View Full Version : [SOLVED] Hawkings Lecture on Blackholes
<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>\nhttp://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html\n\nIt seems that Stephen Hawkings did revise his ideas at the recent\nDublin conference. Does anyone know where a transcript of what he\nsaid, or at least a more indepth discussion of the mathematics behind\nthis lecture can be found?\n\nNM\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>http://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html
It seems that Stephen Hawkings did revise his ideas at the recent
Dublin conference. Does anyone know where a transcript of what he
said, or at least a more indepth discussion of the mathematics behind
this lecture can be found?
NM
<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>\nnpm7@georgetown.edu (Elite) wrote in message news:<ddf73f4d.0407211033.6ec7d956@posting.google. com>...\n> http://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html\n>\n> It seems that Stephen Hawkings did revise his ideas at the recent\n> Dublin conference. Does anyone know where a transcript of what he\n> said, or at least a more indepth discussion of the mathematics behind\n> this lecture can be found?\n>\n> NM\n\nTranscript at http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt .\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>npm7@georgetown.edu (Elite) wrote in message news:<ddf73f4d.0407211033.6ec7d956@posting.google.com>...
> http://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html
>
> It seems that Stephen Hawkings did revise his ideas at the recent
> Dublin conference. Does anyone know where a transcript of what he
> said, or at least a more indepth discussion of the mathematics behind
> this lecture can be found?
>
> NM
Transcript at http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt .
Urs Schreiber
Jul22-04, 08:49 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>"DickT" <rthompson10@new.rr.com> schrieb im Newsbeitrag\nnews:93eecb7c.0407220513.36dd605@post ing.google.com...\n>\n> npm7@georgetown.edu (Elite) wrote in message\nnews:<ddf73f4d.0407211033.6ec7d956@postin g.google.com>...\n> >\nhttp://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html\n> >\n> > It seems that Stephen Hawkings did revise his ideas at the recent\n> > Dublin conference. Does anyone know where a transcript of what he\n> > said,\n\n> Transcript at http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt .\n\n> > or at least a more indepth discussion of the mathematics behind\n> > this lecture can be found?\n\nNo calculations yet. I gather that there will be a paper one day. But from\nreading the transcript I am getting the impression that there is probably\nnot much math involved. It seems that Hawking is more like giving conceptual\nconsiderations.\n\nFor more comments see also Sean Carrols entry\n\nhttp://preposterousuniverse.blogspot.com/2004/07/hawking-speaks.html\n\nor Peter Woit\'s\n\nhttp://www.math.columbia.edu/~woit/blog/archives/000057.html\n\nor the SCT\n\nhttp://golem.ph.utexas.edu/string/archives/000403.html .\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>"DickT" <rthompson10@new.rr.com> schrieb im Newsbeitrag
news:93eecb7c.0407220513.36dd605@posting.google.co m...
>
> npm7@georgetown.edu (Elite) wrote in message
news:<ddf73f4d.0407211033.6ec7d956@posting.google.com>...
> >
http://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html
> >
> > It seems that Stephen Hawkings did revise his ideas at the recent
> > Dublin conference. Does anyone know where a transcript of what he
> > said,
> Transcript at http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt .
> > or at least a more indepth discussion of the mathematics behind
> > this lecture can be found?
No calculations yet. I gather that there will be a paper one day. But from
reading the transcript I am getting the impression that there is probably
not much math involved. It seems that Hawking is more like giving conceptual
considerations.
For more comments see also Sean Carrols entry
http://preposterousuniverse.blogspot.com/2004/07/hawking-speaks.html
or Peter Woit's
http://www.math.columbia.edu/~woit/blog/archives/000057.html
or the SCT
http://golem.ph.utexas.edu/string/archives/000403.html .
<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>npm7@georgetown.edu (Elite) wrote in message news:<ddf73f4d.0407211033.6ec7d956@posting.google. com>...\n> http://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html\n>\n> It seems that Stephen Hawkings did revise his ideas at the recent\n> Dublin conference. Does anyone know where a transcript of what he\n> said, or at least a more indepth discussion of the mathematics behind\n> this lecture can be found?\n>\n> NM\n\nHawking\'s recent flap on television is of no physics signifiance\nwhatsoever. He had his\npublicist send out a press release to the Associated Press, so all the\nmedia outlets would report that Hawking solved all the mysteries of\nthe universe, in some vague unspecified way. He constantly compares\nhimself with Einstein and Newton. He never passes up the chance to\nremind people that he holds the same chair as Newton, as if everyone\nwho held that chair was therefore equal to Newton. He charges\nludicrous sums of money as speaking fees for his lecture tour. The\nonly reason his popular is because he\'s quadraplegic, which the public\nfinds irresistable. He shamelessly uses his disability for his own\nself-promotion. His only significant contribution to physics was\nHawking radiation, which was 30 years ago, and which the public never\nheard of. Since then, he\'s become increasingly irrelavant in terms of\nreal physics, including his recent claim that information lost to a\nblack hole in somehow magically recovered, for which he makes no\nattempt to explain how that might be possible. Yet every news program\nran a story about Hawking\'s recent "breakthrough". A real physicist\nwould be trying to convince his collegues, not the general public.\n\nDavid\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>npm7@georgetown.edu (Elite) wrote in message news:<ddf73f4d.0407211033.6ec7d956@posting.google.com>...
> http://www.cnn.com/2004/TECH/space/07/21/hawking.blackholes.ap/index.html
>
> It seems that Stephen Hawkings did revise his ideas at the recent
> Dublin conference. Does anyone know where a transcript of what he
> said, or at least a more indepth discussion of the mathematics behind
> this lecture can be found?
>
> NM
Hawking's recent flap on television is of no physics signifiance
whatsoever. He had his
publicist send out a press release to the Associated Press, so all the
media outlets would report that Hawking solved all the mysteries of
the universe, in some vague unspecified way. He constantly compares
himself with Einstein and Newton. He never passes up the chance to
remind people that he holds the same chair as Newton, as if everyone
who held that chair was therefore equal to Newton. He charges
ludicrous sums of money as speaking fees for his lecture tour. The
only reason his popular is because he's quadraplegic, which the public
finds irresistable. He shamelessly uses his disability for his own
self-promotion. His only significant contribution to physics was
Hawking radiation, which was 30 years ago, and which the public never
heard of. Since then, he's become increasingly irrelavant in terms of
real physics, including his recent claim that information lost to a
black hole in somehow magically recovered, for which he makes no
attempt to explain how that might be possible. Yet every news program
ran a story about Hawking's recent "breakthrough". A real physicist
would be trying to convince his collegues, not the general public.
David
<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"DickT" <rthompson10@new.rr.com> wrote in message\nnews:93eecb7c.0407220513.36dd605@posting. google.com...\n\n> Transcript at http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt .\n\nThe transcript was fascinating. I\'m sure I\'ll never understand the preprint,\nso I\'ll ask my questions of the experts based on that.\n\nDid I read it correctly to understand that, at least in Hawking\'s view,\none can *never* be sure that a Black Hole has formed? (in the real\nworld, which I accept must be described by a quantum theory of gravity).\n\nIf so, black holes are a funny kind of Schrodinger\'s cat. By that, I mean\nthat no matter how you probe, you\'re still not sure if the cat is alive or dead\nand there is no experiment you can ever do, even in principle, to determine it.\nIs that his view?\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>"DickT" <rthompson10@new.rr.com> wrote in message
news:93eecb7c.0407220513.36dd605@posting.google.co m...
