Eric Gisse ha escrito:

Juan R. wrote:
Eric Gisse ha escrito:

Wald obtains the correct potential and the correct definition of
acceleration (a = -del*phi) on page 77.

MTW and "Spacetime and Geometry" obtain the same metrics as Wald.

I fail to see what you are complaining about.


Exactly! You see page 77 of Wald and you think "equation (4.4.21) of
Wald is Newtonian law".

I should have qualified that by explaining what phi was. My mistake.

The phi obtained is GM/r.

already explained why Wald equation is not Newtonian equation!! I will
explain again Phy (x,t) is not Phy(R(t))

'r' in Wald equation is not 'r' in Newtonian equation. Moreover, 'GM/r'
in Wald equation contains c in a hidden manner via retardation of the
field. 'M' in Wald equation computed at t_{ret} is not 'M' in Newton
equation computed at tau, etc.


Moreover, i already explained why the rest of the equation and
derivation are just wrong.

The derivation is incorrect as i will prove AGAIN.

1) Derivation in the linear regime is WRONG.

In the linear regime a=0; newer (repeat NEWER) a=-grad (Phi). In fact,
you see Wald derivation and you believe because you have not revised
details -see below- that derivation is correct -just as you cite the
MTW- but derivation is INCORRECT. The linear regime predicts a=0 and
Newtonian gravity predicts a = - grad(Phi).

["NEWER" ?]

That isn't a proof, that is a statement unsupported by fact.

Read Wald before doing irrelevant claims. Wald clearly proves why in
the linear regime a=0.


***Therefore GR does not reduce to NG in the linear regime***. Usual
textbooks are wrong.

Then if you cannot understand an elementary derivation WHY are you
doing wrong claims? Note i would be not as hard with you if you had
claimed "Hey Juan R. I think that you are not correct by this and
this". But you categorically claimed "you wrong" even without the most
basic understanding of the topic!

Again, I remember you that we are doing serious stuff, this is not
string theory or general relativity, this is canonical science.

*snicker*

Read elementary stuff and after understanding basic stuff read more
advanced literature and after understanding it continue reading still
more advanced literature. Do not make irrelevant claims at first
undergraduate level.


If you have time you would read pag 78 of Wald:

"If one stays consistently within the linear approximation, one
predicts that test bodies are unaffected by gravity. Thus, in obtaining
equation (4.4.21) we actualy have gone beyond the linear
approximation".

That is the reason why i said that Wald derivation is NON-linear, since
in the strict rigorous linear regime a=0. All textbooks claiming that
in the linear regime a is different from zero are wrong and simply are
modifing *reality* for consistency with Newtonian law. Ok, then next
Wald claims that in the non-linear regime, the derivation is already
correct, but, again, that is not true.

How you extend a=0 from just test bodies to ALL bodies is a mystery
beyond my understanding.

I guess it is easier to assume that everyone is wrong and you are
right, I suppose.

What is the link of this nonsense with Wald's proof on linear regime a
= 0 and gravitation is not correclty modelled? Do you know that word
'proof' mean?


2) Wald (4.4.21) is not Newton equation. The 'Phi' in (4.4.21) is not
Newtonian potential it is a retarded LW potential. The 'a' in (4.4.21)
is not Newton aceleration because 'x' is not Newtonian 'x'. Moreover
't' in (4.4.21) is not Newtonian time.

I am not going to argue about this when it is all explained on the very
same page which you are referencing.

Nonsense. Wald is just deriving the weak field slow velocity limit
which is NOT the Newtonian limit. The Newtonian limit is in rigor the
c-- infinite limit. Do you know NC theory? Perhaps you would study
first before doing claims...

If you think a = -del*phi isn't the Newtonian potential, your
understanding of Newton is suspect.

It is not 'if your think'. You appear unable to distinguish between a
Newtonian potential with functional dependence phy = phy(R(t)) with the
nonrelativisitc limit of a LW 'potential' -really field- with
dependence phy = phy(x, t). I only can recomend to you read literature
on the topic. I cited several articles where the correct dependence is
highlighted. Also cited a chapter on a well known book on dynamics (the
Goldstein). I also cited a web page where you can see the diference on
functional dependence. No worry i will cite again the online page.

Look the first V in http://www.mathpages.com/home/kmath527/kmath527.htm

That is a potential with functional dependence V = V(R, dR/dt)

Taking limit c-- infinite one recovers Newton potential V = V(R) =
V(R(t))

Now scroll down the page and looks in the LW potential just before
equation (2). The phy in Wald equation has the same functionality phi =
phi(x, t). There are published literature (i already cited) where it is
proven that mathematically the phi(x, t) is incorrect.

Moreover V(R(t)) is different from V(x, t). Do you know what is a
function?

Moreover you just ignore the rest of criticisms.

What is more, (4.4.21) is not a nonrelativistic equation because it
contains c in both terms left and right and this is an authentic
absurdity. Non relativistic equations do not contain c. Moreover, the
metric used by Wald also contains c and does not correspond with
Newtonian physics.

It is close enough. If you want authentic Newton, use Newton. I really
don't understand why you are complaining about this...

No, that 'option' is not valid on physics. 'Close enough' is not
suficient. Or you can explain data or cannot explain data. In Wald
equation experimental data is not explained and this is the reason that
authors doing serious research in the topic does not follow that way.

If GR cannot reduce to NG then GR is unable to explain experimental
data that Newtonian gravity CAN explain.

Moreover, GR says that gravity is caused by spacetime curvature and in
the nonrelativistic limit there is no curvature, therefore the causal
structure is just wrong.

Then one has the same problem that with relativisitic quantum field
thoery that cannot explain non-relativistic quantum mechanical
experiments. In Dirac words:

"Most physicists are very satisfied with this situation. They argue
that if one has rules for doing calculations and the results agree with
observation, that is all that one requires. But it is not all that one
requires. One requires a single comprehensive theory applying to all
physical phenomena. Not one theory for dealing with non-relativistic
effects and a separate disjoint theory for dealing with certain
relativistic effects."

You cannot use GR for computing certain relativistic phenomena (light
bending radar delay, Mercury perihelion, etc) AND Newtonian gravity for
computing other phenomena. for example computer programs use Newtonian
gravity for computing orbits and in the final step time delays for
aparent image of celestial bodies or formulas for correcting perihelion
are introduced /ad hoc/. That is more, both theories GR and NG are so
incompatible as GR and QM.

