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The astrophysicist Laurent Nottale develops since 1984 the scale relativity, which aims to unify quantum physics and relativity theory, using a fractal space-time.

I would like to understand why this theory, which seems have a good potential, is not taken seriously by the physics community, in the sense that it is not as developed as (of course) the string theory, but also the loop quantum gravity or the noncommutative geometry model of Alain Connes. Is it a political problem or a communication problem, or are they serious obstructions for such a theory to be valid?

Edit: Scale relativity is not at all in the category of "unpublished personal theories", see these references from the wikipedia page: the theory admits several papers published in peer-reviewed journals.

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    $\begingroup$ I have the feeling that hardly anybody knows of the theory (which in part is an answer to the question too). Like with Fractional anything, if no big solution to an old problem through it is being made popular and/or if the author isn't popular, getting ideas known is very hard. Nobody's who isn't payed for it is gonna invest the time to look into it in the first place - to take the time must presuppose a suspicion you can get something out of it. There are also tools like Gyrovector spaces nobody uses for SRT, and so on and so on. $\endgroup$
    – Nikolaj-K
    Commented Aug 2, 2015 at 12:41
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    $\begingroup$ I'm voting to close this question as off-topic because it is asking why scientists might not accept a particular theory and not physics. $\endgroup$
    – Kyle Kanos
    Commented Aug 2, 2015 at 14:40
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    $\begingroup$ I would like to understand why this theory, which seems have a good potential, is not taken seriously by the physics community is asking for opinions why scientists might not accept a particular theory. Given the Wiki article contains about 17,000 words in 28 subsections, the request is way too broad for this Q&A format as an answer would have to incorporate most (if not all) of those subsections. So it's off topic for a variety reasons: non-mainstream, too broad, opinion-based & not about physics. $\endgroup$
    – Kyle Kanos
    Commented Aug 2, 2015 at 14:54
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    $\begingroup$ @KyleKanos: I don't see any contradiction. I'm interesting in physics reasons (on-topic) why scientists do not accept this theory; otherwise the reason is purely politics, and the marginality of the theory would be not scientifically justified. Do you understand the nuance? $\endgroup$ Commented Aug 3, 2015 at 13:35
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    $\begingroup$ @KyleKanos: I'm not interesting in opinions (subjective) of physicists, but obstructions (objective and physics content). If there is no obstruction, then this theory is not mainstream physics only because of subjective reasons, which is not fair in science. $\endgroup$ Commented Aug 3, 2015 at 13:45

3 Answers 3


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 Polchiski string theory book.

Over this consistency postulate, Nottale adds a 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 post-hoc: given that we know Plank mass and electron mass, it could be just a guess)


I also don't think I can give a definitive answer. But maybe no one can because maybe no one knows enough about the theory and about why people don't know about the theory. But I will do my best.

As mentioned by Nikolajs maybe fee people think they can contribute to it or make use of it. This is partly because of the success of quantum mechanics and relativity in there domains of applicability which covers almost everything we have an opportunity to see. And partly because of having to learn new things.

But let's not confuse the issues. Peer review is one thing, and reviewers should be fair. But choosing to study an area is a personal choice, everyone chooses what to specialize it. Just because you choose an area because you think you skills and background and interests will allow you to make meaningful contributions down mean you think other specializations are wrong, they just aren't your cup of tea. At least right now (people do change their specializations).

So if you think another researcher is way ahead of you and isn't likely to be a coauthor, then that might discourage you. In a robust and healthy field you can have interplay between different subarea experts, for instance theorists and experimentalists can work together. And then their collaborations with other theorists and other theorists can lead to more people becoming aware of their work. You like to know what your collaborators are up to. Maybe not at first, but in a long term collaboration you find out the other things your collaborators are up to. In an area without active collaboration between for instance experiment and theory, there is a barrier to awareness.

But you specifically asked about comparison with loop gravity and string theory, surely those areas have just as much a disconnect with experiment. Fair enough. String theorists have a particular culture, of lots of people working on specific hard mathematical problems in a very competitive way. So if there is a large group of people working on the same problem you know others will appreciate your work, not just because they are a built in audience that understands it, but because of the competitive nature where if you publish first you can get their respect for doing hard work very quickly. This means lots of people can say good things about you, good things that speak well about you even outside of physics, which means there a clear payoff for succeeding. And since there are many strong leaders in the field that have a history of success their are expectations that success is possible, there is also a rich field of hypothesis that haven't been completed yet. Researchers like open problems, have them and make them clear and this is encouraging to research, that's why papers have sections about future work.

Now, not all of those things were always true of string theory so you could ask about the history and try to find out how it got that way. But any specific theory's history could be too accidental so let's talk a out what makes different theories appealing.

