The Fractal nature of reality

[Brian G Turner]

So I was refreshing my science reading with a few books...

A few weeks ago I was reading an introduction to Relativity, that mentioned how a ball can look like a two-dimensional circle from a distance, but as a sphere closer up. Apparently this is a key part in Einstein's description of space-time.

Today I was reading an introduction to Chaos theory, when I came across this page:

And it suddenly occurred to me that space-time would more likely be fractal.

Additionally, the issue of bifurcations reminds me a lot of Quantum Mechanics - and if you can explain gravity and QM in terms of fractals then you're on the way to a unifying theory.

I did a little Googling and this is exactly the approach some physicists have taken:
Scale relativity - Wikipedia
https://phys.org/news/2009-03-spacetime-fractal-properties-quantum-scale.html

Additionally, I'm wondering if the process of applying chaos theory to genetics can explain a whole range of issues with Evolution, not least Convergent Evolution.

It's been some time since I last read up on Chaos Theory - I think it may be interesting to catch up again.

 

[Dave]

You sound just like Dr. Ian Malcolm (the Jeff Goldblum character) in Jurassic Park who also wanted to explain everything with Chaos Theory.

 

[Cathbad]

Reality - such a chaotic thing!

 

[J Riff]

"they exist primarily to satisfy mathematical equations."
"short scales spacetime might appear foamy, fuzzy, fractal or similar."
"in jargon it is said to be non-renormalizable"

Renormalisable shows up, as a Brit spelling only though.

 

[Brian G Turner]

You sound just like Dr. Ian Malcolm (the Jeff Goldblum character) in Jurassic Park who also wanted to explain everything with Chaos Theory.

I can live with that comparison.

What was interesting about the two descriptions is that I bet in Einstein's description, the ball would be a perfect sphere and perfectly smooth - a mathematical ideal that doesn't relate fully to the real world. Describing space-time in terms of fractal geometry I suspect would only involve minor modifications to relativity, yet address some of the outstanding problems that result from it.

I'll try and keep an eye out for more stories in this area of research.

 

[Venusian Broon]

Describing space-time in terms of fractal geometry I suspect would only involve minor modifications to relativity, yet address some of the outstanding problems that result from it.

You have much to learn Padawan .

The two models he build he picks are because, no doubt, he can actually solve them mathematically - reality is clearly different but could happily just obey GR but the 'real' equation, even although you could imagine it, is so difficult it is virtually certain to be impossible to solve - remember we can't solve the three body problem exactly, never mind the ~10^82 particles in the universe! Note that all models are just that - models of reality. Really they are so unbelievably simple it is amazing they can tell us something about real life.

The whole point of the paper was to 'hide' the fractal space-time from GR i.e make it so that it only appears on very small scale, so that you didn't need to apply any fractal stuff to GR. Which is good as he points out that GR can't have fractal geometry so 'making minor modifications' to it is clearly not possible. He does state that it is much easier to treat gravity in two dimensions on these scales, which might be a way of building a new theory, but I still see this as brushing all this stuff away from GR.

If anything I think it continues to show how incompatible GR and QM really are.

If it is the case that Space-time becomes fractal on Quantum scales - (note: we don't know - you have to do experiments to find out!) then the 'theory of everything' that replaces GR/QM will have to describe this transition as well as everything else. Or it might just be some cute mathematics (as most of chaos theory and fractal stuff tends to be - it's not usually very practical)

 

[Serendipity]

Geek alert - if you're not a geek, look away NOW!

Apparently a certain gentlemen, Fournier D'Albe had a go at examining the fractal dimension of the universe and wrote it up more like fiction than serious science in 1907 (warned you this was geekish) See - Two New Worlds: I. The Infra-World II. The Supra-World: Amazon.co.uk: E. E. Fournier d'Albe: 9781523981700: Books

This novel was acknowledged as relevant by Mandelbrot himself in his original textbook on The Fractal Nature of Geometry.

Apparently Fournier and Hoyle said the fractal dimension of the universe should theoretically be 1. The measured fractal dimension is 1.23. This discrepancy was tackled by P J E Peebles by relativity theory. The full treatment of the physics and statistics concerned is reported to be written up in his book, The Large Scale Structure of the Universe, Princeton University Press, 1980.

End of Geek Alert!