We need is a NEW gravitational theory explaining all phenomena,
relativistic and nonrelativisitic, and without the further difficulties
of GR (self-action, singularities, problem of energy, quantization,
frames, etc.).


3) Moreover functional dependence is wrong. In (4.4.21), phy = phi(x,
t). In Newtonian physics, phi = phi(R(t)). Wald simply writes 'phy',
without details, and then it appears that one has derived Newtonian
law.

The details you seek are between 4.4.20 and 4.4.21. Wald simply writes
"phi" because he DID explain it not but a moment before.

But since you have a bit of difficulty reading, I will explain.

phi is dependant on x^i, i=1,2,3. It is explained, as I said, on the
very same page of which you reference. phi is not dependant on time -
it is explained, as I said, on the page of which you reference.

When I said your understanding of Newton is suspect, I was correct. In
Newtonian gravity, phi is dependant on r, not t.

You obviously do not understand.

In Wald derivation, phy = phi(x, t) is a LW potential (field). Taking
the limit of low motion does that retardation effects in velocity are
negigible but those do not make t dissapear`since is stiull present in
te retarded density. In fact the 'M' in Wald LW potential is M =
M(t_{ret}) because that term is independent of velocity.

Even ignoring time dependence of M and writting just phy = phi(x) THAT
is NOT Newtonian potential because Newtonian potential functional form
is

phy = phi(R(t)) = phi(R)

and R is different from x and moreover CONTAINS implicit time
dependence on t, because R = R(t).

Still even ignoring all of this the a in a = -grad(Phi) is not
Newtonian a.


4) The fixing of the gauge of the GR phi is done via asymptotic regime.
This regime is called 'island universe asumption' and it is wrong,
because it is not verified by experimental data. In Christian's own
words:

"However, physical evidence clearly suggests that we are not living in
an 'island
universe' "

In Penrose's own words:

"universe is not 'an island of matter surrounded by emptiness'"

I would hope Penrose, of all people, understands the utility of an
approximation.

I think that Penrose know what is an approximation. Approximation means
that if you put the approximate answer you obtain and approximate
answer (more good if approximation was better). If you put the real
answer you may obtain the correct
answer. This is not the situation with island asumption. If you put the
real boundary of universe which is not island one you obtain a WRONG
Newtonian limit.

100 is an approximation to 101, because the difference between real
value and approximate value is small of order of 1/100. Substitution of
approximated (100) by real values (101) imply a better fiting of data.

In GR boundaries if flatness was an approximation then that mean that
substitution of approximated boundary by real (observed) boundary would
imply a better fiting of data. BUT IS NOT!!! If you use the observed
boundary of the universe instead of flatness one, one does not obtain a
better result one obtains JUST WRONG results.

Etc.

Wald derivation is a complete nonsense. If GR is consistent, the
Newtonian limit may BE the c-- infinite limit of GR. But Wald did NOT
the c-- infinite limt. Wald only took the slow motion weak field
limit.

Which is close enough.

No, 'post-Minkoskian' way is not! and this is the reason in the
research in alternative ways (post-Newtonian ones). Moreover Wald
approach is internally inconsistent and implies that one may substitute
***by hand*** incorrect mathematical expresions by correct ones.

For example, Wald obtains

d^2 x_{Einstein} / d t_{Einstein}^2 = - grad { -G M(t_{ret}) / [x -
y(t_{ret})] }

and may FIRST know Newtonian gravity and then one may after do, by
hand, the ***substitutions****

x_{Einstein} === x_{Newton}

t_{Einstein} === t_{Newton}

M(t_{ret}) === M

[x - y(t_{ret})] === [R(t)]

Etc.

And this only for the ONE body problem. For the N-body problem the
number of ad hoc substitutions is greater.

Moreover, there is conceptual and theoretical difficulties. Why one may
ignore c dependence in a kinetic term but c is still present in the
potential term. How is possible that an instantaneous interaction is
derived from a retarded interaction maintaining c finite (if one
maintain retardation in a Newtonian potential then orbits are destroyed
in simulations becaue momenta is not conservedl, etc.), etc.

This is the reason that limit only can be c--- infinite that,
curiously, IS the limit studied in research literature. Textbooks are
only that... textbooks.


I repeat again that people doing research does not follow textbook
wrong derivation.

If you take the c-- infinite limit you discover that gravity breaks
down and cannot explain Newtonian gravity. This is not so difficult to
understand in the c--infinite limit there is no curvature. The metric
is

What is the curvature scalar for the Newtonian limit if you allow c to
go to infinity?


(1 -1 -1 -1)

That isn't the metric that results if c is infinite. Steve Carlip
explained this to you before.

Yes Carlip 'explained'... using a wrong metric with wrong Minkoskian
limit, incorrect dimensions (when metric is adimensional), violating
the /XXIVth International Astronomical Union General Assembly
recomendations. Moreover, Carlip obtain wrong functional dependence
(violating causality), wrong boundaries (violating cosmological data),
wrong derivatives (due to the use of 00-connection), wrong time
(obtained a dimension and time is not a dimension in Newtonian physics)
and finally was unable to prove that curvature interpretation holds in
the limit.

If that is a explanation for you i repsect your criteria. however, it
is very interesting that people doing research in those topics
(including Penrose) do not hold Carlip views.
For example, Penrose clearly reject island asumption as *unphysical*,
Carlip is still unable to understand why.

The metric for flat space, with c restored, is diag(-c^2,1,1,1)
assuming the -+++ sign convention.

But that is not the correct metric. Take a basic book on SR, EM,
particle physics, etc. The metric is (1 -1 -1 -1). The c is NOT
introduced into the metric, the c is introduced into the x^0 component
of spacetime.

I already cited an online textbook on GR

pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf

see page 2 of Sean Carrol basic manual, x^0 = ct and the metric is (1
-1 -1 -1). Carlip does x^0 = t and his metric is (c^2 -1 -1 -1), which
is wrong. For example, in Carlip's wrong metric there is not
four-currents because the c term in the temporal dimension is mising.
Moreover, Carlip obtains a full couple of mistakes in the limit c--
infinite as proven.


Therefore if GR was a consistent theory would have no gravity.

That is stupid. Seriously, it is.

It is well-known that GR is not a consistent theory of gravity. It is
also known by people who has done serious stuff in Newtonian limit (and
Carlip is not one of them) that the Newtonian limit cannot be obtained
from GR without invoking aditional equations and ad hoc postulates.


