Hello Jerry, 

What do you mean by smallest possible scale? And can you clarify these degeneracies you are talking about? 

I find your comment about "exact description of nature" puzzling. Nothing is exact and theoretical developments can only be proven wrong and can not be proven right. They can only be proven as being satisfying given the precision with which measurements to test them were performed. 

Now, I think there is no question about the fact that enforcing a relativistic approach to resolution at a fundamental level as Nottale did results in a straightforward manner into quantum mechanics. In fact that is the simplest thing SR does. So the way I see it, Saeed's question opens up on two directions: 

1) Is the SR approach valuable to provide a new understanding of elementary physics? Can it generate progress toward an understanding of some reasons for the microphysical world to be the way it is by, for example, fixing some relations between parameters of the standard model. 

2) Is the SR approach valuable to provide a physics approach to complex systems that are usually not studied from a physicist approach. The reason why complex systems might appear under a new light with SR specifically resides in the fact that the structure or evolution of these systems always depend on many scales, a situation making physicists uncomfortable because it makes approximations difficult or even impossible. SR might change that.

I do not think we can give a definite answer to any of the two aspects of the question but interesting developments have been pursued in both directions with very promising results.

Steph.   

This is the question for which I also want to get replies. On the Internet, I have found the long discussion on a related question:

http://www.physicsoverflow.org/32836/technical-obstructions-prevent-relativity-quantum-gravity

Dear Al Rashid

The scale relativity theory was  a new theory in physics but not complet all fields just applied in afew regions

Dear RG colleagues

scale relativity theory is valid to many regions in physics , Laruent Nottale and his team applied it to many applications so you look for it on web.

https://www.researchgate.net/profile/Laurent_Nottale?_sg=TvogSsu_TGA7DsV4KAIXkDIs8gROJNaFbvTfYkbT7crmRhfQLJ6D3PGExivGTpkdPU3by6plrR5fPD0L0PaLMg.jDEg-pQ126ZiUpUKm66wEnD9XzEDkhpVa_XV1qrhoK69b2pu3vzXCiAA9xEn61gp

best regards 

 You have an interesting question, which cannot be answered simply.  One also needs to take due care in commenting on any theory within a public forum.  What I would suggest to anyone interested in any theory, is to ask if it offers new insights into your field of study.  If you find this to be the case then it is worthwhile exploring  the theory and its implications in a rigorous way to either confirm or refute its applicability/validity for yourself.  We are both fortunate and cursed (information overload) to have such a large and diverse range of ideas/theories at our finger tips.  One never knows where the next insight is going to come from.  For my self it is important to keep an open mind on any theory until you really understand it, even if it does not answer all the questions.  No theory of unification does this yet.  If it did we would not be having a debate.  

The history of physics is littered with examples of ideas that took years to be accepted and become mainstream.  Later we wonder why it took so long.  Often it takes a key piece of new information/evidence or a well respected new champion for the theory to gain acceptance.  Scientists also have a tendency to follow trends (we are all guilty of this to some extent).

Its ultimately up to individuals to decide if a theory such as scale relativity is part of the big picture in physics.  There are still many outstanding issues to resolve.  I think that one of the big challenges is to explore the links/synergies between different theories rather than focus on the differences.  I think every theory has some insight to contribute to the debate (even if one doesn't accept the full picture), otherwise people would not be spending their lives working on them. Ultimately we all want the same thing, to understand the nature of the world in which we live.  Having personally made considerable effort to understand the theory of Scale relativity, I believe it has an important contribution to make towards this goal, but it is clear that there are still many things that remain outstanding for us to explore and develop.

Dear Philip Turner

Thank you very much for your interesting answer, you are working on Scale relativity theory by Nottale so you know more concepts about this theory . As I see ,after appearing the concept of Cantorian fractal space-time by El-Naschie's, the SCR was not publishing in physics field well. The goal of my question is remembering  by SCR theory and let researchers  discuss it in many fields. I believe by this theory so I founded its correct for many quantum systems also found there are a deep idea in this theory , and I do not why Nottale stopping research on his theory. Again,  thank you, so I invited  Nottele , Hermann and Stephan to comment on this question and I hope you will invite any one you knowing that he care of  this theory.

