## Can Fractals Make Sense of the Quantum World? 236

Posted
by
CmdrTaco

from the cuz-i-sure-can't dept.

from the cuz-i-sure-can't dept.

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."*
## Quantum Exploration (Score:5, Funny)

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.

## Re:Quantum Exploration (Score:5, Funny)

God is one of these role-play nerds then, with his 20 dimensional dice.

## Re:Quantum Exploration (Score:4, Informative)

## Re: (Score:3, Informative)

## Re: (Score:3, Funny)

Roll 4 Time Cubes and beat DC orange!

Foolish! You lose!

## Re: (Score:2, Funny)

God is one of these role-play nerds then, with his 20 dimensional dice.

Typical ignorance from a whole number dimensional being. God's fractal dice have 23.5 dimensions.

No, his dice has e^pi dimensions. How could you ever think God's dice would not be transcendental?

## Re: (Score:2)

And evalNum("googol"++plexes) sides, where

plexes = "plex" ++ plexes

as ++ bs = string concatenation

Oh yeah. he can count to infinite. And beyond!

## Re: (Score:2)

Oh yeah, and e tokk my ablity to speel korektily, two...

## Re: (Score:2)

It sounds like Buzz Lightyear's mission was actually a spiritual quest.

## Blasphemers! (Score:2)

God is one of these role-play nerds then, with his 20 dimensional dice.

Typical ignorance from a whole number dimensional being. God's fractal dice have 23.5 dimensions.

No, his dice has e^pi dimensions. How could you ever think God's dice would not be transcendental?

God's dice have exactly e^(i*pi) dimensions! Either that or factorial(e^(i*pi)) dimensions. Or maybe both at the same time...

## Re:Quantum Exploration (Score:5, Funny)

So, the problem wasn't that God was playing dice with the universe, rather, it's just a nice Julia set?

Actually, it's just that God's dice have a complex number of sides.

## And suddenly LOGO (Score:5, Funny)

And suddenly LOGO turns out to be the programming language we need to encode the formula for everything.

Go, little turtle, go!

## Re:And suddenly LOGO (Score:5, Funny)

## Re:And suddenly LOGO (Score:5, Funny)

"Where'd the damn turtle go?"

"Ah, it fell off the edge of the universe again." Start over from the flat spot on that atom, would you?

## Don't give the turtle a hard time (Score:2)

That turtle is working hard holding up the whole Universe [wikipedia.org].

## Re:And suddenly LOGO (Score:5, Funny)

It really *is* turtles all the way down??

## Re: (Score:2)

No, of course not, that's ridiculous. Everyone knows there's just one turtle with four elephants on it. The turtle

swims, because it's a turtle.## Re: (Score:2)

thesandtiger writes:

"

And suddenly LOGO turns out to be the programming language we need to encode the formula for everything."Oh crap. So it's turtles all the way down??!

## Poppycock (Score:4, Insightful)

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 (Score:5, Interesting)

Well, the point of the article is that if the underlying structure of the universe is fractal, then it shows why, for instance, you can measure the position or the velocity of an electron, but not both; the general idea is that instead of a linear reality, the universe exists along a fractal edge, and answers derived using current quantum methods are literally falling off the edge because they're not finely enough resolved - they don't take the foaminess of the edge into account, so they miss the answer and land in a space that literally isn't part of the real universe - they're undefined. This is an illuminating and interesting idea, and it may point directly to how we

couldmeasure both at the same time, which would make a lot more sense to some of us. Me included.He's not incorporated all of quantum theory into his fractal idea, so this is far from certain, but it is a lovely idea.

## All it really means. (Score:5, Interesting)

## Re: (Score:3, Insightful)

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. (Score:4, Insightful)

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

## Re: (Score:2)

Fractals, being objects with a well defined fractal dimension, are not required to be iteratively defined or discontinuous, they just have to satisfy the limit formula for fractal dimension. Brownian motion, for example.

## Re: (Score:2)

How come the formal definition of the Mandelbrot set [wikipedia.org] lacks those switch-loop-and-jump statements?

## Re: (Score:3, Insightful)

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: (Score:3, Insightful)

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

setis simplyrecursively defined.ie: /. dont like the html or symbols)

f1(z)=C restricted to the domain 0 less than C less than 2 in complex (goddamn

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 Com

## Re: Poppycock (Score:5, Insightful)

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: (Score:2, Insightful)

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

## Re: Poppycock (Score:4, Insightful)

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.

## Re: Poppycock (Score:5, Insightful)

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 (Score:4, Insightful)

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: (Score:2)

Maybe in this wonderful world of Quantum Mechanics logic doesn't apply in the same way, but hey, being able to measure both makes no sense to me whatsoever.

Please don't make me bring out the cars...

## Re: (Score:2)

Actually, the uncertainty principle comes from the pure mathematics of Fourier transforms, and applies to all kinds of waves. For example, the kick of a drum is well defined in time, and contains a wide range of frequencies. An ideal sine wave, on the other hand, has only one frequency, and extends infinitely in time.