 

[Brian G Turner]

he points out that GR can't have fractal geometry

I suspect what would need to happen is that rather than directly modify relativity, someone would need to go back to the beginning of Einstein's assumptions - and try to include fractal geometry from the start. That could be similar to how Einstein modified Newton's equations and why the result might look like modified relativity, even though it was rebuilt from scratch.

It would seem strange to try and keep any fractal geometry reduced to the quantum level, because the principle of self-similarity means that scale should not be an issue for Chaos theory.

2 more c.

 

[Venusian Broon]

It would seem strange to try and keep any fractal geometry reduced to the quantum level, because the principle of self-similarity means that scale should not be an issue for Chaos theory.

2 more c.

Hence the issue with actually trying to do as you suggest! As far as we are aware the nature of spacetime is not self-similar in a way that is required for fractals - in large scales it's pretty dull . So it doesn't make sense trying to put 'fractal' geometry into relativity because it would just be wrong.

If this speculation is correct it's actually much more complex - it's the large limit approximation again, when QM gets large enough somehow it becomes Newtonian/Einsteinian. In some cases you can show this 'happening', in other cases it's really not clear why this happens at all. From my basic understanding he's saying that in the large limit the speculated fractal nature of spacetime just evaporates away.

Remember also that fractals are not reality too - they are a mathematical tool. A 'real' fractal is infinitely self-similar - see the videos of 'deep' Mandlebrot as they focus ever downward. As numbers are infinite it is theoretically possible to do this infinitely. In real life we actually know there are hard limits, so 'fractal-icality' is just another model of reality that doesn't actually quite add up.

 

[Dave]

Interesting discussions.

In real life we actually know there are hard limits, so 'fractal-icality' is just another model of reality that doesn't actually quite add up.

I was under the belief that anything could be explained, when written as a beautiful mathematical equation. Are you saying here that "fractical-icality" is not really a direct function of mathematics, but rather just our human need to see patterns in everything, even when they are not there (canali on Mars, Christ on toast.) I'm not very well read on this, but I thought otherwise.

 

[Venusian Broon]

Interesting discussions. I was under the belief that anything could be explained, when written as a beautiful mathematical equation. Are you saying here that "fractical-icality" is not really a direct function of mathematics, but rather just our human need to see patterns in everything, even when they are not there (canali on Mars, Christ on toast.) I'm not very well read on this, but I thought otherwise.

A fractal can be imagined perfectly- but it's a 'platonic' mathematical entity - you can define it and calculate things about it, like what fractal dimension a Koch star is (~1.26 according to Wikipedia). In reality there is a limit to how far we can 'see' something - eh, off the top of my head the Planck length (but the actual limit is probably much bigger!) - so we know that at some point, looking at objects and things in reality, we just can't continue being self-similar & fractal!

You can't physically construct a real fractal Koch star, only do so in your imagination

 

[hej]

And it suddenly occurred to me that space-time would more likely be fractal.

Additionally, the issue of bifurcations reminds me a lot of Quantum Mechanics - and if you can explain gravity and QM in terms of fractals then you're on the way to a unifying theory.

I did a little Googling and this is exactly the approach some physicists have taken:
Scale relativity - Wikipedia
https://phys.org/news/2009-03-spacetime-fractal-properties-quantum-scale.html

Additionally, I'm wondering if the process of applying chaos theory to genetics can explain a whole range of issues with Evolution, not least Convergent Evolution.

You are correct, likely much more so than you realize.

As I state and imply in my writing (which I will share elsewhere on the forum when I get up the gumption), the cosmos is fractal at every level.

The photon is within the electron (see Jablonski diagrams for an illustration); the electron, within water (not merely as covalent and hydrogen bonds but as a flow from which we see waves); water, within carbohydrate; carbohydrate, within phospholipid bilayers; and all the way up!

This work is (1) published in a paper (that destroyed the career of the author) and (2) both too complex and, paradoxically, too simple for scientists to accept.

The paper has been available online for several years. Downloads of the full article exceed views of the abstract -- and still occur at about ten per day.

I won't share it out of respect for the author's wishes (he finds it to be a deep embarrassment). Too, it is loaded with gobbledygook. It is beyond the comprehension of most readers -- who, unable to understand, largely chose to mock the language and the content -- but not the science.

Defending the paper in this environment of hostility is a fool's errand, as I found with my efforts.

 

[Cathbad]

I'm so glad I never decided to become a scientist...