> Transcript at http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt .
The transcript was fascinating. I'm sure I'll never understand the preprint,
so I'll ask my questions of the experts based on that.
Did I read it correctly to understand that, at least in Hawking's view,
one can *never* be sure that a Black Hole has formed? (in the real
world, which I accept must be described by a quantum theory of gravity).
If so, black holes are a funny kind of Schrodinger's cat. By that, I mean
that no matter how you probe, you're still not sure if the cat is alive or dead
and there is no experiment you can ever do, even in principle, to determine it.
Is that his view?
<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"Alan" <info@optioncity.REMOVETHIS.net> wrote in message\nnews:48udnf6aI7AbgZ3cRVn-ug@adelphia.com...\n>\n> Did I read it correctly to understand that, at least in Hawking\'s view,\n> one can *never* be sure that a Black Hole has formed? (in the real\n> world, which I accept must be described by a quantum theory of gravity).\n\nDear Alan,\n\nthere seems to be some confusion about what Hawking was\nactually talking about. This confusion has to do with what meaning\none attributes to the term "black hole".\n\nHawking talks about "black holes" for which an event horizon never\nforms.\n\nActually, this is a contradiction in itself.\n\nIf, as Hawking claims, an event horizon *never forms* in realistic\ngravitational collapse, then clearly the space-time representing the\ncollapsed object *cannot* be a black hole space-time.\n\nEvery graduate student learns, that it is most important to properly\ndefine the terms that one uses in scientific statements. The proper\ndefinition for the term "black hole" goes as follows: A black hole\nis a (non-vanishing) region in space-time , which is causally\ndisconnected from asymptotic infinity. The event horizon is the\n(non-vanishing!) boundary between the black hole region and the\nasymptotic region.\n\nIt is obvious from this definition, that if there is no boundary\nbetween two causally disconnected regions, i.e. no event horizon,\nthere is no black hole. It is as simple as that.\n\nThere is another contradiction in Hawking\'s talk, which has the\nsame origin as the first. To quote from the manuscript:\n\n"This result indicates that a black hole evaporates, while\nremaining topologically *trivial*."\n\nHowever, some lines before Hawking has informed us, that\nthe black hole metrics are topologically *non-trivial*. Let us\nlook at the relevant quotes:\n\n"Any topologically non-trivial metric will have a fixed point\nin the Euclidean regime which corresponds to a horizon in the\nLorentzian."\n\nAnd shortly thereafter:\n\n"There are two important cases, topologically trivial metrics,\nand the black hole. The black hole is eternal. It can not become\ntopologically trivial at late times."\n\nClearly black hole space-times are topologically non-trivial.\nHow then can "black holes" evaporate while the black hole\nspace-time remains topologically trivial? This seems impossible.\n\nOne might therefore ask oneself, what did Hawking really mean\nto say? Or rather, why does he still talk about "black holes" (or\nmore generally about topologically non-trivial metrics), when he\nhas something completely different in mind? Obviously Hawking\nnow uses the term "black hole" in a way, that is not in agreement\nwith the well known definition for the technical term "black hole".\nOne can only wonder why Hawking secretly has changed the\ndefinition of an important technical term without telling. Why\nshould we call the "horizonless, topologically trivial compact\nobject", which he apparently has in mind as the end-stage of\nrealistic gravitational collapse, by the already occupied name\n"black hole", which has just the opposite meaning? This makes\nno sense at all. Or does the continued usage of the technical\nterm "black hole" in Hawking\'s presentation suggest, that\nHawking still believes that black hole space-times (*with*\nevent horizon!) still can be used to describe the *new*\nend-state of realistic gravitational collapse that he is envisaging\nnow, i.e. a compact object without event horizon? Maybe\nHawking will eventually tell us what logic is behind this\nconfusion.\n\nHowever, until this might happen one has to find out by oneself,\nwhat Hawking\'s talk might mean: If one pastes away the obscuring\nmathematics and the ill-defined usage of the technical term "black\nhole", the true message of Hawking\'s talk - according to it\'s\nown logic - can only be, that neither the Kerr-Newman family\nof vacuum black hole solutions, nor any other topologically\nnon-trivial solution of the field equations, can be the physically\nrealized solution that describes the end-state of realistic gravitational\ncollapse. According to Hawking\'s reasoning *none* of these\nsolutions contribute to the Euclidean path integral! However, if\nthey don\'t contribute, (and if the Euclidean path integral is the\ncorrect approach to quantum gravity, as Hawking believes) why\nthen should we include these solutions at all in our search for the\nproper classical limit of a consistent theory of quantum gravity?\n\nSo if one takes Hawking\'s arguments seriously, there must be\n*other* solutions of the field equations, which describe the\n*realistic* end-state of gravitational collapse in the classical\nlimit. The only solutions that need to be considered, are the\nones that *contribute* to the Euclidean path integral. These\nare the topologically trivial ones. But topologically trivial\nsolutions *don\'t* have an event horizon!\n\nFollowing the logic of Hawking\'s talk then inevitably leads\nto the conclusion, that the *physically realistic* solutions of\nthe classical field equations we must look for (in the classical limit),\nare solutions describing a (compact) self-gravitating object\n*without* event-horizon!. Clearly any such solution, however\ncompact it may be, cannot be a black hole!\n\nUnfortunately this is a very destructive argument. It basically\nsays, that the solutions we have been working with so far\n(the black hole solutions), are not adequate in describing\nthe physically realistic end-state of gravitational collapse.\n\nOne could now ask the question, whether there are any such\nsolutions of the field equations, which give some sense to\nHawking\'s talk in a constructive way. There are at least two:\nThe gravastar and the holostar. However, before rushing into\na discussion about alternative solutions I would rather like to\ndiscuss Hawking\'s arguments as a first step.\n\nWhat do you think? Has he been talking about black holes\n(in the correct technical sense of the term) or about something\nelse? And if he talked about something else, what?\n\nMP\n\nYou might find a quote from Max Planck interesting (not literally):\n\n"wrong scientific ideas usually don\'t die because their practitioners\nhave become convinced to something better. They die, because\ntheir practitioners die"\n\nAt least Hawking seems to have changed his mind. If for good\nor for bad, who knows?\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>"Alan" <info@optioncity.REMOVETHIS.net> wrote in message
news:48udnf6aI7AbgZ3cRVn-ug@adelphia.com...
>
> Did I read it correctly to understand that, at least in Hawking's view,
> one can *never* be sure that a Black Hole has formed? (in the real
> world, which I accept must be described by a quantum theory of gravity).
Dear Alan,
there seems to be some confusion about what Hawking was
actually talking about. This confusion has to do with what meaning
one attributes to the term "black hole".
