Request for information: Observables in GR and QG. [Archive]

Dean Rickles

May11-04, 07:05 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>\nI have a simple request for information: which physicists have endored\nthe ``correlation\'\' view of observables (i.e. the view that the\nobservables of GR and quantum gravity are gauge *invariant*,\n*relative* quantities decribing correlations between gauge *dependent*\nquantities)? I would appreciate sources too. I know of quite a few, but\nI would rather like an exhaustive list.\n\nSo far, I have: DeWitt, Rovelli, Smolin, Page and Wooters. I think\nEinstein and Bergmann (with Komar) may have held this view, but it\nisn\'t completely clear that they intend the form I described above.\n\nWould it be fair to say that this is the majority view? And would it be\nfair to say that relationism (i.e. about space(time)) is generally seen\nto be implied by this view? Do you agree with this latter implication?\n\n\nTa,\n\nDean\n\n-----------------------------\n\nDean Rickles,\nDivision of History & Philosophy of Science,\nSchool of Philosophy,\nUniversity of Leeds,\nLS2 9JT\n\nhttp://www.personal.leeds.ac.uk/~phldpr/index.html\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 have a simple request for information: which physicists have endored
the ``correlation'' view of observables (i.e. the view that the
observables of GR and quantum gravity are gauge *invariant*,
*relative* quantities decribing correlations between gauge *dependent*
quantities)? I would appreciate sources too. I know of quite a few, but
I would rather like an exhaustive list.

So far, I have: DeWitt, Rovelli, Smolin, Page and Wooters. I think
Einstein and Bergmann (with Komar) may have held this view, but it
isn't completely clear that they intend the form I described above.

Would it be fair to say that this is the majority view? And would it be
fair to say that relationism (i.e. about space(time)) is generally seen
to be implied by this view? Do you agree with this latter implication?

Ta,

Dean

-----------------------------

Dean Rickles,
Division of History & Philosophy of Science,
School of Philosophy,
University of Leeds,
LS2 9JT

http://www.personal.leeds.ac.uk/~phldpr/index.html

Robert C. Helling

May14-04, 04:06 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>On 11 May 2004 08:05:00 -0400, Dean Rickles <dean.rickles@ntlworld.com> wrote:\n>\n> I have a simple request for information: which physicists have endored\n> the ``correlation\'\' view of observables (i.e. the view that the\n> observables of GR and quantum gravity are gauge *invariant*,\n> *relative* quantities decribing correlations between gauge *dependent*\n> quantities)? I would appreciate sources too. I know of quite a few, but\n> I would rather like an exhaustive list.\n>\n> Would it be fair to say that this is the majority view? And would it be\n> fair to say that relationism (i.e. about space(time)) is generally seen\n> to be implied by this view? Do you agree with this latter implication?\n\nAre there people who disagree with this? I am not sure I understand\nyour criteria. Anybody would agree that observables are gauge\ninvariant (that\'s quasi the definition of observable). However, I am\nnot sure what you mean by "relative" and why you mention "gauge\ndependent". Could you give some examples and a technical definition as\nall the definitions I could think of would make the above statement\ncontroversal. Could you give me a sensible point of view that would\nnot agree with the above statement?\n\nSome months ago, we had a thread here discussing the nature of\nobservables in quantum gravity. The upshot was that in some sense\nthere are no local observables in GR (meaning at fixed values of\ncoordinates, but this is a rather trivial statement. It\'s much harder\nto define "local observables" in a non-trivial way) and some people\n(not including me) held the view that only the S-matrix (or something\nsimilar as in AdS/CFT) will be observable. You should be able to find\nthe thread on google.\n\nRobert\n\n--\n..oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oO o.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oO\nRobert C. Helling Department of Applied Mathematics and Theoretical Physics\nUniversity of Cambridge\nprint "Just another Phone: +44/1223/766870\nstupid .sig\\n"; http://www.aei-potsdam.mpg.de/~helling\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>On 11 May 2004 08:05:00 -0400, Dean Rickles <dean.rickles@ntlworld.com> wrote:
>
> I have a simple request for information: which physicists have endored
> the ``correlation'' view of observables (i.e. the view that the
> observables of GR and quantum gravity are gauge *invariant*,
> *relative* quantities decribing correlations between gauge *dependent*
> quantities)? I would appreciate sources too. I know of quite a few, but
> I would rather like an exhaustive list.
>
> Would it be fair to say that this is the majority view? And would it be
> fair to say that relationism (i.e. about space(time)) is generally seen
> to be implied by this view? Do you agree with this latter implication?

Are there people who disagree with this? I am not sure I understand
your criteria. Anybody would agree that observables are gauge
invariant (that's quasi the definition of observable). However, I am
not sure what you mean by "relative" and why you mention "gauge
dependent". Could you give some examples and a technical definition as
all the definitions I could think of would make the above statement
controversal. Could you give me a sensible point of view that would
not agree with the above statement?

Some months ago, we had a thread here discussing the nature of
observables in quantum gravity. The upshot was that in some sense
there are no local observables in GR (meaning at fixed values of
coordinates, but this is a rather trivial statement. It's much harder
to define "local observables" in a non-trivial way) and some people
(not including me) held the view that only the S-matrix (or something
similar as in AdS/CFT) will be observable. You should be able to find
the thread on google.

