Awareness of Nottale's scale relativity work
Christophe de Dinechin
awareness about Nottale's scale relativity work, and I would like to
know if you have an explanation. First, I let me give a quick
overview, since I have to assume that readers here are not familiar
with the ideas (this was apparently not discussed much on s.p.r since
about 2002).
Nottale starts with the following observation: there is a non-
dimensionless constant hbar that appears in Schrödinger's equation.
Just like c in Maxwell's equation suggested that there was a
"speed" (the speed of light) that did not obey the "normal" additive
combination of speed at the time (v = v1+v2), the existence of hbar
suggests that Planck's length is similarly invariant under the
"normal" multiplicative combination of scales (s = s1 * s2). For
special relativity, the solution was to state that c was indeed
invariant, and to use the Lorentz transform as the correct combination
law. Scale relativity, taking the log of scales, applies the same
reasoning. It postulates that Planck's length is indeed invariant by
scaling, and that the correct law for a change of scale is (after
taking the log) similar to Lorentz (Nottale called it non-Galilean).
Nottale developed the idea quite a bit. I will refer your to his
articles (http://luth2.obspm.fr/~luthier/nottale/ukdownlo.htm) or his
book ("Fractal Space time and Microphysics",
http://www.amazon.com/Fractal-Space-Time-Microphysics-Towards-Relativity/dp/9810208782).
The consequence of the postulate is that we need to give up
differentiability of space-time, which gives space-time a "fractal"
structure.
What I find particularly thought-provoking is the number of
cosmological predictions and retrodictions that this simple hypothesis
leads to:
- Large scale stellar structures (look at the pictures in section
4.4.3 of astro-ph/0310036, see also classification in astro-ph/
0310031) without any need for dark matter
- More than 3/4 of the anomalous Pioneer acceleration (gr-qc/0307042),
- An interesting toy model of the electron (http://luth2.obspm.fr/
~luthier/nottale/arDNB.pdf)
- Quantization of planetary systems (http://luth2.obspm.fr/~luthier/
nottale/arA&A322.pdf, http://luth2.obspm.fr/~luthier/nottale/arA&A315.pdf).
- Prediction of the structure of extrasolar systems (http://
luth2.obspm.fr/~luthier/nottale/ukmenure.htm)
That last result alone, which is a true prediction (made in 1996,
still verified today as far as I know), should in my opinion have
received a lot of attention. But my impression is that this work is
largely ignored. There is a striking constrat between string theory,
which has yet to make a single firm prediction that is not flatly
contradicted by experiments, but receives a lot of media coverage, and
scale relativity, which made a number of pretty detailed predictions
that were later confirmed, but which nobody seems to know about.
I don't know why this is. Maybe the mathematics is just too bizarre
and nobody wants to learn it. On the other hand, for me at least, it
does not require the same gigantic leap of faith ("it works therefore
it's mathematically valid") as, say, the renormalization group (to
take something that deals with similar issues).
So, any idea why physicists do not seem interested by this approach?
Is the work published in the wrong journals? Does Nottale have
insufficient connections within the research community? Is the work
clearly wrong but I can't see it?
dougsw...@gmail.com
The only web page that was reachable for me was the amazon page. All
other pages claimed: "The connection has timed out." That is one basic
reason :-)
For people who work on the edge of physics, I wish I could impose a
standard that all the math has to be run through a symbolic math
checker, such as Mathematica or Maple.
As a relevant example, the rotation profile of thin disk galaxies
doesn't work for two reasons: based on the mass seen by light and
using Newton's law of gravity (using GR would not materially change
the calculation), the predicted velocity profile falls off instead of
what is observed, which is the velocities are flat as R increases.
Less well known is that disk galaxies are unstable to a perturbation
along the axis: they should collapse when another galaxy passes by!
Any alternative must answer both problems, and be backed up
numerically.
I have my own differential equation I'd like to apply to this
problem. I've even found a description of the mass profile written as
an exponential function for one particular galaxy. Yet I don't
understand the nuts and bolts of elliptical integrals that were first
used by Alar Toomre to solve this problem. I also don't get how to do
numerical integration on the problem. I am not going to buy any
claims of a prediction from an independent researcher until it has
passed through a symbolic math package. Such software is a first
level screen, one that my own work has from time to time failed.
doug
Tom Roberts
> When I discuss with various physicists, I am surprised by the very low
> awareness about Nottale's scale relativity work, and I would like to
> know if you have an explanation.
How does this compare to "Doubly Special Relativity", in which there are
two invariant scales: the speed of light and the Planck length/mass/energy?
There are dozens of preprints on arXiv.org related to it.
Tom Roberts
Christophe de Dinechin
wrote:
> Hello:
>
> The only web page that was reachable for me was the amazon page. All
> other pages claimed: "The connection has timed out." That is one basic
> reason :-)
Yup, it seems to be down today. It worked when I posted. Well, you
should be able to get at least the arXiv articles, that's where the
pictures are ;-)
Christophe de Dinechin
> Christophe de Dinechin wrote:
> > When I discuss with various physicists, I am surprised by the very low
> > awareness about Nottale's scale relativity work, and I would like to
> > know if you have an explanation.
