This Week's Finds in Mathematical Physics (Week 206)

... so if you're an expert who knows a lot about this, let me
know what you think - or better yet, post an article about this to
sci.physics.research!

I've never read anything about MOND other than what you have written
above, but I have taken separate astronomy courses from two professors
who I thought were great teachers, Rosanne DiStefano and Eric
Chaisson.

DiStefano was the first person to teach me that there is no
significant difference between dark matter and dark energy other than
pressure. I haven't looked closely at this issue for about two years
but AFAIK this is still the conventional view.

Anyways, there is brand new and reasonably good evidence for dark
energy [1]. Additionally, recent experiments done only with electrons
have found parity violation in electroweak interactions, thus
providing further and somewhat non-trivial evidence for the SM [2].


[1] http://www.washingtonpost.com/wp-dyn...2004May18.html

[2] http://sciencenow.sciencemag.org/cgi...ull/2004/426/2

"Tobias Fritz" schreef in bericht
...


Lee Smolin told me some neat stuff about MOND - that's "Modified
Newtonian Dynamics", which is Mordehai Milgrom's way of trying
to explain the strange behavior of galaxies without invoking
dark matter. The basic problem with galaxies
is that the outer parts rotate faster than they
should given how much mass we actually see.

If you have a planet in a circular orbit about the Sun,
Newton's laws say its acceleration is proportional to 1/r^2,
where r is its distance to the Sun. Similarly, if almost all the
mass in a galaxy were concentrated right at the center, a star orbiting
in a circle at distance r from the center would have acceleration
proportional to 1/r^2. Of course, not all the mass is right at the
center!
So, the acceleration should drop off more slowly than 1/r^2
as you go further out. And it does.
But, the observed acceleration drops off a lot more slowly than
the acceleration people calculate from the mass they see.
It's not a small effect: it's a HUGE effect!

One solution is to say there's a lot of mass we don't see: "dark matter"
of some sort. If you take this route, which most astronomers do,
you're forced to say that *most* of the mass of galaxies is in
the form of dark matter.


That is one solution but may be there is a slightly different point of view.
First of all a galaxy consists of a bulge and a disc.
To simulate the bulge (a sphere) using Newton's Law is easy
and what you get is a rotation curve with lineair increases
with distance.
To simulate the disc is a slightly different endavour.
When the disc only consists of some sun sized test stars
(like the planets around the sun)
then the rotation curve will follow the curve: sqroot(M*G/r)

However that picture is too simple.
First of all there are not some sun sized visible stars in the disc
but many and when you take those into acount the rotation curve
becomes more flat.
Secondly the number of visible stars to make the rotation flatter
is not large, specific along the rim the density becomes small
Third even outside the visible rim of the galaxy it is easy possible
that that there are sun sized stars (or slightly smaller) which
are overall invisible because the density is so low.
This becomes the more of a problem the further away the galaxy is.

My point is that before you can introduce dark matter
first you must make a 3D picture of ALL the visible matter included
and calulate the rotation curve based on that.
The question is if this calulated curve matches which what is
observed.
If it matches there is no reason to introduce dark matter.
If it does not match you could introduce dark matter in this 3D
picture such that it matches.
But my guess is that no HUGE amounts are required
nor that *most* of the mass is in the form of dark matter

However you have to be carefull where you envision
this dark matter.
It can not be in the close neighbourhood of our Sun,
because it will effect the trajectories of our planets,
nor it can be close to any Star in the disc,
because why should out Sun be special.
Also in a sphere around the visible rim of the galaxy
(like the oort cloud outside the kuiper belt around our Sun)
is tricky because it will only effect the rim.

In short a 3D picture of a Galaxy, with dark matter included,
is complicated.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

(alistair) writes:

Can MOND make any useful predictions about electromagnetic phenomena?

