# Weinberg on GR

8 views

### Pmb

Jan 29, 2004, 6:28:26 PM1/29/04
to
In Weinberg's GR text he writes in the preface

-------------------------------------
But now the the passage of time has taught us not to expect that the
strong, weak, and electromagnetic interactions can be understood in
geometrical terms, and too great an emphasis on geometry can only
obscure the deep connections between gravitation and the rest of
physics.
-------------------------------------

Someone claims that this is now wrong. Why is this supposed to be wrong? The
person's claim is

------------------------
The standard model is fundamentally
geometrical in its approach -- it is the geometry of fiber bundles on
spacetime, of course, and of gauge transforms on them. But the
Lagrangian is the geometrical curvature of the fields on the bundle,
just as in GR the Lagrangian is the curvature of the metric field on
spacetime.
------------------------

If this is correct how does it make Weinberg wrong. When did Weinberg become
wrong and does he know that he's wrong?

Pmb

>
> This is now known to be wrong.

### Doug Sweetser

Feb 2, 2004, 4:58:07 PM2/2/04
to
Hello Peter:

One problem with Weinberg's statement is that we still do not have a
direct link between gravity and the rest of physics. Gravity is about
the metric field, the standard model about the potentials for EM, the
weak and strong forces within the group structure of the standard
model. I want the link to be obvious, since all these forces play a
role in everything I do :-)

We have always been able to see connections at a mathematical level.
After all, both use the variation of the action to generate field
equations. Both theories allow gauge transformations. It appears like
the uncited claimant holds that gauge transformations can be viewed as
part of a geometric approach. If valid, then that would be another
content.

So I don't agree with Weinbergs statement, nor the critique. This is
purely a judgment call, so people can agree to disagree.

doug
quaternions.com

### Lubos Motl

Feb 2, 2004, 4:58:34 PM2/2/04
to
Steven Weinberg wrote in his book:

> But now the the passage of time has taught us not to expect that the
> strong, weak, and electromagnetic interactions can be understood in
> geometrical terms, and too great an emphasis on geometry can only
> obscure the deep connections between gravitation and the rest of
> physics.

Let me just say that this is a very deep and important formulation. There
are technical differences between gravity and gauge theories - gravity has
spin 2 particles (instead of spin 1) and it can't be described by a
renormalizable local quantum field theory, unlike the gauge theories. The
gravitational loop divergences (in 4 dimensions) are much more serious
than those in gauge theories. Geometry and the existence of spacetime
seems psychologically to be something entirely necessary for our lives.

But that's it. The conceptual character of both these theories is very
similar. Both of these theories are theories, which at long distances
admit a description in terms of field theories with a local gauge
symmetry, although its details can differ, and they admit analogous
semiclassical quantization. At a higher level - string theory, or perhaps
Kaluza-Klein theory is enough as an example - gravity and gauge theories
are unified, and the separation of physics into the "gravitational" and
"gauge/matter" sector becomes artificial at higher energy scales.

There is no canonical separation of geometry from the rest of physics.
Moreover, geometry seems to be an emergent property of a quantum
mechanical system, and different "interpretations" with different
geometrical backgrounds can be dual/equivalent to each other. The topology
change is just another phase transition and it is allowed in a quantum
theory of gravity.

> If this is correct how does it make Weinberg wrong. When did Weinberg become
> wrong and does he know that he's wrong?

Weinberg is not wrong, of course. Weinberg is very deep, and his sentence
indicates that he understands the unity of Nature. Even if someone likes
geometry a lot, physics is more than just geometry - geometry is just one
approximate aspect of reality, and already GR has taught us that it is not
a fixed background that influences others but is not influenced by
anything else. Geometry is just another player in the dynamical laws of
our Universe, and separating the players into boxes is arbitrary once we
go beyond the low-energy approximations.

All the best
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

### Serenus Zeitblom

Feb 2, 2004, 5:21:11 PM2/2/04
to
"Pmb" <peter.bro...@verizon.net> wrote in message news:<5edSb.10152>

When did Weinberg become
> wrong

In 1971, when he wrote it.

and does he know that he's wrong?

This is an observational question to which we still
await an answer from somebody in Austin. Any progress
on the observational front, Aaron?

### Bartosz Milewski

Feb 2, 2004, 5:37:21 PM2/2/04
to
I think it's a matter of interpretation. If you consider fiber bundles based
on arbitrary groups "geometric" than the Standard Model is geometric. More
commonly, it's theories like Kaluza-Klein that are considered geometric,
since the "fiber" there can be interpreted as a compactified dimension.
This is trivially so in the case of electromagnetism, whose gauge group U(1)
is the same as SO(2)--the group of rotations in the compactified dimension.

"Pmb" <peter.bro...@verizon.net> wrote in message

news:5edSb.10152$bx....@nwrdny02.gnilink.net... ### Arkadiusz Jadczyk unread, Feb 5, 2004, 10:57:38 AM2/5/04 to On Mon, 2 Feb 2004 22:37:21 +0000 (UTC), "Bartosz Milewski" <bar...@nospam.relisoft.com> wrote: >I think it's a matter of interpretation. If you consider fiber bundles based >on arbitrary groups "geometric" than the Standard Model is geometric. More >commonly, it's theories like Kaluza-Klein that are considered geometric, >since the "fiber" there can be interpreted as a compactified dimension. >This is trivially so in the case of electromagnetism, whose gauge group U(1) >is the same as SO(2)--the group of rotations in the compactified dimension. The case of electromagnetism shows, at the same time, why Weinberg can have been right. We have U(1) in electromagnetism, and we have U(1) in quantum theory (complex Hilbert space with U(1)-unobservable overall phase of the wave function). They are somehow, mysteriously related. Quatenionic quantum mechanics (with SU(2) as the gauge group) is just a theoretical concept. Complex quantum mechanics seems to be right. Quantum theory and electromagnetism are also intertwined via the fine structure constant. On the other hand electromagnetism seems to be intertwined with gravity in Kaluza-Klein theories (where Planck constant comes in again). That suggests that gravity may be somehow intertwined with quantum theory, and its linear framework in infinite number of dimensions (noncommutative geometry?) In other words: fiber bundles can lead us into infinite dimensional geometry, which cleser to algebra than geometry. But, as Bartosz indicated, "it's matter of interpretation". ark -- Arkadiusz Jadczyk http://www.cassiopaea.org/quantum_future/homepage.htm -- ### Arvind Rajaraman unread, Feb 5, 2004, 11:00:20 AM2/5/04 to "Pmb" <peter.bro...@verizon.net> wrote in message news:<5edSb.10152$bx....@nwrdny02.gnilink.net>...

Geometry plays a much more significant role in GR than in the standard
model. For instance, I know of no way to calculate the force between
particles in the SM using just geometry, whereas in GR, of course, the
gravitational force is an effect of geometry. So I would say that
while the classical action of the Standard Model can maybe be
described by geometrical notions, it is not true of the dynamics.

I am also confused by the statement above stating that "the Lagrangian
is the geometrical curvature of the fields on the bundle": the
curvature of course corresponds to the field strength, while the
classical Lagrangian is the field strength squared. The quantum
effective action has all allowable powers of the field strength, and
the coefficients of these terms cannot be derived from geometry alone.
So geometry does not specify the dynamics of the SM.

IOW, Weinberg is not wrong.

Weinberg's point is that the same thing must be true of GR; once we go
to the quantum theory, it is practically certain that geometrical
notions will play a much less vital role. (Geometry is possibly only a
semiclassical notion.) It is for that reason, I believe, that Weinberg
deemphasizes the geometrical picture; it is unlikely to be
fundamental. Treating GR as "a theory of a spin-2 particle" is the
right way to set it up to go to the quantum theory.

### Serenus Zeitblom

Feb 6, 2004, 3:16:03 AM2/6/04
to
arvin...@hotmail.com (Arvind Rajaraman) wrote in message news:<cc21857b.04020...@posting.google.com>...

>
> Weinberg's point is that the same thing must be true of GR; once we go
> to the quantum theory, it is practically certain that geometrical
> notions will play a much less vital role. (Geometry is possibly only a
> semiclassical notion.) It is for that reason, I believe, that Weinberg
> deemphasizes the geometrical picture; it is unlikely to be
> fundamental.

First of all, you have to put Weinberg's comments in the historical
context. He was writing at a time when cosmology was not taken
very seriously and black holes were speculation. At that time
you could argue --- not very convincingly, but you could do
it --- that GR was just spin-2 excitations propagating in
Minkowski space, plus a few bits added on for consistency.
Stir in SW's provocative personality and serve.