Robert

--
..oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo. oOo.oOo.oOo.oOo.oOo.oOo.oOo.oO
Robert C. Helling Department of Applied Mathematics and Theoretical Physics
University of Cambridge
print "Just another Phone: +44/1223/766870
stupid .sig\n"; http://www.aei-potsdam.mpg.de/~helling

Dean

May14-04, 11:58 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>On 2004-05-14 10:06:10 +0100, "Robert C. Helling"\n<helling@ariel.physik.hu-berlin.de> said:\n\n>\n> Are there people who disagree with this? I am not sure I understand\n> your criteria. Anybody would agree that observables are gauge\n> invariant (that\'s quasi the definition of observable). However, I am\n> not sure what you mean by "relative" and why you mention "gauge\n> dependent". Could you give some examples and a technical definition as\n> all the definitions I could think of would make the above statement\n> controversal. Could you give me a sensible point of view that would\n> not agree with the above statement?\n>\n\n\nYes, of course most people would agree that observables in a gauge\ntheory are gauge-invariant. Kuchar might possibly be read a one who\ndenies this, since he denies that the observables of GR commute with\nthe Hamiltonian constraint. But he might just as well say that the\nconstraint doesn\'t in fact generate gauge transformations, therefore\nobservables don\'t have to commute with it. Of course, this is leading\ninto the problems of time in the canonical theory, and I don\'t want to\nget into that.\n\nAnyway, that wasn\'t my point - we can agree that observables have to be\ngauge invariant. My point concerned a particular view of what kind of\nanimal these observables are in (canonical) GR and QG (perhaps I wasn\'t\nclear that I meant the canonical approach? apologies). You mentioned a\nthread debating the observables of GR, and that there can be no local\nobservables (I think Torre proved this, and what it shows is simply\nthat the points of spacetime and the metric (or whatever field) are\nentwined). So the options seem to be global or non-local. Global\nobservables don\'t seem to be what we deal with when we work with GR, so\nforget those. The problem then is: how do we understand the non-local\nobservables?\n\nDeWitt\'s view was that we simply use objects to pick out space points\nand instants of time. This line of thought leads to Page and Wooters\nconditional probability approach, and to Rovelli\'s evolving constants\nof motion and partial/complete observables strategies. The latter\nexplicitly uses quantities defined on the extended phase space\n(gauge-dependent variables) to construct observables defined on the\nphysical phase space. The idea is to use correlations between pairs of\ngauge-dependent variables to get a gauge-invariant quantity (an\nobservable). (I should have said `relational\' instead of `relative\' in\nmy post: the idea is that these relational quatities are what the\ntheory is about.) To give a well used example, we don\'t measure\nposition, but intsead measure position at a time (on a physical clock).\nThe basic thought is, as Isham says somewhere, \\phi (x,t) is not\ngauge-invariant but \\phi (thing) is; so localization is carried out\nwith respect to things, and observables are constructed from\ncorrelations between things. (An initial serious problem is getting\nthese expressed as phase functions; not to mention factor ordering in\nthe quantum theory).\n\nNow a ``sensible point of view\'\' that might make you disagree is\nUnruh\'s: he says that the correlation understanding of the non-local\nobservables implies that the gauge-dependent quantities must be\nmeasurable, which cannot be the case. In his paper on partial\nobservables Rovelli explicitly states that the variables on the\nextended phase space have a robust physical reality; he seems to think\nhe needs this to underwrite his idea that the observables of GR are\ncomposed of just such quantities. That might be ``controversial\'\', we\nmight expect the physical stuff to be given by the reduced space only.\nI should point out that Kuchar makes a similar point against Rovelli\'s\nevolving constants approach.\n\n\n\n-----------------------------\n\nDean Rickles,\nDivision of History & Philosophy of Science,\nSchool of Philosophy,\nUniversity of Leeds,\nLS2 9JT\n\nhttp://www.personal.leeds.ac.uk/~phldpr/index.html\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>On 2004-05-14 10:06:10 +0100, "Robert C. Helling"
<helling@ariel.physik.hu-berlin.de> said:

>
> Are there people who disagree with this? I am not sure I understand
> your criteria. Anybody would agree that observables are gauge
> invariant (that's quasi the definition of observable). However, I am
> not sure what you mean by "relative" and why you mention "gauge
> dependent". Could you give some examples and a technical definition as
> all the definitions I could think of would make the above statement
> controversal. Could you give me a sensible point of view that would
> not agree with the above statement?
>

Yes, of course most people would agree that observables in a gauge
theory are gauge-invariant. Kuchar might possibly be read a one who
denies this, since he denies that the observables of GR commute with
the Hamiltonian constraint. But he might just as well say that the
constraint doesn't in fact generate gauge transformations, therefore
observables don't have to commute with it. Of course, this is leading
into the problems of time in the canonical theory, and I don't want to
get into that.

Anyway, that wasn't my point - we can agree that observables have to be
gauge invariant. My point concerned a particular view of what kind of
animal these observables are in (canonical) GR and QG (perhaps I wasn't
clear that I meant the canonical approach? apologies). You mentioned a
thread debating the observables of GR, and that there can be no local
observables (I think Torre proved this, and what it shows is simply
that the points of spacetime and the metric (or whatever field) are
entwined). So the options seem to be global or non-local. Global
observables don't seem to be what we deal with when we work with GR, so
forget those. The problem then is: how do we understand the non-local
observables?