>
> How does this compare to "Doubly Special Relativity", in which there are
> two invariant scales: the speed of light and the Planck length/mass/energy?
One difference is about 10 years: the first DSR paper that I know of
was published in october 2002 (gr-qc/0210063), and does refer to
Nottale's work (section 9.2 and reference 51 in the above) dating from
1989 and 1992. I cannot say that I find the characterization of scale
relativity in 9.2 particularly enlightening, however.
Technically, they differ slightly in the mathematical apparatus being
used. ScR uses a lot of tools developed for fractals, and gives up the
hypothesis of differentiability, which I don't think DSR does. Having
read papers on both sides, I tend to find the predictions on the ScR
side much more clear-cut and convincing, but the mathematics much more
difficult to validate.
As far as predictions are concerned, they even have pictures comparing
the observed shapes with the predicted shapes (again, that's 4.4.3 in
astro-ph/0310036), even when the predicted shapes look pretty bizarre
at first sight for cosmic objects. I have never seen this kind of
precision on the DSR side, only comparatively vague statements.
In my opinion, DSR at the age of 6 (hep-th/0612280) had a lot less to
show than ScR at the same age. But maybe that's just me.
> There are dozens of preprints on arXiv.org related to it.
That's one aspect of this lack of awareness I was referring to. There
is also a Wikipedia entry for DSR, but not for ScR. That is so
peculiar, as Calvin would say.
Surfer
<chris...@dinechin.org> wrote:
>
>Nottale starts with the following observation: there is a non-
>dimensionless constant hbar that appears in Schrödinger's equation.
>Just like c in Maxwell's equation suggested that there was a
>"speed" (the speed of light) that did not obey the "normal" additive
>combination of speed at the time (v = v1+v2), the existence of hbar
>suggests that Planck's length is similarly invariant under the
>"normal" multiplicative combination of scales (s = s1 * s2). For
>special relativity, the solution was to state that c was indeed
>invariant, and to use the Lorentz transform as the correct combination
>law. Scale relativity, taking the log of scales, applies the same
>reasoning. It postulates that Planck's length is indeed invariant by
>scaling, and that the correct law for a change of scale is (after
>taking the log) similar to Lorentz (Nottale called it non-Galilean).
>
>Nottale developed the idea quite a bit. I will refer your to his
>articles (http://luth2.obspm.fr/~luthier/nottale/ukdownlo.htm) or his
>book ("Fractal Space time and Microphysics",
>http://www.amazon.com/Fractal-Space-Time-Microphysics-Towards-Relativity/dp/9810208782).
>The consequence of the postulate is that we need to give up
>differentiability of space-time, which gives space-time a "fractal"
>structure.
>
Something that impressed me is that the addition of this simple
postulate allowed Nottale to derive the Schrodinger and Dirac
equations.
The reason being, that if space-time is non-differentiable, then the
speed of an entity following a geodesic cannot be represented by a
single value, but rather needs to be represented by a combination of a
tendency to move forwards and a tendency to move backwards. Also, in a
non-differentiable space there are an infinity of geodesics between
any two points, so between measurements, the motion of a particle must
be represented by a wavefunction. The competing tendencies to move
forward and backward are encoded in a complex value--a real component
representing average motion, and an imaginary component representing
the difference between the back and forth tendences.
Raphael P Hermann showed that using these ideas "one can get numerical
prediction of quantum mechanical particle behaviour without using the
Schrödinger equation".
Numerical simulation of a quantum particle in a box
J. Phys. A: Math. Gen. 30 (1997) 3967–3975.
http://luth2.obspm.fr/~luthier/nottale/arRHeJPh.pdf
>
>What I find particularly thought-provoking is the number of
>cosmological predictions and retrodictions that this simple hypothesis
>leads to:
>- Large scale stellar structures (look at the pictures in section
>4.4.3 of astro-ph/0310036, see also classification in astro-ph/
>0310031) without any need for dark matter
>
I found those predictions very interesting also.
Good questions. I don't know the answers.
-- Surfer
Al.R...@gmail.com
wrote:
> Nottaledeveloped the idea quite a bit. I will refer your to his> book ("Fractal Space time and Microphysics",http://www.amazon.com/Fractal-Space-Time-Microphysics-Towards-Relativ...).
> So, any idea why physicists do not seem interested by this approach?
> Is the work published in the wrong journals? DoesNottalehave
> insufficient connections within the research community? Is the work
> clearly wrong but I can't see it?
I have the book and I am ashamed I had not noticed that Nottale
formula is the usual formula for electromagnetic mass of the electron
in function of a natural cutoff. For instance, EXACTLY THE SAME
FORMULA, except for 3/8 that is substituted by O(1) approximation,
APPEARS IN VOLUME 2 OF POLCHINSKI STRING THEORY BOOK: section 16.2
(Spacetime susy) formula 16.2.2.
The formula has being around half a century. The only merits of
Nottale are to suggest 3/8 and to suggest that alpha should be
evaluated in running, at the point $m_e$. The demerit is that he does
not point out that standard theory gives the same results. The mistery
is if nobody has told him.