Nowadays nobody talks like that, apart from a few wild-eyed
extremists. Let me give you an example of what I am thinking
of. As you know, it is *wrong* to think of a black hole as
something with an event horizon, such that, if you venture
inside, you will find a point-like singularity waiting for
you. [Although, to my shock, I have seen recent papers with
pictures of the interior of a black hole which looked like
that!] *In fact* the singularity is spacelike; it does not
yet exist even for observers inside the event horizon. Now
*how* are you going to get something like the Kruskal diagram
out of a quantum theory, starting with Minkowski space? I'm
sure you won't try the old trick, "string theory allows
topology change, so it will spit out the Kruskal diagram
eventually...." Classical GR ought to be an approximation
to the quantum theory, so the latter has to generate the
K diagram somehow. How?

I agree that the geometric picture may not be fundamental,
hand-waving, as above. But in the same
way you could say that quantum mechanics, as presently
understood, probably isn't fundamental either. Why do
I say that? Because I want to sound profound, even
though I have no idea about how to go beyond quantum
mechanics in a meaningful way. Just as nobody knows
how to go beyond the geometric picture of gravity in
a meaningful way.

I'm tempted to conjecture that there is some sociology
here: we all learn QM when we have posters of Einstein
riding a bike on our dorm walls and walk about with
Maxwell's equations on our wrinkled T-shirts, whereas
we don't really hit GR until grad school when we are
less apt to become passionately attached to theories.
So: GR can be discarded like last term's girlfriend,
but QM is our First True Love. On revient toujours
and all that.

Isn't it obvious that we need some genuinely *new* ideas
about *both* spacetime geometry and QM? I note that
Juan Maldacena seems to have a great faith in geometry,
even when discussing very fundamental aspects of quantum
gravity, see for example http://arxiv.org/abs/hep-th/0106112
That's the way to go: you have to take BOTH QM and GR
that seriously....

Treating GR as "a theory of a spin-2 particle" is the
> right way to set it up to go to the quantum theory.

Then why has it been such a flop? And I don't mean
that kind of "flop" either....

### Lubos Motl

Feb 6, 2004, 9:50:00 AM2/6/04
to

On Fri, 6 Feb 2004, Serenus Zeitblom wrote:

> First of all, you have to put Weinberg's comments in the historical
> context. He was writing at a time when cosmology was not taken
> very seriously and black holes were speculation.

Weinberg's book was the first major and comprehensible book that explained
these subjects (cosmology, black holes) and argued in favor of their
existence. Yes, it is even older than MTW. You must be talking about a
different book.

> At that time you could argue --- not very convincingly, but you could
> do it --- that GR was just spin-2 excitations propagating in Minkowski
> space,

If someone advocated this point of view in 1972, she would be many years

> ... plus a few bits added on for consistency. Stir in SW's
> provocative personality and serve.

Anyone who looks at http://www.amazon.com/exec/obidos/tg/detail/-/0471925675
which is the web page of the book at amazon.com will see that Weinberg's
book and Weinberg's personality are *not* so controversial. His book's
score is 4.5 stars, and people like the book because it is a very physical one
that avoids meaningless mathematical cliches. It is always possible to
criticize a book because of many reasons, but a more important thing is
whether the book can bring something *positive* for its readers.

> Nowadays nobody talks like that, apart from a few wild-eyed
> extremists.

These "extremists" are normally called "mainstream modern physicists".
Gravity *is* dynamics of massless spin-two messenger particles, and the
gauge invariance necessary to exclude the unphysical polarizations (called
"general covariance") forces the nonlinear terms to behave according to
the rules of GR, and agree with a very geometric (Riemannian)
interpretation. This is *the* modern point of view. An excited focus on
geometry and its properties is a great tool to learn and love classical
GR, including some advanced topics, but it is also a prejudice that
prevents many people from understanding quantization of gravity and its
unification with other forces and particles.

> Let me give you an example of what I am thinking
> of. As you know, it is *wrong* to think of a black hole as

> something with an event horizon, ...

Physical black holes are *defined* as compact objects with event horizons.

> such that, if you venture inside, you will find a point-like
> singularity waiting for you.

The shape of the singularity depends on the precise black hole that you
choose, but nevertheless the general statement that a singularity is
waiting for you is morally correct. Indeed, the singularity is point-like
in the sense that its worldline is one-dimensional.

> *In fact* the singularity is spacelike; it does not
> yet exist even for observers inside the event horizon.

Some black holes have space-like singularities, some black holes have
time-like singularities.

> Now *how* are you going to get something like the Kruskal diagram out
> of a quantum theory, starting with Minkowski space?

The Kruskal diagram is a diagram describing *classical* physics. Classical
physics of GR is included in the classical limit of any good theory of
quantum gravity (which means that it is included in the classical
low-energy limit of string theory), and therefore the Kruskal diagrams -
if correct - are guaranteed to be included, too. But it is misleading to
think that the quantum theory should lead to causal diagrams directly and
exactly. It certainly does not because geometry is a quantum, fluctuating
variable in quantum gravity and the causal diagrams only describe a
classical solution, a result of classical averaging.

By the way, classical physics is *guaranteed* to break down - and be
replaced by more complete physical description - near the singularities
(in fact, by the very definition of the word "singularity"), and there are
also some very interesting recent quantitative arguments in favor of the
idea that the classical description already breaks down at the point we
used to call the horizon. If true, many properties of the causal diagrams
would be an artifact of classical averaging.

> I agree that the geometric picture may not be fundamental,
> hand-waving, as above.

Nope. The non-fundamental nature of geometry has been quantitatively and
more or less rigorously showed in many articles that described topology
change; T-duality, mirror symmetry, and other dualities involving
geometry; short-distance corrections to GR, and so on. What remains a
piece of handwaving is a dreamed about formulation of quantum gravity that
starts with *no* geometry whatsoever, and generates everything it needs.

> But in the same way you could say that quantum mechanics, as presently
> understood, probably isn't fundamental either.

According to all insights collected so far (as for 2004), quantum
mechanics seems totally fundamental and it is likely that it will survive
in the final formulation of the ultimate theory in the same form, or in a
very slightly generalized form. The period of 1990s has showed that it is
possible to describe black holes in a completely orthodox quantum
mechanical framework.

> > Treating GR as "a theory of a spin-2 particle" is the
> > right way to set it up to go to the quantum theory.
>
> Then why has it been such a flop? And I don't mean
> that kind of "flop" either....

Why has it been such a flop? Good question. It can be partly blamed on
Mach's principle. There were many people who thought that General
Relativity reflected Mach's principle - a principle that young Einstein
himself was influenced by. Mach's principle tries to eliminate the reality
of space (and spacetime) itself. If correct, it would imply that the
gravitational waves can't exist. Therefore it was very difficult for the
physicists to realize that the gravitational waves were a real prediction
of GR, much like the electromagnetic waves followed from Maxwell's theory:
many wrong papers argued that all such waves in GR were pure gauge (i.e.
flat space in different coordinates).

Once the reality of the gravitational waves was established, people had
all the tools to deal with GR in the same way as with other field
theories. However the quantization of GR is subtle. First of all, we
don't have any direct experiments that test quantum gravity. Second,
gravitational Feynman's diagrams lead to divergences. Third, the nature of
the gravitational gauge invariance (general invariance) raises many
conceptual issues - for example what does it mean for two operators to
commute at space-like separation if the spacelike separation is determined
by the metric that is itself a fluctuating quantum field?

It was really the success of the old string theory in describing the
gravitational S-matrix (Scherk, Schwarz) that started to diminish the

Cheers,

Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Only two things are infinite, the Universe and human stupidity,
and I'm not sure about the former. - Albert Einstein

### Pmb

Feb 6, 2004, 11:28:25 AM2/6/04
to

"Lubos Motl" <mo...@feynman.harvard.edu> wrote

> These "extremists" are normally called "mainstream modern physicists".

Bravo Lubos!! Bravo!!! Well said Sir!!

It's a shame that so many people are only willing to simlply 'go with the
flow' - The most important discoveries are often made when one questions the
flow.

> Gravity *is* dynamics of massless spin-two messenger particles, and the
> gauge invariance necessary to exclude the unphysical polarizations (called
> "general covariance") forces the nonlinear terms to behave according to
> the rules of GR, and agree with a very geometric (Riemannian)
> interpretation. This is *the* modern point of view. An excited focus on
> geometry and its properties is a great tool to learn and love classical
> GR, including some advanced topics, but it is also a prejudice that
> prevents many people from understanding quantization of gravity and its
> unification with other forces and particles.
>
> > Let me give you an example of what I am thinking
> > of. As you know, it is *wrong* to think of a black hole as
> > something with an event horizon, ...
>
> Physical black holes are *defined* as compact objects with event horizons.