Best regards 

Saeed 

Dear RG colleagues

I did have an experience in scale relativity theory , shown as following:

((The theory of scale relativity (ScR) is based on the extension of the principle of relativity of motion to include relativity of scale. Fractal space-time is the basis of this new theory as formulated by Nottale. Applications of this theory encompass diverse fields from microphysics, cosmology and complex systems. Previously, direct numerical simulations using this theory in quantum physics as performed by Hermann have resulted in the appearance of the correct quantum behavior without resorting to the Schrödinger equation. However these simulations were performed for only one limited case of a particle in an infinite one-dimensional square well. Hence, there is a need for more such applications using this theory to establish its validity in the quantum domain.

 In the present work, and along the lines of Hermann, ScR theory is applied to other standard one-dimensional quantum mechanical problems. These problems are: a particle in a finite one-dimensional square well, a particle in a simple harmonic oscillator (SHO) potential and a particle in a one-dimensional double-well potential. Some mathematical problems that arise when obtaining the solution to these problems were overcome by utilizing a novel mathematical connection between ScR theory and the well-known Riccati equation. Then, computer programmes were written using the standard MATLAB 7 code to numerically simulate the behavior of the quantum particle in the above potentials utilizing the solutions of the fractal equations of motion obtained from ScR theory. Several attempts were made to fix some of the parameters in the numerical simulations to obtain the best possible results in a practical computer CPU time within the limited local computer facilities. 

Comparison of the present results for the particle probability density in the three potentials with the corresponding results obtained from conventional quantum mechanics by solving the Schrödinger equation, shows very good agreement. This agreement was improved further for some cases by utilizing the idea of thermalization of the initial particle state and by optimizing the parameters used in the numerical simulations such as the time step and number of coordinate divisions.

 It is concluded from the present work that ScR theory can be used as a basis for describing the quantum behavior without reference to conventional quantum mechanics. Hence, it can also be concluded that the fractal nature of space-time, which is the basis of ScR theory, is the origin of the quantum behavior observed in these problems.

 More applications to potentials in more than one-dimension, including asymmetric potentials, would give greater confidence along these lines. Also, the novel mathematical connection between ScR theory and the Riccati equation, that was previously used in quantum mechanics without reference to ScR theory, needs further investigation in future work.))

So I work on paper that proof that Ricatti equation( has deep idea in physics specially in quantum mechanics ) connect with scale relativity theory.

Regards 

Sorry for having been so slow getting back to your invitation Saeed. I was busy with the end of the semester and I am new to this so it took me sometime to get there. 

To react to your question and Philips comment, I think Scale Relativity (SR) is not so much a theory as it is a program the value of which is to be set by the theories it may give access to. 

The first "stage" in the development of this program (while maintaining an absolute time) lands naturally and simply on standard quantum mechanics (as you have nicely illustrated for a number of systems). It does not provide answers to all the usual quantum mechanics interpretation questions. It does not even provide any particular or even efficient new way to calculated anything quantum mechanical.  But it achieves something very interesting: it brings up the postulates of quantum mechanics in a very simple manner from the extension of the relativity principle to scaling. The use of the term scaling can be misleading: what is scaled are not the objects in natures but the level of resolution with which they are considered. Sensitivity to resolution is (one of) the aspect(s) of quantum mechanics which makes it so "weird". By "injecting" resolution in the relativity method, the first thing that is encountered is standard quantum mechanics. I am not surprised by the fact SR is not of much interest to the "users" of quantum mechanics. It does not bring them much.  I am however puzzled by the fact SR has generated so little of an interest among science philosopher and people interested in foundational questions as it definitely provides a new angle of approach.

Application of SR to microphysics has been pushed further with relativistic quantum mechanics and quantum field theories. While this is an achievement, I find this less spectacular or striking than the first appearance of standard quantum mechanics even if there are vey beautiful ideas in there. They remain as great successes of the SR approach. 

These  successes can be regarded as validations of the SR method and the question is not so much to know if SR is "true", correct or valid but whether it can be used to describe the structure of the microphysical world even further. In the light of the connection between SR and quantum mechanics the question seems very worthwhile but I think only Laurent has published in this direction. I am wrong here?

As for  "unification", I am not sure what you mean Philip but if it is a comment about gravitation, I do not think much claims are made by SR (yet). But as SR provides a relativistic method approach to quantum mechanics, it provides a natural framework within which one may hope to describe both the quantum nature and gravitation and as you say there is certainly a lot to explore and develop. 

