\n\nhttp://groups.google.de/groups?selm=c3p23d%242au24e%241%40ID-168578.news.uni-berlin.de&output=gplain\n\nand\n\nhttp://golem.ph.utexas.edu/string/archives/000299.html .\n\n\nWhat I find fascinating is that, while it is not clear that we have found\nany theory that describes the observed world including its gravitational and\nquantum aspects, we know that there are consistent quantizations of _some_\ngravitational theories of sorts - not necessarily of the gravitational\ntheory describing our world, but certainly of some theories containing (some\napproximation to) Einstein-Hilbert gravity. If you don\'t want to trust in\nthe higher loop finiteness of the superstring think of the regularized\nsupermembrane/BFSS model at finite N, for instance, or of AdS/CFT. This are\nexamples of quantum theories which undoubtly do contain (nontrivial)\ngravity - plus other stuff, including possibly higher dimensions, etc, of\ncourse.\n\nSo I think it is fair to say that quantizations of theories that include\n(approximations/generalizations of) gravity have been found. I find it\ninteresting to consider what it would imply if these theories do _not_ apply\nto our world. That would mean that there would exist at least two different\nways to find a notion of "quantum gravity". I would find that surprising.\nEven more so as the know theories of quantum gravity show an amazing unity,\nas nicely summarized yesterday on sci.physics.strings:\n\nhttp://groups.google.de/groups?selm=Pine.LNX.4.31.0405242013120.2886-100000%40lamb.physics.harvard.edu .\n\nBut of course that does not prove anything - yet.\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>"Martin Lohmann" <martin_lohmann@t-online.de> schrieb im Newsbeitrag
news:f38a1178.0405251009.373793ee@posting.google.c om...
>
> alistair@goforit64.fsnet.co.uk (alistair) wrote in message
news:<861c1b21.0405230924.72e700b8@posting.google.com>...
> > If so, can the gravitational field be quantized
> > independently of the electric field?
>
> Mathematically, yes, but it would not match experiment. Notice that
> quantization of gravity is actually a mathematical problem.
This statement seems to assume that we know in principle what we'd have to
do, in order to "quantize gravity", i.e. that some general prescription is
known, that there is a generally accepted well-posed problem which could be
submitted to the math department for them to figure out how to do it in
detail.
But I think this is not quite what is going on. There is indeed one naive
general prescription, based on ordinary QFT - but this one is well known to
fail!
So now the problem is to change the rules of the game somehow, in order to
find a new general prescription which should approximate the naive one to
some degree but without inheriting its inconistencies.
This is genuinely a question of physics: "Find a new theory with more
desireable features." And that's also the reason why it is not easily
possible to rule out (or to confirm!) proposals for quantum gravity.
Actually, when it comes to quantum gravity there is apparently not only no
general agreement on what it means to "quantize gravity" but even on what it
means to "quantize anything". For some recent discussion on this point see
http://groups.google.de/groups?selm=c3p23d%242au24e%241%40ID-168578.news.uni-berlin.de&output=gplain
and
http://golem.ph.utexas.edu/string/archives/000299.html .
What I find fascinating is that, while it is not clear that we have found
any theory that describes the observed world including its gravitational and
quantum aspects, we know that there are consistent quantizations of _some_
gravitational theories of sorts - not necessarily of the gravitational
theory describing our world, but certainly of some theories containing (some
approximation to) Einstein-Hilbert gravity. If you don't want to trust in
the higher loop finiteness of the superstring think of the regularized
supermembrane/BFSS model at finite N, for instance, or of AdS/CFT. This are
examples of quantum theories which undoubtly do contain (nontrivial)
gravity - plus other stuff, including possibly higher dimensions, etc, of
course.
So I think it is fair to say that quantizations of theories that include
(approximations/generalizations of) gravity have been found. I find it
interesting to consider what it would imply if these theories do _not_ apply
to our world. That would mean that there would exist at least two different
ways to find a notion of "quantum gravity". I would find that surprising.
Even more so as the know theories of quantum gravity show an amazing unity,
as nicely summarized yesterday on sci.physics.strings:
http://groups.google.de/groups?selm=Pine.LNX.4.31.0405242013120.2886-100000%40lamb.physics.harvard.edu .