Hawking talks about "black holes" for which an event horizon never
forms.
Actually, this is a contradiction in itself.
If, as Hawking claims, an event horizon *never forms* in realistic
gravitational collapse, then clearly the space-time representing the
collapsed object *cannot* be a black hole space-time.
Every graduate student learns, that it is most important to properly
define the terms that one uses in scientific statements. The proper
definition for the term "black hole" goes as follows: A black hole
is a (non-vanishing) region in space-time , which is causally
disconnected from asymptotic infinity. The event horizon is the
(non-vanishing!) boundary between the black hole region and the
asymptotic region.
It is obvious from this definition, that if there is no boundary
between two causally disconnected regions, i.e. no event horizon,
there is no black hole. It is as simple as that.
There is another contradiction in Hawking's talk, which has the
same origin as the first. To quote from the manuscript:
"This result indicates that a black hole evaporates, while
remaining topologically *trivial*."
However, some lines before Hawking has informed us, that
the black hole metrics are topologically *non-trivial*. Let us
look at the relevant quotes:
"Any topologically non-trivial metric will have a fixed point
in the Euclidean regime which corresponds to a horizon in the
Lorentzian."
And shortly thereafter:
"There are two important cases, topologically trivial metrics,
and the black hole. The black hole is eternal. It can not become
topologically trivial at late times."
Clearly black hole space-times are topologically non-trivial.
How then can "black holes" evaporate while the black hole
space-time remains topologically trivial? This seems impossible.
One might therefore ask oneself, what did Hawking really mean
to say? Or rather, why does he still talk about "black holes" (or
more generally about topologically non-trivial metrics), when he
has something completely different in mind? Obviously Hawking
now uses the term "black hole" in a way, that is not in agreement
with the well known definition for the technical term "black hole".
One can only wonder why Hawking secretly has changed the
definition of an important technical term without telling. Why
should we call the "horizonless, topologically trivial compact
object", which he apparently has in mind as the end-stage of
realistic gravitational collapse, by the already occupied name
"black hole", which has just the opposite meaning? This makes
no sense at all. Or does the continued usage of the technical
term "black hole" in Hawking's presentation suggest, that
Hawking still believes that black hole space-times (*with*
event horizon!) still can be used to describe the *new*
end-state of realistic gravitational collapse that he is envisaging
now, i.e. a compact object without event horizon? Maybe
Hawking will eventually tell us what logic is behind this
confusion.
However, until this might happen one has to find out by oneself,
what Hawking's talk might mean: If one pastes away the obscuring
mathematics and the ill-defined usage of the technical term "black
hole", the true message of Hawking's talk - according to it's
own logic - can only be, that neither the Kerr-Newman family
of vacuum black hole solutions, nor any other topologically
non-trivial solution of the field equations, can be the physically
realized solution that describes the end-state of realistic gravitational
collapse. According to Hawking's reasoning *none* of these
solutions contribute to the Euclidean path integral! However, if
they don't contribute, (and if the Euclidean path integral is the
correct approach to quantum gravity, as Hawking believes) why
then should we include these solutions at all in our search for the
proper classical limit of a consistent theory of quantum gravity?
So if one takes Hawking's arguments seriously, there must be
*other* solutions of the field equations, which describe the
*realistic* end-state of gravitational collapse in the classical
limit. The only solutions that need to be considered, are the
ones that *contribute* to the Euclidean path integral. These
are the topologically trivial ones. But topologically trivial
solutions *don't* have an event horizon!
Following the logic of Hawking's talk then inevitably leads
to the conclusion, that the *physically realistic* solutions of
the classical field equations we must look for (in the classical limit),
are solutions describing a (compact) self-gravitating object
*without* event-horizon!. Clearly any such solution, however
compact it may be, cannot be a black hole!
Unfortunately this is a very destructive argument. It basically
says, that the solutions we have been working with so far
(the black hole solutions), are not adequate in describing
the physically realistic end-state of gravitational collapse.
One could now ask the question, whether there are any such
solutions of the field equations, which give some sense to
Hawking's talk in a constructive way. There are at least two:
The gravastar and the holostar. However, before rushing into
a discussion about alternative solutions I would rather like to
discuss Hawking's arguments as a first step.
What do you think? Has he been talking about black holes
(in the correct technical sense of the term) or about something
else? And if he talked about something else, what?
MP
You might find a quote from Max Planck interesting (not literally):
"wrong scientific ideas usually don't die because their practitioners
have become convinced to something better. They die, because
their practitioners die"
At least Hawking seems to have changed his mind. If for good
or for bad, who knows?
Jake Mannix
Jul25-04, 08:16 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\n\n\nulmo@cheerful.com (Ulmo) wrote in message\n\n> Hawking\'s recent flap on television is of no physics signifiance\n> whatsoever. He had his publicist send out a press release to the\n> Associated Press, so all the\n\n<a bunch of rude personal attacks snipped>\n\n>From what people I\'ve talked to at Stanford\'s physics dept, it\'s\nnowhere nearly so harshly thought of ("no physics signifigance").\n\n> His only significant contribution to physics was\n> Hawking radiation, which was 30 years ago, and which the public never\n> heard of.\n\nAnd the Hawking-Penrose singularity theorems, and the Hawking-Page\nphase transition, and... or did you mean "signifigant contribution"\nas "contribution which fundamentally changed the way we look at\na branch of physics"? Most theorists never have one of those.\n\n> Since then, he\'s become increasingly irrelavant in terms of\n> real physics, including his recent claim that information lost to a\n> black hole in somehow magically recovered, for which he makes no\n> attempt to explain how that might be possible. Yet every news program\n> ran a story about Hawking\'s recent "breakthrough". A real physicist\n> would be trying to convince his collegues, not the general public.\n\nI think there\'s a big difference between saying that Hawking is not\nTHE ONE AND ONLY MOST AMAZING PHYSICIST ALIVE TODAY (which\nmany in the public believe), and saying he\'s irrelevant and not a\nreal physicist. Showmanship is not terribly uncommon among theorists,\nand while not necessarily positivley correlated with talent, it\'s not\nnecessarily *negatively* correlated either.\n\nBerate the media for treating Hawking as a celebrity beyond all\ncelebrities. But personal attack belittle yourself more than\nanyone else.\n\n-jake\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>ulmo@cheerful.com (Ulmo) wrote in message
> Hawking's recent flap on television is of no physics signifiance
> whatsoever. He had his publicist send out a press release to the
> Associated Press, so all the
<a bunch of rude personal attacks snipped>
>From what people I've talked to at Stanford's physics dept, it's
nowhere nearly so harshly thought of ("no physics signifigance").
> His only significant contribution to physics was
> Hawking radiation, which was 30 years ago, and which the public never
> heard of.
And the Hawking-Penrose singularity theorems, and the Hawking-Page
phase transition, and... or did you mean "signifigant contribution"
as "contribution which fundamentally changed the way we look at
a branch of physics"? Most theorists never have one of those.