Then finally there is the question of the applicability to complex/chaotic systems which happen to share with quantum mechanics this aspect of resolution sensitivity which opens itself to the same type of description that landed on quantum mechanics. Maybe Laurent will object to this but I have the impression that the classes of systems for which some systematic tests were carried out to establish wether or not SR signatures are visible are those systems which can be effectively described as memory-less random processes. For these systems there seems to be interesting indications which do not generate much attention either despite the significance of the implications if these results were solidly confirmed. But the interesting features of complex/chaotic systems can not be described as memory less random processes and call for the development of a generalized form of quantum-like mechanics. Whether or not such theories would be applicable or valuable is probably impossible to tell as long as we do not have them. And so again, as Philip says, there is a lot to explore.

So I do not know how to answer your question either but while we do not understand quantum mechanics or scale relativity I have the impression that the idea of SR as a tool or as a method should be promoted and better exposed because it brings in a different way to think about resolution and offers a chance include the role of measurements at the very fundamental level in the description of the world.  

Thank you for starting such a discussion, I am curious to see other inputs. 

Best regards

Steph. 

Dear Steph.

I did wait your answer long time but it is OK, First, Thank you for your comment that you explaining SR in your viewing and the problems that faced when we try to applied it specially in Q.M.. I still waiting comment from Nottale and Hermann, to let SR well known to us and other people.

Best Regards

Dear Stephan

I think that you capture some important points with respect to SR.  Your comment on chaotic systems is particularly relevant and this is in fact that a key area where SR has an important contribution to make and to show critical links with the foundations of QM.  You can see some links here in the latest work published by Laurent and myself on self-organization in plants.  Whilst the paper uses plants as a case study it is directly relevant to all living systems as well as condensed matter in general. There is considerable new activity around the area of chaos and SR at the moment and so we can anticipate some very interesting new publications in this area soon.  Laurent is very active in this work.

Reverting back to my comment on the applicability of a theory, I would recommend that people look at the following link which highlights physics grand challenges that the EPSRC has identified: 

https://www.epsrc.ac.uk/newsevents/pubs/outputs-from-epsrc-physics-grand-challenge-surveys/ 

The EPSRC has identified 4 grand challenges.  What I find particularly striking is that in the latest work Laurent and I have published (2015 & 2016) is that the principles we have established (within the framework of SR) lead to a natural unification into a single challenge.  This for me gives some comfort that the foundations of SR are on a sound footing, which we will be working on further in future work.  I am in the process of establishing one or two multidisciplinary research projects in this area.  Let me know if you are interested in participating via email: [email protected].

On a further note relating to Saeeds comment,  I welcome any initiative that aims to promote the work on SR and am very happy to play a role in supporting this.  During next year I hope to establish a new network of active researchers active in this field and possibly organise a workshop relating to the field in the next 12 months.  If this is of interest to anyone please let me know via email

Dear Dimiter Prodanov

Nelson's stochastic is one of  the principles that scale relativity theory by Laurent Nottale , he did talk on  it as a historical survey of physics geometrical.

Regards

Well, I think there is a big difference. In Nelson's approach, the particle actually follows one trajectory of Brownian nature as postulated. On the contrary, in the Scale Relativity approach to quantum mechanics there is a loss of the meaning of the question about the position of the particle which results from the abandonment of the differentiability assumption. The numerical simulations are the same because of the finite nature of the time step used in the integration. In the SR approach each step corresponds to a position measurement selecting a bundle of indistinguishable paths. The difference is in the interpretation. I have been struggling with this and I tried to clarify this for myself in two papers now available in the archive: 

Scale relativistic formulation of non-differentiable mechanics I: Application to the harmonic oscillator

and 

Scale relativistic formulation of non-differentiable mechanics II: The Schroedinger picture

Cheers, 

Steph. 

https://arxiv.org/abs/1601.07778

https://arxiv.org/abs/1701.00530

Dear Steph

I know there are different between SR and Nelson's stochastic  but also there are similarity.  At first sight, scale relativity and Nelson's stochastic mechanics share features, such as the derivation of the Schrödinger equation.However, Nelson's mechanics has been refuted, with multitime correlations in repeated measurements.By contrast, scale relativity is not founded on a stochastic approach, and doesn’t fall into the refutation of stochastic mechanics. As Nottale writes:  Here, the fractality of the space-time continuum is derived from its nondifferentiability, it is constrained by the principle of scale relativity and the Dirac equation is derived as an integral of the geodesic equation. This is therefore not a stochastic approach in its essence, even though stochastic variables must be introduced as a consequence of the new geometry, so it does not come under the contradictions encountered by stochastic mechanics.

