I'm not an expert.. when I was studying physics in college I never got
a satisfying answer to this question and to how one could go about
proving it.
I assume almost everyone will tell me that it is zero, but how
could/can you demonstrate this is so?

The answer given in comment by  hfsha-ga has some merit -
 and is supported by this expert opinion:
http://www.physlink.com/Education/AskExperts/ae230.cfm
(This may be opinion of the same person, of course)
but I think it does not fully answers your question.

 There is some debate between the experts on the issue:
http://www.madsci.org/posts/archives/apr2002/1017882364.As.r.html
and the topic had to do with a profound issue of the
SEARCH TERM : Mach Principle
://www.google.com/search?q=Mach+principle
which was so far not fully resolved to universal satisfaction.

So - I will not give you a final, definitive answer, but I will comment on
(possible) meaning of the question itself:
The term 'angular momentum' is usually used on the context of
classical physics - as a vector in 3D space. Defind e.g. here:
 http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html
http://en.wikipedia.org/wiki/Angular_momentum

This are two problems with answer given by hfshaw and others:
1) Vector quantity does not have a value. Only it's components 
  in some frame of reference have value. Meaning: if you are a man,
  standing on the Earth, a spinning bullet passing by has a (non
zereo)   angular momentum.
  If you are a bug (or a microbe) sitting on that bullet , that same moment
is zero.
 The value depends on the  frame of reference (aka coordinate system).

 Hfshaw (and others) make an implicit assumption, that you are thinking of
certain 'preferred' system of coordinates, implied by today's accepted
(big bang) model of the universe - which is frame defined by microwave
background and by the stars - and then the answer is sort of a
tautology:
 with respect to the stars, the stars do not move (too much).
(This is ignoring the question of the 'missing mass' or 'dark mass'-
mass which is not visible (like stars) and is, according to some
speculations,
http://www.amazon.com/exec/obidos/tg/detail/-/0465037402/103-5666594-0955800?v=glance
http://www.ebicom.net/~rsf1/missmass.htm
making 90% of the total).

2) The second problem I see with glib answer to this question is that it shows
 a 3D thinking, while cosmological theories are inherently 4D, and the
concept of angular momentum in relativistic (4D) theory is a topic for
a PhD thesis in itself.
 The 3D thinking has some validity - since the big-bang moment defines
a special frame - in which there is e.g. universal time, but that
these do not have universal validity. There are (alternative) theories
which try to explain
red-shift (caused by expansion) by 'rotation of the whole universe' - however
the question 'rotation with respect to what' needs to be answered before the
concept of rotation has meaning - in relativistic (4D) universe.

So - in conclusion: your question is touching issues which are not
well defined and resolved. More simple questions: "For an observer on
the Earth
- what is the angular momentum of our galaxy?" can be answered. The visible
stars clearly rotate around the Earth - and stars we see by naked eye are
in the Milky Way.
The questions about the whole universe, it's mass, energy, linear or
angular momentum, require either relativistic appoach, or an
assumption that one particular model (such as Big Bang) is valid, and
also that you specify a frame of reference. For the 'special frame of
reference implied by the Big-Bang' model - and assuming that the 'dark
mass' behaves -- well -
 zero value is a good guess.

So - real answers is: no one really knows, as yet.

Hedgie

---

Request for Answer Clarification by yates9-ga on 19 Nov 2004 01:09 PST

Hedgie-ga, thank you for the work, but in a sense the line of thinking
I was always interested in is more like racecar-ga's comment.  This
was my argument with my professors that perhaps the argument that the
universe is isotropic is actually not really that strong.
I don't know if this is possible, if it isn't I'll accept the answer,
but can you tell me or conjecture if we did have a positive angular
momentum, what consequences would appear?  For one there would be a
center of the universe, there would have to be... or there would have
to be an intertial reference frame for the whole and the whole
universe would have some kind of tails like galaxies do? Then the real
tricky thing for me to imagine would be that probably the curvature of
space would follow the outlines of this galaxy like structure?

The thing that makes this question a bit relevant is that afterall
most structure we see in the universe appears spinning around
somehow...

---

Clarification of Answer by hedgie-ga on 19 Nov 2004 01:53 PST

yates9-ga 
           To get a  'right' answer, one should disclose purpose and
if possible, motive when first asking the question. By default (that
is unless told otherwise) I assume that people ask about current 
mainstream theories.
There are always alternative theories - and some are interesting: 

http://www.amazon.com/exec/obidos/tg/detail/-/0521662230/103-5666594-0955800?v=glance
http://titles.cambridge.org/catalogue.asp?isbn=0521662230
and imaginative. For example guess that our universe is a black hole
or that we are part of computer  model .. (I like the last one as
possible explanation of the QM weirdness :-)

One alternative theory, speculates that red shift of remote galaxies is caused
by rotation of the universe, not by expansion...

the SEARCH TERM "rotating universe" 
://www.google.com/search?hl=en&lr=lang_en&ie=ISO-8859-1&c2coff=1&q=rotating+universe&btnG=Search

brings quite a few such  theories, some of them quite interesting.

