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| Robert L. Oldershaw... |
 Posted: Wed Oct 21, 2009 1:35 pm |
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Regarding arxiv:0910.3374v1 (another just-so story)
Hogg says: "a fractal universe is untenable".
He looks at nature and can only see a homogeneous blur.
Ah, but the porcines are so notoriously near-sighted, don't you know.
RLO
www.amherst.edu/~rloldershaw |
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| Roger Bagula... |
| Posted: Thu Oct 22, 2009 7:12 am |
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On Oct 21, 4:35 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]Regarding arxiv:0910.3374v1 (another just-so story)
Hogg says: "a fractal universe is untenable".
He looks at nature and can only see a homogeneous blur.
Ah, but the porcines are so notoriously near-sighted, don't you know.
RLO
www.amherst.edu/~rloldershaw
[/quote]
This paper is an essay pushing one sort of model:
what he calls ACDM and contrasting it in words only to the DGP
and fractal universe type models.
He calls the fractal model "inhomogeneous".
He talks about the Darwin ship Beagle
without really seeming to know that the sand pile self-organization
type fractal model is the best one known for evolution
on all physical scales.
What he is saying has been the doctrine of
Cambridge educated cosmologists who dominate
the world at the moment.
That he says it really doesn't make him less ignorant,
it appears.
That he doesn't back it with equations, but relies on argument
shows that he really isn't prepared to back his words up
with actual facts?
Since it is an essay we are free to argue and disagree
from our own base of facts.
1) galaxy distributions are Levy flights distributions
2) black hole mass scales seem quantum
and not homogeneously distributed or continuous.
3) distributions of planets/ asteroids in all known solar systems
are Henon type area conserving fractals
4) at the particle level the mass scale appears to be alpha
in a quantum massive form
So the evidence in the evidence of the information that we have
is that the universe in it's distribution of mass
is quantum and scaled from the smallest to the largest.
Roger Bagula |
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| Roger Bagula... |
| Posted: Thu Oct 22, 2009 7:22 am |
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On Oct 21, 4:35 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]Regarding arxiv:0910.3374v1 (another just-so story)
Hogg says: "a fractal universe is untenable".
He looks at nature and can only see a homogeneous blur.
Ah, but the porcines are so notoriously near-sighted, don't you know.
RLO
www.amherst.edu/~rloldershaw
[/quote]
Robert L. Oldershaw
I think that name calling
as bad as the essay paper appears to be
is in bad taste:
http://howdy.physics.nyu.edu/index.php/Hogg
You can contact time directly with your comments at:
david.hogg at (no spam) nyu.edu
Really essays like this "proving the existence of God"
were historically part of theology, not science.
The doctrine changes with time
but university the pedagogy doesn't.
Roger Bagula |
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| Roger Bagula... |
| Posted: Thu Oct 22, 2009 11:24 am |
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http://www.merriam-webster.com/dictionary/homogeneous
Main Entry: ho·mo·ge·neous
Pronunciation: \-ˈjē-nē-əs, -nyəs\
Function: adjective
Etymology: Medieval Latin homogeneus, homogenus, from Greek homogenēs,
from hom- + genos kind — more at kin
Date: 1641
1 : of the same or a similar kind or nature
2 : of uniform structure or composition throughout <a culturally
homogeneous neighborhood>
3 : having the property that if each variable is replaced by a
constant times that variable the constant can be factored out : having
each term of the same degree if all variables are considered <a
homogeneous equation> |
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| Robert L. Oldershaw... |
| Posted: Sat Oct 24, 2009 4:15 pm |
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On Oct 22, 5:24 pm, Roger Bagula <roger.bag... at (no spam) gmail.com> wrote:
[quote]
---------------------------------------------------------------------------------[/quote]
From COSMOCOFFEE Blog
----------------------------------------------------------------------------------
Greetings High School "Anonymous",
I am confused by your question. General Relativity already
demonstrates how to calculate and understand the advance
in the perihelion of Mercury.
General Relativity is the theory of gravitational interactions
involving Stellar Scale systems [technically within a Stellar
Scale system but exterior to any Atomic Scale system].
I really don't think I can improve upon GR in this context,
especially with high school math.
If you ask me to model something on the Atomic Scale,
it might be a more interesting request.