> Since then, he's become increasingly irrelavant in terms of
> real physics, including his recent claim that information lost to a
> black hole in somehow magically recovered, for which he makes no
> attempt to explain how that might be possible. Yet every news program
> ran a story about Hawking's recent "breakthrough". A real physicist
> would be trying to convince his collegues, not the general public.
I think there's a big difference between saying that Hawking is not
THE ONE AND ONLY MOST AMAZING PHYSICIST ALIVE TODAY (which
many in the public believe), and saying he's irrelevant and not a
real physicist. Showmanship is not terribly uncommon among theorists,
and while not necessarily positivley correlated with talent, it's not
necessarily *negatively* correlated either.
Berate the media for treating Hawking as a celebrity beyond all
celebrities. But personal attack belittle yourself more than
anyone else.
-jake
<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> What do you think? Has he been talking about black holes\n> (in the correct technical sense of the term) or about something\n> else? And if he talked about something else, what?\n\nMP,\n\nThank you for your comments. As a non-expert, my sense of\nit was that in a putative quantum gravity one has to consider\nmany types of \'paths\' at once in some sort of path integral.\nThis is a general principle that will hold even if the details aren\'t quite\nknown.\nThe classical technical black-hole solution would only be\nan approximate path integral contribution that ignored radiation --\na WKB-style solution as hbar->0.\n\nThe radiation would come from other path integral pieces involving\nsmooth metrics with no horizon, if I have it right.\nI guess the relative importance of these types\nof pieces depend on the mass of the object and the time scale\nof the experiment among other things. Besides radiation, these\nsmooth metrics also allow the theory to be \'unitary\', preserving\ninformation, which was the motivation for the problem.\n\nI took Hawking\'s remarks to be general principles\nthat would hold in *any* quantum theory of gravity, regardless\nof the details. The idea that in some final theory, that one will sum\nover various metrics has been around for a long time.\nBut to me, and I could be completely wrong here, the\nassociation of the radiative effects with the path sums over\nall the \'smooth metrics\' seemed like a new insight. Not\nonly that, it seems quite agreeable with his earlier\nsemi-classical insight that the radiation causes the classical black\nhole with a classical horizon to evaporate, returning\na classical spacetime to a smooth state. It all seems quite\nconsistent in a qualitative way.\n\nPlease ... somebody correct me if I have totally mangled it.\n\nalan\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>What do you think? Has he been talking about black holes
> (in the correct technical sense of the term) or about something
> else? And if he talked about something else, what?
MP,
Thank you for your comments. As a non-expert, my sense of
it was that in a putative quantum gravity one has to consider
many types of 'paths' at once in some sort of path integral.
This is a general principle that will hold even if the details aren't quite
known.
The classical technical black-hole solution would only be
an approximate path integral contribution that ignored radiation --
a WKB-style solution as \hbar->0.
The radiation would come from other path integral pieces involving
smooth metrics with no horizon, if I have it right.
I guess the relative importance of these types
of pieces depend on the mass of the object and the time scale
of the experiment among other things. Besides radiation, these
smooth metrics also allow the theory to be 'unitary', preserving
information, which was the motivation for the problem.
I took Hawking's remarks to be general principles
that would hold in *any* quantum theory of gravity, regardless
of the details. The idea that in some final theory, that one will sum
over various metrics has been around for a long time.
But to me, and I could be completely wrong here, the
association of the radiative effects with the path sums over
all the 'smooth metrics' seemed like a new insight. Not
only that, it seems quite agreeable with his earlier
semi-classical insight that the radiation causes the classical black
hole with a classical horizon to evaporate, returning
a classical spacetime to a smooth state. It all seems quite
consistent in a qualitative way.
Please ... somebody correct me if I have totally mangled it.
alan
<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\n"Alan" <info@optioncity.REMOVETHIS.net> wrote in message\nnews:mrKdnakBeP2tdJ7cRVn-hQ@adelphia.com...\n>\n\n\n> As a non-expert, my sense of\n> it was that in a putative quantum gravity one has to consider\n> many types of \'paths\' at once in some sort of path integral.\n> This is a general principle that will hold even if the details aren\'t\n> quite known.\n\nYou described it quite accurately for a "non-expert".\n\nHawking\'s method belongs to the class of variational\napproaches, which has turned out to be quite a powerful tool in\ntheoretical physics in general (not only in quantum mechanics).\nPut in simple terms, the crucial difference between the Euclidean\npath integral approach and the well known Feynman path\nintegral approach is, that in the second we sum over different\n(intermediate, virtual) processes whereas in the first we sum over\nall "possible" space-time metrics.\n\nIn the Feynman path integral approach each (virtual) process\ncontributes to the total probability of a particular outcome with a\n(complex) probability amplitude less than 1. All probability\namplitudes are summed up and give us the probability amplitude\nfor the whole process. Any (intermediate) process that has a\nprobability amplitude of zero does not need to be considered in the sum. In\nHawking\'s approach the "Euclidean path integral" over a particular\nspace-time metric takes on a similar role as the\nFeynman diagram for a certain topology of the scattering\nprocess.\n\nNow Hawking tells us, that the probability amplitude of the\nblack hole space-times (with event-horizon) in the Euclidean\npath integral approach is zero (or rather goes to zero exponentially at low\ntemperatures, if I understand him correctly).\nI don\'t know if this truly is the case, as I am not an expert in the\nEuclidean path integral approach. However, nobody seems to\nhave criticized this particular statement and some have even\nremarked that it is quite an old result, already derived by others.\n\nSo let us assume that\n\ni) the Euclidean path integral approach is the correct way to do\nquantum gravity\n\nii) the black hole metrics (or rather all non-trivial metrics) don\'t\ncontribute to the probability amplitude in this approach.\n\nHowever, if this is the case, why should we include metrics with\n*zero* probability amplitude at all in our classical (!) picture?\n\nSome might say, the classical picture is never 100% correct.\nOne always has to include *all* possibilities , however low their\nprobabilities are, at least as intermediate stage. But this is not a\ngood argument, as you will see shortly:\n\nFirst remember the Bohr-correspondence principle. This principle\ntells us, that a system which consists of a large number of\nquantum states has a well defined classical limit. The limit is the\n(hopefully) unique state with the "highest" quantum mechanical\nprobability amplitude.\n\nNow for quantum mechanical processes involving very few\ndegrees of freedom it is generally impossible to single out one\nsingle process with the highest probability amplitude. As JB\nremarked in the companian thread "Hawking in Dublin", in\nscattering processes involving elementary particles it is (at least)\nproblematic to attribute too much meaning to the intermediate\nprocesses, or even to a whole class of intermediate processes,\nsuch as the class of processes described by a single Feynman-\ndiagram. There are many cases known, where a sensible answer\nto a scattering problem can only be obtained, if one includes all\nFeynman-diagrams of a certain order (see e.g. the infrared-\nproblem in electron scattering).\n\nHowever, in the large N-limit we know from experience, that it\nis always possible to find a single process, whose probability\ndominates so vastly over all other processes, that it makes\nimminent sense to refer to this process as a unique single process.