True. How could anyone conclude otherwise? I.e. How could anyone conclude
that it is wrong to think of a black hole as something with an event
horizon???????????

> Some black holes have space-like singularities, some black holes have
> time-like singularities.

What does that mean? What does it mean for a singularity to be
spacelike/timelike etc?

Pmb

### Hendrik van Hees

Feb 7, 2004, 9:17:42 AM2/7/04
to
Lubos Motl wrote:

>> At that time you could argue --- not very convincingly, but you could
>> do it --- that GR was just spin-2 excitations propagating in
>> Minkowski space,
>
> If someone advocated this point of view in 1972, she would be many

If I remember right, in "Feynman Lectures on Gravity" they say about the
history of this book that the lectures where given already in the
60ies, and there Feynman takes exactly this point of view.

He derives the Einstein equations (or equivalently the Hilbert-Einstein
action) from this idea and a consistency argument.

Of course, at the end the result of both approaches, i.e., Einstein's
geometrical and Feynman's field theoretical one, is the same, namely
the Einstein equations of gravitation. So physically there is no
difference in both approaches.

So the only question is, which is didactically the best one. I'd say
it's only a question of the order, in which you present the subject.
I'd say the Feynman approach is only good for people who are already
trained in relativistic field theory and some representation theory of
the Poincare group, while Einstein's is starting from a relatively
simple empirical fact, namely the equivalence of inertial and
gravitational mass.

On the other hand, Weinberg's book is known to be very economic in the
sense that the reader is lead by the physics rather than the
mathematics of differential geometry.

I think it is good to know both approaches and I'd not reject the one or
the other.

> These "extremists" are normally called "mainstream modern physicists".
> Gravity *is* dynamics of massless spin-two messenger particles, and
> the gauge invariance necessary to exclude the unphysical polarizations
> (called "general covariance") forces the nonlinear terms to behave
> according to the rules of GR, and agree with a very geometric
> (Riemannian) interpretation. This is *the* modern point of view. An
> excited focus on geometry and its properties is a great tool to learn
> and love classical GR, including some advanced topics, but it is also
> a prejudice that prevents many people from understanding quantization
> of gravity and its unification with other forces and particles.

Why should one have a prejudice preventing people to quntize gravity,
only because you use a geometric approach to derive the classical
Einstein equations or the Hilbert-Einstein action?

You can also take a geometrical point of view towards Yang-Mills theory,
and nobody ever was prevented from quantizing it since their
(re)invention by Yang and Mills.

--
Hendrik van Hees Cyclotron Institute
Phone: +1 979/845-1411 Texas A&M University
Fax: +1 979/845-1899 Cyclotron Institute, MS-3366
http://theory.gsi.de/~vanhees/ College Station, TX 77843-3366

### Steve McGrew

Feb 7, 2004, 9:16:53 AM2/7/04
to
On 6 Feb 2004 09:50:00 -0500, Lubos Motl <mo...@feynman.harvard.edu>
wrote:

>Some black holes have space-like singularities, some black holes have
>time-like singularities.

Please explain to a layman what the observable differences would be
between black holes with timelike and spacelike singularities, and
what sorts of situations might lead to their creation--

Steve

### Bartosz Milewski

Feb 7, 2004, 9:22:11 AM2/7/04
to
My impression so far is that the words "Quantum Gravity" are used in place
of an older term, "magic". Any time GR runs into problems (e.g.,
singularities), it is postulated that the magic of QG will solve them. Roger
Penrose goes even further by postulating that QG will solve the
philosophical problems of our mind--brains are not finite automata because
of the mysterious QG activity in the microtubules inside the neurons. The
fact is that there is no QG in the sense of "renormalizable quantum theory
of spin 2 particles". Not even supersymmetry makes it renormalizable. Since
the theory doesn't exist, it can be postulated that it could solve _any_
problem.

"Lubos Motl" <mo...@feynman.harvard.edu> wrote in message
news:Pine.LNX.4.31.04020...@feynman.harvard.edu...

[Moderator's note: Entire quoted article deleted. Please trim quoted
material rather than quoting entire articles. Also, please don't
responding to, not before. Finally, let me note that the general
point of view expressed here is something that we've gone over quite
a bit in the newsgroup in the past. I urge everyone to think about
whether their response would really move the discussion forward in a
substantive way before hitting "Send." -TB]

### Arvind Rajaraman

Feb 8, 2004, 6:34:04 AM2/8/04
to
serenusze...@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.04020...@posting.google.com>...

> arvin...@hotmail.com (Arvind Rajaraman) wrote in message news:<cc21857b.04020...@posting.google.com>...

>At that time

> you could argue --- not very convincingly, but you could do
> it --- that GR was just spin-2 excitations propagating in
> Minkowski space, plus a few bits added on for consistency.
> Stir in SW's provocative personality and serve.

Massless spin 2 particles can only interact classically in one way if
you want to get a consistent theory. That theory is GR. So the phrase
"theory of a massless spin 2 particle" is identical classically to the
phrase "general relativity". This is the content of various theorems
proven by Weinberg and Witten.

>
> Nowadays nobody talks like that, apart from a few wild-eyed
> extremists.

You don't say. Do all string theorists qualify as "wild-eyed
extremists"?

>Let me give you an example of what I am thinking
> of. As you know, it is *wrong* to think of a black hole as
> something with an event horizon, such that, if you venture
> inside, you will find a point-like singularity waiting for
> you. [Although, to my shock, I have seen recent papers with
> pictures of the interior of a black hole which looked like
> that!] *In fact* the singularity is spacelike; it does not
> yet exist even for observers inside the event horizon. Now
> *how* are you going to get something like the Kruskal diagram
> out of a quantum theory, starting with Minkowski space? I'm
> sure you won't try the old trick, "string theory allows
> topology change, so it will spit out the Kruskal diagram
> eventually...." Classical GR ought to be an approximation
> to the quantum theory, so the latter has to generate the
> K diagram somehow. How?
>

Obviously I don't know the details, and I won't pretend the problem
has been solved. Nevertheless the qualitative pictures provided by the
brane models of black holes seem to me to be on the right track to
generate the geometry you want. After all, how do we figure out the
geometry of a black hole, or of anything? You scatter stuff from
it,and figure out the radius etc. of the object. Such calculations
work very well for extremal black holes in string theory. The
calculation cannot yet be done for the Schwarzchild case, but I see no
in principle problems. Such a calculation would identify the horizon.

As to finding the singularity inside, who knows? Maybe quantum effects
smooth it out. Maybe something like the Horowitz-Maldacena idea works.
It is true in some cases that the same calculation can be done in
several different ways, some of which look at the black hole interior,
and some that only look at the outside (Reference: Kraus, Ooguri,
Shenker). In this language, the way the singularity shows up would be
that if you tried to reformulate your calculation by including states
in the black hole interior, you would find a singular behaviour
somewhere. All these are possibilities, which do not seem to me to be
ruled out a priori.

>
> Isn't it obvious that we need some genuinely *new* ideas
> about *both* spacetime geometry and QM? I note that
> Juan Maldacena seems to have a great faith in geometry,
> even when discussing very fundamental aspects of quantum
> gravity, see for example http://arxiv.org/abs/hep-th/0106112
> That's the way to go: you have to take BOTH QM and GR
> that seriously....

Possibly. But nobody knows how to modify QM. If a consistent idea
comes along, it will certainly be considered.

>
> Treating GR as "a theory of a spin-2 particle" is the
> > right way to set it up to go to the quantum theory.
>
> Then why has it been such a flop? And I don't mean
> that kind of "flop" either....

The only working theory of quantum gravity treats the graviton as a
massless spin-2 particle, so I don't know what you mean.

### Serenus Zeitblom

Feb 9, 2004, 10:16:20 AM2/9/04
to

> > such that, if you venture inside, you will find a point-like

> > singularity waiting for you.
>
> The shape of the singularity depends on the precise black hole that you
> choose, but nevertheless the general statement that a singularity is
> waiting for you is morally correct. Indeed, the singularity is point-like
> in the sense that its worldline is one-dimensional.

I'm sorry, but *this is not correct*. It's true that Reissner-
Nordstrom black holes have timelike singularities, but it is
generally believed that these are not realistic because of the
instability of the Cauchy horizon. The general belief is that
a *real* black hole would have a *spacelike* singularity, and
as you know very well it does not make sense to talk about
the "worldline" of something spacelike. So it is *not* true,
even "morally" [we all know that those who insist most on
morality are rarely very moral themselves....] that the
singularity is waiting for you. It does not yet exist. The
whole causal structure is utterly different from anything that
you could ever regard as a perturbation of Minkowski space.