But of course that does not prove anything - yet.
alistair
May29-04, 11:55 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>The principle of general relativity as realized in Einstein\'s\ngravitational theory of 1915 implies that the components of the\ngravitational energy-momentum are not localizable. Therefore, as was\nmentioned by Einstein (1954b), "electro-magnetic waves can be put into\na container, gravitational waves cannot." As a consequence, for the\ngravitational field, one cannot either follow the road of canonical\nquantization or define numerable gravitons as field quanta ascribed to\nEinstein\'s metrical field of gravity.\n--------------------------------------------------------------------------------\nPage 2\nPage 144APEIRON Vol. 5 Nr. 3-4, July-October 1998\n\n"electro-magnetic waves can be put into a container, gravitational\nwaves cannot."\n\nAlistair writes:\n\nBut what if the gravitational waves contain themselves?\nWhat if a gravitational wave is a set of waves that are confined as\nquarks are?\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 principle of general relativity as realized in Einstein's
gravitational theory of 1915 implies that the components of the
gravitational energy-momentum are not localizable. Therefore, as was
mentioned by Einstein (1954b), "electro-magnetic waves can be put into
a container, gravitational waves cannot." As a consequence, for the
gravitational field, one cannot either follow the road of canonical
quantization or define numerable gravitons as field quanta ascribed to
Einstein's metrical field of gravity.
--------------------------------------------------------------------------------
Page 2
Page 144APEIRON Vol. 5 Nr. 3-4, July-October 1998
"electro-magnetic waves can be put into a container, gravitational
waves cannot."
Alistair writes:
But what if the gravitational waves contain themselves?
What if a gravitational wave is a set of waves that are confined as
quarks are?
Martin Lohmann
May29-04, 11:55 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>> > > If so, can the gravitational field be quantized\n> > > independently of the electric field?\n> >\n> > Mathematically, yes, but it would not match experiment. Notice that\n> > quantization of gravity is actually a mathematical problem.\n>\n> This statement seems to assume that we know in principle what we\'d have to\n> do, in order to "quantize gravity", i.e. that some general prescription is\n> known, that there is a generally accepted well-posed problem which could be\n> submitted to the math department for them to figure out how to do it in\n> detail.\n>\n> But I think this is not quite what is going on. There is indeed one naive\n> general prescription, based on ordinary QFT - but this one is well known to\n> fail!\n\nIt does fail, thats why I said that quantization of gravity is a\nmathematical problem. The ordinary (and well-known) procedures of\nquantization lead to infinities (and other interesting stuff) if\napplied to gravity, but this only means that an ordinary quantized\ntheory of gravity is (mathematically, but also physically)\ninconsistent. If nature had chosen gravity to be quantized in the\nordinary way, then there would be infinities all over the place, so\nthats why I said it doesnt fit experiment.\n\n\n\n>\n> So now the problem is to change the rules of the game somehow, in order to\n> find a new general prescription which should approximate the naive one to\n> some degree but without inheriting its inconistencies.\n>\n\nThat is, we have to replace quantization by a more general procedure.\n\n\n\n\n> Actually, when it comes to quantum gravity there is apparently not only no\n> general agreement on what it means to "quantize gravity" but even on what it\n> means to "quantize anything".\n\nI think there is. The path-integral approach shows very directly what\nyou have to do to go from the classical theory to its quantum\ncounterpart. The fact that this method does not always lead to\nmathematical consistent theories is another problem but this does not\ntell us that quantization is an unkown procedure but rather that it is\nnot the procedure realized in nature.\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>> > > If so, can the gravitational field be quantized
> > > independently of the electric field?
> >
> > Mathematically, yes, but it would not match experiment. Notice that
> > quantization of gravity is actually a mathematical problem.
>
> This statement seems to assume that we know in principle what we'd have to
> do, in order to "quantize gravity", i.e. that some general prescription is
> known, that there is a generally accepted well-posed problem which could be
> submitted to the math department for them to figure out how to do it in
> detail.
>
> But I think this is not quite what is going on. There is indeed one naive
> general prescription, based on ordinary QFT - but this one is well known to
> fail!
It does fail, thats why I said that quantization of gravity is a
mathematical problem. The ordinary (and well-known) procedures of
quantization lead to infinities (and other interesting stuff) if
applied to gravity, but this only means that an ordinary quantized
theory of gravity is (mathematically, but also physically)
inconsistent. If nature had chosen gravity to be quantized in the
ordinary way, then there would be infinities all over the place, so
thats why I said it doesnt fit experiment.