No. In fact, one of the major arguments against MOND is its total
inability to make any useful prediction of any type whatsoever
about the "gravitational lensing" effect produced by galaxies,
since light-bending is a general relativistic effect, and MOND
is incompatible with General Relativity, combined with the fact
that the gravitational lensing produced by most non-dwarf galaxies
as computed using General Relativity is entirely consistent with
estimates of the masses of "Dark Matter" they must contain based
on their rotation curves and non-MOND Newtonian stellar dynamics.


It's a modification of Newton's laws and they can be used in gravity
and electromagnetism.

Actually, Newton's Laws _CAN'T_ be used to handle electromagnetism,
which is one of the reasons why Einstein invented Special Relativity.
Moreover, Newton's Laws have also been shown to be inadaquate to handle
gravity except in the simultaneous limit of weak fields and slow motion;
for particles moving at a significant fraction of the speed of light,
or near bodies whose escape velocity is a significant fraction of the
speed of light, Newton's Laws fail miserably.


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'

Lubos Motl wrote in message news:

On Sat, 15 May 2004, John Baez wrote:

Someone: This [a paper on discretization of gravity] is pretty exciting.
http://www.arxiv.org/abs/hep-th/0404156

I'm glad you think so! I sure do!

Well, I am sure that you would be even more happy if I agreed, too. But I
don't. There is just no evidence that the resulting physics is physics of
gravity, and there is evidence against the conjecture that it will be
locally Lorentz-invariant. Below, I will argue that this unjustified
excitement about these models returns again and again, and that these
models never lead anywhere.

So do I win a prize win I agree with Lubos for the 100th time ?
I hope so because I must be close !

Here are three other reasons to be skeptical of discretized approaches
to gravity:


1) How are such approaches to be made compatible with vector
supersymmetry (or vsusy) which is a topological type of symmetry that
appears in both gravity and topological gauge theories [1].

2) How are such approaches to be made compatible with Bell- like
correlations, non-locality and non-causality which are each present in
the experiment described in this brief four page paper [2].

3) To paraphrase a sentence that Stephen Hawking once wrote, to not
believe in the beauty and unity of the dualities of M-theory is like
believing that evolution did not occur because instead God placed by
hand all the fossils in the Earth just to play a joke on the
paleontologists :-)


[1] http://arxiv.org/abs/hep-th/0111273

http://arxiv.org/abs/hep-th/0010053

[2] http://arxiv.org/abs/quant-ph/0102109

It's interesting that MOND splits Newtonian gravity into two cases
and the Modified version of Newtonain dynamics seems to happen in
galaxies and clusters of galaxies with magnetic fields.What is the
physical reason that MOND could be right?
If we assume that there is another force interacting with the stars in
a galaxy –
which modifies the Newtonian force law, what generates this force?

One answer to this question could be this:
suppose some charged particles flow over the plane of a spiral galaxy
and parallel to the plane, from intergalactic space. They encounter
the magnetic field lines of the galaxy and a force acts on them
obeying the equation force = qvB.
Assuming q v and B stay roughly constant as the charged particles
cross the galaxy,and
since in normal Newtonian dynamics acceleration = Force / mass of
charged particle,
the charged particles experience a constant acceleration as they move
(we will assume the particles are separated widely enough to make
their coulomb attractions and repulsions insignificant).
Negative charges will experience a push in the opposite direction to
positive charges-
the negative and positive charges will move closer together.
How much do they move?
Using s= ut + (a t ^ 2) / 2 , s = sideways distance moved,
and setting u, the initial and sideways speed of the charges as they
just reach edge of the spiral galaxy disc ( we are assuming that this
location is an approximation that will yield useful results) to zero:

s = (a t ^ 2) / 2

since the normal Newtonian acceleration on the charges is constant,
s is proportional to t ^ 2.

A charge moving towards the centre of the galaxy takes half the time
to move
to a position 0.75 the distance from the centre to the edge of the
disc, as it does to move to 0.5 that distance from the centre to the
edge.