Don't mistake me: the Strominger-Horowitz entropy stuff was
brilliant work. But it still falls vastly short of a
"derivation of black holes from string theory"!

### Urs Schreiber

Feb 9, 2004, 10:35:45 AM2/9/04
to

"Serenus Zeitblom" <serenusze...@yahoo.com> schrieb im Newsbeitrag

>[...] At that time

> you could argue --- not very convincingly, but you could do
> it --- that GR was just spin-2 excitations propagating in
> Minkowski space, plus a few bits added on for consistency.

I'd like to better understand what you are objecting to. To me there seem to
be two components of this statement, namely:

1) GR is just spin-2 excitations
2) propagating in Minkowski space

I'd think that 1) is uncontroversial, while 2) is maybe not sufficiently
precise to be either right or wrong.

How about an easier analogy, YM theory. Would you object to the statement
that "YM solitons are made up of spin-1 excitations propagating in
field-free space."?

### Serenus Zeitblom

Feb 9, 2004, 11:00:27 AM2/9/04
to

arvin...@hotmail.com (Arvind Rajaraman) wrote in message news:<cc21857b.0402...@posting.google.com>...

> Massless spin 2 particles can only interact classically in one way if
> you want to get a consistent theory. That theory is GR. So the phrase
> "theory of a massless spin 2 particle" is identical classically to the
> phrase "general relativity". This is the content of various theorems
> proven by Weinberg and Witten.

I think that the situation is a little more subtle. I have heard
people who claimed that GR is *nothing but* spin-2 particles
propagating in Minkowski space. This is the view I am attacking.
I have also heard other people [string theorists] say that
spin-2 particles propagating on Minkowski space is a way
of describing *certain configurations* in GR, but no
*complete equivalence* is claimed. We know how to get
certain pieces of GR out of string theory, but the jury
is still out as to whether we can ever get all of it.

>
> Obviously I don't know the details, and I won't pretend the problem
> has been solved.

That's because you are *not* wild-eyed. :)

Nevertheless the qualitative pictures provided by the
> brane models of black holes seem to me to be on the right track to
> generate the geometry you want. After all, how do we figure out the
> geometry of a black hole, or of anything? You scatter stuff from
> it,and figure out the radius etc. of the object. Such calculations
> work very well for extremal black holes in string theory. The
> calculation cannot yet be done for the Schwarzchild case, but I see no
> in principle problems. Such a calculation would identify the horizon.

The calculations work really well, to the extent that there
must be something right about them. But they don't give you
the Kruskal diagram or anything close to it. So the work is
still far from finished.

> As to finding the singularity inside, who knows?

*Exactly*. But I will bet money that when we do
understand this, it *won't* be in terms of gravitons
propagating on Minkowski space!

Maybe quantum effects
> smooth it out. Maybe something like the Horowitz-Maldacena idea works.
> It is true in some cases that the same calculation can be done in
> several different ways, some of which look at the black hole interior,
> and some that only look at the outside (Reference: Kraus, Ooguri,
> Shenker). In this language, the way the singularity shows up would be
> that if you tried to reformulate your calculation by including states
> in the black hole interior, you would find a singular behaviour
> somewhere. All these are possibilities, which do not seem to me to be
> ruled out a priori.

I agree, there's lots of extremely clever work being done, see
eg the paper by Hubeny and that gang. But again, they don't talk
about gravitons propagating on flat space. They draw very fancy
Penrose diagrams for Ads black holes and what not. All I am
saying is that someone who really took Weinberg's words to
heart would not be able to write any of these excellent papers!

### Peter Woit

Feb 10, 2004, 4:48:50 AM2/10/04
to

"Urs Schreiber" <Urs.Sc...@uni-essen.de> wrote in message
news:c08948$144dun$1...@ID-168578.news.uni-berlin.de...

> How about an easier analogy, YM theory. Would you object to the statement
> that "YM solitons are made up of spin-1 excitations propagating in
> field-free space."?
>

I hope someone objects to this. Even assuming "solitons" is a
typo for "solutions".

You can't understand confinement in QCD if you believe that gauge theory is
nothing but a theory of spin-1 quanta, with interactions determined by gauge
symmetry. This kind of perturbative definition of the theory is fine if you
just
want to talk about short distance effects, but useless if you want to
understand
the spectrum of the theory. For this you need a non-perturbative definition
like lattice gauge theory. If you don't like lattices and want to work
directly
in the continuum, the general conjecture is that confinement is a sort of
dual
Meissner effect, with magnetic monopole-like configurations condensing in
the
vacuum. No one knows exactly how to do this, but all perturbative QCD
tells you about long distances is that it has broken down and you need to
do something else.

The notion of a connection is the most fundamental notion in modern
geometry,
whether you're talking about the Riemannian geometry of a metric connection
in the frame bundle or the geometry of a connection in an arbitrary bundle.
A connection has precisely the properties of a gauge field, so to claim
gauge fields aren't geometrical is simply being perverse.

If you only want perturbative quantum gravity, maybe you can get away
with just thinking about spin-2 quanta, whether part of a string theory or
not.
If you want a theory that makes sense outside of perturbation
theory, I'll bet that, like in YM, you'll need to properly understand the
geometry you're dealing with.

### Serenus Zeitblom

Feb 10, 2004, 12:01:58 PM2/10/04
to

"Urs Schreiber" <Urs.Sc...@uni-essen.de> wrote in message news:<c08948$144dun$1...@ID-168578.news.uni-berlin.de>...

> "Serenus Zeitblom" <serenusze...@yahoo.com> schrieb im Newsbeitrag
>
> >[...] At that time
> > you could argue --- not very convincingly, but you could do
> > it --- that GR was just spin-2 excitations propagating in
> > Minkowski space, plus a few bits added on for consistency.
>
> I'd like to better understand what you are objecting to. To me there seem to
> be two components of this statement, namely:
>
> 1) GR is just spin-2 excitations
> 2) propagating in Minkowski space
>
> I'd think that 1) is uncontroversial,

I don't agree. The key word here is *JUST*! I would say
that GR can be thought of in those terms *in some cases*,
say, weak gravitational waves. But not in all cases.

while 2) is maybe not sufficiently
> precise to be either right or wrong.

I'm not sure I understand you. Where are they
propagating then? Anyway I am just taking this
from the standard Feynman argument.

>
> How about an easier analogy, YM theory. Would you object to the statement
> that "YM solitons are made up of spin-1 excitations propagating in
> field-free space."?

I was going to answer this but I see that Peter Woit has already
done so. Let me just add that the case in GR is even worse, because
unlike a YM soliton a black hole changes the very causal structure
of spacetime. Step inside an event horizon and you are in a world
that is completely alien to Minkowski spacetime, or even "Minkowski
spacetime plus a pointlike singularity with a timelike worldline".

Of course you are entitled to claim that according to String Theory
the interior of a black hole is nothing like the Kruskal diagram.
But then string theory doesn't reproduce GR, even just inside the
event horizon of a large black hole, where everything is classical
because the curvature is small.

### Urs Schreiber

Feb 10, 2004, 12:17:31 PM2/10/04
to

"Serenus Zeitblom" <serenusze...@yahoo.com> schrieb im Newsbeitrag

> "Urs Schreiber" <Urs.Sc...@uni-essen.de> wrote in message
news:<c08948$144dun$1...@ID-168578.news.uni-berlin.de>...
> > "Serenus Zeitblom" <serenusze...@yahoo.com> schrieb im Newsbeitrag

> > 1) GR is just spin-2 excitations

> > 2) propagating in Minkowski space
> >
> > I'd think that 1) is uncontroversial,
>
> I don't agree. The key word here is *JUST*! I would say
> that GR can be thought of in those terms *in some cases*,
> say, weak gravitational waves. But not in all cases.

But an excitation need not be weak. It may be a condensate of gravitons.

> Of course you are entitled to claim that according to String Theory
> the interior of a black hole is nothing like the Kruskal diagram.
> But then string theory doesn't reproduce GR, even just inside the
> event horizon of a large black hole, where everything is classical
> because the curvature is small.

This is hardly a controversial issue. String theory implies that all
condensates of elementary excitations satisfy the respective equations of
motions, which to lowest order are those of Einstein gravity coupled to some
other fields. Whatever black hole solution you can find to these equations
is a condensate of graviton-states of string.

