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. 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 sci.physics.research since
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 or his book (Fractal Space time and Microphysics).
The consequence of the postulate is that we need to give up
differentiability of space-time, which gives space-time a “fractal”
What I find particularly thought-provoking is the number of
cosmological predictions and retrodictions that this simple hypothesis
- 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.
- Quantization of solar and extrasolar planetary systems.
- Prediction of the distribution of planets in extrasolar systems.
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 contrast 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 fractal mathematics he uses 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?