Carlip has done an attempt to derive Newtonian limit on both
sci.physics.resesarch and sci.physics.relativity but:

i) He uses a wrong metric that forces to us to rewritte all relativity.
For example, in his nonstandard approach there is no four currents and
there is not four space. The EM four 'current' is a strange mixture of
densities and true currents in Carlip nonstandard approach.

Where did your nitpickery go? In Newton there is no 4-anything.

I was talking of the Minkoskian limit of Carlip wrong metric when i
talked of Em currents, it is obvious!!! Moreover, you do not understand
Carlip's approach. In my approach the nonrelativistic limit of (ct, x)
looks like (infinite, x). the zero-dimension collapses and one is
forced to use a 3-space parametrized by the invariant tau. In Carlip
wrong approach, his nonrelativistic limit is (t, x) and one obtains a
four spacetime which has no sense in the newtonian limit!!!

My metric is standard, verifies all experimental data and is consistent
with particle physics, special relativity and Maxwell EM. Moreover my
chossing of metric is recommended by Astronomical societies.

Ooooh.

??????

It all makes sense now. Actually learning and changing your opinions is
impossible for you because you have a vested interest in how you
currently have your theory written - no matter how absurd it is.

I stopped taking you seriously at all right about....here.

That is you ignore published literature, you ignore math, and you put
in words of one author the mistakes done by other authors. For example
you critize to me that in your words "In Newton there is no
4-anything." when precisely i am obtaining a 3-space and Carlip is who
obtained a wrong 4-space with time like a dimension, which is a
complete absurdity!!!!


ii) Carlip takes the wrong spacetime (t, x) which looks like (t, x) in
the nonrelativisitc limit. That is, Carlip think that in Newtonian
physics time is a dimension which violates the most basic understanding
of Newtonian physics!!!

God, stop whining.

GR isn't Newton because they are fundamentally different. To expect
otherwise is foolish.

Or either you obtain Newtonian physics exactly or your theory is just
wrong. Moreover you appears completely ignorant of NC theory and
similar.

In my own spacetime (ct, x), the limit is the correct (infinite, x).
The zeroth dimension of spacetime collapse, doing time as dimension a
wrong concept, and this is good. One recovers time as an evolution
parameter (x^0 collapses by t does NOT collapse), WHICH is the correct
Newtonian concept of time. In any elementary textbook of mechanics one
can verify that the state of the system is (p,q) parametrized for one
single evolution parameter t called absolute Newtonian time.

Sounds like you are one of those MOND people, except with 100% more
crank.

Your insults do not mistakes. Perhaps you would read a basic textbook
on Newtonian physics...

Your usage of "collapse" is completely unmotivated and confusing.

No it is not, the collapse of the topology of the dimension zeroth does
you cannot use it as a valid physical dimension distance between two
physical intervals is of measure zero, and only other three dimensions
survive. Curiously this is also 'predicted' by NC theory. Yes NC is
just complex enough for doing not appear in the Wald or in other
elementary textbooks but does not mean that was not a research topic.


iii) By taking the wrong spacetime and wrong limit, Carlip obtains the
functional dependence Phi(x,t) when the correct dependence in
Newtonian physics is Phi(R(t)) because time is NOT a dimension in
Newtonian physics and interactions are not field-theoretic ones.
Moreover, there are difficulties with the use of Phi(x,t) for example
violation of causality in the transition to stationary regimes, etc.

Get the functional dependance of phi correct and try again.

?????

I am obtaining the correct functional dependance R(t). It is Wald and
Carlip and other who obtain incorrect dependence (x, t)!!!


My work on gravity corrects this and one obtains the correct functional
dependence without lack of continuity, etc.

Your "work" on gravitation is based on Newton and GR's Newtonian limit?
Are you kidding?

You do not understand.

iv) Carlip choosing of wrong spacetime and wrong metric does that he
obtains a nonzero 00-connection. This is wrong. In GR, the covariant
derivatives are physical derivatives, therefore in Carlip approach the
only measured (physical) derivatives are

What the hell is a "physical" derivative? It sounds like you are
inventing new terminology as you go along.

New terminology? "Physical derivative" is a standard term. I explain
again, in presence of a nonzero 00-connection the flat derivative is
unobservable ad this is the basic reason for the minimal coupling
standard rule

flat derivative --- covariant derivative.

The reason the 00 connections are nonzero is because of the metric. If
you wish to argue about that, you will have to dig a little deeper and
complain about how the metric was derived.

If the 00 connection is not zero you are forced to substitute the flat
derivatives by covariant ones in the Newtonian limit. In Newtonian
physics the physical derivatives are flat ones.


This is of course WRONG, any textbook of Newtonian mechanics explains
that the correct derivatives are usual partial ones.

For the love of god, stop whining. This is a different theory. It is
not Newton.

WE ARE ATEMPTING TO OBTAIN THE NEWTONIAN LIMIT. THEREFORE YOU MAY
OBTAIN ALL OF NEWTONIAN LIMIT.

In fact, this is the reaos that textbooks only focuse on the derivation
(so say) of Newtonian law for one single body. Newtonian mechanics is
not equivalent to Newton law for an single body. Newtonian mechanics is
some more.

For example what is the continuity equation in Carlip approach.


In my own work, the 00-connection is zero therefore Newtonian
derivatives are partial ones. This is correct.

..and you get a = 0

Completely WRONG, you have no idea. The 00-connection is zero but a is
NOT zero if you are computing the nonrelativistic limit of the
trajectory ;-)

Which is....incorrect.

Incorrect is your profound misunderstading of even the most elementary
stuff.

Moreover the physical derivative is the flat one just as in Newton
physics.


v) The scalar curvature in Carlip approach is R = R_00/g_00. Since he
introduces the c^2 term into g_00, in the limit he obtains R -- 0.
That is, in GR, gravity is spacetime curvature, even ignoring all four
points of above doing Carlip derivation just wrong, one obtains that in
the nonrelativistic limit the curvature of spacetime is ZERO. If A is
the cause of B, then elimination of A may eliminate B. The curvature
interpretation of GR is not only artificial (as proved by teleparallel
gravity or FTG) is also incorrect.

So what are you saying, R *doesn't* go to 0 as r goes to infinity?

?????


In my own metric, the curvature is zero as correspond to Newtonian
physics. Are you heard in some textbook of Newtonian physics that
spacetime, time, or space is curved?