Have you thoroughly studied:
http://arxiv.org/ftp/physics/papers/0701/0701132.pdf
Already published in ApSS, 2007.
This paper explains how, in a discrete self-similar cosmos,
GR must be modified in order to model the dynamics of
Atomic Scale or Galactic Scale systems.
Here's something really ironic. GR can be abreviated: R = kT.
In groping for a unified theory that would apply in the microcosm
as well as the macrocosm, theoretical physicists tinkered with
the R and the T, but assumed that the k was inviolate and
therefore of little interest.
Actually it is in the k = 8piG/c4 that the needed breakthrough
was waiting all along. If you want to know how the discrete
fractal scaling for k works, read the friggin' paper. But the
key concept is that G is not scale invariant [even t'Hooft
has finally figured that out. Well better 33 years late than never];
each Scale has its specific value of G and it only takes high
school math, actually only elementary school math, to understand
the scaling.
Please read the paper. Discrete Scale Relativity is the new
paradigm for physics in the 21st century. When the physical
characteristics of the dark matter are revealed, the new
paradigm will be fully vindicated. So far we see mostly the
high mass tail: neutron stars, BHs, gamma ray sources,
RRATS, etc, and there are billions of these ultracompact
objects, but the main DM components are in much lower
states and are stellar mass black holes with 0.1 < M < 0.7
solar masses.
Any questions?
Yours in the new paradigm,
RLO
www.amherst.edu/~rloldershaw |
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| Roger Bagula... |
| Posted: Sun Oct 25, 2009 9:30 am |
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When these cosmologist are talking about "homogeneous"
that means what Weyl calls the metric ground form
of the universe.
When the Poincare conjecture was confirmed as proved
then all the manifolds in the Thurston classification
of manifolds could be reduced by transform to a simple sphere
type manifold.
So they aren't talking about quantum gravity,
quantum masses or the groupings of matter in the observed universe
but the 3 manifold that is observed as being very close
to the Einstein general relativity in a 4 dimensional space-time.
Fractals of the Weierstrass or Biscovitch-Ursell/ Mandelbrot function
type
(which I named Mandelbrot space about 1993) are ones that
have derivative trouble ( disjoint, cusps, or points)
where the derivative can't be defined for the complete
metric or manifold ( they may have what are called quantum jumps , for
instance).
Weierstrass functions of this type were actually invented to
make an exception to the derivative limit.
So they are termed as hetro-geneous or inhomogeneous in terms
of their metrical behavior. To deal with this sort of
topology that gives inbetween/fractal dimensions
Hausdorff space was invented.
The distinction here is between the metric of the space-time
and that of the quantum clumps of matter that inhabit it.
To put this in simple terms:
They are looking at the hole in the donut
and we are looking at the donut.
The relationship of particles ( bosons and fermions ) to black holes
is sometimes thought of as that of self-similar "holes"
in the structure of the metric ( toral self-similar geometry).
Let us say that at the Planck mass we have a particle singularity
and that using some scaling like alpha
we have other smaller ( electrons, protons, mesons, etc. )
and maybe larger
particles ( Black holes).
Then we also have a metrically singularity of a quantum sort.
The current theory is that the quantum particles in the
standard model of physics that deals with the symmetry breaking of an
SU(5) or Cartan A_4 manifold ( pure electromagnetic alpha structure
constant) to an
U(1)*SU(2)*SU(3) ( weak field U(1)*SU(2) , strong nuclear field of SU
(3)).
The Higgs Boson is the largest such particle that confers
mass to all the rest during the symmetry breaking mechanism.
This set of ideas is strongly believed by PHD's in physics
before they get their degrees: they mostly defend it
as a doctrine taken on the faith of their teachers in that model.
The idea that there may be self-similar levels of mass above and below
the Higgs
boson( that black holes may be a kind of very large boson)
is one that has been kick around since the 80's
and Mandelbrot's appearance on the scene.
Things like the Casimir quantum effect and the states
of very cold helium ( superfliudity, Bose-Einstein fluids/
condensates)
make the vacuum
seem to have other than homogeneous propertities
at very small distances and very low kinetic energies.
The discovery of other nonlinear higher derivative
waves in terms of solitons ( Korteweg and de Vries)
has also opened up new ideas in smooth differential
geometry.