### Arvind Rajaraman

Feb 11, 2004, 5:43:03 AM2/11/04
to

"Peter Woit" <wo...@cpw.math.columbia.edu> wrote in message news:<3nXVb.8403$Lp....@twister.nyc.rr.com>... Maybe we're talking past each other. Certainly it is not true that the spectrum of Yang-Mills theory is given only by spin-1 particles. However, it is also true that if we say that Yang-Mills theory is fundamentally (i.e. asymptotically) a theory of spin-1 particles, then the rest of the stuff follows i.e. the asymptotic Lagrangian must be the standard one of Yang-Mills theory, and confinement etc. should follow from the running of the coupling constants at low energies. I do not see how geometry helps us in this at all. From geometry, how would you derive the Lagrangian (not to speak of confinement)? Yes, gauge fields can be interpreted geometrically, but their dynamics is not obviously geometrical. Interestingly, the only stable particles in pure gravity are the gravitons, so the S-matrix of the theory really is only the interactions of spin-2 particles. So it might be that you only need to think about spin-2 quanta. ### Arvind Rajaraman unread, Feb 11, 2004, 5:43:07 AM2/11/04 to serenusze...@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.0402...@posting.google.com>... > "Urs Schreiber" <Urs.Sc...@uni-essen.de> wrote in message news:<c08948$144dun$1...@ID-168578.news.uni-berlin.de>... > > "Serenus Zeitblom" <serenusze...@yahoo.com> schrieb im Newsbeitrag > > news:c7fd6c7a.04020...@posting.google.com... > > > > How about an easier analogy, YM theory. Would you object to the statement > > that "YM solitons are made up of spin-1 excitations propagating in > > field-free space."? > > I was going to answer this but I see that Peter Woit has already > done so. Let me just add that the case in GR is even worse, because > unlike a YM soliton a black hole changes the very causal structure > of spacetime. Step inside an event horizon and you are in a world > that is completely alien to Minkowski spacetime, or even "Minkowski > spacetime plus a pointlike singularity with a timelike worldline". > > Of course you are entitled to claim that according to String Theory > the interior of a black hole is nothing like the Kruskal diagram. > But then string theory doesn't reproduce GR, even just inside the > event horizon of a large black hole, where everything is classical > because the curvature is small. Disclaimer: I can't prove any of the statements below, but it is important to understand how this problem is treated in string theory. 1. The real question is whether there are observables in Minkowski space quantum gravity other than the S-matrix, and in string theory, there are not. If this is the case, then questions about geometry must be answered by a detailed examination of the results of a S-matrix calculation. But an S-matrix, by definition describes the interactions of particles coming in from infinity, and such particles do not fall through the horizon, as seen by an observer at infinity. In this sense, the inside of a black hole does not exist. 2. This is all to the good, since as Hawking showed, the existence of states outside as as well as inside the horizon inevitably leads to information loss. If the current lore about string theory is correct, it does not make sense to think of states existing inside the horizon. In this way we can avoid information loss. 3. The creation of a black hole does not change the asymptotics of the geometry. The black hole inevitably decays, and the final state is Minkowski space plus widely separated gravitons. So where did the singularity, or for that matter the inside of the horizon, go? Well, it was an artifact of semiclassical reasoning anyway, so who cares? 4. The creation of the black hole will show up as a long-lived resonance in the S-matrix. No singularity will appear, since the quantum theory of gravity should be well defined. 5. Can we have a theory of somebody falling through the horizon? This is controversial. Some people claim that the horizon is actually physical i.e. somebody crossing the horizon would see objects there, even though GR says the horizon is smooth. Others say that there is nothing at the horizon, but a complementary description exists of this observer. In any case, as long as we have a complete description of the observer at infinity, we should have the full physics. ### Thomas Larsson unread, Feb 11, 2004, 9:11:11 AM2/11/04 to "Urs Schreiber" <Urs.Sc...@uni-essen.de> wrote in message news:<c08948$144dun$1...@ID-168578.news.uni-berlin.de>... > > 1) GR is just spin-2 excitations > 2) propagating in Minkowski space > > I'd think that 1) is uncontroversial, while 2) is maybe not sufficiently > precise to be either right or wrong. > Do not gravitons on Minkowski have severe problems with microcausality? In flat-space QFT, a correlator <phi(x) phi(y)> vanishes whenever x and y are spacelike separated. This holds, I believe, to all orders in perturbation theory. However, the notion of spacelike separation is defined by the metric, which in perturbation theory is the unphysical Minkowski metric rather than the physical metric that solves Einstein's equations. So the correlator will vanish, to all orders in perturbation theory, if x-y is spacelike w.r.t. the background metric, even if it is timelike w.r.t. the physical metric. Worse, the correlator may be nonzero even if x-y is spacelike w.r.t. the true metric. This seems to me as a serious and possibly fatal problem with the graviton picture. ### Mihai Cartoaje unread, Feb 11, 2004, 9:11:09 AM2/11/04 to > gauge invariance necessary to exclude the unphysical polarizations (called > "general covariance") forces the nonlinear terms to behave according to > the rules of GR, and agree with a very geometric (Riemannian) References for the geometrical part? ### Peter Woit unread, Feb 11, 2004, 12:10:38 PM2/11/04 to Arvind Rajaraman wrote: >Certainly it is not true that the spectrum of Yang-Mills theory is >given only by spin-1 particles. However, it is also true that if we >say that Yang-Mills theory is fundamentally (i.e. asymptotically) a >theory of spin-1 particles, then the rest of the stuff follows i.e. >the asymptotic Lagrangian must be the standard one of Yang-Mills >theory, and confinement etc. should follow from the running of the >coupling constants at low energies. > >I do not see how geometry helps us in this at all. From geometry, how >would you derive the Lagrangian (not to speak of confinement)? Yes, >gauge fields can be interpreted geometrically, but their dynamics is >not obviously geometrical. > > It's not true that confinement, etc follow from knowing the short distance Lagrangian and running of the coupling constants. All this tells you is that at long enough distances the conceptual framework of perturbative YM theory breaks down and you need a better one. It really is a misconception to believe that all you need to know is the Lagrangian to have a well-defined non-perturbative QFT. In path integral terms, you also need an appropriate measure. In perturbation theory this comes down to defining Gaussian integrals, outside of perturbation theory it is a whole new ball-game. The only known way of making sense of quantum YM theory non-perturbatively is using lattice gauge theory. The basic variables of this theory are not a linear space of spin-1 fields, but non-linear spaces of group elements describing parallel transport (this is what geometry tells you to look at: connections are the infinitesimal version of parallel transport). The observables and the action are gauge-invariant functionals of parallel transport around closed loops. Geometry tells you that conjugation invariant functions of these "holonomy" group elements are the gauge-invariant information to consider. The standard Wilson action just uses the simplest such conjugation-invariant function: the trace in the fundamental representation. The renormalization group tells you that, as you take the continuum limit you can ignore more complicated functions (traces in larger representations) and just consider Wilson's choice. Quantum YM theory is certainly not purely geometry. In the path integral language it is supposed to be a measure on some infinite dimensional space. The correct infinite dimensional space is one defined in terms of geometry, not spin-1 linear fields. The definition of the measure on this geometrical space is something that goes beyond geometry, but to even get started on the problem you need geometry to choose which space you are going to integrate over. ### tes...@tum.bot unread, Feb 11, 2004, 1:45:59 PM2/11/04 to On Sat, 7 Feb 2004, Steve McGrew asked: > On 6 Feb 2004 09:50:00 -0500, Lubos Motl <mo...@feynman.harvard.edu> > wrote: > > >Some black holes have space-like singularities, some black holes have > >time-like singularities. Yes, and for the simplest examples of this phenonmenon (e.g. rotating versus non-rotating Kerr vacuums, Vaidya null dust, etc.), see the discussion of black hole interiors near the end of this page: > Please explain to a layman what the observable differences would be > between black holes with timelike and spacelike singularities, For Kerr models, the "answer" is very simple: rotating <-> timelike, nonrotating <-> spacelike. But this "answer" is obviously absurd! > and what sorts of situations might lead to their creation-- Alas, I feel that anything I might say will only confuse a layman! But you asked a good question, and I dare say that some graduate students out there, who have taken a basic g.t.r. course, would also like to see an answer. Unfortunately, it would be impossible to "explain" anything much, even to a well-prepared student, in a short post, but for those students, I would suggest thinking about several related questions: 1. What is "a solution" of the e.f.e.? What role is played by standard "energy conditions" in answering this question? These conditions are convenient for defining "g.t.r.", but are they perhaps physically misleading? What role is played by the degree of smoothness demanded? What is the physical interpretation (if any) of a "solution"? If one has a "local solution" (all the classical exact solutions start life as a local solution which one then tries to extend), does it have a unique "maximal extension"? What does it mean physically when a maximal extension includes a Cauchy horizon? 2. What is a "geometric singularity" in a Lorentzian manifold? What are their physical interpertations? E.g. what are their effects upon an ideal observer? What plausible physical scenarios could result in the formation of a given type of singularity? 3. What does it mean to "perturb" a solution? Is there a global/local distinction here? What are the observable consequences (if any) of "perturbing" a given solution in such a way as to change its conformal structure, e.g. to change from a spacelike to a null singularity in the interior of a black hole solution? (As always, you should retort: observable by -whom-?) Does it help to distinguish between "radiative" and "non-radiative"? 4. Suppose you have a black hole solution defined far into the past, but allow the possibility for influx of matter/radiation. Distant external observers can expect to observe, after a delay, radiation carrying some information concerning the "interaction" (but perhaps not the ultimate fate of the infalling stuff). The no hair theorems lead us to expect that "eventually" the hole will settle back into a Kerr exterior state, in which case distant external observers can in principle eventually measure the altered mass/angular momentum. But what about observers in the -interior-? 