*sigh*

GR IS NOT NEWTON.

WE ARE ATEMPTING TO OBTAIN THE NEWTONIAN LIMIT. THEREFORE YOU MAY
OBTAIN ALL OF NEWTONIAN LIMIT not just the part what is of interest for
you and the part that is not of interst for you because breaks the
consistency of GR just is ignored. Ignorance of data is not a good
attitude for a scientist

GR IS NOT NEWTON.

To expect otherwise is foolish.

Is wait that GR reduce to the correct Newtonian limit foolish?

Is "your own metric" even a valid solution to Einstein's field
equations and does it even reduce to the Newton at the proper limit?

??????


vi) In the derivation from GR one may fix the 'gauge'. Carlip uses
asymptotic limit. This is again wrong. As explained by Christian,
Penrose and others, the island asumptions is ***experimentally***
false.

BFD.

You are looking for something to complain about. The "island
assumption" is perfectly valid because we aren't trying to find the
metric of the universe, just for a specific case under specific
assumptions.

Yes it is so valid that we know that is experimentally invalid. Great!

"However, physical evidence clearly suggests that we are not living in
an 'island universe' (cf. Penrose 1996, 593-594) - i.e., universe is
not 'an island of matter surrounded by emptiness' (Misner et al. 1973,
295)."


Other people, as Christian, does use of aditional equations and
constraints do NOT derived from GR.

There is still more points and very very sophisticated that i do not
discuss with Carlip, but since he is unable to recognize difference
between a Newtonian potential (R(t)) and the nonrelativistic limit of a
retarded LW field (x, t), i consider unnecesary to discuss advanced
stuff with him.

Get the functional dependance of phi right first.

I already obtained the correct functional dependence (R(t)). From GR,
one obtains the incorect functional dependence (x, t).

I see it as you are advocating a pet theory of your own and you haven't
dedicated the necessary time to properly learn GR. You keep making
mistakes, and often repeat them even when corrected by others.

It is really interesting as people who has studied those points on
detail concide with me.

But do not worry if you want believe that GR reduces to NG in the
linear regime you can do it : -)


Juan R.

Center for CANONICAL |SCIENCE)

Gregory L. Hansen ha escrito:
Juan R. wrote:
Where is there a complete bound-state theory in Weinberg manual for
example?

It doesn't have to be in Weinberg manual. No single textbook is
comprehensive, or can represent work done after it was published.

Where is there a complete and consistent relativistic bound-state
theory?


R-QFT clearly states that only possible observables are those derived
from S-matrix, which is only valid for independent particles (remember
the cluster decomposition principle). In rigor R-QFT only deal with
free fields.

The S-matrix is a particular method of solving the equations of motion.
Specifically, it's useful when the end states are mostly the free particle
states.

Correction, the S-matrix is the only possible observable on R-QFT and
it is only defined for free particles. The only well-defined fields on
R-QFT are free fields.

Crank the Lagrangian through Euler-Lagrange equations and you'll get an
equation of motion, like the Dirac equation with electromagnetic
interaction. Solve it any way you like. The S-matrix is one way.

There is not equation of motion in R-QFT defined for full interacting
states and only scattering states can be defined. This is reason that
S-matrix is the only observable. Only free fields are defined in R-QFT.

So I haven't specifically seen bound state problems solved in QFT, but I'm
suspicious of claims that they can't be.

Difficult to believe that you can find them because the only physical
states on R-QFT are free particle states. There is nothing on R-QFT as
the wavefunction of two bound electrons.

...
Bethe-Salpeter and others are incorrect. At one hand, one claims that
two body state is a 16 component wavefunction. At the other hand in the
interaction regime one uses propagators derived from formals series of
QED which clearly state that there is not two body wavefunction for the
two electrons.

The propagators themselves are arbitrary. Greiner makes that clear in his
book "Field Quantization" by delaying the choice of a basis for as long as
possible. Eventually he chooses a basis of momentum eigenstates, like
everyone else does. But I've wondered what you could do with, for
instance, a basis of hydrogen orbitals. I know from condensed matter,
another study where quantum field theory is usefully applied, that the
choice of a basis can make the difference between a practical solution and
a mess, although theoretically the choice of a basis makes no difference.

I clearly said that only propagators on R-QFT are formal propagators
for asymptotic scattering. Care! do not confound quantum field theory
with relativistic quantum field theory. Full bounded states are defined
in nonrelativistic quantum field theory. The only defined states on
relativistic quantum field theory are free fields and whereas that can
be useful in certain regimes of condensed matter (basically when
thermodynamic limit applies) the R-QFT is not applied to a single
molecule of water.


Juan R.

Center for CANONICAL |SCIENCE)

Juan R. wrote:

So I haven't specifically seen bound state problems solved in QFT, but I'm
suspicious of claims that they can't be.


Difficult to believe that you can find them because the only physical
states on R-QFT are free particle states. There is nothing on R-QFT as
the wavefunction of two bound electrons.

By a well-known theorem, poles of the S-matrix are located at energies
corresponding to bound states. Since renormalized R-QFT can calculate
the S-matrix with perfect accuracy, it can also find the bound
state energies. That's what is done in the Bethe-Salpeter approach.

The problem, however, is with finding the wave functions of these
bound states in the framework of R-QFT. I agree with you that
R-QFT has no consistent solution for the wave functions.

This
becomes clear from the following point of view: If we know energies
and wave functions of stationary states then we can reconstruct the
full Hamiltonian. However, there is no finite Hamiltonian in
R-QFT. In the renormalized theory, the Hamiltonian expressed in terms
of bare particles has infinite counterterms.

The simple and natural solution for both energies and wave functions
of bound states is given by the "dressed particle" approach.
A finite Hamiltonian can be found by a unitary transformation of the
R-QFT Hamiltonian. The usual diagonalization of this
Hamiltonian provides the solution for bound states.

See, for example,

Shebeko, A. V.; Shirokov, M. I., Unitary transformations in quantum
field theory and bound states, nucl-th/0102037

Eugene.

In article om,
wrote:


"Judge not, and ye shall not be judged."

Usenet has taught me that this is not true.


--
"The main, if not the only, function of the word aether has been to
furnish a nominative case to the verb 'to undulate'."
-- the Earl of Salisbury, 1894

Gregory L. Hansen wrote:
In article om,
wrote:


"Judge not, and ye shall not be judged."

