The Infinite Fractal Universe by Robert L. Oldershaw

Dear Mr. Oldershaw,

I have to admit, I did not paid the right amount of attention to your essay. Yes eternal inflation solves undoubtedly many core problems, but there are my questions.

If once the inflation starts, it cannot really be stopped and if it is eternal, I would expect it to be much more widespread all around us. In other words, why is our observable universe so stable and uniform? (Yes, we seem to observe a positive cosmological constant, but it is really tiny.)

Let's also compare this with biology (a usual inspirational ground on string landscape and multiverse ideas). We see new life forms being born all the time all around us (just think of all the bacteria we are killing all the time with chemicals). If inflation does not have a beginning in time and is truly eternal, then why we are not witnessing nearby galaxies just disappearing suddenly in a burst of inflation? A truly fractal structure would also manifest at smaller scales as well, and why is the atom stable and electrons are not extracted from the atom in a mini local inflation?

I'm afraid that cosmogenesis still belongs as much to the domain of metaphysics as it did in pre-Copernican times, never mind the impressive arsenal of instruments we have at our disposal today, the theories the ingeniousness of which seem to pass for proof, nor the huge amount of data which, if I'm right, can support a much simpler and consistent scenario of a self-creating universe which cannot but produce a homogenous, isotropic universe and answers questions Big Bang hypothesis doesn't even try to: the mechanics and why of its creation. Your statement that 'the Big Bang model of the Universe has provided an excellent explanation for the basis cosmological observations' seems to me far too optimistic, 'excellent' being a self-congratulating adjective hiding the true state of affairs in cosmology, which is that of a building only standing because it hasn't yet realized that it was founded on sand.

As some other essays of the contest touch similar matters, I have posted my arguments among the discussion posts at my essay 'Mechanics of a Self-Creating Universe' -see my post of 25 september.

Cheers Robert,

Embarrassingly, for the second time I misunderstood your position: I thought you were for a fractal structure and inflation.

Your web page clarified many things, and the fractal position promises a very interesting solution to the dark matter problem. What I do not believe however is that this fractal pattern is repeatable at scales above the galactic ones (or below the atomic ones). In my opinion, the pattern's root cause is gravity's and electromagnetism's infinite ranges and different strengths, and therefore it is not really a true fractal. Please convince me otherwise. A true fractal structure is observed in quantum field theories via virtual particles in the renormalization group approach. When scale does not matter, the only remaining relevant structure is the symmetry group which determines the nature of the interaction.

Dear Robert L. Oldershaw,

In a top-to-bottom approach, the cluster-matter universe model has a hierarchy of embedded cluster-matters and sub-cluster-matters up to infinity at the bottom, and not describes any inflationary universe in entirety.

With best wishes

Jayakar

Hi Robert,

There is no contradiction. The fractal idea looks only like an empirical explanation, and not the actual root cause. I believe the root cause for the successful predictions to be the infinite range of electromagnetism and gravity and their respective relative strength. What if your parameters 5.2 x 1017 and 3.174 can be obtained from G, and alpha for example? Now if you can derive your parameters from the fundamental constants, and have a lot of successful data fits, then your dark matter origin prediction will suddenly become very credible and be accepted as the new paradigm.

But maybe I am putting the problem in the wrong way. The very first thing one should look is to try to derive the parameters from fundamental constants within existing theories. Only if unsuccessful, the case should me made for a new explanation like a fractal structure.

I am not aware of t'Hooft's preprint you are mentioning. Do you have an archive reference?

FM

PS: I am not a fan of anthropic reasoning, landscapes, multiverses, extra dimensions, etc.

Hi Robert,

I can tell you about some recent development. I was hoping to derive the Klein-Gordon equation (see note [1] on page 4 on my essay) in the near future but Emile Grgin just beat me to it. (There goes one paper I was hoping to write.)

Hi Robert,

Everyone should be free to pursue whatever questions he likes to answer. In math there are important open questions like Riemann's hypothesis, and in the past there were questions regarding the set theory axiomatization. Same thing in physics.

From your set of questions, I think I know the answer for no. 6. In QM one can experimentally ask simultaneous questions for complete set of commuting observables. Those observables form an algebra (a Jordan algebra) which is a linear structure and this is why nonlinearity does not occur at this level.

Nonlinearity can and does occur at higher levels in emergent phenomena.

For lower levels, 't Hooft works on a theory where he hopes to show that nonlinearity and chaos characterizes the vacuum and QM is only an emergent phenomena from a deterministic theory, but there are no experimental verifications for this theory yet.

Greetings Robert,

I liked your essay for clearly stating your views, while neatly avoiding some of the complications inherent in this subject. I gave a talk last month on Fractals in the Cosmos, and cited the work of three scientists whose theories predict a fractal aspect to the universe in my contest essay. I also have some published papers on related topics. So I guess you could say I am fractal friendly. But I do have some comments.

