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Can Fractals Make Sense of the Quantum World?
Keith found a New Scientist story about fractals and quantum theory. The article says "Take the mathematics of fractals into account, says Palmer, and the long-standing puzzles of quantum theory may be much easier to understand. They might even dissolve away."
So, the problem wasn't that God was playing dice with the universe, rather, it's just a nice Julia set?
Einstein must be rolling in the dimensions of his grave. Fractionally, of course.
I've fallen off your lawn, and I can't get up.
And suddenly LOGO turns out to be the programming language we need to encode the formula for everything.
Go, little turtle, go!
Since I can't tell them apart, I treat all ACs as the same person.
Using fractals as a way of viewing a problem can be useful, but it doesn't fundamentally offer any new ways to solve a problem over conventional methods.
Fractals are basically the incorporation of decisions into iteratively applied functions of some kind. Physics normally uses mathematics of varying degrees of curves and shapes and spaces to describe things and these functions are continuous to a degree, and so its pretty reasonable to think that such descriptions could be imprecise. Math tends to see "switch and loop and jump" statements as inelegant and those are the essence of fractals.
This is my sig.
An old Canadian friend's brother turned out to be a mathematical physicist working at a Canadian university researching fractal spacetime. Garnet Ord's work supposedly reconciles the notoriously conflicting relativity and quantum mechanical models of spacetime. It seems that the time axis used to be treated as an integer variable, when in fact it's a fractional dimension: a fractal.
I'd say that making relativity and QM interoperate is a good way to "make sense of the quantum world".
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make install -not war
again EVIL people deny that only TIME CUBE can make sense of the world
If, as the article suggests, Palmer's theory eventually does away the need for multiple universes, then incalculable damage has been done to the world of science fiction. What fun is it if there isn't a world where the Nazi's won WW2? What's there in that for anyone?
So if I understand this correctly, Palmer is saying that the universe has a finite amount of information variables and at some certain point it will reach that limit? And that every time we try a thought experiment to measure either the position or a velocity of a particle, we risk overstepping that finite limit and thus get results where we can only measure one or the other because to do both sets us beyond the limit? So then can it be inferred that he's saying the universe has a limit then?
Here's to hot beer, cold women, and Glaswegian kisses for all.
Wow, and I thought it was only in computer science that you could talk buzzwords like this.
My first program:
Hell Segmentation fault
Or he could use quantum theory to explain fractals to me, didn't quite get it when John Gleick wrote about chaos in the late 80's
Anyway, want credits for the word 'Quantals' and now I'm off to RTFA.
The problem is that Bell's Thm. tests for hidden variables - essentially "deeper physics".
And Bell's Thm. has been verified repeatedly.
So, either he's arguing that Bell's Theorem is taking us down a blind alley, or he's going to have to figure out someway to make both the fractal understanding and Bell's true. The article in New Scientist doesn't discuss that at all.
In illa quae ultra sunt
Since I couldn't bother with RTFA, I'm gonna go with a definite maybe.
After applying fractal math on quantum problems you could notice something dissolving... but is your mind, not the problem.
No. No, they can't.
Squirrel!
Thank you. I would say it is still an untested hype-o-thesis.
Yes. Yes, they can.
Squirrel!
>The article was pretty vague handwaving. It didnt actually how any problem was solved with fractal mathematics. It could have tried to explain one example.
By coincidence I just looked through a text book on 'quantum chaos' today, paying attention to an example they had for the quantum mechanics of the Helium atom. (something I know something about, as a chemical physicist).
What they did there, was model Helium semi-classically as 'colinear'; as if the two electrons and the nucleus were in a straight line. A pretty weird model from a physics standpoint, but I suppose necessary from their perspective since that dynamical system apparently displays chaotic behavior. After some math, they managed to show how this replicated the overall spectrum of Helium.
Now that's nice and fairly impressive. But I don't actually see any direct usefulness of it. It's not a better or more accurate way than solving the Schrödinger equation for the electrons. It does illustrate that the main properties of atoms/molecules are due to the nonlinear dynamics of electron motion. But we knew that already. So in a way it was like a lot like how you react to fractals: "Well, that does look a lot like a fern leaf!... So?"
Now I'm not entirely certain if this is representative of the work in TFA. But there's a definitely the risk when you attempt to mate 'buzzword topics' like this, that you start doing stuff for its own sake, and always end up with rather contrived connections. Now, if chaos theory can really explain quantum physics at a more fundamental level, that's one thing. But I don't think coming up with chaotic systems that share properties with quantum ones is doing so, any more than a fractal image of a fern leaf 'explains' the biology of ferns.
The article loses me almost immediately when it states that information is lost in a black hole. Anyone who's read Susskind's book knows that this implies all sorts of unpleasantness like the irreversibility of the the S-matrix, and so it is likely incorrect; ie, information is not lost when objects fall into a black hole. This makes sense, because to an outside observer, an object never falls into a black hole, it only approaches the event horizon without ever quite reaching it. Therefore, one would expect that information from objects falling into a black hole is written on the surface of the event horizon. This represents the highest information density possible. This is Susskind's thesis, and it was my understanding that it is becoming the accepted view. Stephen Hawking was a proponent of black-hole information loss, and Palmer was a student of Hawking (20 years ago). Therefore, it is not surprising his theory is based on rejected premises.
From the author's abstract at http://arxiv.org/abs/0812.1148
The Invariant Set Hypothesis: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity
T.N.Palmer
"Combining these, an entirely analysis is given of the standard "mysteries" of quantum theory: superposition, nonlocality, measurement, emergence of classicality, the ontology of uncertainty and so on."
I feel you're on to something here: Along the lines of the parent post I put on... let's assume that fractals are correct and that Palmer's right. Would that then mean that there is a limit to the universe, in terms of using fractals to make sure we get the calculation just right to avoid 'hitting nothing' when calculating position and velocity? If so, is non-existence quantifiable? Or does the act of measuring it increase existence? My head is starting to hurt here, so I'd like to ask if someone far more knowledgable than I am can answer this. What I'm thinking though, is that if Palmer's correct, then we might have found an edge of the universe (so to speak), and if we have, then wouldn't that put us a whole lot closer towards determining whether or not we are in a simulation (a better way to put it would be : we are the simulation?)
Here's to hot beer, cold women, and Glaswegian kisses for all.
It's more like the Readers' Digest of science.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."