Usenet has taught me that this is not true.

Amen.



--
"The main, if not the only, function of the word aether has been to
furnish a nominative case to the verb 'to undulate'."
-- the Earl of Salisbury, 1894

Juan R.:

Bilge ha escrito:
i.e., the uncertainty relations permitting the short term violation
of conservation of energy.

This is a common misconception.

Then tell eugene. Do you make a habit of quoting out of context?


This means that there exists a substance
that penetrates everywhere, effects real things, but cannot be
directly observed. This looks very much like long forgotten aether.

Only to you.

This is not correct. Similar claims were done by people so smart like
Einstein, Dirac or Feynmann or Wheeler between others.

You mean they told eugene the same thing?

As history showed us, physics is doing much better if such
unobservable "substances" like aether or virtual photons are removed
from the theory and the theory is formulated in terms of directly
observable things, like real physical photons, electrons, etc.

Please explain precisely how to observe a real electron. Every
signal which is observed from a detector is observed through the
forces produced by virtual interactions, i.e., the motion of an
indicator on a meter, the chemical reactions in ones retina
which propagate via more chemical reactions through the visual
cortex, etc. I could claim the exact opposite with greater
veracity. Give me a single example of any observation in which
the final step in the observation involves any of the free
particles you call real.

It is well known that fields are -by definition- unobservables, and
that one only measure particles and motion of particles. Have you read
chapter 3 of Weinberg manual? There Weinberg clearly states that one
measures in particle physics experiments are particles. One NEWER
measures fields.

Try posting something without deliberately misconstruing what
I've written.


In fact your above discussion proves that you do not know even that a
field is!!!! Even if one does the hyphotesis of the field exists and
even if one does hypothesis one is measuring via meters, chemical
reactions, etc. One is NOT measuring the field.

You appears to mix the concept of *FIELD* with the concept of *strengh
of the FIELD* at one point.

That is, even if could prove that we are measuring the *strengh of the
FIELD* at one point x in an instant t, that is VERY different from
proving that the FIELD exist. If you want prove that field exist, you
would measure the *strengh of the FIELD* not only in the point where
the test particle is sited. You may also measure the *strengh of the
FIELD* in the rest of points of the universe (even beyond observable
universe) and remember that you cannot use tests particles (because if
you use test particles you are measuring really forces newer fields).
Can do that guy? Can you prove that fields exist?

Juan R.

Center for CANONICAL |SCIENCE)

Eugene Stefanovich:


Bilge wrote:

On the other hand, it's very easy to see how specific diagrams contribute
to observable effects. For example, the diagram,

\ is the first order correction to the magnetic moment.
.\ It is easily interpreted that way, too. The virtual
. \ photon which connects to the ingoing and outgoing
. /~~~~ electron lines carries momentum. That modifies the
/ momentum at the vertex in the middle. A charge which
/ scatters from the electron then sees the modified
momentum present at the middle vertex which connects
the exchanged photon.


Does it bother you that this graph makes infinite contribution to
the scattering amplitude?

No, because I didn't include the two other graphs that go with
that one.

Bilge wrote:
Eugene Stefanovich:


Bilge wrote:

On the other hand, it's very easy to see how specific diagrams contribute
to observable effects. For example, the diagram,

\ is the first order correction to the magnetic moment.
.\ It is easily interpreted that way, too. The virtual
. \ photon which connects to the ingoing and outgoing
. /~~~~ electron lines carries momentum. That modifies the
/ momentum at the vertex in the middle. A charge which
/ scatters from the electron then sees the modified
momentum present at the middle vertex which connects
the exchanged photon.


Does it bother you that this graph makes infinite contribution to
the scattering amplitude?

No, because I didn't include the two other graphs that go with
that one.

Does it bother you that these additional graphs result from
infinite renormalization counterterms in the Hamiltonian?

Infinite Hamiltonian operator doesn't make sense, does it?

Eugene.

Juan R. wrote:
Eric Gisse ha escrito:

Juan R. wrote:
Eric Gisse ha escrito:

Wald obtains the correct potential and the correct definition of
acceleration (a = -del*phi) on page 77.

MTW and "Spacetime and Geometry" obtain the same metrics as Wald.

I fail to see what you are complaining about.


Exactly! You see page 77 of Wald and you think "equation (4.4.21) of
Wald is Newtonian law".

I should have qualified that by explaining what phi was. My mistake.

The phi obtained is GM/r.

already explained why Wald equation is not Newtonian equation!! I will
explain again Phy (x,t) is not Phy(R(t))

I repeat myself, because it bears repeating.

There is *no* time dependence in the potential in Newtonian
gravitation.


'r' in Wald equation is not 'r' in Newtonian equation. Moreover, 'GM/r'
in Wald equation contains c in a hidden manner via retardation of the
field. 'M' in Wald equation computed at t_{ret} is not 'M' in Newton
equation computed at tau, etc.

That is because GR is not Newton.

Considering how the potential is derived, I am going to disagree and
say the Ms are the same. But if you are insistant, you can work out the
Komar integral for this case and see what you get, which I think I
should do as an exercise anyway.



Moreover, i already explained why the rest of the equation and
derivation are just wrong.

....except that your entire line of thought is poorly concieved.


The derivation is incorrect as i will prove AGAIN.

1) Derivation in the linear regime is WRONG.

In the linear regime a=0; newer (repeat NEWER) a=-grad (Phi). In fact,
you see Wald derivation and you believe because you have not revised
details -see below- that derivation is correct -just as you cite the
MTW- but derivation is INCORRECT. The linear regime predicts a=0 and
Newtonian gravity predicts a = - grad(Phi).

["NEWER" ?]

That isn't a proof, that is a statement unsupported by fact.

Read Wald before doing irrelevant claims. Wald clearly proves why in
the linear regime a=0.

I guess on page 77, where acceleration is trivially not zero, is
clearly a mistake in my reading comprehension abilities.



***Therefore GR does not reduce to NG in the linear regime***. Usual
textbooks are wrong.

Then if you cannot understand an elementary derivation WHY are you
doing wrong claims? Note i would be not as hard with you if you had
claimed "Hey Juan R. I think that you are not correct by this and
this". But you categorically claimed "you wrong" even without the most
basic understanding of the topic!

Again, I remember you that we are doing serious stuff, this is not
string theory or general relativity, this is canonical science.