I agree with your assessment of chaotic or eternal inflationary cosmologies being a large-scale fractal breeding grounds, although I would have given some credit to Linde. It seems that sometimes people would rather brush that fractality away, by asserting that the other branches of the fractal tree are in adjacent bubbles which are in another universe, but this is a semantic evasion in my opinion.

And there seems to be plenty of evidence that large scale structure continues up to levels of scale where it was thought it would smooth out. The void near the CMB cold-spot, for one (see Rudnick, et al. - Extragalactic Radio Sources and the WMAP Cold spot). I also recently read a paper by John Hartnett at UWA, on evidence for the largest structures yet observed, which might be of interest. And an article in Scientific American by Clifton and Ferreira suggests that what appears to be Dark Energy may actually be evidence we are in an immense void.

This begs the question about how the characteristics of the local neighborhood affect our views of large scale structure. Some statements about fractal dimension and hierarchality depend on whether we are on a 'structure point' or in one of the lacunae, or voids. That is, the overall fractal dimension may be different from what we can observe.

I wonder about the limits at the lower end. I tend to feel that natural fractals like the growth pattern of certain ferns provide a good example. Though each smaller level of form looks like a copy of the whole fern, it is fattened with each smaller generation, as it must also obey the natural laws of fluid flow, and so on.

But it was a well-written essay overall.

All the Best,

Jonathan J. Dickau

Thank you Robert!

Your candor is appreciated. Too much good work gets ignored, and I too would be bogged down listing all the sources of my sources. But in all fairness, Linde studied with Starobinski so had a jump on thinking about Inflationary Cosmos over Guth, and it was his idea that brought the fractal aspect out in inflationary theory. It was no foul, on your part, however.

As to the other comment, I was just pointing out that perfect mathematical fractals, which have infinite depth, are not often seen in nature in their pristine form. My comment was not meant to imply that there is no fractality at the bottom, simply that we would be naive to assume things at the smallest scale can do the same things as larger aggregates of form.

This does not rule out some form of scale relativity, and it is agreed a discrete formulation avoids some of the complications thereof. Personally I like the idea from CDT and QEG that reality is 2-d down there at the Planck scale, but they are talking a fractal universe too. What we'll actually find remains to be seen.

Regards,

Jonathan

Hello again,

As I am completely unfamiliar with Cabibo-Snot theory, I want to steer things back to the topic of your essay, and try to relate it back to things I do know about. FYI - the result from CDT and Quantum Einstein Gravity, that reality is 2-d near the Planck scale, is very satisfying to Loop Quantum Gravity and Spin Foam folks. When numerous theories all converge on a similar result, I take this as evidence that there is something special worth examining there.

You should note that I apply this rule to the Fractal Universe paradigm, as well. As you point out in your essay, there are a bunch of theories under serious consideration, all of which point to a universe that is fractal. And as I pointed out both here and on Richard Easther's essay page, folks would rather talk about a 'multiverse' than admit that things are fractal even up to the ultra-large scale beyond observability. I find this curious and somewhat disturbing, as calling it a fractal makes far more sense, in my view.

In my own essay, I point out that I too feel there has been an over-dependence on Math, sometimes at the expense of good logic and clear conceptual thinking. But I am a constructivist through and through. I am firmly of the belief that the existence of the universe is clear evidence that it could be constructed from earlier constituents and ultimately from first principles. That is; there had to be some process or procedure by which the form we see could come into existence, for it to exist at all. But I hold Math to the same standard, even while believing that the shape of Mathematics may be a 'mold' or 'template' for physical reality.

For the sake of understanding how your approach is similar to - or different from - other theories with which I am familiar, I would like to summarize and ask you to make a comparison or clarification. As I remember, your Discrete Scale Relativity results in a modified Planck Scale, but I'm not sure how this works.

First; it seems that all the related ideas describe a reality whose dimension is resolution dependent. I find this idea satisfying as it links up with the view from Constructive Math that a space has no definite dimensionality, apart from what is observable, measurable, or computable. What does DSR say about this?

Nottale's Scale Relativity describes a fabric of reality that is continuous but non-differentiable, like the Peano curve. It appears as a solid membrane, because it fills space. In Connes' approach from NCG, the resolution-dependent aspect arises in a manner similar to the situation on a flower like a daisy, where a tiny bug is constrained to walk around each petal and a larger insect can walk across them and travel a much shorter distance. In ElNaschie's Cantorian Space approach, it is as though the petals are separable as well, so that gaps appear between them. This translates the Math into a conceptual framework.

How does your Discrete Scale Relativity fit with these examples, if at all, and why does it result in a modified Planck Scale?

Regards,

Jonathan