DeWitt's view was that we simply use objects to pick out space points
and instants of time. This line of thought leads to Page and Wooters
conditional probability approach, and to Rovelli's evolving constants
of motion and partial/complete observables strategies. The latter
explicitly uses quantities defined on the extended phase space
(gauge-dependent variables) to construct observables defined on the
physical phase space. The idea is to use correlations between pairs of
gauge-dependent variables to get a gauge-invariant quantity (an
observable). (I should have said `relational' instead of `relative' in
my post: the idea is that these relational quatities are what the
theory is about.) To give a well used example, we don't measure
position, but intsead measure position at a time (on a physical clock).
The basic thought is, as Isham says somewhere, \phi (x,t) is not
gauge-invariant but \phi (thing) is; so localization is carried out
with respect to things, and observables are constructed from
correlations between things. (An initial serious problem is getting
these expressed as phase functions; not to mention factor ordering in
the quantum theory).

Now a ``sensible point of view'' that might make you disagree is
Unruh's: he says that the correlation understanding of the non-local
observables implies that the gauge-dependent quantities must be
measurable, which cannot be the case. In his paper on partial
observables Rovelli explicitly states that the variables on the
extended phase space have a robust physical reality; he seems to think
he needs this to underwrite his idea that the observables of GR are
composed of just such quantities. That might be ``controversial'', we
might expect the physical stuff to be given by the reduced space only.
I should point out that Kuchar makes a similar point against Rovelli's
evolving constants approach.

-----------------------------

Dean Rickles,
Division of History & Philosophy of Science,
School of Philosophy,
University of Leeds,
LS2 9JT

http://www.personal.leeds.ac.uk/~phldpr/index.html

Urs Schreiber

May14-04, 12:28 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>"Dean" <phldpr@leeds.ac.uk> schrieb im Newsbeitrag\nnews:2004051417565716807%phldpr@leeds acuk...\n> On 2004-05-14 10:06:10 +0100, "Robert C. Helling"\n> <helling@ariel.physik.hu-berlin.de> said:\n\n> the Hamiltonian constraint. But he might just as well say that the\n> constraint doesn\'t in fact generate gauge transformations\n\nI am surprised about this statement, but probably just because I don\'t know\nthe precise context. Why should the Hamiltonian constraint be on different\nfooting than the spatial diffe constraints?\n\n> Of course, this is leading\n> into the problems of time in the canonical theory, and I don\'t want to\n> get into that.\n\nHeh, but in the following paragraphs you do! :-)\n\n> The problem then is: how do we understand the non-local\n> observables?\n\nOk.\n\n> The basic thought is, as Isham says somewhere, \\phi (x,t) is not\n> gauge-invariant but \\phi (thing) is; so localization is carried out\n> with respect to things, and observables are constructed from\n> correlations between things.\n\nThat\'s the idea, and in simple covariant theories, like in 2d gravity\ncoupled to scalar matter, one can even explicitly see how this works,\nclassically and quantumly.\n\nSo consider 2d gravity with scalar matter taking values in a flat\nsigma-model space with indefinite signature, for definiteness. As expected,\nthings like the momentum density at a point "sigma" in the 1d space are not\ngauge invariant observables, because they makes recourse to the physically\nmeaningless parameter "sigma".\n\nBut it turns out that one can construct a certain combination X+ of the\nbosonic fields in the theory such that the equations of motion imply that X+\nis a bijective function of sigma.\n\nWe may then ask: "What is the momentum density at a point where X+ takes a\ngiven value?"\n\nThis is a physically meaningful question, since X+ is just one of the fields\n(\'things\' in your terminology) of the theory. Accordingly, one finds that\nthe respective functions on phase space Poisson-commutes with the\nHamiltonian and diffeo constraints and is hence gauge invariant.\n\nThis is precisely an implementation of Isham\'s idea above. The nice thing is\nthat it is possible to consistently quantize this 2d gravity theory,\nincluding a full resolution of all operator ordering, normal ordering\nissues, etc. So this is a nice toy example where the idea of quasi-local\nquantum gravity observables can be fully implemented.\n\nMost probably similar constructions have been done for 2+1d gravity, but I\nam no expert on that. The only reason that I happen to be familiar with the\nabove examle of gauge invariant observables in 2d gravity is that this was a\nspin-off thought (most probably not a new one, of course) of some\nconsiderations that I recently did with respect to such a 2d theory. I know\nthat it is a little shameless, but see the footnote on page 13 of\nhttp://www.iop.org/EJ/abstract/1126-6708/2004/05/027\nfor the details of what I indicated above. :-)\n\n> (An initial serious problem is getting\n> these expressed as phase functions; not to mention factor ordering in\n> the quantum theory).\n\nThe canonical quantum theory for anything covariant with d>3 is notoriously\nunknown, where operator ordering not even arises as a problem because\nalready the very definition of the elementary canonical operators is\nproblematic.\n\n> Now a ``sensible point of view\'\' that might make you disagree\n\nDisagree with the above recipe by Isham? At least for toy models it can be\nconstructively demonstrated to be correct! (But that need not imply anything\nfor d>3 gravity, of course.)\n\n> is\n> Unruh\'s: he says that the correlation understanding of the non-local\n> observables implies that the gauge-dependent quantities must be\n> measurable,\n\nWhy?\n\n> which cannot be the case. In his paper on partial\n> observables Rovelli explicitly states that the variables on the\n> extended phase space have a robust physical reality; he seems to think\n> he needs this to underwrite his idea that the observables of GR are\n> composed of just such quantities. That might be ``controversial\'\', we\n> might expect the physical stuff to be given by the reduced space only.\n> I should point out that Kuchar makes a similar point against Rovelli\'s\n> evolving constants approach.\n\nI don\'t quite recall the details of Rovelli\'s constructions, although I\nhappily remember having had some discussion about this stuff here on spr\nback in the old days:\nhttp://www-stud.uni-essen.de/~sb0264/CovExpValue.html .\n\nBut recent disucssions about similar issues at\nhttp://golem.ph.utexas.edu/string/archives/000299.html\nconvinced me that it is probably best to first test all these ideas about\ncanonical quantization of gravity in the simplest non-trivial toy examples\nthat are available. That helps not to get lost in abstract considerations\nbut to instead get a hands-on experience in terms of some actually tractable\nexamples.\n\nTherefore I would be interested in if you can identify Rovelli\'s point and\nUnruh\'s and Kuchar\'s objection concretely in the 2d toy example mentioned\nabove. That should help us better understand the controversial point.\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>"Dean" <phldpr@leeds.ac.uk> schrieb im Newsbeitrag
news:2004051417565716807%phldpr@leedsacuk...
> On 2004-05-14 10:06:10 +0100, "Robert C. Helling"
> <helling@ariel.physik.hu-berlin.de> said:

> the Hamiltonian constraint. But he might just as well say that the
> constraint doesn't in fact generate gauge transformations

I am surprised about this statement, but probably just because I don't know
the precise context. Why should the Hamiltonian constraint be on different
footing than the spatial diffe constraints?

> Of course, this is leading
> into the problems of time in the canonical theory, and I don't want to
> get into that.

Heh, but in the following paragraphs you do! :-)

> The problem then is: how do we understand the non-local
> observables?

Ok.

> The basic thought is, as Isham says somewhere, \phi (x,t) is not
> gauge-invariant but \phi (thing) is; so localization is carried out
> with respect to things, and observables are constructed from
> correlations between things.

That's the idea, and in simple covariant theories, like in 2d gravity
coupled to scalar matter, one can even explicitly see how this works,
classically and quantumly.

So consider 2d gravity with scalar matter taking values in a flat
\sigma-model space with indefinite signature, for definiteness. As expected,
things like the momentum density at a point "\sigma" in the 1d space are not
gauge invariant observables, because they makes recourse to the physically
meaningless parameter "\sigma".

But it turns out that one can construct a certain combination X+ of the
bosonic fields in the theory such that the equations of motion imply that X+
is a bijective function of \sigma.

We may then ask: "What is the momentum density at a point where X+ takes a
given value?"

This is a physically meaningful question, since X+ is just one of the fields
('things' in your terminology) of the theory. Accordingly, one finds that
the respective functions on phase space Poisson-commutes with the
Hamiltonian and diffeo constraints and is hence gauge invariant.

This is precisely an implementation of Isham's idea above. The nice thing is
that it is possible to consistently quantize this 2d gravity theory,
including a full resolution of all operator ordering, normal ordering
issues, etc. So this is a nice toy example where the idea of quasi-local
quantum gravity observables can be fully implemented.

Most probably similar constructions have been done for 2+1d gravity, but I
am no expert on that. The only reason that I happen to be familiar with the
above examle of gauge invariant observables in 2d gravity is that this was a
spin-off thought (most probably not a new one, of course) of some
considerations that I recently did with respect to such a 2d theory. I know
that it is a little shameless, but see the footnote on page 13 of
http://www.iop.org/EJ/abstract/1126-6708/2004/05/027
for the details of what I indicated above. :-)

> (An initial serious problem is getting
> these expressed as phase functions; not to mention factor ordering in
> the quantum theory).

The canonical quantum theory for anything covariant with d>3 is notoriously
unknown, where operator ordering not even arises as a problem because
already the very definition of the elementary canonical operators is
problematic.

> Now a ``sensible point of view'' that might make you disagree

Disagree with the above recipe by Isham? At least for toy models it can be
constructively demonstrated to be correct! (But that need not imply anything
for d>3 gravity, of course.)

> is
> Unruh's: he says that the correlation understanding of the non-local
> observables implies that the gauge-dependent quantities must be
> measurable,

Why?

> which cannot be the case. In his paper on partial
> observables Rovelli explicitly states that the variables on the
> extended phase space have a robust physical reality; he seems to think
> he needs this to underwrite his idea that the observables of GR are
> composed of just such quantities. That might be ``controversial'', we
> might expect the physical stuff to be given by the reduced space only.
> I should point out that Kuchar makes a similar point against Rovelli's
> evolving constants approach.

I don't quite recall the details of Rovelli's constructions, although I
happily remember having had some discussion about this stuff here on spr
back in the old days:
http://www-stud.uni-essen.de/~sb0264/CovExpValue.html .

But recent disucssions about similar issues at
http://golem.ph.utexas.edu/string/archives/000299.html
convinced me that it is probably best to first test all these ideas about
canonical quantization of gravity in the simplest non-trivial toy examples
that are available. That helps not to get lost in abstract considerations
but to instead get a hands-on experience in terms of some actually tractable
examples.

Therefore I would be interested in if you can identify Rovelli's point and
Unruh's and Kuchar's objection concretely in the 2d toy example mentioned
above. That should help us better understand the controversial point.