*snicker*

Read elementary stuff and after understanding basic stuff read more
advanced literature and after understanding it continue reading still
more advanced literature. Do not make irrelevant claims at first
undergraduate level.

Well if you say so, I must follow for you are a member of the Center
for CANONICAL |SCIENCE)



If you have time you would read pag 78 of Wald:

"If one stays consistently within the linear approximation, one
predicts that test bodies are unaffected by gravity. Thus, in obtaining
equation (4.4.21) we actualy have gone beyond the linear
approximation".

That is the reason why i said that Wald derivation is NON-linear, since
in the strict rigorous linear regime a=0. All textbooks claiming that
in the linear regime a is different from zero are wrong and simply are
modifing *reality* for consistency with Newtonian law. Ok, then next
Wald claims that in the non-linear regime, the derivation is already
correct, but, again, that is not true.

How you extend a=0 from just test bodies to ALL bodies is a mystery
beyond my understanding.

I guess it is easier to assume that everyone is wrong and you are
right, I suppose.

What is the link of this nonsense with Wald's proof on linear regime a
= 0 and gravitation is not correclty modelled? Do you know that word
'proof' mean?

I guess on page 77, where acceleration is trivially not zero, is
clearly a mistake in my reading comprehension abilities.

Read, and understand, your sources before you cite them.



2) Wald (4.4.21) is not Newton equation. The 'Phi' in (4.4.21) is not
Newtonian potential it is a retarded LW potential. The 'a' in (4.4.21)
is not Newton aceleration because 'x' is not Newtonian 'x'. Moreover
't' in (4.4.21) is not Newtonian time.

I am not going to argue about this when it is all explained on the very
same page which you are referencing.

Nonsense. Wald is just deriving the weak field slow velocity limit
which is NOT the Newtonian limit. The Newtonian limit is in rigor the
c-- infinite limit. Do you know NC theory? Perhaps you would study
first before doing claims...

Would a rose by any other name smell just as sweet?

Small pertubation, weak field, slow particles [although extendable].
Newtonian limit!


If you think a = -del*phi isn't the Newtonian potential, your
understanding of Newton is suspect.

It is not 'if your think'. You appear unable to distinguish between a
Newtonian potential with functional dependence phy = phy(R(t)) with the
nonrelativisitc limit of a LW 'potential' -really field- with
dependence phy = phy(x, t). I only can recomend to you read literature
on the topic. I cited several articles where the correct dependence is
highlighted. Also cited a chapter on a well known book on dynamics (the
Goldstein). I also cited a web page where you can see the diference on
functional dependence. No worry i will cite again the online page.

Look the first V in http://www.mathpages.com/home/kmath527/kmath527.htm

That is a potential with functional dependence V = V(R, dR/dt)

Taking limit c-- infinite one recovers Newton potential V = V(R) =
V(R(t))

a = -del * phi

phi = GM/r.

r = sqrt( (x-x_0)^2 + (y-y_0)^2 + (z-z_0)^2)

NO TIME!

If you are going to be so nitpicky about my definition of Newton you
shouldn't be so lax about yours.


Now scroll down the page and looks in the LW potential just before
equation (2). The phy in Wald equation has the same functionality phi =
phi(x, t). There are published literature (i already cited) where it is
proven that mathematically the phi(x, t) is incorrect.

Moreover V(R(t)) is different from V(x, t). Do you know what is a
function?

Moreover you just ignore the rest of criticisms.

Instead of correcting me, you just repeat your assertion so I have no
idea if I missed something or not.

I don't care about Lagrangian formalisms, mostly because I am not
familiar with them.


What is more, (4.4.21) is not a nonrelativistic equation because it
contains c in both terms left and right and this is an authentic
absurdity. Non relativistic equations do not contain c. Moreover, the
metric used by Wald also contains c and does not correspond with
Newtonian physics.

It is close enough. If you want authentic Newton, use Newton. I really
don't understand why you are complaining about this...

No, that 'option' is not valid on physics. 'Close enough' is not
suficient. Or you can explain data or cannot explain data. In Wald
equation experimental data is not explained and this is the reason that
authors doing serious research in the topic does not follow that way.

If GR cannot reduce to NG then GR is unable to explain experimental
data that Newtonian gravity CAN explain.

Newtonian gravitation can't explain **** no matter how much you patch
it up because it is *wrong* at a fundamental level.


Moreover, GR says that gravity is caused by spacetime curvature and in
the nonrelativistic limit there is no curvature, therefore the causal
structure is just wrong.

No, it means Newton is wrong since Newton fails to predict correctly
and GR does. Expecing a correct theory to be incorrect is....pointless.


Then one has the same problem that with relativisitic quantum field
thoery that cannot explain non-relativistic quantum mechanical
experiments. In Dirac words:

"Most physicists are very satisfied with this situation. They argue
that if one has rules for doing calculations and the results agree with
observation, that is all that one requires. But it is not all that one
requires. One requires a single comprehensive theory applying to all
physical phenomena. Not one theory for dealing with non-relativistic
effects and a separate disjoint theory for dealing with certain
relativistic effects."

My QFT book isn't here yet.


You cannot use GR for computing certain relativistic phenomena (light
bending radar delay, Mercury perihelion, etc) AND Newtonian gravity for
computing other phenomena. for example computer programs use Newtonian
gravity for computing orbits and in the final step time delays for
aparent image of celestial bodies or formulas for correcting perihelion
are introduced /ad hoc/. That is more, both theories GR and NG are so
incompatible as GR and QM.

Oh please.

Whine about the semantics until you run out of breath and die, the weak
field limit of GR predicts correctly, even if its simply deflecting
your massive ego.

Just because *you* do not understand how they are derived does not mean
they are done ad-hoc.

But yes, GR and NG are incompatable because one is correct and the
other is WRONG. GR can reduce to the Newtonian limit to explain things
with easier math but that doesn't mean you should expect GR to reduce
to Newton exactly.




We need is a NEW gravitational theory explaining all phenomena,
relativistic and nonrelativisitic, and without the further difficulties
of GR (self-action, singularities, problem of energy, quantization,
frames, etc.).

What makes you think the new theory will be any nicer than GR?



3) Moreover functional dependence is wrong. In (4.4.21), phy = phi(x,
t). In Newtonian physics, phi = phi(R(t)). Wald simply writes 'phy',
without details, and then it appears that one has derived Newtonian
law.