Obviously limiting towards known results in known regions that have been confirmed is good. It would be nice if there are testable predictions as well, particularly ones that could be tested soon. For instance Einstein had the bending of starlight which was doable. But there is also a desire for principled reasons.

For instance of you took the average global temperatures for the recent history and fit them with a large degree polynomial and then asserted that was your prediction for global temperatures few people would care how well it fits the data because the principles are so unappealing. You predict incredibly high and/ot incredibly low the temperatures for every time except times near now and base it on no physics. Almost no one will bother.

Physicists want to understand the universe. A theory with parameters that come out of no where and aren't stand ins for unknown experimentally measured parameters is unappealing. But partly that is because of high expectations for quantum gravity, some people want a theory of everything and they want it to predict everything, every mass, every coupling, everything. Those will be hard people to please. But even if you don't want all that, you still want a principle that makes sense that makes the universe seem less mysterious and makes it seem more understandable.

What's nice about GR, is that even if you haven't studied the detailed math of curvature, you have some intuition, so if someone says that they can explain why different massed objects more on the same paths as because they follow natural curves (like great circles on the earth). So it feels like it explains.

There are also things that are specifically unappealing about scale relativity. And some of that is cultural too. For instance the Planck length business. The plank length is just a length based on some constants. It is generally considered by physicists to be a length scale where quantum and gravitational effects can both be important. It is considered by lay people to be a minimum length in the universe. If scale relativity reproduces the lay person idea this makes the theory appealing to lay people and unappealing to physicists. Since we haven't observed a minimum length and don't expect to be able to soon (it is so small) and didn't actually think there was one, physicists aren't excited by that "prediction."

But that's just it. What are the principles? When I read the wikipedia article it is vague (which is understandable if I haven't studied fractal geometry and that is the math used) but then it ends up reading like a parody of physics with a bunch of buzzwords. And saying that the whole idea is that only relative scales matter sounds just like the fact that we have to use units. The fractal geometry had to be involved somehow and the way the theory is presented to new people sounds vacuous at best, or a rehash of the fact that we use units. Which doesn't mean that is a fair characterization. But if that's the best description to newcomers that 30 years has produced, maybe it will never catch on.

Think of it this way. If you have a better and principled way of understanding the universe, tell us why the (the principles) involved involved so that we can tell what is wrong with the alternatives. With GR, you can say that spacetime is curved and this explains why different masses follow the same paths, and that assuming spacetime is flat is an assumption not based on a principle.

What can scale relativity say? That we always pick the same scale and this is a problem somehow? We already use constants with different values, is scale relativity supposed to predict those constants in a non ad hoc way? Why would I want to be covariant to scale when my constants already change if I use different units. The principle involved is not articulated well.

And how about reproducing known results? If everything is non linear and hard to solve then how easy is it to see whether you get known results in known areas. People aren't interested in studying something whose predictions have already been disproven experimentally. With GR, there is a weak field limit that reproduces known results from Newtonian physics in the domain where Newtonian physics holds.

These are the kinds of things string theory had to deal with back when it was less popular. And there were promises (or at least strong advertising) that there would be a unique theory, that the constants would be predicted and that one idea would lead to a weak field theory that would agree with the standard model and with GR in the appropriate limits. These things did not pan out, but they did lure people in to help the field grow.

That doesn't mean you should try to lure people in, but it is a reason why people get interested in the early days.

Now, for further problems with scale relativity, that again might be just about how it is presented to people that haven't studied it. Which is a distrust of adjustable parameter explosions. Let's look at renomralizable QFT.

The idea is firstly that restricting to renormalizablr QFTs reduces the number of possible theories quite drastically thus it is a principle to reduce the number of theories, thus when one agrees with observations there is more reason to be excited (if string theory had developed the landscape issue right away fewer people would have joined). Secondly the idea isn't that you renormalize a theory to get finite predictions the point is that you do so with a finite number of experimentally determined parameters.

The introductory explanations of scale relativity make it seem either near pointless (pick a unit, then use it) or like it has an infinite number of parameters (coordinates become functions, so finite degrees of freedom become an infinite number of degrees of freedom) or like it has a landscape of possibilities were you can make whatever you want happen at any scale. It doesn't seem scientific. It doesn't seem like understanding the universe. It doesn't seem principled. It doesn't seem like you can do things other than post hoc retrodictions. And that doesn't mean those things are true, people claim to have predictions.

However, if the introductions don't make it sound like it is good and instead say things that make it sound appealing to lay people, that is not going to encourage people to join that don't personally know people in the field and know that it isn't a crank field.

So if your introductions don't sound appealing to people based on what made people find out theories appealing (uniqueness of theory, small number of parameters explaining lots of results, principles that seem explanatory, etcetera) then people might be more drawn to new/s areas that do those things or to more established/popular areas that have other things going for them like recognition of hard work from large group of other practitioners or from interaction/collaboration with other subspecialties ideally including experimentalists.