John Baez

May15-04, 02:45 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>In article <2004051022171437122%deanrickles@ntlworldcom>,\nDe an Rickles <dean.rickles@ntlworld.com> wrote:\n\n>I have a simple request for information: which physicists have endorsed\n>the ``correlation\'\' view of observables (i.e. the view that the\n>observables of GR and quantum gravity are gauge *invariant*,\n>*relative* quantities decribing correlations between gauge *dependent*\n>quantities)?\n\nYou could make this question more fine-grained by asking first:\n\nwhich physicists endorse the view that observables in GR need to\nbe gauge-invariant (i.e., invariant under those diffeomorphisms\nthat are "pure gauge" from the symplectic point of view)?\n\nand then:\n\nwhich physicists endorse the view that observables in GR need to\nbe gauge-invariant quantities describing correlations between\ngauge-dependent quantities?\n\nThe first one is weaker than the second, and it seems pretty hard\nto argue against it. The only person in GR who seems to question\nit these days is Karel Kuchar - see for example page 21 of this:\n\nKarel Kuchar\nCanonical Quantum Gravity\nhttp://www.arxiv.org/abs/gr-qc/9304012\n\nHere he claims "one can observe dynamical observables which are\nnot perennial". He requires observables to be invariant under\ndiffeomorphisms of *space*, reserving the name "perennial" for those\nobservable that are invariant under diffeomorphisms of space*time*.\n\nBut, it\'s possible I\'m not understanding him, since sometimes he puts\n"dust" in his models of gravity to make previously gauge-dependent\nquantities become gauge-invariant, precisely by making it possible\nto measure positions and times *relative to the dust*! See for example:\n\nJ.D. Brown, K.V. Kuchar\nDust as a Standard of Space and Time in Canonical Quantum Gravity\nhttp://www.arxiv.org/abs/gr-qc/9409001\n\nSo, you\'ll have to make up your own mind about what Kuchar believes.\nHe\'s rather important in this field, so it\'s worth trying.\n\nI assume you\'ve gotten your hands on lots of papers about\nrelational physics by Rovelli and Smolin - they\'re easy to find.\n\nYou didn\'t mention Julian Barbour, who is a crucial person in this\ngame:\n\nJulian B. Barbour,\nAbsolute or Relative Motion?: Volume 1, The Discovery of Dynamics:\nA Study from a Machian Point of View of the Discovery and the\nStructure of Dynamical Theories,\nCambridge University Press, 1989.\n\nAshtekar\'s approach to canonical quantum gravity is all about\nfinding states that are annihilated by all the constraints, and\nthus fully gauge-invariant... so I feel sure he agrees with the weaker\nstatement, but I doubt you can find anything where he says\ngauge-invariant observables must be *relational* in character.\n\nIndeed, I don\'t see any reason why gauge-invariant observables\n*must* be relational - perhaps the relational ones are just the\neasiest to get ahold of.\n\n(And actually it\'s even trickier than I\'m suggesting, because these\ndays Ashtekar is interested in quantum states that aren\'t EXACTLY\nannihilated by the constraints, which one can actually "evolve in\ntime". But, he\'s trying to prove these can be used to approximately\ncalculate gauge-invariant information.)\n\n>Would it be fair to say that this is the majority view?\n\nI think almost all people in gravity agree that observables must be\ngauge-invariant. As for whether they "must" be relational in character,\nI\'m not sure. But, surely the observables we most often actually\nobserve are relational in character! - e.g., "the position of this\nthing as measured by that appartus", "the time of this event as measured\nby that stopwatch", and so on. Pretty much everyone in relativity has\ninternalized this viewpoint, I think.\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 <2004051022171437122%deanrickles@ntlworldcom>,
Dean Rickles <dean.rickles@ntlworld.com> wrote:

>I have a simple request for information: which physicists have endorsed
>the ``correlation'' view of observables (i.e. the view that the
>observables of GR and quantum gravity are gauge *invariant*,
>*relative* quantities decribing correlations between gauge *dependent*
>quantities)?

You could make this question more fine-grained by asking first:

which physicists endorse the view that observables in GR need to
be gauge-invariant (i.e., invariant under those diffeomorphisms
that are "pure gauge" from the symplectic point of view)?

and then:

which physicists endorse the view that observables in GR need to
be gauge-invariant quantities describing correlations between
gauge-dependent quantities?

The first one is weaker than the second, and it seems pretty hard
to argue against it. The only person in GR who seems to question
it these days is Karel Kuchar - see for example page 21 of this:

Karel Kuchar
Canonical Quantum Gravity
http://www.arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/9304012

Here he claims "one can observe dynamical observables which are
not perennial". He requires observables to be invariant under
diffeomorphisms of *space*, reserving the name "perennial" for those
observable that are invariant under diffeomorphisms of space*time*.

But, it's possible I'm not understanding him, since sometimes he puts
"dust" in his models of gravity to make previously gauge-dependent
quantities become gauge-invariant, precisely by making it possible
to measure positions and times *relative to the dust*! See for example:

J.D. Brown, K.V. Kuchar
Dust as a Standard of Space and Time in Canonical Quantum Gravity
http://www.arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/9409001

So, you'll have to make up your own mind about what Kuchar believes.
He's rather important in this field, so it's worth trying.

I assume you've gotten your hands on lots of papers about
relational physics by Rovelli and Smolin - they're easy to find.

You didn't mention Julian Barbour, who is a crucial person in this
game:

Julian B. Barbour,
Absolute or Relative Motion?: Volume 1, The Discovery of Dynamics:
A Study from a Machian Point of View of the Discovery and the
Structure of Dynamical Theories,
Cambridge University Press, 1989.