The homogeneous concepts are thus a dated old way
of looking at the manifold of the space-time
without consideration of quantum gravity,
dark matter
and the probable quantum nature of the vacuum itself.
In other words we are dealing with a Clovis first sort of mentality
that has suppressed hundreds of factual discoveries, since
1920 in order to have a simple doctrine they can teach to undergrads. |
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| Robert L. Oldershaw... |
| Posted: Sun Oct 25, 2009 11:10 am |
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On Oct 25, 3:30 pm, Roger Bagula <roger.bag... at (no spam) gmail.com> wrote:
[quote]When these cosmologist are talking about "homogeneous"
that means what Weyl calls the metric ground form
of the universe.
When the Poincare conjecture was confirmed as proved
then all the manifolds in the Thurston classification
of manifolds could be reduced by transform to a simple sphere
type manifold.
So they aren't talking about quantum gravity,
quantum masses or the groupings of matter in the observed universe
but the 3 manifold that is observed as being very close
to the Einstein general relativity in a 4 dimensional space-time.
Fractals of the Weierstrass or Biscovitch-Ursell/ Mandelbrot function
type
In other words we are dealing with a Clovis first sort of mentality
that has suppressed hundreds of factual discoveries, since
1920 in order to have a simple doctrine they can teach to undergrads.
[/quote]
----------------------------------------------------------------------------
Interesting.
Tell me: (1) are you happy with the conventional Planck scale?
(2) Do you have any explanation for the hierarchy problem?
(3) Do you have any explanation for the vacuum energy density
disparity.
(4) Would you agree with t"Hooft that G might NOT be scale
invariant?
Yours in the new paradigm,
RLO
www.amherst.edu/~rloldershaw |
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| Roger Bagula... |
| Posted: Tue Oct 27, 2009 6:26 am |
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On Oct 25, 2:10 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]----------------------------------------------------------------------------
Interesting.
Tell me: (1) are you happy with the conventional Planck scale?
(2) Do you have any explanation for the hierarchy problem?
(3) Do you have any explanation for the vacuum energy density
disparity.
(4) Would you agree with t"Hooft that G might NOT be scale
invariant?
Yours in the new paradigm,
RLOwww.amherst.edu/~rloldershaw
[/quote]
Robert L. Oldershaw
You are an astronomy professor:
maybe you might want to clarify what you mean by:
1) the Planck scale
2) the hierarchy problem
3) vacuum energy density
4) G as scale invariant
I have tried to explain in simple terms what Hogg
probably meant.
Why don't you try to do the same for what you mean?
and tell us how it relates to fractals and self-similar sets
or affine sets.
Try to put it in terms a high school student
with just a little fractal math might understand.
Roger Bagula |
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| Roger Bagula... |
| Posted: Tue Oct 27, 2009 7:40 am |
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On Oct 25, 2:10 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]On Oct 25, 3:30 pm, Roger Bagula <roger.bag... at (no spam) gmail.com> wrote:
When these cosmologist are talking about "homogeneous"
that means what Weyl calls the metric ground form
of the universe.
When the Poincare conjecture was confirmed as proved
then all the manifolds in the Thurston classification
of manifolds could be reduced by transform to a simple sphere
type manifold.
So they aren't talking about quantum gravity,
quantum masses or the groupings of matter in the observed universe
but the 3 manifold that is observed as being very close
to the Einstein general relativity in a 4 dimensional space-time.
Fractals of the Weierstrass or Biscovitch-Ursell/ Mandelbrot function
type
In other words we are dealing with a Clovis first sort of mentality
that has suppressed hundreds of factual discoveries, since
1920 in order to have a simple doctrine they can teach to undergrads.
----------------------------------------------------------------------------
Interesting.
Tell me: (1) are you happy with the conventional Planck scale?
(2) Do you have any explanation for the hierarchy problem?
(3) Do you have any explanation for the vacuum energy density
disparity.
(4) Would you agree with t"Hooft that G might NOT be scale
invariant?