So if it moves to 0.75 the distance the value of s is (1/2) ^2 i.e
1 / 4 of what it would be for a movement of a particle to halfway
across the galactic plane.So the force exerted on a star would be a
force exerted by 1/4
the number of particles because the negative and positive charged
particles
will not have moved so much sideways and so will not be so densely
packed at 0.75 units distance as they would be at 0.5 units distance
from the galactic centre.
The gravitational force depends on 1/ r^2 so at 0.75 units it would be
( 0.75 / 0.5 ) ^ 2 2.25 times weaker than at 0.5 units distance from
the galactic centre.


So if at 0.5 units distance a star experiences a force due to gravity
of X newtons
and a force due to the charged particles of Y Newtons, the force on
the star
is X + Y Newtons towards the galactic centre.

at 0.75 units distance, the star would experience a force of:

1 / 2.25 X + 0.25 Y
This will apply only for charged particles moving through a
homogeneous region
of the galactic magnetic field and it is assumed that the electric
forces between charges are negligible.The idea outlined above may need
modifying but
hopefully it gives some insight into a physical mechanism for MOND.
It attempts to show that Newton's laws are still valid and that MOND
is right just because it considers only the gravitational force and
not other forces that could act upon stars.

Charlie Stromeyer Jr. skrev i
diskussionsgruppsmeddelandet:61773ed7.0405240822.1 ...

So do I win a prize win I agree with Lubos for the 100th time ?
I hope so because I must be close !

Dear Zirkus,

Motl has of course completely missed the main point. Distler's
objection from 3 years ago was that he didn't believe in a good
continuum limit in 4D; a "miracle" as he puts it. This may have
been good point at that time; I thought so myself, although I
would have been much less pessimistic if I had known that
Ambjorn and Loll had already succeeded in 2 and 3D.

The new thing is that AJL have presented rather compelling
numerical evidence for a good continuum limit in 4D, thus making
Distler's objection obsolete. It is the fact that AJL have
apparently succeeded in quantizing gravity numerically that
people are so excited about.


Here are three other reasons to be skeptical of discretized approaches
to gravity:


1) How are such approaches to be made compatible with vector
supersymmetry (or vsusy) which is a topological type of symmetry that
appears in both gravity and topological gauge theories [1].

The term vector susy is a misnomer, since the superalgebras
appearing in those papers can hardly qualify as susies. Physical
fields obey the spin-statistics theorem, so susy generators must
be spinors rather than vectors. Instead, what these authors do
is to treat the diffeomorphism constraint in the BV formalism,
which is the Lagrangian counterpart of the BRST method in
Hamiltonian quantization. This is a neat way to treat a gauge
symmetry, at least in the absense of anomalies: one identifies
physical states with cohomology classes of a nilpotent BRST
operator. A superalgebra structure arises naturally since the
BRST operator is fermionic, but this has nothing to do with
supersymmetry.

In the AJL model, the gauge is already fixed;they formulate the
action in terms of diff-invariant edge lengths rather than the
metric, there is a privileged time direction, etc. Since their
model only contains gauge-invariant quantities, there are no
diffeomorphism constraints left, and thus no need for ghosts.


2) How are such approaches to be made compatible with Bell- like
correlations, non-locality and non-causality which are each present in
the experiment described in this brief four page paper [2].

Causality seems to be the whole point with the AJL approach -
lack of causality, i.e. singular metrics, is explicitly thrown
out. Whereas things like the EPR paradox are constantly
confusing, it does not imply a violation of neither causality
nor special relativity. One should ponder what Bert Schroer
writes in http://arxiv.org/abs/hep-th/0405105, p 3:

"In fact nowadays it is generally excepted among experts that
among all physical principles which underlie standard QFT,
Einstein causality for local observables is the most sturdy
property from a conceptual point of view; no matter how many
words have been spoken and how many papers had been written on
cut-offs, regularizations and other ad hoc modifications, nobody
has any idea (beyond a wishful incantation) what such
manipulations really mean in terms of operators in a Hilbert
space. Hence it comes as no surprise that most attempts of
introducing deviations from micro-causality actually amount to
violating macro-causality in the wake; but macro-causality is
the absolute borderline between physics and the realm of
poltergeists."