\nThis process, if it exists, is called the classical trajectory.\n\nTo give an example how this works computationally, consider\nthe following classical analogue: The principle of least action.\nYou find an excellent introduction to this principle in the\nFeynman lectures. Let me summarize: In order to find the\n(classical) path of a particle going from A to B you consider all\npaths that take this particle from A to B. You calculate the action\nfor each possible path. The classical path is the one that\nextremizes the action. Now calculating the action for each path is\nquite cumbersome, often impossible. Therefore in practice you\nresort to an approximation procedure: You look at differences\nbetween paths close to each other, i.e. you look at how a small\nvariation of the path changes your calculated value for the action.\nThe path that extremizes the action is the one, for which small\nlocal variations of the path leave the action stationary. This\napproximation procedure in a sense demands, that a classical\nlimit truly exists: In the difference-approach you only consider\npaths which are very close to the "classical" path. But if the\nclassical limit exists, it does not make sense to attribute any\nmeaning to paths which are very far away from the classical path\nand therefore have zero probability of occurring (or rather\nexponentially decaying probability).\n\nHawking is doing something very similar, when he expands in a\nsaddle-point approximation. Clearly he presumes that the\nclassical limit exists. This is a very reasonable assumption for a\nlarge system. In this respect GR is no different from any other\nclassical theory. Hawking implicitly invokes the Bohr\ncorrespondence principle, which guarantees that the classical\nlimit exists for large N.\n\nHowever, Hawking does not minimize the action, rather he\ncalculates probability amplitudes. But as we well know from\nquantum mechanics (see also the Feynman lectures or the little\ncute Feynman book on QED) complex probability amplitudes\nand action are related (somewhat like A = e^iS), meaning that a\nnon-stationary action leads to a heavy oscillatory behaviour of\nthe complex probability amplitude for any small section of the\npath, which gives nearly zero when averaged over the whole\npath.\n\nHawking has found out (or maybe he just re-interpreted a known result), that\nall space-times with non-trivial topology (i.e.\nall black hole space-times) don\'t contribute to the probability\namplitude. As I said, I don\'t know if this is correct. But if this is\nthe case, it makes no sense at all to include these space-times in\nthe *classical* (!) picture. To include space-times with\nexcruciatingly low probability in the classical picture would be as\ncrazy as if you would demand, that in a classical analysis of a\ncannon ball flying from A to B you have to consider the path\nwhere the cannon-ball flies to the moon and back again.\nAlthough such a path is quantum mechanically possible, and\ntherefore in principle should be included in a full quantum\nmechanical calculation, it\'s probability of occurrence is so low,\nthat no sane physicist would ever think that such a process might\nactually occurr in the real world, not even as an "intermediate"\nprocess. Therefore a process with (exponentially) zero\nprobability amplitude has no place at all in the classical theory.\n\n> The classical technical black-hole solution would only be\n> an approximate path integral contribution that ignored radiation\n> a WKB-style solution as hbar->0.\n\nCorrect, but its probability amplitude is zero (if Hawking is\ncorrect) and therefore it is madness to include this in the list of\npossible classical space-times, even as an intermediate state.\n\n> The radiation would come from other path integral pieces\n> involving smooth metrics with no horizon, if I have it right.\n\nIf Hawking is correct, you have it right.\n\nHowever why would it only be radiation that originates from the\nsmooth metrics with no horizon? We know very well that small\nblack holes can "radiate" particles...\n\nAlso note, that the compact object formed at the end-stage of\ngravitational collapse has no horizon (according to Hawking),\nand therefore is not a black hole. Still it will very much look like\na black hole from the outside, so that one can assume that a\nsufficiently small compact collapsed object would be very hot\nand therefore will also radiate particles. But even if the\nhorizonless compact object that belongs to the "path integral\npieces with no horizon" is very large, so that only Hawking\nradiation can escape its gravitational pull, this does not\nnecessarily mean that the object itself is composed exclusively\nout of radiation. No?\n\n> I guess the relative importance of these types\n> of pieces depend on the mass of the object and the time scale\n> of the experiment among other things.\n\nYes, the more we approach the classical limit (in the Bohr\ncorrespondence principle this means: the higher the number of\nquantum states N becomes, which implies the more massive the\nobject becomes, which implies the longer the relevant time-\nscales are, ...) the more important will the "pieces with no event\nhorizon" (you called these the "pieces with radiation") will\nbecome relative to the "pieces with event horizon" (i.e. black\nholes). This means that the more massive a compact object\nbecomes (i.e. the higher its number of internal degrees of\nfreedom) the more will the topologically *trivial* metrics with no\nhorizon dominate the probabililty amplitude. At least this will be\nthe case if Hawking is correct, and the "black hole pieces" have\namplitudes approaching zero very quickly.\n\n> Besides radiation, these\n> smooth metrics also allow the theory to be \'unitary\', preserving\n> information, which was the motivation for the problem.\n\nThese smooth metrics are the only ones that need to be\nconsidered (in the large N limit!), because *only* these smooth\nmetrics make a noticeable contribution to the overall probability\namplitude. Therefore, in the large N-limit the theory quite\ncertainly is unitary. But it is unitary *only* because the black hole\nmetrics, which quite evidently "destroy" information\n(Hawking says so himself), are *not* part of the classical limit of\nthe theory. Why would you wan\'t a space-time, which has zero\n(!!!) contribution to the total probability amplitude, be part of the\nclassical theory? Do you include virtual cannon balls flying from\nthe earth to the moon and back again in your classical calculation\nof the trajectory of a cannon ball going from A to B?\n\nHowever, the result of (nearly) zero probability amplitude for the\nblack hole space-times can only be correct within the limits of\nthe approximation that Hawking is using. The approximation\npresumes that the classical limit exists.\n\n(it is reasonable to assume, that the correct classical limit will be\nan exact solution of the field equations. But keep in mind that not\nevery exact solution of the field equations is a black hole. Many\nare not! And then there is the - remote - possibility, that Einsteins\nfield equations must be modified already in the classical regime.\nI don\'t believe this, but some do.).\n\nIf the classical limit exists, the approximations used by Hawking\nwill become better, the higher N becomes. For macroscopic\nobjects one would assume, that the approximation is excellent.\nFor low N one must keep in mind though, that the approximation\nmight fail. Therefore it is very well possible that small (quantum\nsized) "black holes" might still play a role in collision processes\nof elementary particles at high energies. But for large objects N\nis very high, so "zero" should be "0" to an excellent\napproximation for any macroscopic compact object (recall that\nthe exponential function is involved, for instance 10^(-1000) is\nby all practical purposes zero!).\n\n> I took Hawking\'s remarks to be general principles\n> that would hold in *any* quantum theory of gravity, regardless\n> of the details. The idea that in some final theory, that one will\n> sum over various metrics has been around for a long time.