Ashtekar's approach to canonical quantum gravity is all about
finding states that are annihilated by all the constraints, and
thus fully gauge-invariant... so I feel sure he agrees with the weaker
statement, but I doubt you can find anything where he says
gauge-invariant observables must be *relational* in character.

Indeed, I don't see any reason why gauge-invariant observables
*must* be relational - perhaps the relational ones are just the
easiest to get ahold of.

(And actually it's even trickier than I'm suggesting, because these
days Ashtekar is interested in quantum states that aren't EXACTLY
annihilated by the constraints, which one can actually "evolve in
time". But, he's trying to prove these can be used to approximately
calculate gauge-invariant information.)

>Would it be fair to say that this is the majority view?

I think almost all people in gravity agree that observables must be
gauge-invariant. As for whether they "must" be relational in character,
I'm not sure. But, surely the observables we most often actually
observe are relational in character! - e.g., "the position of this
thing as measured by that appartus", "the time of this event as measured
by that stopwatch", and so on. Pretty much everyone in relativity has
internalized this viewpoint, I think.

Charles Torre

May17-04, 07:57 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>Dean <phldpr@leeds.ac.uk> wrote\n\n> My point concerned a particular view of what kind of\n> animal these observables are in (canonical) GR and QG (perhaps I wasn\'t\n> clear that I meant the canonical approach? apologies). You mentioned a\n> thread debating the observables of GR, and that there can be no local\n> observables (I think Torre proved this, and what it shows is simply\n> that the points of spacetime and the metric (or whatever field) are\n> entwined). So the options seem to be global or non-local. Global\n> observables don\'t seem to be what we deal with when we work with GR, so\n> forget those. The problem then is: how do we understand the non-local\n> observables?\n>\n\nJust to be clear: The "local observables" in this context\nare defined as spatial integrals of densities\nconstructed *locally* from the fields and their derivatives (to any order).\nThe theorem is: if these functionals Poisson commute with the\nconstraints, then they must vanish (all modulo the constraints).\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>Dean <phldpr@leeds.ac.uk> wrote

> My point concerned a particular view of what kind of
> animal these observables are in (canonical) GR and QG (perhaps I wasn't
> clear that I meant the canonical approach? apologies). You mentioned a
> thread debating the observables of GR, and that there can be no local
> observables (I think Torre proved this, and what it shows is simply
> that the points of spacetime and the metric (or whatever field) are
> entwined). So the options seem to be global or non-local. Global
> observables don't seem to be what we deal with when we work with GR, so
> forget those. The problem then is: how do we understand the non-local
> observables?
>

Just to be clear: The "local observables" in this context
are defined as spatial integrals of densities
constructed *locally* from the fields and their derivatives (to any order).
The theorem is: if these functionals Poisson commute with the
constraints, then they must vanish (all modulo the constraints).

charlie

theos ek mechanes

May17-04, 08:05 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>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote...\n>\n> "Dean" <phldpr@leeds.ac.uk> wrote...\n>\n> > the Hamiltonian constraint. But he might just as well say that\n> > the constraint doesn\'t in fact generate gauge transformations\n>\n> I am surprised about this statement, but probably just because I\n> don\'t know the precise context. Why should the Hamiltonian\n> constraint be on different footing than the spatial diffe constraints?\n>\n\nA good reference on this is section 2.4 of Carlip\'s "Quantum\nGravity in 2+1 Dimensions." Hopefully not misrepresenting\nCarlip\'s argument too much, as he\'s likely listening...\n\nGR is not a "gauge theory," where a gauge theory is under-\nstood to be a theory in which the constraints generate infi-\nnitesimal gauge transformations off and on-shell, because\nthe Hamiltonian constraint generates diffeomorphisms in\nthe time direction but only on-shell. However, the other\nconstraints in GR generate spatial diffeomorphisms off\nand on-shell, thus the two types of constraints are on a\ndifferent footing.\n\nThis is I think the origin for the idea that the Hamiltonian\nconstraint does not generate "gauge transformations." It\nonly generates "gauge transformations" up to terms which\nvanish on-shell.\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>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote...
>
> "Dean" <phldpr@leeds.ac.uk> wrote...
>
> > the Hamiltonian constraint. But he might just as well say that
> > the constraint doesn't in fact generate gauge transformations
>
> I am surprised about this statement, but probably just because I
> don't know the precise context. Why should the Hamiltonian
> constraint be on different footing than the spatial diffe constraints?
>

A good reference on this is section 2.4 of Carlip's "Quantum
Gravity in 2+1 Dimensions." Hopefully not misrepresenting
Carlip's argument too much, as he's likely listening...

GR is not a "gauge theory," where a gauge theory is under-
stood to be a theory in which the constraints generate infi-
nitesimal gauge transformations off and on-shell, because
the Hamiltonian constraint generates diffeomorphisms in
the time direction but only on-shell. However, the other
constraints in GR generate spatial diffeomorphisms off
and on-shell, thus the two types of constraints are on a
different footing.

This is I think the origin for the idea that the Hamiltonian
constraint does not generate "gauge transformations." It
only generates "gauge transformations" up to terms which
vanish on-shell.