Yours in the new paradigm,
RLOwww.amherst.edu/~rloldershaw
[/quote]
The "hierarchy problem" has to do with the infinities that
Feynman renormalization theory was invented for:
http://en.wikipedia.org/wiki/Hierarchy_problem
The science newsman Baez has this page on the vacuum energy density:
http://math.ucr.edu/home/baez/vacuum.html
Aside: Baez is known for having given the fractal theory fellow
Michael Lapidus who
is a close personal friend of Dr. Mandlbrot
a hard time for checking out the same books as him.
(Lapidus's book on Feynman path integrals is rapidly becoming a
classic).
Baez also calls people he doesn't agree with cranks and puts them on a
list.
Reminds me of somebody up Mass. way doesn't it?
I have explained the Planck scale several times:
Suppose that you have a quantum particle radius at the limiting
velocity of c:
r= hbar/(m*c)
that has a gravitational singularity radius ( black hole radius) of:
r=2*m*G/c^2
such that they approach the same radius.
hbar/(m*c)=2*m*G/c^2
(actually Planck took out the two and solved for m)
He, then, plugged back in and got a radius as well.
Suppose that the black hole radius has a Sierpinski scale of two:
r[n_]=2^n*m[n]*G/c^2
That gives the quantum masses:
Solve[hbar/(m*c) == 2^n*m*G/c^2, m]
m[n_]=2^(-n/2)*Sqrt[hbar*c/G]
The Weyl gauge formulation of G goes like:where gamma is a Feynman
alpha like renormalization constant like that in the magnetic moments
of the electron and muon
as Feynman diagram weighted photon exchanges)
G=gamma*(hbar*c/e)
That gives:
m[n_] = 2^(-n/2)*Sqrt[hbar*c/G] /. G -> gamma[n]*(hbar*c/e)= 2^(-n/2)
*Sqrt[e/gamma[n]]
All these gamma[n]'s are close to one.
For n to get to the size of an electron or a super nova black hole
it has to be either large positive or large negative.
Each of the particles has an n like Feynman renormalization parameter.
The point Robert Oldershaw is making about the Planck scale is that
it is very far from any observed mass in the real universe.
The question about the scale invariance of G is pretty much answered
by this kind of Sierpinski scaling scheme using the Weyl gauge
for gravity.
The Baez spin foam sort of approach to the vacuum
seems to fit the Penrose tile idea and the Hadmard
self-similar approach to orthogonal conglomeration.
When you once get a photo large enough, you first make
neutrino pairs:
hv+vacuum-> nu(m)+nu(am)
That massive particle that violates the standard model of physics
is at this point in time the lowest known form of mass.
The extended uncertainty and the Parkeron observation
places another mass seen in the spectra of the formation of
supernova black holes of about 10^(-56) gm ( as a boson I think).
If we take out the gamma[n]'s,you get an hierarchy of masses
Table[2^(-n/2)*Sqrt[4.80325*10^(-10)], {n, -320, 160, 10}]
that starts at a black hole mass and ends just below the electron
mass;
\!\({3.2030734818744184`*^43, 1.0009604630857558`*^42, \
3.1280014471429868`*^40, 9.775004522321834`*^38,
3.054688913225573`*^37, \
9.545902853829916`*^35, 2.9830946418218486`*^34,
9.322170755693277`*^32, \
2.913178361154149`*^31, 9.103682378606716`*^29,
2.8449007433145987`*^28, \
8.890314822858121`*^26, 2.7782233821431628`*^25,
8.681948069197384`*^23, \
2.7131087716241824`*^22, 8.47846491132557`*^20,
2.6495202847892406`*^19, \
8.279750889966377`*^17, 2.5874221531144928`*^16,
8.08569422848279`*^14, \
2.526779446400872`*^13, 7.896185770002725`*^11,
2.4675580531258514`*^10, \
7.711118916018286`*^8, 2.4097246612557143`*^7, 753038.9566424107`, \
23532.467395075335`, 735.3896060961042`, 22.980925190503257`,
0.7181539122032268`, 0.022442309756350837`,
0.0007013221798859636`, \
0.000021916318121436364`, 6.848849412948864`*^-7,
2.14026544154652`*^-8, \
6.688329504832875`*^-10, 2.0901029702602734`*^-11,
6.531571782063354`*^-13, \
2.0411161818947982`*^-14,
6.378488068421244`*^-16, 1.993277521381639`*^-17, \
6.228992254317621`*^-19, 1.9465600794742567`*^-20,
6.083000248357052`*^-22, \
1.9009375776115788`*^-23, 5.940429930036184`*^-25,
1.8563843531363074`*^-26, \
5.801201103550961`*^-28, 1.8128753448596752`*^-29}\)
With the right gamma[n]'s these can be renormalized to the observed
scale masses.