Another reason to believe in strict causality comes from the
quantum analogue of tensor calculus. The objects that build up
projective representations of the diffeomorphism algebra live on
the observer's trajectory, and are thus automatically causally
related. This can be traced back to the apparent paradox that
energy is both a scalar (a number that is bounded from below by
the mass) and a vector (the zeroth component of
energy-momentum), which is a version of the problem of time.
That people haven't cared enough about causality may very well
be the reason why there hasn't been any real progress in quantum
gravity; the work of AJL and collaborators may be an exception.


3) To paraphrase a sentence that Stephen Hawking once wrote, to not
believe in the beauty and unity of the dualities of M-theory is like
believing that evolution did not occur because instead God placed by
hand all the fossils in the Earth just to play a joke on the
paleontologists :-)

Beauty lies in the eyes of the beholder. The AJL model is
admittedly not very beautiful, but one does not expect that of a
gauge-fixed and discretized model. A gauge-fixed version of
lattice gauge theory is not terribly beautiful either, but we
nevertheless believe that it is a valid quantization of gauge
theories.

Can MOND make any useful predictions about electromagnetic phenomena?
It's a modification of Newton's laws and they can be used in gravity
and electromagnetism

The effect of MOND is supposed to be important when acceleration is
less than
10 ^- 10 m / s ^ 2.
If this is true then if I place a postive electric charge at a
distance from a negative electric charge, such that the acceleration
predicted by
k q1 q2/ r ^ 2 on each charge should be 10 ^ - 11 m / s ^ 2,then
according to MOND an experimental measurement of the acceleration
would show that the prediction of k q1 q2 / r ^ 2 was wrong!
Has anyone ever performed a test of this kind on MOND?

I am also cross-posting this reply to s.p.s. since it contains some
commentary about string theory.


(John Baez) wrote in message news:

1) How are such approaches to be made compatible with vector
supersymmetry (or vsusy) which is a topological type of symmetry that
appears in both gravity and topological gauge theories [1].

This "vector supersymmetry" is a mathematical feature of certain
field theories - not something that anyone has observed experimentally.

Okay, but note that vsusy is an inherent aspect of your type of
approach to spin foam models of BF theory and quantum gravity as well
as the Ashtekar action. I discuss this some in post [1].

(Btw, there is also a newer paper about the role of vsusy in a general
supergauge which is more general than WZ gauge and here there does not
need to be a metric which is nonsingular at every space-time point,
i.e. the vielbein matrix doesn't have to be invertible in superspace
[2].)

Nobody has yet constructed a background-free quantum theory that has
general relativity as its limit at large distance scales. The Ambjorn-
Jurkiewicz-Loll model is the closest anyone has come. If they succeed,
this will be of interest regardless of whether their model displays
mathematical features that appear in certain other theories!

2) How are such approaches to be made compatible with Bell-like
correlations, non-locality and non-causality which are each present in
the experiment described in this brief four page paper [2].

As a quantum theory, the Ambjorn-Jurkiewicz-Loll model automatically
has Bell-like "entanglement" and all that jazz.

At first, I thought that the AJL model must be flawed for reasons
mentioned in post [1], however, this may no longer be the case because
there are two recent papers which argue for separate reasons that
superluminal signals may actually be compatible with GTR [3].

As I told Tony Smith in another thread, it will take me some time to
read more literature and try to understand these issues better, and I
have never even read any of the Smolin or Magueiro papers on VSL and
DSR and so this may take me a few weeks or even two months.

3) To paraphrase a sentence that Stephen Hawking once wrote, to not
believe in the beauty and unity of the dualities of M-theory is like
believing that evolution did not occur because instead God placed by
hand all the fossils in the Earth just to play a joke on the
paleontologists :-)

We resort to theological arguments in physics only when better arguments
are lacking. If a scintilla of experimental evidence for M-theory is
ever found, people will instantly stop making arguments of the sort
you mention here.