The details you seek are between 4.4.20 and 4.4.21. Wald simply writes
"phi" because he DID explain it not but a moment before.

But since you have a bit of difficulty reading, I will explain.

phi is dependant on x^i, i=1,2,3. It is explained, as I said, on the
very same page of which you reference. phi is not dependant on time -
it is explained, as I said, on the page of which you reference.

When I said your understanding of Newton is suspect, I was correct. In
Newtonian gravity, phi is dependant on r, not t.

You obviously do not understand.

In Wald derivation, phy = phi(x, t) is a LW potential (field). Taking
the limit of low motion does that retardation effects in velocity are
negigible but those do not make t dissapear`since is stiull present in
te retarded density. In fact the 'M' in Wald LW potential is M =
M(t_{ret}) because that term is independent of velocity.

The potential is static, like the metric. No time dependance. It is
written explicitly many times, too.

Where do you get this ****?


Even ignoring time dependence of M and writting just phy = phi(x) THAT
is NOT Newtonian potential because Newtonian potential functional form
is

phy = phi(R(t)) = phi(R)

and R is different from x and moreover CONTAINS implicit time
dependence on t, because R = R(t).

Still even ignoring all of this the a in a = -grad(Phi) is not
Newtonian a.

I cannot fix your reading disabilities, so I am not even gonna try.

[snip]


The metric for flat space, with c restored, is diag(-c^2,1,1,1)
assuming the -+++ sign convention.

But that is not the correct metric. Take a basic book on SR, EM,
particle physics, etc. The metric is (1 -1 -1 -1). The c is NOT
introduced into the metric, the c is introduced into the x^0 component
of spacetime.

Do you even know what you are talking about?


I already cited an online textbook on GR

pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf

see page 2 of Sean Carrol basic manual, x^0 = ct and the metric is (1
-1 -1 -1). Carlip does x^0 = t and his metric is (c^2 -1 -1 -1), which
is wrong. For example, in Carlip's wrong metric there is not
four-currents because the c term in the temporal dimension is mising.
Moreover, Carlip obtains a full couple of mistakes in the limit c--
infinite as proven.

Carrol works in units where c = 1, it is explained many times
throughout his book which I have sitting below Wald. It is also where I
learned what I know sofar.



Therefore if GR was a consistent theory would have no gravity.

That is stupid. Seriously, it is.

It is well-known that GR is not a consistent theory of gravity. It is
also known by people who has done serious stuff in Newtonian limit (and
Carlip is not one of them) that the Newtonian limit cannot be obtained
from GR without invoking aditional equations and ad hoc postulates.

It serves no purpose to speculate about what Steve Carlip thinks or
does. Especially by people who make assertions such as "GR is
inconsistent".



Carlip has done an attempt to derive Newtonian limit on both
sci.physics.resesarch and sci.physics.relativity but:

i) He uses a wrong metric that forces to us to rewritte all relativity.
For example, in his nonstandard approach there is no four currents and
there is not four space. The EM four 'current' is a strange mixture of
densities and true currents in Carlip nonstandard approach.

Where did your nitpickery go? In Newton there is no 4-anything.

I was talking of the Minkoskian limit of Carlip wrong metric when i
talked of Em currents, it is obvious!!! Moreover, you do not understand
Carlip's approach. In my approach the nonrelativistic limit of (ct, x)
looks like (infinite, x). the zero-dimension collapses and one is
forced to use a 3-space parametrized by the invariant tau. In Carlip
wrong approach, his nonrelativistic limit is (t, x) and one obtains a
four spacetime which has no sense in the newtonian limit!!!

hahahahahaha


My metric is standard, verifies all experimental data and is consistent
with particle physics, special relativity and Maxwell EM. Moreover my
chossing of metric is recommended by Astronomical societies.

Ooooh.

??????

It all makes sense now. Actually learning and changing your opinions is
impossible for you because you have a vested interest in how you
currently have your theory written - no matter how absurd it is.

I stopped taking you seriously at all right about....here.

That is you ignore published literature, you ignore math, and you put
in words of one author the mistakes done by other authors. For example
you critize to me that in your words "In Newton there is no
4-anything." when precisely i am obtaining a 3-space and Carlip is who
obtained a wrong 4-space with time like a dimension, which is a
complete absurdity!!!!

Allowing one component of the metric to go infinite doesn't mean it
goes to zero and you can treat it as good ol' 3-space.



ii) Carlip takes the wrong spacetime (t, x) which looks like (t, x) in
the nonrelativisitc limit. That is, Carlip think that in Newtonian
physics time is a dimension which violates the most basic understanding
of Newtonian physics!!!

God, stop whining.

GR isn't Newton because they are fundamentally different. To expect
otherwise is foolish.

Or either you obtain Newtonian physics exactly or your theory is just
wrong. Moreover you appears completely ignorant of NC theory and
similar.

Thats a new one.

"Either your theory reproduces an incorrect theory, exactly, or it is
WRONG".


In my own spacetime (ct, x), the limit is the correct (infinite, x).
The zeroth dimension of spacetime collapse, doing time as dimension a
wrong concept, and this is good. One recovers time as an evolution
parameter (x^0 collapses by t does NOT collapse), WHICH is the correct
Newtonian concept of time. In any elementary textbook of mechanics one
can verify that the state of the system is (p,q) parametrized for one
single evolution parameter t called absolute Newtonian time.

Sounds like you are one of those MOND people, except with 100% more
crank.

Your insults do not mistakes. Perhaps you would read a basic textbook
on Newtonian physics...

Is Symon suitably basic for your cultivated tastes?


Your usage of "collapse" is completely unmotivated and confusing.

No it is not, the collapse of the topology of the dimension zeroth does
you cannot use it as a valid physical dimension distance between two
physical intervals is of measure zero, and only other three dimensions
survive. Curiously this is also 'predicted' by NC theory. Yes NC is
just complex enough for doing not appear in the Wald or in other
elementary textbooks but does not mean that was not a research topic.

If you tell the time dimension to **** off by allowing c to be infinite
you have a metric that is unchanging in time because time nolonger has
a meaningful existance.

Obviously the "NC" theory predicts it because you have been vague about
what exactly the "NC" theory is. In fact, not once have you explained
what "NC" theory is.



iii) By taking the wrong spacetime and wrong limit, Carlip obtains the
functional dependence Phi(x,t) when the correct dependence in
Newtonian physics is Phi(R(t)) because time is NOT a dimension in
Newtonian physics and interactions are not field-theoretic ones.
Moreover, there are difficulties with the use of Phi(x,t) for example
violation of causality in the transition to stationary regimes, etc.