Best Regards 

 Steph

Notalle Said : the hypothesis that the space-time is nondifferentiable and fractal implies that there are an infinity of geodesics between any couple of points  and provides us with a fundamental and universal origin for the double Wiener

process of Nelson

http://luth2.obspm.fr/~luthier/nottale/arCSF94.pdf

also;

https://www.researchgate.net/profile/Laurent_Nottale/publication/237244087_Fractal_Space-Time_and_Microphysics_Towards_a_Theory_of_Scale_Relativity/links/00b4952a2e69d52416000000.pdf?origin=publication_detail

Regards

Article Fractal Space-Time and Microphysics: Towards a Theory of Sca...

Dear Philip, dear all,

Thanks for starting this important discussion.

Stephan and I are just starting a blog, zooming in and out on some key aspects of scale relativity. Stay tuned!

https://medium.com/zooming-on-scale-relativity

Best,

Clément.

Dears Clément Vidal and Dimiter Prodanov

Thank you to join on my question and your interesting comments, I did work on Scale relativity theory on my Ph.D study " Some applications of SR theory in quantum physics"

So it is suitable in this region. If you like you can see my paper on my page.

Regards 

Scale SR might find application on the smallest possible scale where degeneracy is believed to occur or at the fastest possible speed where another degeneracy is thought  to occur. In other cases scale SR is built of fractals in geometries which might be used as approximations but are unlikely to represent an exact description of nature. It is a math tool that might be mistaken for a physical system, a common failing in physical science.

Hello Jerry, 

What do you mean by smallest possible scale? And can you clarify these degeneracies you are talking about? 

I find your comment about "exact description of nature" puzzling. Nothing is exact and theoretical developments can only be proven wrong and can not be proven right. They can only be proven as being satisfying given the precision with which measurements to test them were performed. 

Now, I think there is no question about the fact that enforcing a relativistic approach to resolution at a fundamental level as Nottale did results in a straightforward manner into quantum mechanics. In fact that is the simplest thing SR does. So the way I see it, Saeed's question opens up on two directions: 

1) Is the SR approach valuable to provide a new understanding of elementary physics? Can it generate progress toward an understanding of some reasons for the microphysical world to be the way it is by, for example, fixing some relations between parameters of the standard model. 

2) Is the SR approach valuable to provide a physics approach to complex systems that are usually not studied from a physicist approach. The reason why complex systems might appear under a new light with SR specifically resides in the fact that the structure or evolution of these systems always depend on many scales, a situation making physicists uncomfortable because it makes approximations difficult or even impossible. SR might change that.

I do not think we can give a definite answer to any of the two aspects of the question but interesting developments have been pursued in both directions with very promising results.

Steph.   

Dear Rashid,

The main result of Nottale is well known as just a consistency postulate of quantum gravity: that if the electromagnetic renormalisation of electron mass is cut off at Planck Scale, the correction is of the same order of magnitude that the electron mass itself. This is remarked eg in Polchinski string theory book.

Over this consistency postulate, Nottale adds an O(1) coefficient, I think that it was a 3/8 fraction, so that the mass is not just the same order but exactly electron mass. This coefficient looks ad-hoc, (and posthoc: given that we know Plank mass and electron mass, it could be just a guess)

The link gives some interesting facts about the theory.

Thankyou.

http://antispirituality.net/nottale-scale-relativity

SR is not main stream of physics, so it faced many big problems 

After my previous comment I found SR useful in the study of Deep Space Transport At High Speed, together with the TGD theory that relates to it. The fractals of SR must be thought of as an averaging geometry with the quantum states they contain.

My conclusion is that kinetic energy resides in local space as convex curvature, not an entirely new idea. Einstein requested something like this in his autobiographical notes published in 1949. Convex is necessary to agree with the standard use of Lagrangians in predicting actions. In this way frame dragging was brought into Polarizable Vacuum theory at high speed. PV was further developed as an engineering device, not intended as a fundamental cosmology. 