\n\nThis is the essential idea. And it seems to be an approach that is\nquite conservative and well within the scope of main stream\nphysics. However, if Hawking is right in his particular variant of\nthe general approach, the logical outcome of his approach is,\nthat the black hole metrics are not "members" of the classical\nlimit. For a classical calculation in the high N regime the black\nhole metrics are as significant as the cannon-ball flying from the\nearth to the moon and back again. I repeat: Hawking says that\nany black hole state has (exponentially) zero probability\namplitude!\n\nIt is clear, that anybody who has invested much time and effort\ninto the study of black hole space-times will not be very happy\nto hear this. Hawking seems to have known this. I would\npresume that this is the reason why he plays a game with\nnames: What has formerly been called black hole (i.e. a space\ntime *with* event horizon) is now called the "eternal black hole".\nWhat is *not* a black hole (i.e. a space-time *without* event\nhorizon) is called "black hole". This apparently slight shift of\nnames, retaining the old name "black hole" (but radically\nchanging its true meaning) and giving an obscure modifier\n(eternal) to the true term black hole, will make all those who yet\nbelieve in black holes happy for a while. Most of them have not\neven realized what happened: The "eternal black hole" is nothing\nelse than Hawking\'s new name for the Schwarzschild or Kerr\nNewman space-times. Think! These classical space-times have\nall the properties that Hawking now attributes to the term\n"eternal black hole". They have\n\n- an event horizon\n\n- they are static (Schwarzschild/Reissner-Nordstroem) or\nstationary (Kerr-Newman), i.e. there is no time-evolution in such\nspace-times. They are truly eternal.\n\n- They can never become non-trivial (at least not classically),\nbecause in classical theory the event horizon never shrinks.\n\nAnd they don\'t contribute to the probability amplitude: the\namplitude is zero.\n\nHawking must know, that a state with zero probability amplitude\ncannot be realized in the classical theory. He has told us, that\n"space-times with event horizon" have *zero* probability\namplitude. He knows the correct definition for the technical term\nblack hole (He is the "father" of the event horizon!). So he must\nknow that black holes are dead. However, being the wizard that\nhe is, he has left the crowd their favorate name: "black hole".\nAnd he has given them a name to bash on: the "eternal black\nhole". All of us know, that the "eternal" black hole is physically\nunrealistic. A physically realistic black hole radiates. So we will\nbash the eternal black hole to death.\n\nNow consider the following (the next par is science fiction):\n\nWhen the funeral ceremonies are over, Hawking gets on stage again. He will\ninform the stupefied crowd, that the "eternal black\nhole" that just has been buried is nothing else than the Kerr-\nNewman family of space-time metrics. If he is a really great\nwizard, he will then present us what he thinks is the physically\nrealistic solution for a compact self gravitating object. This\nsolution will have *trivial* topology and it will *not* have an\nevent horizon. He will still call this soluton a black hole. And\nthis will be correct in a certain sense, because from the outside\nthe new solution will look exactly as a black hole. But clearly\nits interior will be quite different. So what do *you* think what\nthe interior of this object will be? The interior Kerr-Newman\nsolution?\n\n> But to me, and I could be completely wrong here, the\n> association of the radiative effects with the path sums over\n> all the \'smooth metrics\' seemed like a new insight. Not\n> only that, it seems quite agreeable with his earlier\n> semi-classical insight that the radiation causes the classical\n> black hole with a classical horizon to evaporate, returning\n> a classical spacetime to a smooth state. It all seems quite\n> consistent in a qualitative way.\n\nThe "radiative effects" you are talking about, are the effects that\nyou can measure in the space-time exterior to the compact\nobject that forms in gravitational collapse, far far away from the\nstrong field regime. But as Hawking says himself, the radiation\nmeasured at spatial infinity gives you no information about the\ninterior structure of the compact object from which the radiation\noriginates. As Hawking says, one can never know whether an\nevent horizon has actually formed.\n\nHowever, this does not mean that the compact object without\nevent horizon can have arbitrary properties. It\'s metric must be\nquite similar to a black hole metric in the exterior space-time. A\nsolution of the field equations with surface red-shift z ~ 2 will not\ndo. The surface-redshift must be enormous. If the compact body has high\nsurface redshift, as the holostar or gravastar have, they\nwill also radiate Hawking radiation. Therefore Hawking radiation\nin itself does not give you any insights about the interior metric of\nthe compact body that formed in gravitational collapse.\n\nBut let me repeat: If the compact object has no event horizon\nand if it has trivial topology (as Hawking claims), then the\ncompact object that evaporates via Hawking radiation is not a\nblack hole. It is a compact body without event horizon and its\ninterior cannot be described by a black hole space-time, not\neven as an "intermediate" state. According to Hawking the\nspace-time containing the compact object formed during\ngravitational collapse is topologically trivial *all the time*. There\nis no event horizon, no black hole, no trapped surface and\nbecause of this most likely no singularity. No black hole ever\nforms, has formed or will form, in the classical limit, unless the\nclassical canon ball actually flies to the moon and back again on\nits path from A to B.\n\n\n> Please ... somebody correct me if I have totally mangled it.\n\nDon\'t ever belittle yourself in this newsgroup. You didn\'t mangle\nat all. You are asking good questions. Continue.\n\nQuestions are much more important than answers. Answers can\nbe wrong. But a well posed question will make you think for\nyourself. This is what physics is about: Think for yourself! Don\'t\nlet the others do the thinking for you, at least if you wan\'t to\nunderstand things. Even more so if you are interested in\nprogress. Be wary about answers you don\'t understand, from\nwhatever source (and especially from me ;-)! Keep in mind:\nAuthoritative statements from prestigeous sources have a very\nhigh likelyhood of being correct. However, there is a non-zero\nprobability that authorities are wrong.\n\nThis is not fantasy, it has been historically proven over and over.\nYou might wonder, how high the probability of a particular\nstatement upheld by the crowd in the course of history (such as\n"space is absolute", "the Galilei transformations are correct",\n"black holes have been proven to exist" etc.) actually is. Is the\nprobability of a statement being wrong "exponentially decaying",\ni.e. P = e^-N, with N being the number of (independent)\nutterances? Unfortunately no human source has ever been or\never will be independent. There are historical examples, where\none single person stood against the opinions of thousands and\nprevailed (Kopernikus, Galileo, Newton, Einstein,\nChadrasekhar, etc.) It happens not very often, but it happens\noften enough to realize, that P not e^-N.\n\nYet be wary of the crackpots, too. It is the *quality* of the\narguments that count. Not big words or big statements.\n\nMP\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>"Alan" <info@optioncity.REMOVETHIS.net> wrote in message
news:mrKdnakBeP2tdJ7cRVn-hQ@adelphia.com...
>
> As a non-expert, my sense of
> it was that in a putative quantum gravity one has to consider
> many types of 'paths' at once in some sort of path integral.
> This is a general principle that will hold even if the details aren't
> quite known.
You described it quite accurately for a "non-expert".
Hawking's method belongs to the class of variational
approaches, which has turned out to be quite a powerful tool in
theoretical physics in general (not only in quantum mechanics).
Put in simple terms, the crucial difference between the Euclidean
path integral approach and the well known Feynman path
integral approach is, that in the second we sum over different
(intermediate, virtual) processes whereas in the first we sum over
all "possible" space-time metrics.