Actually, Hawking and I were making an argument which you have also
made before, but which is not really an argument so much as a truism:

Thousands of years of the history of mathematics have taught us that
new and non-trivial math which is beautiful and profound never turns
out to be completely useless. Why is it that M-theory has contributed
to or inspired so much variety of important new mathematics? Is this
merely some kind of fluke or joke that Nature is fooling people with?

Here is another important point about this issue for critics of string
theory such as Peter Woit:

During the 1990s, I would occasionally take courses at the Harvard
Extension School. I was once seeing what a particular course would be
like by sitting in the classroom of a mathematical logic course taught
by the famous logician Gerald Sachs who is now at MIT.

One student asked a question about the mathematical rigor of
string/M-theory. I don't remember what her question was but Sachs
explained why it is that string theorists have to make things up as
they go along, i.e. that there is an unavoidable degree of uncertainty
and speculation involved in such an ongoing endeavor.

I also would guess that Sachs realized something that I realized later
which is that it took about 2,100 years until Hilbert and others
showed that classical Euclidean geometry was logically incomplete.

If string theory turns out to be correct then mathematicians will
probably investigate the degree of consistency and completeness of
string theory's mathematical foundations. In the meantime, it does not
make sense to demand too much rigor before the time is ready.
Otherwise, to use Lubos' analogy, theorists risk being like
hypothetical 19th century physicists trying to use Newton's equations
to calculate the expansion of the universe.

For more on this topic, also see my post in sci.physics.strings in
reply to the question about "what is OPE?".

I'm not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll
model is "right". M-theory makes too few definite predictions to be wrong.

This point is not necessarily true, but I won't go on a long spiel
about it right now because Lubos, others and I have already discussed
this issue in more detail in s.p.s. and there are also plenty of
papers in the Arxiv about potential tests of QG, including potential
tests of string theory.

The AJL model does not include matter, so it cannot be right. But the
AJL model is *interesting*, because it represents the best attempt so far
to find a background-free quantum theory that reduces to general relativity
in the large-scale limit!

Okay, I accept that their model might be interesting and I will now
even read their paper !-) Btw, the distinction between discrete and
continuous have a variety of different meanings in physics and math,
and e.g. it was even the great polymath genius, von Neumann, who
invented the field of math known as continuous geometry from
considering a series of discrete instances of projective geometry, and
this field has since been more generalized.

My point is that some of the distinctions between discrete vs.
continous may turn out to be somewhat trivial, and this is one reason
why I asked if Ashetkar's action might be compatible with the AJL
model in post [1], but I will now also read the AJL paper.


[1]

Thomas Larsson wrote:

"In the AJL model, the gauge is already fixed;they formulate the
action in terms of diff-invariant edge lengths rather than the
metric, there is a privileged time direction, etc. Since their
model only contains gauge-invariant quantities, there are no
diffeomorphism constraints left, and thus no need for ghosts."

Hi Thomas, I think you have misunderstood what I wrote and so before I
read the AJL or Bert Schroer papers let us try to clarify what we are
talking about and to make sure that we are considering the same
concepts.

Despite the particularities of the specific BV approach to vsusy, it
is the case that vsusy is an essential part of the origin of
perturbative finiteness of BF theory, and it helps with the algebraic
renormalization of topological YM theory, and vsusy may have a role in
constructing physical observables in addition to perhaps being the
symmetric origin for the IR safety of topologically massive YM theory
in Landau gauge.

Well, at least this is more established for CS theory defined on an
arbitrary space-time three-manifold for Landau gauge choice in which
vsusy is a renormalizable local supersymmetry which derives
perturbative (UV) finiteness at all orders [1].

It is also interesting to note that YM field configurations on 3 and 4
dimensional manifolds generate an effective Riemann-Cartan (in certain
models, Riemann) geometry on a space (or spacetime) and vice versa,
i.e. R-C geometry can yield YM gauge fields. The YM equations can
perhaps be written without the use of any metric on an arbitrary
smooth manifold [2].