A quantum function describes the exchange of energy between the fast moving vehicle and the local space it passes through. This is where the scale relativity is helpful. A large number of quantum actions can be described as a continuous function.

dE / df = n * h

The scale parameter n changes from one to five in steps as the vehicle accelerates continually, and space is squeezed in front of the vehicle.

Scale of one is just General Relativity in which h is constant. A consensus was reached that GR must be modified to join with Quantum Mechanics at high energy and short distance. In my project this is the TGD and scaling of h, which effectively becomes variable.

Scale of four was found to be the opening of a worm hole powered by kinetic energy, a 4D flat space inside a 6D warp field. Scale five was computed to be a thermal destruction of the vehicle from Doppler shifiing. Scale three is the 6D folding of space and scale two is the 5D of Kaluza Klein and others.

Without the scaling parameter n, the GR would allow infinities which are not found in nature. Also GR and QM would not join together at high energy.

So I have moderated my opinions about Scale Relativity and made good use of it in my completed project.

Dear everybody,

Thank you all for beginning this discussion. I have a lot searched on internet for such serious discussion about scale relativity. I'm a young student that will become this year an astrophysics master. I have discovered this theory by having a thought on the possibility to explain the rotation curves of the galaxies by a quantum like phenomena at large scale. To support this, I made the hypothesis that all the physics must be in a way or an other the same independently of the scale at which we observe it.

I have begun to read the last book of Laurent Nottale about the topic, "Scale Relativity and Fractal Space-Time",  and I am writting a short summary of the theoretical part of it. I think that there is something realy interesting that happens with scale relativity. This is first philosophically satisfying because it gives the foundation of Quantum Mechanics as a result of relativity principles. I am young but I'm not serene with the idea that nature is fundamentally based on abstract mathematical "dogmas" instead of first principles.

I didn't have yet the time to read it in detailled but a lot of predictions are done on astrophysical structures and planetary systems that have experimental confirmations. Why isn't it enough to get the attention of the physisist communauty? This is for me really paradoxical...  I would be really interested if you know where discussions on the topic can be done. 

On the future of the developments I think there is a lot of potentiality that links with the present big theories that are trying to unify physics appears. The tensorial nature of the resolution variable seems to be not yet totally exploited.

Best regards,

Julien

Right Jerry Decker, thank you 

Thank you Karlos 

Dear Julien Foerster

The approach to overcoming the conceptual difficulties of quantum mechanics based on scale relativity (ScR) method as formulated by Nottale  is one of them. It's main idea is to give up the differentiability of space-time and, hence, use fractal geometry as a basis to predict the quantum behavior  .

This approach is usually considered as lying outside main stream physics . However, its reliance on the well-founded mathematics of fractal geometry makes it one of the plausible approaches in this field. Applications of the scale relativistic approach to many fields in quantum physics have been discussed by many authors . Also, applications in other fields are available

best wishes  .

 Hi Julien ,

I do not know why scale relativity does not get much attention nor does it receive constructed criticism. To tell the truth it is even difficult to get publications through. One aspect might be that it is not a theory when people often expect it to be a theory. It is a principle from which theories can be built. The construction of quantum mechanics, as you and Saeed were saying, are brilliant illustrations. The transposition to macroscopic complex or chaotic dynamics rests on analysis of various systems, mostly astrophysical done primarily by Laurent and a few others are exciting indications but what would be needed I think is an experimental (reproducible) lab based observation implying a the existence of a new dynamics that could then possibly be described in terms of quantum potentials. The difficulty there is that it is difficult to identify systems simple enough to be analyzed in those terms or to be prepared in a specific quantum-like state whose recognition would provide a signature.   

Since you are not too far away from Brussels you may want to get in touch with Clement Vidal who is at the Free University there. He is on research-gate too. 

Best regards

Steph, you are right about difficult to get publications on SR method, I did send many paper to ISI journals but they are always answer in same words " sorry we can not find reviewer " even I did suggest reviewers like Notalle, Phlip and you. I like to tell you that I get accepted to my paper about harmonic oscillator in Journal of Quantum Information Science (JQIS), Scientific Research Publishing,but I will not publish it because this journal  not  in Scopus or Thomson routers journals.

Best wishes