In the Feynman path integral approach each (virtual) process
contributes to the total probability of a particular outcome with a
(complex) probability amplitude less than 1. All probability
amplitudes are summed up and give us the probability amplitude
for the whole process. Any (intermediate) process that has a
probability amplitude of zero does not need to be considered in the sum. In
Hawking's approach the "Euclidean path integral" over a particular
space-time metric takes on a similar role as the
Feynman diagram for a certain topology of the scattering
process.
Now Hawking tells us, that the probability amplitude of the
black hole space-times (with event-horizon) in the Euclidean
path integral approach is zero (or rather goes to zero exponentially at low
temperatures, if I understand him correctly).
I don't know if this truly is the case, as I am not an expert in the
Euclidean path integral approach. However, nobody seems to
have criticized this particular statement and some have even
remarked that it is quite an old result, already derived by others.
So let us assume that
i) the Euclidean path integral approach is the correct way to do
quantum gravity
ii) the black hole metrics (or rather all non-trivial metrics) don't
contribute to the probability amplitude in this approach.
However, if this is the case, why should we include metrics with
*zero* probability amplitude at all in our classical (!) picture?
Some might say, the classical picture is never 100% correct.
One always has to include *all* possibilities , however low their
probabilities are, at least as intermediate stage. But this is not a
good argument, as you will see shortly:
First remember the Bohr-correspondence principle. This principle
tells us, that a system which consists of a large number of
quantum states has a well defined classical limit. The limit is the
(hopefully) unique state with the "highest" quantum mechanical
probability amplitude.
Now for quantum mechanical processes involving very few
degrees of freedom it is generally impossible to single out one
single process with the highest probability amplitude. As JB
remarked in the companian thread "Hawking in Dublin", in
scattering processes involving elementary particles it is (at least)
problematic to attribute too much meaning to the intermediate
processes, or even to a whole class of intermediate processes,
such as the class of processes described by a single Feynman-
diagram. There are many cases known, where a sensible answer
to a scattering problem can only be obtained, if one includes all
Feynman-diagrams of a certain order (see e.g. the infrared-
problem in electron scattering).
However, in the large N-limit we know from experience, that it
is always possible to find a single process, whose probability
dominates so vastly over all other processes, that it makes
imminent sense to refer to this process as a unique single process.
This process, if it exists, is called the classical trajectory.
To give an example how this works computationally, consider
the following classical analogue: The principle of least action.
You find an excellent introduction to this principle in the
Feynman lectures. Let me summarize: In order to find the
(classical) path of a particle going from A to B you consider all
paths that take this particle from A to B. You calculate the action
for each possible path. The classical path is the one that
extremizes the action. Now calculating the action for each path is
quite cumbersome, often impossible. Therefore in practice you
resort to an approximation procedure: You look at differences
between paths close to each other, i.e. you look at how a small
variation of the path changes your calculated value for the action.
The path that extremizes the action is the one, for which small
local variations of the path leave the action stationary. This
approximation procedure in a sense demands, that a classical
limit truly exists: In the difference-approach you only consider
paths which are very close to the "classical" path. But if the
classical limit exists, it does not make sense to attribute any
meaning to paths which are very far away from the classical path
and therefore have zero probability of occurring (or rather
exponentially decaying probability).
Hawking is doing something very similar, when he expands in a
saddle-point approximation. Clearly he presumes that the
classical limit exists. This is a very reasonable assumption for a
large system. In this respect GR is no different from any other
classical theory. Hawking implicitly invokes the Bohr
correspondence principle, which guarantees that the classical
limit exists for large N.
However, Hawking does not minimize the action, rather he
calculates probability amplitudes. But as we well know from
quantum mechanics (see also the Feynman lectures or the little
cute Feynman book on QED) complex probability amplitudes
and action are related (somewhat like A = e^{iS}), meaning that a
non-stationary action leads to a heavy oscillatory behaviour of
the complex probability amplitude for any small section of the
path, which gives nearly zero when averaged over the whole
path.
Hawking has found out (or maybe he just re-interpreted a known result), that
all space-times with non-trivial topology (i.e.
all black hole space-times) don't contribute to the probability
amplitude. As I said, I don't know if this is correct. But if this is
the case, it makes no sense at all to include these space-times in
the *classical* (!) picture. To include space-times with
excruciatingly low probability in the classical picture would be as
crazy as if you would demand, that in a classical analysis of a
cannon ball flying from A to B you have to consider the path
where the cannon-ball flies to the moon and back again.
Although such a path is quantum mechanically possible, and
therefore in principle should be included in a full quantum
mechanical calculation, it's probability of occurrence is so low,
that no sane physicist would ever think that such a process might
actually occurr in the real world, not even as an "intermediate"
process. Therefore a process with (exponentially) zero
probability amplitude has no place at all in the classical theory.
> The classical technical black-hole solution would only be
> an approximate path integral contribution that ignored radiation
> a WKB-style solution as \hbar->0.
Correct, but its probability amplitude is zero (if Hawking is
correct) and therefore it is madness to include this in the list of
possible classical space-times, even as an intermediate state.
> The radiation would come from other path integral pieces
> involving smooth metrics with no horizon, if I have it right.
If Hawking is correct, you have it right.
However why would it only be radiation that originates from the
smooth metrics with no horizon? We know very well that small
black holes can "radiate" particles...
Also note, that the compact object formed at the end-stage of
gravitational collapse has no horizon (according to Hawking),
and therefore is not a black hole. Still it will very much look like
a black hole from the outside, so that one can assume that a
sufficiently small compact collapsed object would be very hot
and therefore will also radiate particles. But even if the
horizonless compact object that belongs to the "path integral
pieces with no horizon" is very large, so that only Hawking
radiation can escape its gravitational pull, this does not
necessarily mean that the object itself is composed exclusively
out of radiation. No?
> I guess the relative importance of these types
> of pieces depend on the mass of the object and the time scale
> of the experiment among other things.
Yes, the more we approach the classical limit (in the Bohr
correspondence principle this means: the higher the number of
quantum states N becomes, which implies the more massive the
object becomes, which implies the longer the relevant time-
scales are, ...) the more important will the "pieces with no event
horizon" (you called these the "pieces with radiation") will
become relative to the "pieces with event horizon" (i.e. black
holes). This means that the more massive a compact object
becomes (i.e. the higher its number of internal degrees of
freedom) the more will the topologically *trivial* metrics with no
horizon dominate the probabililty amplitude. At least this will be
the case if Hawking is correct, and the "black hole pieces" have
amplitudes approaching zero very quickly.
> Besides radiation, these
> smooth metrics also allow the theory to be 'unitary', preserving
> information, which was the motivation for the problem.
These smooth metrics are the only ones that need to be
considered (in the large N limit!), because *only* these smooth
metrics make a noticeable contribution to the overall probability
amplitude. Therefore, in the large N-limit the theory quite
certainly is unitary. But it is unitary *only* because the black hole
metrics, which quite evidently "destroy" information
(Hawking says so himself), are *not* part of the classical limit of
the theory. Why would you wan't a space-time, which has zero
(!!!) contribution to the total probability amplitude, be part of the
classical theory? Do you include virtual cannon balls flying from
the earth to the moon and back again in your classical calculation
of the trajectory of a cannon ball going from A to B?
