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."

Comments

Poppycock

[the eric conspiracy]

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.

Re: Poppycock

[Black Parrot]

This is an illuminating and interesting idea, and it may point directly to how we could measure both at the same time, which would make a lot more sense to some of us. Me included.

Whence the presumption that "makes sense" is a relevant criterion for evaluating hypotheses?

Our brains didn't evolve to operate on scales where quantum or cosmological phenomena are relevant. There's not the slightest reason to suppose that such phenomena, or their explanations, would "make sense" to us.

Re: Poppycock

[Anonymous Coward]

Of course, if the universe is indeed fractal in nature, then perhaps all levels of it are similar enough to our own that they would 'make sense.'

Re: Poppycock

[Anonymous Coward]

And here i thought that the origins of calculus and physics were an attempt to explain the universe in a way that "makes sense". By your logic, we didn't evolve to work on interstellar or interplanetary scales, and because the mechanics of orbital momentum and gravity on a planetary scale didn't "make sense", Newton invented calculus after proving the orbital shape of planets using geometry.

Your opinion is just as bad as those of the creationists in that if we can't comprehend it now, then we aren't meant to comprehend it.

Re: Poppycock

[GauteL]

There's not the slightest reason to suppose that such phenomena, or their explanations, would "make sense" to us.

If we were always to accept that a solution would never make sense to us, we would have missed out on a lot of our scientific discoveries.

Also, "reason to suppose" is not the only argument for investigating an issue. Sometimes "because it would be great if it was so" is an equally good reason.

In this case, it would be fantastic if there is an explanation behind it that makes sense to us. It would make the theories immeasurably easier to work with and might provide us with answers we could otherwise not comprehend.

Since it turns out that we have found many answers that "makes sense" to us in other areas of science, it is perfectly reasonable to hope that we can make sense of quantum mechanics one day as well, as long as we don't take for granted that there is a sensible explanation and mistake 'hope' for 'assumption'.

Re: Poppycock

[greg_barton]

Our brains didn't evolve to operate on scales where quantum or cosmological phenomena are relevant.

Our brains didn't evolve in the sky, and yet we make machines that fly, and it sure "makes sense" to a whole lot of people.

Re: Poppycock

[cjfs]

Your opinion is just as bad as those of the creationists in that if we can't comprehend it now, then we aren't meant to comprehend it.

I think he's referring to the feeling that we need to break things down into traditional categories (think wave vs particle) for them to "make sense" on an intuitive level. This is very different than never being able to comprehend them.

And the science is?

[Anonymous Coward]

Well after a brief scan of the actual article I have to admit it is an interesting idea that should be developed further however it isn't science yet. As I keep reminding some the students I work with, in science you create a theory that makes a prediction, test the prediction and if the prediction and experiment agrees go out for a beer otherwise you rethink the theory. If Palmer has developed a prediction, it is not mentioned in the article (or I didn't catch it in my brief glance).

Still an interesting idea that hopefully will eventually lead to some new theories and predictions about how particles behave.

Science 2.0

[fph il quozientatore]

Wow, and I thought it was only in computer science that you could talk buzzwords like this.

Re:All it really means.

[Anonymous Coward]

Uh? Some fractals are the infinite sum of a bunch of cosines. No "switch and loop and jump" statements -- just a plain sum of continuous functions. See http://en.wikipedia.org/wiki/Weierstrass_function

Re:All it really means.

[tjstork]

He selects a subset of integers... if positive then... :-)

Re:All it really means.

[tepples]

How come the formal definition of the Mandelbrot set lacks those switch-loop-and-jump statements?

Loop: iterate z := z * z + c. Switch: Is abs(z) > 2?

Re:All it really means.

[daver00]

Geez guys who would have thought a bunch of nerds would be so bad at this. Looping != inelegant intervention or whatever you called it. The mandelbrot set is simply recursively defined.

ie:
f1(z)=C restricted to the domain 0 less than C less than 2 in complex (goddamn /. dont like the html or symbols)
then fn=fn-1^2+C or fn=fn-1^2+f1 if you like, for all n greater than 1.
ie:
f = f(f(f(f(f(f(f(f(f(f(f(...)))))))))))) tending to infinity.
Then the set is defined in the exact same way you define any set:
M={C in Complex such that fn is bounded}
(Incidentally, does slashdot do latex? cos this stuff is hard to write out in ascii)

A recursively defined function is no different (in principle) to a recursively defined sequence, or a recursively defined differential equation which are all normal, fundamental concepts in mathematics. Not inelegant and tricky.

Like it or not, ALL analysis (read: advanced calculus) involves basically the same notions of abstracted set theory, I mean sure its obvious to you that continuity, curvature etc can be defined by derivatives which are defined by limits right? Well define limit, and no "zoom in and the line gets straighter" does not count. And then what on earth does limit mean? I mean when is it useful or even valid? How do you abstract that idea to general scenarios? What you find is that just about all of maths is defined within the confines of: {Some bunch of numbers, such that all of the numbers satisfy some property}

In short: fractals count, now hand in your nerd badges!