Urs Schreiber

May20-04, 11:47 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>"theos ek mechanes" <theosekmechanes@yahoo.com> schrieb im Newsbeitrag\nnews:e4daf466.0405160825.6ba4d14f@pos ting.google.com...\n> "Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote...\n> >\n> > "Dean" <phldpr@leeds.ac.uk> wrote...\n> >\n> > > the Hamiltonian constraint. But he might just as well say that\n> > > the constraint doesn\'t in fact generate gauge transformations\n> >\n> > I am surprised about this statement, but probably just because I\n> > don\'t know the precise context. Why should the Hamiltonian\n> > constraint be on different footing than the spatial diffe constraints?\n> >\n\n> GR is not a "gauge theory," where a gauge theory is under-\n> stood to be a theory in which the constraints generate infi-\n> nitesimal gauge transformations off and on-shell, because\n> the Hamiltonian constraint generates diffeomorphisms in\n> the time direction but only on-shell. However, the other\n> constraints in GR generate spatial diffeomorphisms off\n> and on-shell, thus the two types of constraints are on a\n> different footing.\n\nOk. But you would still want physical observables to (Poisson-)commute with\n_all_ the constraints, diffeos+Hamiltonian, right? If not, why not?\n\n\n\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>"theos ek mechanes" <theosekmechanes@yahoo.com> schrieb im Newsbeitrag
news:e4daf466.0405160825.6ba4d14f@posting.google.c om...
> "Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote...
> >
> > "Dean" <phldpr@leeds.ac.uk> wrote...
> >
> > > the Hamiltonian constraint. But he might just as well say that
> > > the constraint doesn't in fact generate gauge transformations
> >
> > I am surprised about this statement, but probably just because I
> > don't know the precise context. Why should the Hamiltonian
> > constraint be on different footing than the spatial diffe constraints?
> >

> GR is not a "gauge theory," where a gauge theory is under-
> stood to be a theory in which the constraints generate infi-
> nitesimal gauge transformations off and on-shell, because
> the Hamiltonian constraint generates diffeomorphisms in
> the time direction but only on-shell. However, the other
> constraints in GR generate spatial diffeomorphisms off
> and on-shell, thus the two types of constraints are on a
> different footing.

Ok. But you would still want physical observables to (Poisson-)commute with
_all_ the constraints, diffeos+Hamiltonian, right? If not, why not?

carlip@no-physics-spam.ucdavis.edu

May20-04, 11:48 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>Dean <phldpr@leeds.ac.uk> wrote:\n\n[...]\n> Anyway, that wasn\'t my point - we can agree that observables have to be\n> gauge invariant. My point concerned a particular view of what kind of\n> animal these observables are in (canonical) GR and QG (perhaps I wasn\'t\n> clear that I meant the canonical approach? apologies). You mentioned a\n> thread debating the observables of GR, and that there can be no local\n> observables (I think Torre proved this, and what it shows is simply\n> that the points of spacetime and the metric (or whatever field) are\n> entwined). So the options seem to be global or non-local.\n\nI think this is a false dichotomy. Presumably both can be observables,\nand I see no reason to assume that they\'re either mutually exclusive or\nindependent. Asymptotically anti-de Sitter string theory, for example,\nprovides a good example in which ``global\'\' observables -- those defined\nin a dual conformal field theory that lives, in some sense, at infinity\n-- can provide interesting ``almost local\'\' information, perhaps all such\ninformation. This example also illustrates how hard it is to extract\nsuch information from global observables, but this is not obviously very\ndifferent from what we would expect from any quantum theory of gravity.\n\n\n> The problem then is: how do we understand the non-local observables?\n\n> DeWitt\'s view was that we simply use objects to pick out space points\n> and instants of time.\n\nThis makes sense as an approximation, but it\'s not clear it\'s well-\ndefined in a full quantum theory. If you look at how astronomers do\n*classical* relativity, this is what they do; instead of referring,\nsay, to ``the position of Mercury at time t,\'\' they translate that\ninformation into, for instance, ``the time for a radar signal leaving\na specified location X on Earth to bounce off Mercury and return, as\nmeasused by an atomic clock located at X and at rest with respect to\nthe transmitter and receiver.\'\'\n\nThe trouble is that such a definition, while classically invariant,\nrequires that Mercury, the Earth, location X, and an atomic clock\nexist. Presumably this is itself a probablistic statement; it seems\nunlikely that the wave function of the Universe is one that makes\nthese existences all true with probability one. So the question\nbecomes how you determine an object to use to pick out a position\nand time.\n\n> This line of thought leads to Page and Wooters\n> conditional probability approach,\n\nYes, perhaps this is the best one can do: give conditional probabilities\n(``if Mercury, the Earth, location X, and an atomic clock exist and\nhave certain properties...\'\').\n\n> and to Rovelli\'s evolving constants\n> of motion and partial/complete observables strategies. The latter\n> explicitly uses quantities defined on the extended phase space\n> (gauge-dependent variables) to construct observables defined on the\n> physical phase space.\n\nI think this is meant as a short-cut, not as a point of principle. I\nhave not gone through this carefully, but I believe that it is possible\nto reexpress Rovelli\'s ``partial/complete observables strategy\'\'\nentirely in terms of the reduced phase space.\n\nSteve Carlip\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>Dean <phldpr@leeds.ac.uk> wrote:

[...]
> Anyway, that wasn't my point - we can agree that observables have to be
> gauge invariant. My point concerned a particular view of what kind of
> animal these observables are in (canonical) GR and QG (perhaps I wasn't
> clear that I meant the canonical approach? apologies). You mentioned a
> thread debating the observables of GR, and that there can be no local
> observables (I think Torre proved this, and what it shows is simply
> that the points of spacetime and the metric (or whatever field) are
> entwined). So the options seem to be global or non-local.