However, the result of (nearly) zero probability amplitude for the
black hole space-times can only be correct within the limits of
the approximation that Hawking is using. The approximation
presumes that the classical limit exists.
(it is reasonable to assume, that the correct classical limit will be
an exact solution of the field equations. But keep in mind that not
every exact solution of the field equations is a black hole. Many
are not! And then there is the - remote - possibility, that Einsteins
field equations must be modified already in the classical regime.
I don't believe this, but some do.).
If the classical limit exists, the approximations used by Hawking
will become better, the higher N becomes. For macroscopic
objects one would assume, that the approximation is excellent.
For low N one must keep in mind though, that the approximation
might fail. Therefore it is very well possible that small (quantum
sized) "black holes" might still play a role in collision processes
of elementary particles at high energies. But for large objects N
is very high, so "zero" should be "" to an excellent
approximation for any macroscopic compact object (recall that
the exponential function is involved, for instance 10^(-1000) is
by all practical purposes zero!).
> I took Hawking's remarks to be general principles
> that would hold in *any* quantum theory of gravity, regardless
> of the details. The idea that in some final theory, that one will
> sum over various metrics has been around for a long time.
This is the essential idea. And it seems to be an approach that is
quite conservative and well within the scope of main stream
physics. However, if Hawking is right in his particular variant of
the general approach, the logical outcome of his approach is,
that the black hole metrics are not "members" of the classical
limit. For a classical calculation in the high N regime the black
hole metrics are as significant as the cannon-ball flying from the
earth to the moon and back again. I repeat: Hawking says that
any black hole state has (exponentially) zero probability
amplitude!
It is clear, that anybody who has invested much time and effort
into the study of black hole space-times will not be very happy
to hear this. Hawking seems to have known this. I would
presume that this is the reason why he plays a game with
names: What has formerly been called black hole (i.e. a space
time *with* event horizon) is now called the "eternal black hole".
What is *not* a black hole (i.e. a space-time *without* event
horizon) is called "black hole". This apparently slight shift of
names, retaining the old name "black hole" (but radically
changing its true meaning) and giving an obscure modifier
(eternal) to the true term black hole, will make all those who yet
believe in black holes happy for a while. Most of them have not
even realized what happened: The "eternal black hole" is nothing
else than Hawking's new name for the Schwarzschild or Kerr
Newman space-times. Think! These classical space-times have
all the properties that Hawking now attributes to the term
"eternal black hole". They have
- an event horizon
- they are static (Schwarzschild/Reissner-Nordstroem) or
stationary (Kerr-Newman), i.e. there is no time-evolution in such
space-times. They are truly eternal.
- They can never become non-trivial (at least not classically),
because in classical theory the event horizon never shrinks.
And they don't contribute to the probability amplitude: the
amplitude is zero.
Hawking must know, that a state with zero probability amplitude
cannot be realized in the classical theory. He has told us, that
"space-times with event horizon" have *zero* probability
amplitude. He knows the correct definition for the technical term
black hole (He is the "father" of the event horizon!). So he must
know that black holes are dead. However, being the wizard that
he is, he has left the crowd their favorate name: "black hole".
And he has given them a name to bash on: the "eternal black
hole". All of us know, that the "eternal" black hole is physically
unrealistic. A physically realistic black hole radiates. So we will
bash the eternal black hole to death.
Now consider the following (the next par is science fiction):
When the funeral ceremonies are over, Hawking gets on stage again. He will
inform the stupefied crowd, that the "eternal black
hole" that just has been buried is nothing else than the Kerr-
Newman family of space-time metrics. If he is a really great
wizard, he will then present us what he thinks is the physically
realistic solution for a compact self gravitating object. This
solution will have *trivial* topology and it will *not* have an
event horizon. He will still call this soluton a black hole. And
this will be correct in a certain sense, because from the outside
the new solution will look exactly as a black hole. But clearly
its interior will be quite different. So what do *you* think what
the interior of this object will be? The interior Kerr-Newman
solution?
> But to me, and I could be completely wrong here, the
> association of the radiative effects with the path sums over
> all the 'smooth metrics' seemed like a new insight. Not
> only that, it seems quite agreeable with his earlier
> semi-classical insight that the radiation causes the classical
> black hole with a classical horizon to evaporate, returning
> a classical spacetime to a smooth state. It all seems quite
> consistent in a qualitative way.
The "radiative effects" you are talking about, are the effects that
you can measure in the space-time exterior to the compact
object that forms in gravitational collapse, far far away from the
strong field regime. But as Hawking says himself, the radiation
measured at spatial infinity gives you no information about the
interior structure of the compact object from which the radiation
originates. As Hawking says, one can never know whether an
event horizon has actually formed.
However, this does not mean that the compact object without
event horizon can have arbitrary properties. It's metric must be
quite similar to a black hole metric in the exterior space-time. A
solution of the field equations with surface red-shift z ~ 2 will not
do. The surface-redshift must be enormous. If the compact body has high
surface redshift, as the holostar or gravastar have, they
will also radiate Hawking radiation. Therefore Hawking radiation
in itself does not give you any insights about the interior metric of
the compact body that formed in gravitational collapse.
But let me repeat: If the compact object has no event horizon
and if it has trivial topology (as Hawking claims), then the
compact object that evaporates via Hawking radiation is not a
black hole. It is a compact body without event horizon and its
interior cannot be described by a black hole space-time, not
even as an "intermediate" state. According to Hawking the
space-time containing the compact object formed during
gravitational collapse is topologically trivial *all the time*. There
is no event horizon, no black hole, no trapped surface and
because of this most likely no singularity. No black hole ever
forms, has formed or will form, in the classical limit, unless the
classical canon ball actually flies to the moon and back again on
its path from A to B.
> Please ... somebody correct me if I have totally mangled it.
Don't ever belittle yourself in this newsgroup. You didn't mangle
at all. You are asking good questions. Continue.
Questions are much more important than answers. Answers can
be wrong. But a well posed question will make you think for
yourself. This is what physics is about: Think for yourself! Don't
let the others do the thinking for you, at least if you wan't to
understand things. Even more so if you are interested in
progress. Be wary about answers you don't understand, from
whatever source (and especially from me ;-)! Keep in mind:
Authoritative statements from prestigeous sources have a very
high likelyhood of being correct. However, there is a non-zero
probability that authorities are wrong.
This is not fantasy, it has been historically proven over and over.
You might wonder, how high the probability of a particular
statement upheld by the crowd in the course of history (such as
"space is absolute", "the Galilei transformations are correct",
"black holes have been proven to exist" etc.) actually is. Is the
probability of a statement being wrong "exponentially decaying",
i.e. P = e^-N, with N being the number of (independent)
utterances? Unfortunately no human source has ever been or
ever will be independent. There are historical examples, where
one single person stood against the opinions of thousands and
prevailed (Kopernikus, Galileo, Newton, Einstein,
Chadrasekhar, etc.) It happens not very often, but it happens
often enough to realize, that P not e^-N.
Yet be wary of the crackpots, too. It is the *quality* of the
arguments that count. Not big words or big statements.
MP
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