5. Chandrasekhar discovered a local isometry (since generalized) between a class of "colliding plane wave solutions" and a class of "black hole interior solutions". There are various kinds of exact solutions modeling (suggestive but not terribly realistic) situations in which shells of various kinds of "radiation" collapse to form a black hole; in the literature, however, these are usually presented as exact plane colliding plane waves, so if you don't know about Chandrasekhar duality, you would never see the relevance! The point is that it turns out that, depending upon the nature of the radiation and the asymmetry of the collapse, the conformal structure of the resulting solution can be quite different. So: what is one to make of this? And more important, what happens for -physically realistic- influx? This is very much a topic of current research in classical g.t.r. As I said, all of these questions are much too subtle and/or difficult to address in a short post. But try searching for past posts here with keywords like "Penrose diagram", "Cauchy horizon", "mass inflation", "Vaidya models", "generic black hole interior", "colliding plane wave", "Chandrasekhar duality". Next, for background on (5), see author = {J. B. Griffiths}, title = {Colliding Plane Waves in General Relativity}, publisher= {Oxford University Press}, year = 1991} Then search the ArXiv for authors "Brill" and "Visser", in addition to the key words above. Sorry I don't have time to give more references! "T. Essel" (hiding somewhere in cyberspace) ### Arvind Rajaraman unread, Feb 11, 2004, 2:01:00 PM2/11/04 to serenusze...@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.04020...@posting.google.com>... > arvin...@hotmail.com (Arvind Rajaraman) wrote in message news:<cc21857b.0402...@posting.google.com>... > > > Massless spin 2 particles can only interact classically in one way if > > you want to get a consistent theory. That theory is GR. So the phrase > > "theory of a massless spin 2 particle" is identical classically to the > > phrase "general relativity". This is the content of various theorems > > proven by Weinberg and Witten. > > I think that the situation is a little more subtle. I have heard > people who claimed that GR is *nothing but* spin-2 particles > propagating in Minkowski space. This is the view I am attacking. > I have also heard other people [string theorists] say that > spin-2 particles propagating on Minkowski space is a way > of describing *certain configurations* in GR, but no > *complete equivalence* is claimed. We know how to get > certain pieces of GR out of string theory, but the jury > is still out as to whether we can ever get all of it. Ah, so maybe you are saying that the spin-2 excitations are just the weakly coupled excitations, but the full quantum theory requires other input? If so, yes of course. All string theorists agree that to get a consistent theory, you need more stuff (the string excitations, naturally). Whether we can get black holes/singularities from string theory is an open question, but I see no reason in principle for it to fail. That's all one can say at the moment. And of course, Strominger-Vafa is strong evidence for the claim. > > > Maybe quantum effects > > smooth it out. Maybe something like the Horowitz-Maldacena idea works. > > It is true in some cases that the same calculation can be done in > > several different ways, some of which look at the black hole interior, > > and some that only look at the outside (Reference: Kraus, Ooguri, > > Shenker). In this language, the way the singularity shows up would be > > that if you tried to reformulate your calculation by including states > > in the black hole interior, you would find a singular behaviour > > somewhere. All these are possibilities, which do not seem to me to be > > ruled out a priori. > > I agree, there's lots of extremely clever work being done, see > eg the paper by Hubeny and that gang. But again, they don't talk > about gravitons propagating on flat space. They draw very fancy > Penrose diagrams for Ads black holes and what not. All I am > saying is that someone who really took Weinberg's words to > heart would not be able to write any of these excellent papers! I'm not sure why you say this. In AdS/CFT, the graviton is most definitely thought of as a spin 2 excitation. Furthermore, there is evidence, for example in the Maldacena paper you cited, that topology change occurs and that black holes can be understood as excitations of (possibly multiple) AdS geometries. The Penrose diagram is most definitely only a semiclassical notion here, because an AdS-black hole geometry can spontaneously turn into a geometry with no black holes. ### Starblade Darksquall unread, Feb 11, 2004, 2:10:29 PM2/11/04 to > > Nowadays nobody talks like that, apart from a few wild-eyed > > extremists. > > These "extremists" are normally called "mainstream modern physicists". > Gravity *is* dynamics of massless spin-two messenger particles, I have a big problem with this. A messenger particle is that which travels from one particle to another by means of the space time continuum. Saying that one graviton travels to another on the space time continuum when the graviton itself, which represents gravity, which is ITSELF space and time, not merely something ON space and time, is a contradiction in terms. We are living in a rational universe. If we want to get at the principles of the universe, the first step starts with non-contradictory tenets. (...Starblade Riven Darksquall...) ### Arnold Neumaier unread, Feb 12, 2004, 4:45:57 AM2/12/04 to Peter Woit wrote: > It really is a misconception > to believe that all you need to know is the Lagrangian to > have a well-defined non-perturbative QFT. In path integral > terms, you also need an appropriate measure. In perturbation theory > this comes down to defining Gaussian integrals, outside of > perturbation theory it is a whole new ball-game. Yes. > The only known way of making sense of quantum YM > theory non-perturbatively is using lattice gauge theory. No. There are a variety of resummation techniques which capture some nonperturbative information. For example, I think that prediction of meson and baryon masses from first principles (QCD) have been done more accurately with Dyson equations than with lattice gauge theory. Arnold Neumaier ### Danny Ross Lunsford unread, Feb 12, 2004, 5:29:23 AM2/12/04 to Starblade Darksquall wrote: >> > Nowadays nobody talks like that, apart from a few wild-eyed >> > extremists. >> >> These "extremists" are normally called "mainstream modern physicists". >> Gravity *is* dynamics of massless spin-two messenger particles, > > I have a big problem with this. A messenger particle is that which > travels from one particle to another by means of the space time > continuum. Saying that one graviton travels to another on the space > time continuum when the graviton itself, which represents gravity, > which is ITSELF space and time, not merely something ON space and > time, is a contradiction in terms. I sort of have a big problem with both statements :) "Messenger particles" do not in any palpable sense travel from one particle to another. These pictorial representations are bookkeeping devices in a perturbation series and are not to be literally interpreted (although they usually are). Physical tachyons are still tacky. And massless particles in particular do not even have a rest frame or any physical localization at all (the momentum is definite so the position is totally indeterminate). [Moderator's note: The momentum of a particle's wavefunction of course need not be definite. -usc] -- -drl ### Lubos Motl unread, Feb 12, 2004, 9:47:43 AM2/12/04 to On Wed, 11 Feb 2004, Starblade Darksquall wrote: > I have a big problem with this. A messenger particle is that which > travels from one particle to another by means of the space time > continuum. Saying that one graviton travels to another on the space > time continuum when the graviton itself, which represents gravity, > which is ITSELF space and time, not merely something ON space and > time, is a contradiction in terms. We would be happy to have a theory that can "create" its spacetime from "nothing", but the fact is that such a theory (or formulation of a theory) has not been found yet. In order to make any meaningful quantum calculation today, we must assume a classical background - a nonzero "vev" of the gravitational field - and compute the dynamics of particles obtained by quantizing the fluctuations from the classical background. > We are living in a rational universe. If we want to get at the > principles of the universe, the first step starts with > non-contradictory tenets. That's right. And the approach described above is certainly consistent, even though it might be very difficult for many people to understand why it works. ### Lubos Motl unread, Feb 12, 2004, 9:47:49 AM2/12/04 to Serenus Zeitblom wrote: > > I think that the situation is a little more subtle. I have heard > > people who claimed that GR is *nothing but* spin-2 particles > > propagating in Minkowski space. You have heard people claiming this simply because it is the only meaningful description of GR from a particle physics perspective and using the particle physics language. GR is dynamics of spin 2 fields (and particles) with an action whose structure including the nonlinear terms is constrained by the gravitational gauge invariance - namely the general diffeomorphism invariance. It is only a low-energy effective description of a more complex theory. > This is the view I am attacking. Well, one might be attacking various things, but it is the only thing that one can do against the laws of physics. Be sure that one can't change them. :-) > > I have also heard other people [string theorists] say that > > spin-2 particles propagating on Minkowski space is a way > > of describing *certain configurations* in GR, but no > > *complete equivalence* is claimed. We know how to get > > certain pieces of GR out of string theory, but the jury > > is still out as to whether we can ever get all of it. You seem to misunderstand that the goal of string theory is certainly *not* to get exactly what classical GR gives us. No one wants to derive something like that - especially because we know many contexts in which the classical GR is either ambiguous or just plain wrong: the singularities, highly-curved regions of spacetime, divergent quantum loop processes, and topology change (which is forbidden in GR) count as examples, and the independence of the black hole interior from the exterior is becoming another example, as we start to understand the nature of black hole complementarity that reveals that the degrees of freedom inside the black holes are not quite independent from the rest of the Universe. String theory is a theory that goes beyond GR; it reduces to GR in the situations where GR is correct, but it gives us a lot of new and different physics in other regimes! For example, perturbative string theory shows that gravity is just a single component of a more complex field that contains an infinite tower of other possible stringy excitations. Arvind Rajaraman wrote: > Ah, so maybe you are saying that the spin-2 excitations are just the > weakly coupled excitations, but the full quantum theory requires other > input? I think it is pretty obvious that Serenus Zeitblom wants to claim just the opposite: namely that the theory of everything has already been discovered in 1916 and no string theory has any right to change a single detail about it. All the best Lubos ### Steve McGrew unread, Feb 13, 2004, 2:16:14 PM2/13/04 to On Wed, 11 Feb 2004 18:45:59 +0000 (UTC), tes...@tum.bot wrote: >On Sat, 7 Feb 2004, Steve McGrew asked: > >... >> Please explain to a layman what the observable differences would be >> between black holes with timelike and spacelike singularities, > >For Kerr models, the "answer" is very simple: rotating <-> timelike, >nonrotating <-> spacelike. > >But this "answer" is obviously absurd! > >> and what sorts of situations might lead to their creation-- > >Alas, I feel that anything I might say will only confuse a layman! >[good stuff snipped] > >"T. Essel" (hiding somewhere in cyberspace) Hi-- I hoped for answers to these kinds of sub-questions: Would a black hole *look* and *act* the same regardless of whether its singularity were timelike and spacelike? Would it act as a gravitational lens in both cases? Is there a difference in the field outside the horizon? Would a falling observer have the same experience in both cases? Do they both emit the same spectrum of Hawking radiation? Thanks, Steve ### Arvind Rajaraman unread, Feb 13, 2004, 2:17:19 PM2/13/04 to Peter Woit <wo...