It just happens in QM that the momentum of a particle is defined by its wavelength. A narrow range of wavelengths corresponds to a wide range of positions, and vice versa. There are other pa

## Re:Poppycock (Score:5, Funny)

"Your honnor, officer Speedtrap can't know I was there

anddriving too fast. I would like to call Mr. Heisenberg as a witness for the defense."## Re: (Score:3, Informative)

You're confusing the uncertainty principle with the observer effect.

It isn't possible to know the position and velocity of a particle exactly, *even in theory*. I.e. if you could know everything about the particle magically without doing any measurements then you still wouldn't be able to write down its exact position and velocity. In that sense the uncertainty principle is badly named - there isn't really any uncertainty involved.

It's just that velocity and position are macro quantities that don't make muc

## Re:Poppycock (Score:4, Funny)

## Re: Poppycock (Score:2)

And it'll help sell tee-shirts.

Sorry, but a fractal tee-shirt won't fit unless you've got a fractal body plan.

## Quantals (Score:3, Funny)

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.

## Re: (Score:2)

## Re: (Score:2)

None taken.

Thanks for the reference, looks interesting. Especially the 'more mathematical' part.

## Re: (Score:2)

two options:

1. we have finally figured out the beginning of a heisenberg compensator (go go transport booth)

2. you need to get of the catnip for a while, the fractals are making sense.

## Re: (Score:2)

slight correction - we wouldn't be able to measure both at the same time; Palmer suggests that one of the two measurement events itself (either position or velocity) is not part of the real universe. IOW, only one measurement, the one we actually do, is part of the invariant set that makes up the real universe. The other measurement must remain forever hypothetical - it could never have really taken place.

## Re: (Score:2)

I don't read the article that way at all. The article says (emphasis mine):

## Re: (Score:3, Interesting)

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.

I'm good with not being able to directly determine position and velocity simultaneously. The part I have problems with is the position and velocity uncertainty also applies to nothingness. The more sure you are that an area of space contains no particles, the more uncertain you are how fast they are going.

## Re: (Score:2)

If you're going to go off into weird and murky models of existence the holographic model probably makes more sense and seems to interface even better with QM. On the other hand, maybe consensus reality really is the best model; it often seems like you can describe the universe any way you want to :P

## Re: (Score:2)

That's not the way I read it.

From the description in the article (always dangerous) I got the impression it was kind of a cop out.

You do the position or velocity measurement experiment. You choose to measure position and get a result. Then you ask, what if I'd measured velocity instead? From the article it sounds like the explanation is that the universe in which you measured velocity is not a member of the fractal set so that universe cannot exist, so the "what if" is a meaningless question.

Under that i

## Re: (Score:3, Interesting)

Well, the point of the article is that if the underlying structure of the universe is fractal, then it shows why, for instance, you can measure the position or the velocity of an electron, but not both ... This is an illuminating and interesting idea, and it may point directly to how we

couldmeasure both at the same time, which would make a lot more sense to some of us. Me included.IMHO thinking of the position, velocity, energy and lifetime of particles is a hard way to go about things in and of itself. Whilst it's a correct interpretation of quantum mechanics, it's also just as correct to think of everything as waves, which I find easier.

Thinking in this way an electron is simply a wave, as is a photon, and so on. Multi-particle systems are just combinations of these waves added together, and Fourier analysis shows that even these individual waves are just a combination of simple si

## Fractal Math Reconciles Relativity & Quantum M (Score:5, Interesting)

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 [google.com] 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".

## Re: (Score:2)

## Re: (Score:2)

Indeed, I do mean that Ord's work (and work like it) will make sense to only advanced mathematicians. But those people have crossed the border from order in the universe to sense in a human mind. Those people can influence scientists and engineers, who in turn inspire artists, which is when most people get a chance to see it make sense. Between art and products (and the very fuzzy boundary between them), eventually our culture encodes that sense. The math is the watershed, and we might already be across it.

## Re: (Score:2)

## WRONG (Score:5, Funny)

again EVIL people deny that only TIME CUBE can make sense of the world

## Re: (Score:2, Funny)

## Re: (Score:2, Interesting)

http://www.timecube.com/ [timecube.com] *

* I take no responsibility for your sanity if you click the above link.

## No more multiple universes? (Score:5, Funny)

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?

## Re: (Score:2)

## Re: (Score:2)

I think he was referring to the alternate reality where Rimmer is a space fighter hero, super-jock, and ladies man. Rimmerworld was a world populated entirely by genetic clones of Rimmer, both male and female.

## Woof... lots of implications (Score:2, Interesting)

## Re: Woof... lots of implications (Score:5, Funny)

Maybe quantum phenomena appear to be random because the universe's stack has collided with its heap, and all the variables this far down into the recursion are full of garbage.

Mmmmm.... nerd theology. Some hero will come along and separate the stack from the heap with his sword, and the universe will begin anew.