At n=320 we get a Parkeron scale mass of:1.4995753382433074*10^-53
gram
So our quantum fractal self-similar vacuum model of a Sierpinski scale
2
can account for the observed particle physics.
That's is again my simple way of accounting for mass as a fractal
scale
based on gauge gravity theory and fractal geometry.
I'm not saying it is the "right" model,
just that it makes somewhat more sense than the present
standard model doctrine.
This approach also obeys Occam's razor:
http://en.wikipedia.org/wiki/Occam%27s_razor
I think that a larger scale like 137 might be better instead of 2^10
levels:
which is Prime[33]=137~1/alpha.
This long drawn out answer is my effort to give a balanced
picture of how a fractal self-similar model could
produce the observed physic of masses in the universe;
a word picture of how with simple equations.
Roger Bagula |
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| Robert L. Oldershaw... |
| Posted: Tue Oct 27, 2009 2:50 pm |
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On Oct 27, 1:40 pm, Roger Bagula <roger.bag... at (no spam) gmail.com> wrote:
[quote]
[/quote]
Firstly, I am not a professor!
Secondly, I am not an astronomer!
I am a student of nature.
(A) The Hierarchy Problem has many forms but the versions I am most
familiar with all trace back to the fact that the conventional Planck
mass [~ 10^-5 g] corresponds to nothing observed in nature and is
astronomically different from the masses of ALL well-observed
subatomic particles.
(B) The vacuum energy density crisis [HEP gives a value that is 10^120
times higher than is observed in cosmology] is very well known and can
also be traced back to the dopey conventional Planck Mass.
See: http://arxiv.org/abs/0901.3381 for a resolution of the VED crisis
AND the Hierarchy Problem.
(C) Maybe G is NOT scale invariant. This has been assumed since the
Pleistocene, but without any observational evidence to back it up.
Maybe each cosmological Scale has its own value of G, as would be
required in a discrete self-similar cosmos. Are you familiar with
fractals?
(D) John Baez is a world-class crackpot of the educated variety. Last
week he was babbling on about "spin foams" which probably are more
like theoretical bathtub scum. At sci.physics.research and at
sci.math.research I asked him if he could back up his glass bead game
speculations with ANY observational support. So far he has not
succeeded in coming up with anything to report on the subject of the
real world.
(E) Is it true that string theorists wear slippers with bells on the
toes?
Yours in the new paradigm [presented using only elementary school math
at www.amherst.edu/~rloldershaw ],
RLO |
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| Roger Bagula... |
| Posted: Wed Oct 28, 2009 6:54 am |
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On Oct 27, 5:50 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]On Oct 27, 1:40 pm, Roger Bagula <roger.bag... at (no spam) gmail.com> wrote:
Firstly, I am not a professor!
Secondly, I am not an astronomer!
I am a student of nature.
(A) The Hierarchy Problem has many forms but the versions I am most
familiar with all trace back to the fact that the conventional Planck
mass [~ 10^-5 g] corresponds to nothing observed in nature and is
astronomically different from the masses of ALL well-observed
subatomic particles.
(B) The vacuum energy density crisis [HEP gives a value that is 10^120
times higher than is observed in cosmology] is very well known and can
also be traced back to the dopey conventional Planck Mass.
See:http://arxiv.org/abs/0901.3381for a resolution of the VED crisis
AND the Hierarchy Problem.
(C) Maybe G is NOT scale invariant. This has been assumed since the
Pleistocene, but without any observational evidence to back it up.
Maybe each cosmological Scale has its own value of G, as would be
required in a discrete self-similar cosmos. Are you familiar with
fractals?
(D) John Baez is a world-class crackpot of the educated variety. Last
week he was babbling on about "spin foams" which probably are more
like theoretical bathtub scum. At sci.physics.research and at
sci.math.research I asked him if he could back up his glass bead game
speculations with ANY observational support. So far he has not
succeeded in coming up with anything to report on the subject of the
real world.
(E) Is it true that string theorists wear slippers with bells on the
toes?