>
> So now the problem is to change the rules of the game somehow, in order to
> find a new general prescription which should approximate the naive one to
> some degree but without inheriting its inconistencies.
>
That is, we have to replace quantization by a more general procedure.
> Actually, when it comes to quantum gravity there is apparently not only no
> general agreement on what it means to "quantize gravity" but even on what it
> means to "quantize anything".
I think there is. The path-integral approach shows very directly what
you have to do to go from the classical theory to its quantum
counterpart. The fact that this method does not always lead to
mathematical consistent theories is another problem but this does not
tell us that quantization is an unkown procedure but rather that it is
not the procedure realized in nature.
alistair
May29-04, 11:56 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>A graviton is supposedly massless and has spin 2.\nBut these characteristics of the graviton come from quantum mechanics\nin which it is assumed that the graviton does not interact with other\nforce carrying particles.Is it possible that a graviton has a colour\ncharge for example, and interacts with gluons - a graviton is expected\nto have very little energy and it would not interfere noticeably with\nthe mathematics of\nquantum chromodynamics theory, but would the colour force have a\nsignificant effect on gravity? Could the force of gravity be so weak\ncompared to the other\nfield forces because gluons take energy from gravitons? Because dark\nenergy accounts for most of the mass of the universe this would mean\nthat the colour\nforce would have to be associated with dark energy.Is this a\nridiculous idea or something that is reasonably possible?\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>A graviton is supposedly massless and has spin 2.
But these characteristics of the graviton come from quantum mechanics
in which it is assumed that the graviton does not interact with other
force carrying particles.Is it possible that a graviton has a colour
charge for example, and interacts with gluons - a graviton is expected
to have very little energy and it would not interfere noticeably with
the mathematics of
quantum chromodynamics theory, but would the colour force have a
significant effect on gravity? Could the force of gravity be so weak
compared to the other
field forces because gluons take energy from gravitons? Because dark
energy accounts for most of the mass of the universe this would mean
that the colour
force would have to be associated with dark energy.Is this a
ridiculous idea or something that is reasonably possible?
Alfred Einstead
Jun16-04, 03:43 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>alistair@goforit64.fsnet.co.uk (alistair) wrote:\n> The electric field has been quantized independently of the\n> gravitational field\n\nThe *free* electromagnetic field has been quantized. And even\nthat\'s subject to proviso. No free non-Abelian Yang-Mills field\nhas ever been successfully quantized, since it has non-trivial\nself-interaction and is non-linear. The electromagnetic field\nis a non-trivial part of the larger (and non-trivial) electroweak\nfield, which is non-linear -- even within the Maxwell equations.\nThe Maxwell equations, accounting for all of the electroweak field\ncomponents (specifically, the components associated with W+ and W-),\nare actually non-linear; even with non-zero magnetic source terms.\nSo, the quantization of even the free electromagnetic field is still\nup in the air.\n\nThe closest anyone\'s ever gotten to quantizing non-linear theories\nis via a perturbation-theoretic quasi-free-field type approximation\n(e.g., S-matrix theory), which is known or believed to be ill-defined\nand is based on a general formulation (the Interaction Picture)\nthat is already known not to exist.\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@goforit64.fsnet.co.uk (alistair) wrote:
> The electric field has been quantized independently of the
> gravitational field
The *free* electromagnetic field has been quantized. And even
that's subject to proviso. No free non-Abelian Yang-Mills field
has ever been successfully quantized, since it has non-trivial
self-interaction and is non-linear. The electromagnetic field
is a non-trivial part of the larger (and non-trivial) electroweak
field, which is non-linear -- even within the Maxwell equations.
The Maxwell equations, accounting for all of the electroweak field
components (specifically, the components associated with W+ and W-),
are actually non-linear; even with non-zero magnetic source terms.
So, the quantization of even the free electromagnetic field is still
up in the air.
The closest anyone's ever gotten to quantizing non-linear theories
is via a perturbation-theoretic quasi-free-field type approximation
(e.g., S-matrix theory), which is known or believed to be ill-defined
and is based on a general formulation (the Interaction Picture)
that is already known not to exist.
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