@cpw.math.columbia.edu> wrote in message news:<c0dn6p$e6s$1...@newsmaster.cc.columbia.edu>... > Arvind Rajaraman wrote: > > >> The only known way of making sense of quantum YM > theory non-perturbatively is using lattice gauge theory. > The basic variables of this theory are not a linear space of > spin-1 fields, but non-linear spaces of group elements > describing parallel transport (this is what geometry tells > you to look at: connections are the infinitesimal version > of parallel transport). The observables and the action > are gauge-invariant functionals of parallel transport around > closed loops. Geometry tells you that conjugation > invariant functions of these "holonomy" group elements > are the gauge-invariant information to consider. Yes. Geometry is very useful in figuring out the gauge invariant observables. However, it does not tell you about the dynamics. That is done, as you say, by the Wilson action and use of the RG. And geometry doesn't tell you about confinement either. > > Quantum YM theory is certainly not purely geometry. In > the path integral language it is supposed to be a measure > on some infinite dimensional space. The correct infinite > dimensional space is one defined in terms of geometry, not > spin-1 linear fields. The definition of the measure on this > geometrical space is something that goes beyond geometry, > but to even get started on the problem you need geometry > to choose which space you are going to integrate over. Any space may be said to "be defined in terms of geometry". But we agree on the main point, which is that we must go beyond geometry. If only we agreed about this in the case of quantum gravity, we're done. And if your original point was that we can't think of nonperturbative gravity as a perturbative theory of spin 2 particles (or even a field theory), I agree. ### Jerzy Karczmarczuk unread, Feb 13, 2004, 2:22:12 PM2/13/04 to Danny Ross Lunsford wrote: > Starblade Darksquall wrote: ... >>>Gravity *is* dynamics of massless spin-two messenger particles, >> >>I have a big problem with this. A messenger particle is that which >>travels from one particle to another by means of the space time >>continuum. Saying that one graviton travels to another on the space >>time continuum when the graviton itself, which represents gravity, >>which is ITSELF space and time, not merely something ON space and >>time, is a contradiction in terms. > > I sort of have a big problem with both statements :) > > "Messenger particles" do not in any palpable sense travel from one particle > to another. These pictorial representations are bookkeeping devices in a > perturbation series and are not to be literally interpreted (although they > usually are). Physical tachyons are still tacky. And massless particles in > particular do not even have a rest frame or any physical localization at > all (the momentum is definite so the position is totally indeterminate). > > [Moderator's note: The momentum of a particle's wavefunction of > course need not be definite. -usc] I would even be more Jesuit... All "messenger particles" are off-shell. They have no asymptotics, they are represented by propagators (Green's functions), not the Dirac delta of the mass shell. The space localization is not so bad, after all we know about it since Yukawa, don't we? They are "diffused" by the source. The curvature fluctuations may be diffused similarly, and saying that a graviton is ITSELF space and time is a kind of bad poetry... Pauli would say "this is not even wrong...". Jerzy Karczmarczuk ### Danny Ross Lunsford unread, Feb 13, 2004, 2:23:36 PM2/13/04 to Lubos Motl wrote: > We would be happy to have a theory that can "create" its spacetime from > "nothing", but the fact is that such a theory (or formulation of a theory) > has not been found yet. David Finkelstein has the basis for one. Tony Smith has a generalization of the Feynman checkerboard lattice based on the isotetrichoron. The latter is a lattice approach, the former does just what you describe. http://arxiv.org/find/hep-th/1/au:+Finkelstein_D/0/1/0/all/0/1 However there is nothing self-evident about making quantum theory and gravity compatible by abandoning the continuum. -drl ### Danny Ross Lunsford unread, Feb 13, 2004, 2:23:50 PM2/13/04 to Lubos Motl wrote: >>>I think that the situation is a little more subtle. I have heard >>>people who claimed that GR is *nothing but* spin-2 particles >>>propagating in Minkowski space. > > You have heard people claiming this simply because it is the only > meaningful description of GR from a particle physics perspective and using > the particle physics language. GR is dynamics of spin 2 fields (and > particles) with an action whose structure including the nonlinear terms is > constrained by the gravitational gauge invariance - namely the general > diffeomorphism invariance. It is only a low-energy effective description > of a more complex theory. You keep saying this but in fact you are repeating folklore. There is no quantum theory of gravity, and so trivially there is no classical limit to a theory that doesn't exist. There is a formal procedure for investigating the kinematics of spin-2 and noticing a correspondence with linearized gravity, with the spin-2 particle as its gauge boson. The gauge invariance in this theory is not GC, rather hmn -> hmn + Bm,n + Bn,m - Ba,a diag mn This theory has no dynamics because it is not renormalizable. One does not pull the Christoffel connection out of spin-2. -drl ### eb...@lfa221051.richmond.edu unread, Feb 13, 2004, 2:57:04 PM2/13/04 to In article <dn3l205vddn5n49sg...@4ax.com>, Steve McGrew <ste...@nli-ltd.com> wrote: > I hoped for answers to these kinds of sub-questions: >Would a black hole *look* and *act* the same regardless of whether its >singularity were timelike and spacelike? I don't think that the structure of the singularity is relevant to what a black hole looks like on the outside. More or less by definition, the physics outside the horizon is determined entirely by stuff that's outside the horizon, while the singularity is safely hidden away on the inside. Isn't that right? -Ted -- [E-mail me at na...@domain.edu, as opposed to na...@machine.domain.edu.] ### Peter Woit unread, Feb 14, 2004, 3:13:09 AM2/14/04 to Arnold Neumaier wrote: >Peter Woit wrote: > > > >>The only known way of making sense of quantum YM >>theory non-perturbatively is using lattice gauge theory. >> >> > >No. There are a variety of resummation techniques which >capture some nonperturbative information. For example, >I think that prediction of meson and baryon masses from first >principles (QCD) have been done more accurately with Dyson >equations than with lattice gauge theory. > > > I confess my only knowledge about the sort of approach to QCD that you mention comes from a friend who I've heard refer to this in a highly dismissive way. Can you suggest a reference for where to read about it? Based on experience with other things, my guess would be that a problem with this work is that it involves an uncontrolled approximation. Solving the Dyson equations is the differential version of the same problem as constructing the path integral. Typical attempts to solve Dyson equations involve an iterative construction that may behave better than perturbation theory, but my impression was that these things sometimes work, but sometimes don't. Can you really use this to write down the answer to any question about QCD, or is it an approximation scheme that works for some sorts of calculations, fails for others? ### Serenus Zeitblom unread, Feb 14, 2004, 3:14:06 AM2/14/04 to arvin...@hotmail.com (Arvind Rajaraman) wrote in message news:<cc21857b.04021...@posting.google.com>... > > Disclaimer: I can't prove any of the statements below, Excellent start. :) but it is > important to understand how this problem is treated in string theory. > > 1. The real question is whether there are observables in Minkowski > space quantum gravity other than the S-matrix, and in string theory, > there are not. If this is the case, then questions about geometry must > be answered by a detailed examination of the results of a S-matrix > calculation. But an S-matrix, by definition describes the interactions > of particles coming in from infinity, and such particles do not fall > through the horizon, as seen by an observer at infinity. In this > sense, the inside of a black hole does not exist. Well, if this is what most string theorists really believe, then it's good that you are so open about it. I was under two mistaken impressions: [a] That while string theorists usually deal with gravity as if it were defined on a rigid Minkowskian background, they only do this as a stop-gap, while waiting for some better technique, and *not* because they really believe that this is fundamental to string theory. [b] That string theory can reproduce classical GR in the limit of sufficiently weak gravitational fields. Now you are telling me that this is not the case. This is a very important point, so let me spell it out. When people say "black hole" they immediately think "strong gravitational field". But as you probably know, this is not necessarily the case. If you stepped just inside the event horizon of a Schwarzschild black hole with M = 10^10 solar masses, you would feel very comfortable; the gravitational field there is quite weak. And yet string theory claims either that something very spectacular happens in that region of weak fields or that this weak-field region "does not exist". That is pretty hard to swallow. Does string theory also claim that the region behind the deSitter cosmological horizon "does not exist"? Given point [b], what are the precise circumstances in which string theory *does* reproduce classical GR? It isn't when the fields are weak. Is it just when the topology is precisely R^4 or something? > 2. This is all to the good, since as Hawking showed, the existence of > states outside as as well as inside the horizon inevitably leads to > information loss. If the current lore about string theory is correct, > it does not make sense to think of states existing inside the horizon. > In this way we can avoid information loss. Not according to Prof Giddings... > 3. The creation of a black hole does not change the asymptotics of the > geometry. The black hole inevitably decays, and the final state is > Minkowski space plus widely separated gravitons. So where did the > singularity, or for that matter the inside of the horizon, go? Well, > it was an artifact of semiclassical reasoning anyway, so who cares? > 4. The creation of the black hole will show up as a long-lived > resonance in the S-matrix. No singularity will appear, since the > quantum theory of gravity should be well defined. When people speak of the "Music of the Spheres", do they have the song "Don't worry, be happy" in mind? :) I'm not trying to be rude, and I do appreciate your candor in spelling all this out. But I have to say that I find it very disturbing that people think that issues as profound as information loss in black hole evaporation can be dealt with in such a cavalier manner. I have to say that my conclusion from reading what you wrote is that there is something very seriously wrong with string theory. Your mileage may vary. ### Arvind Rajaraman unread, Feb 14, 2004, 3:14:58 AM2/14/04 to Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> wrote in message news:<YQMWb.14627$_H2....@newssvr22.news.prodigy.com>...
> Lubos Motl wrote:
>