Get the functional dependance of phi correct and try again.

?????

I am obtaining the correct functional dependance R(t). It is Wald and
Carlip and other who obtain incorrect dependence (x, t)!!!

"Why is everyone stupid but me?" [Sorry Gregory].



My work on gravity corrects this and one obtains the correct functional
dependence without lack of continuity, etc.

Your "work" on gravitation is based on Newton and GR's Newtonian limit?
Are you kidding?

You do not understand.

iv) Carlip choosing of wrong spacetime and wrong metric does that he
obtains a nonzero 00-connection. This is wrong. In GR, the covariant
derivatives are physical derivatives, therefore in Carlip approach the
only measured (physical) derivatives are

What the hell is a "physical" derivative? It sounds like you are
inventing new terminology as you go along.

New terminology? "Physical derivative" is a standard term. I explain
again, in presence of a nonzero 00-connection the flat derivative is
unobservable ad this is the basic reason for the minimal coupling
standard rule

google.com "physical derivative" 203 hits. Perhaps some standards are
more standard than others.


flat derivative --- covariant derivative.

Only in flat space, which in the linearized limit is manifestly NOT.


The reason the 00 connections are nonzero is because of the metric. If
you wish to argue about that, you will have to dig a little deeper and
complain about how the metric was derived.

If the 00 connection is not zero you are forced to substitute the flat
derivatives by covariant ones in the Newtonian limit. In Newtonian
physics the physical derivatives are flat ones.

You aren't getting it. GR is not Newton.



This is of course WRONG, any textbook of Newtonian mechanics explains
that the correct derivatives are usual partial ones.

For the love of god, stop whining. This is a different theory. It is
not Newton.

WE ARE ATEMPTING TO OBTAIN THE NEWTONIAN LIMIT. THEREFORE YOU MAY
OBTAIN ALL OF NEWTONIAN LIMIT.

Except for the wrong parts, which is most of it.


In fact, this is the reaos that textbooks only focuse on the derivation
(so say) of Newtonian law for one single body. Newtonian mechanics is
not equivalent to Newton law for an single body. Newtonian mechanics is
some more.

Fine. You derive a nice closed-form way of working with multiple bodies
in GR. It might take awhile though.


For example what is the continuity equation in Carlip approach.


In my own work, the 00-connection is zero therefore Newtonian
derivatives are partial ones. This is correct.

..and you get a = 0

Completely WRONG, you have no idea. The 00-connection is zero but a is
NOT zero if you are computing the nonrelativistic limit of the
trajectory ;-)

If all the connection coefficients are zero, which is what you desire,
then there is no acceleration. It is flat space.


Which is....incorrect.

Incorrect is your profound misunderstading of even the most elementary
stuff.

I have been known to make the occasional profound misunderstanding or
three.


Moreover the physical derivative is the flat one just as in Newton
physics.

I am going to assume you mean total derivative, because you don't
explain what a physical derivative means.



v) The scalar curvature in Carlip approach is R = R_00/g_00. Since he
introduces the c^2 term into g_00, in the limit he obtains R -- 0.
That is, in GR, gravity is spacetime curvature, even ignoring all four
points of above doing Carlip derivation just wrong, one obtains that in
the nonrelativistic limit the curvature of spacetime is ZERO. If A is
the cause of B, then elimination of A may eliminate B. The curvature
interpretation of GR is not only artificial (as proved by teleparallel
gravity or FTG) is also incorrect.

So what are you saying, R *doesn't* go to 0 as r goes to infinity?

?????


In my own metric, the curvature is zero as correspond to Newtonian
physics. Are you heard in some textbook of Newtonian physics that
spacetime, time, or space is curved?

*sigh*

GR IS NOT NEWTON.

WE ARE ATEMPTING TO OBTAIN THE NEWTONIAN LIMIT. THEREFORE YOU MAY
OBTAIN ALL OF NEWTONIAN LIMIT not just the part what is of interest for
you and the part that is not of interst for you because breaks the
consistency of GR just is ignored. Ignorance of data is not a good
attitude for a scientist

Newton is wrong.

Why do people here have such a hard time grasping that simple fact?


GR IS NOT NEWTON.

To expect otherwise is foolish.

Is wait that GR reduce to the correct Newtonian limit foolish?

Nope, but to expect GR = Newton at that limit is.


Is "your own metric" even a valid solution to Einstein's field
equations and does it even reduce to the Newton at the proper limit?

??????

I guess not.



vi) In the derivation from GR one may fix the 'gauge'. Carlip uses
asymptotic limit. This is again wrong. As explained by Christian,
Penrose and others, the island asumptions is ***experimentally***
false.

BFD.

You are looking for something to complain about. The "island
assumption" is perfectly valid because we aren't trying to find the
metric of the universe, just for a specific case under specific
assumptions.

Yes it is so valid that we know that is experimentally invalid. Great!

"However, physical evidence clearly suggests that we are not living in
an 'island universe' (cf. Penrose 1996, 593-594) - i.e., universe is
not 'an island of matter surrounded by emptiness' (Misner et al. 1973,
295)."

Again, BFD.

I understand what he is saying, and he is exactly correct, but its a
GOOD ENOUGH approximation.



Other people, as Christian, does use of aditional equations and
constraints do NOT derived from GR.

There is still more points and very very sophisticated that i do not
discuss with Carlip, but since he is unable to recognize difference
between a Newtonian potential (R(t)) and the nonrelativistic limit of a
retarded LW field (x, t), i consider unnecesary to discuss advanced
stuff with him.

Get the functional dependance of phi right first.

I already obtained the correct functional dependence (R(t)). From GR,
one obtains the incorect functional dependence (x, t).

Sure, why not? Making it up as you go along is fun sometimes.


I see it as you are advocating a pet theory of your own and you haven't
dedicated the necessary time to properly learn GR. You keep making
mistakes, and often repeat them even when corrected by others.

It is really interesting as people who has studied those points on
detail concide with me.

I would suggest you make sure those people know what the hell they are
talking about before letting them be advocates of your pet theory,
otherwise it makes you look stupid.


But do not worry if you want believe that GR reduces to NG in the
linear regime you can do it : -)


Juan R.

Center for CANONICAL |SCIENCE)