However, as I said in the answer: Once you abandon (mainstream
Big-Bang model, which fits our 3D intuition) you need to think in
terms of General Relativity.

Your question, and racecar's remark, appear to be based on 3D concepts.
So I see an inherent conflict here. The question would have to be
formulated in 4D terms, before it can be seriously debated.

So answer is not 'NO' - but trather it is a different and even more
complex question.

To get a feel of how 4D reasoning looks (and how much - or how little
can be explain without math) - please have a look at somewhat related
question:
http://answers.google.com/answers/threadview?id=351408

Hedgie

---

Clarification of Answer by hedgie-ga on 19 Nov 2004 02:57 PST

Correction:

The link I wanted to give you (at the end of clarification) is this

http://answers.google.com/answers/threadview?id=31905

The other one may be of interest too, but this one explains
(or maintains) the 'strong principle of relativity' according to which
laws of physics should be formulated in a way independent of the frame
of reference - or as Einstein did put it --by equations which are invariant
- not only with respect to Lorentz group - but for any transformation of
coordinates.

Some experts may disagree (racecar is not included in that group :-)
but it is at least a program --   a worthy goal -- program which
actually preceeds Einstein's relativity. If you accept that principle
-
for universe as whole as well - then the question 'does it rotates'
always requires one to specify 'rotates with respect to what'.
 It makes sense to say 'with respect to me', or Earth - and the link
above explains (or tries ) that such choice could be be a valid choice
of the reference system.  In that frame, universe rotates (around you
- literaly) . However, what physics is really interested in, is not
'how universe appears in a given frame) but what are those invariant laws.



Hedgie

Interesting style of answering... a lot of different kinds of answers.

Current models of the universe are based on the assumption that at
large scales, it is isotropic -- that is, that it has no preferred
directions.  All observational evidence so far seems to support this
assumption.  Insofar as the universe *is*, in fact, isotropic the
total angular momentum of the universe is zero.  This is because
angular momentum is a vector quantity, and if the universe had a net
angular momentum vector, this would define a "special" direction,
violating the assumption of isotropy.

The (classical) angular momentum of an object about its center of mass
is independent of the translational motion of the center of mass, and
so does not depend on reference frame, as long as it's an inertial
frame.  For this reason, the center of mass is a common point about
which to consider the angular momentum; so common that it is often
unnecessary to state explicitly.  For example, if you were to ask
'what is the angular momentum of the earth?' some sticklers might
argue that the question is ambiguous, but really it's pretty clear
that you mean the angular momentum about the earth's center of mass.

The problem with the universe is that every point in it has equal
right to call itself the center of mass.

I resent a bit the statement that "what physics is interested in" is
purely invariant laws.  And actually overall it is odd how a something
that might resemble one of einsteins simple thought experiements
brings up so much resistance.  But this'll become a forum discussion
rather than an answer...
I guess I was hoping it would be possible to physically prove based on
some simple assumptions or specific measurements that it is either not
true or highly unlikely.  But it does not seem the case... Rather we
would much prefer if it is the case because our formulas look nicer.

Thank you for the work, though!

Surely to define an angular momentum for a body you need a frame of
reference outside that body.  For instance, to determine if the earth
is rotating you need to be able to see outside the earth.  This should
be true for the universe too.

Is there an error in the above logic?

Helpfulperson:

There is an error in the logic, if you're willing to concede that the
laws of physics are basically known, and are the same in all inertial
reference frames.  So it is possible, armed with physical laws, to
determine that the earth is spinning without looking outside.  The
reason is that spinning involves acceleration--directions of motions
change.  This gives rise to pseudo-forces, like the Coriolis force, or
the centrifugal force which causes you to weigh less standing on the
equator than at the poles.  A pendulum does not oscillate back and
forth in the same plane, but rotates at the Coriolis frequency (google
Foucault pendulum).  Observing these forces, we could conclude the
earth is spinning without looking outside the earth.  The same is not
true of linear motion.  There is no way to tell without looking
outside the earth how fast the earth is moving in a straight line. 
Even if you do look outside, you still have to pick a (necessarily
arbitrary) frame of reference.  So it would be meaningless to ask what
is the linear momentum of the universe.

Racecar-ga, actually you are almost answering what I was hoping to learn...
So even on the scale of galaxies turning around an axis there would be
a theoretical coriolis effect on a galactical level?
Would this kind of effect not interfere with signals coming from very
distant galaxies? ... so the answer would be something like, it is
unlikely that there is a positive angular momentum because we would
have likely noted its effect on cosmological measures?
hmm...

Einstein's field equations permit an exact solution for a ROTATING
universe, solved by Kurt Godel in the mid- 1940s. (whether or not such
a universe would have an angular momentum is a trickier thought).
Interestingly, EVERY point in this universe would appear to its'
observers to be the center. (I'm the center of mine and you or your's-
doesn't sound too bad). Time would move in 'circles'.
check out:
http://www.discovery.org/scripts/viewDB/index.php?command=view&program=CSC&id=1117

or search for "godel einstein rotating universe"