Yours in the new paradigm [presented using only elementary school math
atwww.amherst.edu/~rloldershaw],
RLO
[/quote]
"Robert L. Oldershaw"
You would probably get further if you were nicer
to everybody?
John Baez is a relatively well recognized
web author and his "blogs" have over the years
at least gaven me stuff that I had to learn
to understand the physics better.
Conpaired to some of the physics crazies
John Baez is mild and relatively helpful.
You will really not get anywhere with the Infinities
and Heirarchy problem until you understand QED as Feynman
has organized it and his Feynman poton exchange diagrams
as physics graphs that represent changes of state.
Renormalization was invented for the infinities problem.
no one has yet a valid Gravitational renormalization
program
so that field still has vacuum and other infinity problems.
Roger Bagula |
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| Roger Bagula... |
| Posted: Wed Oct 28, 2009 7:06 am |
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Over the years I have come to distrust people
who think their approach is the only
and right approach to science or mathematics
and who abuse others for having different views.
It usually helps me to read more
and try to understand what others are talking about.
Roger Bagula |
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| Robert L. Oldershaw... |
| Posted: Wed Oct 28, 2009 11:54 am |
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On Oct 28, 1:06 pm, Roger Bagula <roger.bag... at (no spam) gmail.com> wrote:
[quote]Over the years I have come to distrust people
[/quote]
Loads of bad analysis [both personal and scientific], as usual.
At least you are consistent Roger. |
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| Robert L. Oldershaw... |
| Posted: Thu Oct 29, 2009 6:07 am |
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On Oct 28, 5:54 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]On Oct 28, 1:06 pm, Roger Bagula <roger.bag... at (no spam) gmail.com> wrote:
[/quote]
Good Morning Readers!
And it is a bright and shining day today!
Be sure to see the Oct. 28 issue of Nature: classical GR vindicated.
Spin foams and other quantum gravity fantasies falsified.
On the subject of gravitation, here is a nice example of a particle
physicist using his anti-Midas touch to turn gold into poop:
http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.5167v1.pdf .
Does the Perimeter Insitute have anyone who is interested in anything
besides Glass Bead Games, like maybe, reality?
Reading of the Day: http://arxiv.org/ftp/arxiv/papers/0708/0708.3501.pdf
Omigod, can that possibly be right? Oh Ya!
Yours in the new paradigm,
RLO
www.amherst.edu/~rloldershaw |
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| Robert L. Oldershaw... |
| Posted: Fri Oct 30, 2009 4:14 pm |
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On Oct 29, 12:07 pm, "Robert L. Oldershaw" <rlolders... at (no spam) amherst.edu>
wrote:
[quote]
Good Morning Readers!
Last night I was reading [2nd or 3rd time] Ivars Ekeland's[/quote]
excellent book "The Best Of All Possible Worlds" and the
revolutionary changes wrought by nonlinear dynamical
systems theory.
I was moved once again the ask the following
impertinent question:
Is Perfect Reversibility/Integrability A Myth?
Did Poincare discover this revolutionary idea
already during the 1892-1899 period when modern
chaos theory was founded in his "The New Methods
of Celestial Mechanics"?
Are the examples of "reversibility" that physicists
frequently cite actually one of two basic varieties:
(1) artificial idealizations that do not exist in the real
world [nature], or (2) systems that are briefly maintained
in periodic states, but whose full, and unmanipulated,
range of behavior includes periodic, semi-periodic,
quasi-static and fully chaotic states.
Bottom line: Are reversible/integrable "systems" very
limited artificial idealizations of true systems found in
nature, which are nonlinear dynamical systems?
What are the best examples of real world systems
that appear to be ideally reversible/integrable?
-----------------------------------------
On a related note, it seems to me that the
SubStandard paradigm is tottering around like an
embarrassing drunk. It's going down, and the sooner
the better.
The ingredients of the new paradigm are:
(1) Classical EM, (2) Classical GR, (3) Discrete
Scale Relativity, and (4) Nonlinear Dynamical Systems
Theory. These ingredients cannot be combined randomly
or with force. They must be carefully integrated by those
who study nature and have developed the intuition to do so.
Yours in the new paradigm,
RLO
www.amherst.edu/~rloldershaw |
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