Sometimes it is about getting experimentalists happy. So again, leer review is for fair assessments of right or wrong. Choosing to invest your own time to learn something is a different issue. And making an experimentalist choose or a theorist choose might be different beasts.

I myself made fractal theories of physics on my own as a young person, not having heard about scale relativity, but even so reading the wikipedia page did nothing for making me think we get anything from it whatsoever.

Does it show an existing thing that we do wrong (don't agree with observation) and show how to do it right? It seems to be described as still in progress after 30 years.

And it is not just that the wikipedia article fails to convince me, it actively discourages me. For instance it says

Scientific theories usually do not improve by adding complexity, but rather by starting from a more and more simple basis. This fact can be observed throughout the history of science. The reason is that starting from a less constrained basis provides more freedom and therefore allows richer phenomena to be included in the scope of the theory. Therefore, new theories usually do not contradict the old ones, but widen their domain of validity and include previous knowledge as special cases. For example, releasing the constraint of rigidity of space led Einstein to derive his theory of general relativity and to understand gravitation. As expected, this theory naturally includes Newton's theory, which is recovered as a linear approximation under weak fields.

And if you have anomalies in the old theories (such as Mercury) that is great to have a wider space of theories. But some people are hoping for a smaller space of theories. So I don't get excited about a wider space of theories, this makes me less interested. It is physical principles that reduce the space of theories. So the covariance of scale relativity should be reducing the possibilities, but its not clear (in the introduction) that the covariance does something other than picking units at least without opening the doors to way too many possibilities.

And now for some of the really specific criticisms. Which is that I'm already familiar with theories that personally are easier for me to understand, have principles I understand, and seem to have the same (or at least similar) advantages. And if I do, then others do, so in general this could just mean that the space of theories is crowded do any one has to compete with the rest. So that means every unpopular theory has to compete not just with the popular theories you know but all of the many many many less popular theories.

For me for instance the Gauge Theory of Gravity e.g. by Lasenby, Doran, and Gull at Cambridge University has many of the same advantages. All comparisons are made between fields, the fields can locally change their orientation, boosts, and scale. It derives the equivalence principle instead of assuming it, and basically is based on the fact that we don't know where or when things are happening or a sense of scale but we only know how to compare. And the math it uses is math that is required to be used to study relativistic quantum mechanics, hence it contains things I already know or things I should learn anyway.

Again, I'm not trying to convince you that Gauge Theory of Gravity is better than scale relativity, but I list it as an example that other equally (or more) appealing alternatives exist so any theory has to compete with all the alternatives.

This might be landscape problem (too many possibilities) at a higher level. Making too many competitors for theories that handle scale. If that is the case then maybe an insight that encompasses them all and brings everyone together is the key, something that allows you to study them all easily and objectively sort through them.


Sébastien : I can't give a definitive answer, just an opinion. And I would say that to get anywhere, this theory has to be consistent with relativity, which is one of the best-tested theories we've got. See http://arxiv.org/abs/1403.7377. It has to persuade the "relativists" first, and only then can it gain credence amongst the wider physics community and be taken seriously. But as somebody who knows a thing or two about relativity, I don't find fractal space time at all convincing. Let's take a look at a few things in the Wikipedia article:

If Einstein showed that space-time was curved

There are some issues with this. If you search the Einstein digital papers on curved space-time you only get one hit. Ditto if you search on space-time curvature. But if you search on homogeneous there's lots of hits, including this one where Einstein describes a gravitational field as space that's neither homogeneous nor isotropic.

Nottale has proven a key theorem which shows that a space which is continuous and non-differentiable is necessarily fractal. It means that such a space depends on scale. Importantly, the theory does not merely describes fractal objects in a given space. Instead, it is space itself which is fractal.

The problem here is that Nottale has confused space with space-time. This does not impress a relatavist.

Mathematically, a fractal space-time is defined as a nondifferentiable generalization of Riemanian geometry. Such a fractal space-time geometry is the natural choice to develop this new principle of relativity, in the same way that curved geometries were needed to develop Einstein’s theory of general relativity.

This is totally going against the grain of relativity I'm afraid.

In the same way that general relativistic effects are not felt in a typical human life, the most radical effects of the fractality of spacetime appear only at the extreme limits of scales: micro scales or at cosmological scales.

Only there's no evidence for it. Compare and contrast with GR, which is one of the best-tested theories we've got. It's as if this is attempting to ride on the coat-tails of relativity, and it does not impress me at all. If it doesn't impress me, it's unlikely to impress everybody else. Sorry.

  • $\begingroup$ Well scale relativty can be made as mathematically consistent as relativity. So there is no problem using it. $\endgroup$
    – Dimiter P
    Commented Mar 6, 2016 at 23:11

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