> > You have heard people claiming this simply because it is the only
> > meaningful description of GR from a particle physics perspective and using
> > the particle physics language. GR is dynamics of spin 2 fields (and
> > particles) with an action whose structure including the nonlinear terms is
> > constrained by the gravitational gauge invariance - namely the general
> > diffeomorphism invariance. It is only a low-energy effective description
> > of a more complex theory.
>

>There is a formal procedure for

> investigating the kinematics of spin-2 and noticing a correspondence
> with linearized gravity, with the spin-2 particle as its gauge boson.

There is a very detailed investigation of the DYNAMICS of a spin 2
particle, due first to weinberg, and then to Weinberg and Witten. This
investigation leads to the conclusion that the only way to have a
consistent theory of massless spin 2 partcle g_{ab] is to impose a
gauge symmetry, which is...

> The gauge invariance in this theory is not GC, rather
>
> hmn -> hmn + Bm,n + Bn,m - Ba,a diag mn
>

This is very much the same as GR. This is the linearized form of the
formula

g_{ab} \rightarrow { dy^c\over dx^a} g_{cd} {dy^d\over dx^b}

which is the the transformation of the metric under the coordinate
change x^a \rightarrow y^a. If you take y to be infinitesimally close
to x, you automatically get the transformation law you quoted.

The transformation you wrote therefore is related to the formula I
just gave as the Lie algebra is related to the Lie group. We are
perfectly comfortable in gauge theories with just working with the
transformations in the algebra, and exponentiating them to get the
full group action. It is the same in GR.

> This theory has no dynamics because it is not renormalizable.

Nonrenormalizable theories can of course have dynamics. Consider the
four-fermion theory.

>One does
> not pull the Christoffel connection out of spin-2.

All one has to do is try to couple the metric to ordinary matter in
such a way that the theory is invariant under the gauge transformation
you wrote (and also reduces to the original matter theory when the
metric is decoupled). This will automatically "pull the Christoffel
connection out".

### Danny Ross Lunsford

Feb 15, 2004, 3:45:51 AM2/15/04
to
Jerzy Karczmarczuk wrote:

> All "messenger particles" are off-shell. They have no asymptotics, they
> are represented by propagators (Green's functions), not the Dirac delta
> of the mass shell. The space localization is not so bad, after all we
> know about it since Yukawa, don't we?

Well this is the point - it is "not profitable" to demand a pictorial
interpretation which implies an act of measurement for these off-shell
things. A massless particle as a physical thing has no localization.

-drl

### Arvind Rajaraman

Feb 15, 2004, 3:46:19 AM2/15/04
to
serenusze...@yahoo.com (Serenus Zeitblom) wrote in message news:<c7fd6c7a.04021...@posting.google.com>...

> arvin...@hotmail.com (Arvind Rajaraman) wrote in message news:<cc21857b.04021...@posting.google.com>...
> >
> > 1. The real question is whether there are observables in Minkowski
> > space quantum gravity other than the S-matrix, and in string theory,
> > there are not. If this is the case, then questions about geometry must
> > be answered by a detailed examination of the results of a S-matrix
> > calculation. But an S-matrix, by definition describes the interactions
> > of particles coming in from infinity, and such particles do not fall
> > through the horizon, as seen by an observer at infinity. In this
> > sense, the inside of a black hole does not exist.
>
> Well, if this is what most string theorists really believe, then
> it's good that you are so open about it. I was under two mistaken
> impressions:
>
> [a] That while string theorists usually deal with gravity as if
> it were defined on a rigid Minkowskian background, they only
> do this as a stop-gap, while waiting for some better technique,
> and *not* because they really believe that this is fundamental
> to string theory.

I do not see how this follows from my original statement.
Nevertheless, string theorists do not assume the background is rigid.
Perturbative string theory naturally looks like a calculation on a
rigid background, but even here we can occasionally see that the
background must be corrected for consistency (the Fischler-Susskind
mechanism). Nonperturturbative string theory, i.e. AdS/CFT and matrix
theory, most definitely sum over all allowed geometries.

>
> [b] That string theory can reproduce classical GR in the limit
> of sufficiently weak gravitational fields. Now you are telling
> me that this is not the case. This is a very important point,
> so let me spell it out. When people say "black hole" they
> immediately think "strong gravitational field". But as you
> probably know, this is not necessarily the case. If you stepped
> just inside the event horizon of a Schwarzschild black hole
> with M = 10^10 solar masses, you would feel very comfortable;
> the gravitational field there is quite weak. And yet string
> theory claims either that something very spectacular happens
> in that region of weak fields or that this weak-field region
> "does not exist". That is pretty hard to swallow.