I think this is a false dichotomy. Presumably both can be observables,
and I see no reason to assume that they're either mutually exclusive or
independent. Asymptotically anti-de Sitter string theory, for example,
provides a good example in which ``global'' observables -- those defined
in a dual conformal field theory that lives, in some sense, at infinity
-- can provide interesting ``almost local'' information, perhaps all such
information. This example also illustrates how hard it is to extract
such information from global observables, but this is not obviously very
different from what we would expect from any quantum theory of gravity.

> The problem then is: how do we understand the non-local observables?

> DeWitt's view was that we simply use objects to pick out space points
> and instants of time.

This makes sense as an approximation, but it's not clear it's well-
defined in a full quantum theory. If you look at how astronomers do
*classical* relativity, this is what they do; instead of referring,
say, to ``the position of Mercury at time t,'' they translate that
information into, for instance, ``the time for a radar signal leaving
a specified location X on Earth to bounce off Mercury and return, as
measused by an atomic clock located at X and at rest with respect to
the transmitter and receiver.''

The trouble is that such a definition, while classically invariant,
requires that Mercury, the Earth, location X, and an atomic clock
exist. Presumably this is itself a probablistic statement; it seems
unlikely that the wave function of the Universe is one that makes
these existences all true with probability one. So the question
becomes how you determine an object to use to pick out a position
and time.

> This line of thought leads to Page and Wooters
> conditional probability approach,

Yes, perhaps this is the best one can do: give conditional probabilities
(``if Mercury, the Earth, location X, and an atomic clock exist and
have certain properties...'').

> and to Rovelli's evolving constants
> of motion and partial/complete observables strategies. The latter
> explicitly uses quantities defined on the extended phase space
> (gauge-dependent variables) to construct observables defined on the
> physical phase space.

I think this is meant as a short-cut, not as a point of principle. I
have not gone through this carefully, but I believe that it is possible
to reexpress Rovelli's ``partial/complete observables strategy''
entirely in terms of the reduced phase space.

Steve Carlip

theos ek mechanes

May23-04, 03:13 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>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote ...\n>\n> Ok. But you would still want physical observables to (Poisson-)commute with\n> _all_ the constraints, diffeos+Hamiltonian, right?\n\nYes.\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>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote ...
>
> Ok. But you would still want physical observables to (Poisson-)commute with
> _all_ the constraints, diffeos+Hamiltonian, right?

Yes.

Urs Schreiber

May23-04, 03:45 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\n"theos ek mechanes" <theosekmechanes@yahoo.com> schrieb im Newsbeitrag\nnews:e4daf466.0405220534.589376e4@pos ting.google.com...\n> "Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote ...\n> >\n> > Ok. But you would still want physical observables to (Poisson-)commute\nwith\n> > _all_ the constraints, diffeos+Hamiltonian, right?\n>\n> Yes.\n\nOk. Let me recall that the original statement by Dean was:\n\n> Yes, of course most people would agree that observables in a gauge\n> theory are gauge-invariant. Kuchar might possibly be read a one who\n> denies this, since he denies that the observables of GR commute with\n> the Hamiltonian constraint.\n\nTo this I replied:\n\n> Why should the Hamiltonian constraint be on different\n> footing than the spatial diffeo constraints?\n\nYou kindly pointed out that the physical interpretation of the Hamiltonian\nconstraint is indeed not completely analogous to that of the spatial\ndiffeos. But it seems that we still agree in wondering why Kuchar deduces\nfrom that that physical states/observables don\'t have to commute/be\nannhihalted by the Hamiltonian constraint.\n\nBut I did see John Baez\'s message concerning this point, and it seems that\napparently Kuchar\'s point of view is either controversial or more subtle\nthan it seemed from Dean\'s original remark.\n\nMy point would simply be that in simple toy examples of reparameterization\ninvariant theories we certainly do want the Hamiltonian constraint to\ncommute with observables and to annihilated physical states. This is not\neven a question which can be decided at will, but one that the formalism\nanswers for us.\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>"theos ek mechanes" <theosekmechanes@yahoo.com> schrieb im Newsbeitrag
news:e4daf466.0405220534.589376e4@posting.google.c om...
> "Urs Schreiber" <Urs.Schreiber@uni-essen.de> wrote ...
> >
> > Ok. But you would still want physical observables to (Poisson-)commute
with
> > _all_ the constraints, diffeos+Hamiltonian, right?
>
> Yes.

Ok. Let me recall that the original statement by Dean was:

> Yes, of course most people would agree that observables in a gauge
> theory are gauge-invariant. Kuchar might possibly be read a one who
> denies this, since he denies that the observables of GR commute with
> the Hamiltonian constraint.

To this I replied:

> Why should the Hamiltonian constraint be on different
> footing than the spatial diffeo constraints?

You kindly pointed out that the physical interpretation of the Hamiltonian
constraint is indeed not completely analogous to that of the spatial
diffeos. But it seems that we still agree in wondering why Kuchar deduces
from that that physical states/observables don't have to commute/be
annhihalted by the Hamiltonian constraint.

But I did see John Baez's message concerning this point, and it seems that
apparently Kuchar's point of view is either controversial or more subtle
than it seemed from Dean's original remark.

My point would simply be that in simple toy examples of reparameterization
invariant theories we certainly do want the Hamiltonian constraint to
commute with observables and to annihilated physical states. This is not
even a question which can be decided at will, but one that the formalism
answers for us.