However, the new AJL paper may also be intriguing because coframe
models can have the problem of allowing the existence of non-physical
modes such as ghosts or tachyons [e.g. references 18 and 19 in
gr-qc/0111087].

Anyways, the first question I would like to ask before reading this
new AJL paper is if their approach is compatible with the Ashtekar
action?

I ask because the vsusy of 4d Einstein gravity (in the Palantini first
order formalism) is compatible with the Ashtekar action and may be
compatible with any other actions if such actions have the vierbein
and connection as independent variables and have invariance under
_active_ diffeomorphisms, i.e. diffeos which act on dynamical fields
only, IOW, act quantum mechanically on field operators - the vierbein,
connection and matter fields [hep-th/0005011].

"Causality seems to be the whole point with the AJL approach -
lack of causality, i.e. singular metrics, is explicitly thrown
out."

Here we are thinking of different notions of "causality" which I will
now start attempting to clarify. Also, before discussing the AJL paper
further we might want to consider the important conundrum I ask about
at the bottom of this post.

1) For some as yet unknown and hypothetical reason, it might turn out
to be the case that theorists, e.g. either string theorists, LQG
theorists or discretized gravity theorists, will uncover what seems to
be a reasonable theory of QG but then for decades not be able to
figure out how to make the theory compatible with what we already know
to exist here at the everyday low energy scale.

However, let us presume, for this discussion at least, that a good
theory of QG should be inherently compatible with various low energy
phenomena and then consider the following:

1) Various quantum phenomena have already been demonstrated to be
"noncausal" both theoretically and sometimes even experimentally. I
have been looking at some of this literature recently and so far,
except for the one very important conundrum I ask about below, the
term
"noncausal" means only that there is no discernable and meaningful
dependence upon causality which is different from the idea that there
is some kind of explicit violation of Einstein causality via
superluminal signals.

For instance, experiments with TmYAG crystals have shown that
stimulated photon ehoes (SPEs) can exist in the noncausal direction
[3], and separate experiments have shown that the phase and energy of
a photon pulse can travel faster than c, the speed of light in a
vacuum, but there does not (yet, anyways) seem to be meaningful
information transmitted via superluminal signals due to cancellation
of such potential superluminal signals because of complicated
diffraction and diffusion effects [4].

3) However, now consider the important conundrum:

Suppose that one definition of the presence of "acausality" would be
the existence of uncertainty which is clearly non-statistical (or
non-probabilistic). Well, this is what happens in the photon
experiment decsribed in this brief four page paper [quant-ph/0102109],
yet there are no superluminal communications necssarily entailed !

Furthermore, also consider this paper [quant-ph/9802056] about
acausality in QED which shows that it is theoretically possible for
there to be acausal behavior for photons in both time-like and/or
space-like directions.

Thomas, since you are from Scandinavia you should heed what the Prince
of Denmark once said and also do not forget about ghosts :-)

"I will tell you why; so shall my anticipation precede your discovery,
...."

Hamlet, Act II, Scene 3

I will post more later about noncausality and acausality, but in the
meantime I will demonstrate the existence of acausality by correctly
anticipating what you, Thomas, will write in reply to this post before
you have even started typing on your keyboard !-)


[1] "Local Supersymmetry of the Chern-Simons theory and finiteness",
C. Lucchesi, O. Piguet, Nucl Phys B 381 (1992) 281-300.

[2] "Induced Geometry: Riemann-Cartan from Yang-Mills", Y. Obukhov,
D. Ivaneko Festschrift, JMS, v5 (1995) pp1-20.

[3] "Nutational Stimulated Photon Echoes", Optics Letters, v27(iss
13) (2002), pp.1156-58.

[4] J.J. Carey et al., Phys Rev Lett, v84(no7) (2000), p.1431.


---------- end of post [1] -------------


[2] http://arxiv.org/abs/gr-qc/0402036

[3] http://arxiv.org/abs/gr-qc/0304059

http://arxiv.org/abs/gr-qc/0403121