## Re: (Score:2)

## Re: (Score:3, Funny)

## Re: (Score:3, Interesting)

## Let me throw this out to /. (Score:2, Interesting)

## Re: (Score:2)

## Science 2.0 (Score:2, Insightful)

## So then what about Bell's Inequality (Score:5, Interesting)

The problem is that Bell's Thm. [wikipedia.org] 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.

## Re: So then what about Bell's Inequality (Score:5, Interesting)

or he's going to have to figure out someway to make both the fractal understanding and Bell's true.

Kind of like measuring position and velocity at the same time? Now he needs a fractal unifying meta-theory, I guess.

And then a fractal unifying meta-meta-theory, and then a ...

OK, maybe he has the right idea.

## Re:So then what about Bell's Inequality (Score:5, Interesting)

Bell's Theorem states:

No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Personally, I don't see why people have such an issue with the existence of non-locality. David Bohm did a lot of work in this area, much of which is admittedly over my head but compelling nonetheless. Interestingly, he was drawn towards non-local hidden variables after working with plasmas, whose electrons act as a unified whole instead of individually. To my knowledge, no satisfactory explanation other than non-locality has been offered up for such behavior.

And now I'm stepping out on a limb and will probably be torn to pieces, but it just occurred to me that at its birth, our universe was essentially a point of infinite density, or something very like it. With the knowledge of such a beginning, it seems probable to me that there would be some degree of interconnectedness and therefore non-locality should not be written off so quickly.

## Re: (Score:3, Interesting)

Personally, I don't see why people have such an issue with the existence of non-localityIt's because of how utterly central relativity is to our understanding of the universe. Manifest non-locality would be phenomenologically equivalent to a violation of the law of non-contradiction, or equivalently the law of causality. All the time-travel, grandfather-paradox stuff would become real problems for physics and nobody has the least idea of how to deal with them.

This doesn't mean that nonlocality is impossib

## Re: (Score:3, Interesting)

This doesn't mean that nonlocality is impossible, but it does mean it creates enormous practical problems for physics that no one knows how to approach, much less solve.

Forgive me for such a glib remark, but it's a shame that we're so afraid of entering new territory nowadays. It seems to me that the way things have worked historically is that each generation soaked up the knowledge of the old guard, then poked holes in the existing theories that revealed vast new lands to explore.

Indeed, this appears to be what Bohm did to the work of Einstein and Bohr with his willingness to explore non-locality, but the rest of his colleagues for whatever reason were unwilling to join

## Re: (Score:2)

There is no distance, since the coupled particles are, in fact, the same "particle". Then the problem of "information transfer"

This is indeed the end result of this line of thinking and is the conclusion reached by Bohm. I didn't want to take it that far in my post because a) without presenting the steps to reach that point it sounds like hippie bullshit, and b) since we experience "distance" in day-to-day living, it made sense to me to frame the concept as "non-locality" rather than "identity."

## Re: (Score:2)

If you RTFA, you will see that the article already talks about this, and explains how the authors went beyond this.

It amazes me how a slashdot armchair physicist can even presume that a published peer-reviewd article that then got covered by New Scientist would have ignored Bell's theorem.

## Re: (Score:2, Interesting)

It circumvents Bell's inequality in one of the already known ways.

There are a couple of ways out neither of which are appealing at first glance

-Non-local interaction (against special relativity)

-Super determinism (the experimenter is not free to setup his experiment as he sees fit)

This particular model falls in the later category. We cannot reason about a experiment asking what would have happened if I measured the other complementary thing. That particular history is not a valid configuration (falls outsid

## Re: (Score:2)

Bell's theory states that either the universe is non-local or quantum theory is incorrect. Palmer argues that quantum theory is incorrect in so far that the measurements it makes fall outside of the possible states of the universe and are therefore invalid.

## Can Fractals Make Sense of the Quantum World? (Score:4, Funny)

## Re: (Score:2)

## Who watches the watchers? (Score:5, Funny)

## wheres the beef? (Score:2)

## Re: (Score:3, Interesting)

>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 lin

## Re: (Score:2)

Did it have any pretty pictures?

Huh? No, of course I didn't read it, what do you take me for?

## Can Fractals Make Sense of the Quantum World? (Score:5, Funny)

No. No, they can't.

## Re: (Score:2)

## Can Fractals Make Sense of the Quantum World? (Score:5, Funny)

Yes. Yes, they can.

## Re:Can Fractals Make Sense of the Quantum World? (Score:5, Funny)

Maybe. Maybe, they could, or they couldn't.

## Re: (Score:3, Funny)

Yes. Yes they can.

and

No. No they can't.

## Black hole information loss? (Score:5, Interesting)

## Re: (Score:2)

## Re: (Score:3, Informative)

> ...to an outside observer, an object never falls into a black hole, it only approaches

> the event horizon without ever quite reaching it.

This implies that a black hole can never be observed to come into existence.

## Re: (Score:2)

I still don't understand why people cannot deal with the possibility of information loss in black holes. No, it doesn't fit with the DESIRE for a "tidy" Universe, but it also doesn't prevent the Universe from functioning (just some of our current assumptions).

We currently work with the idea of a "quantum foam", and some experiments on the Casimir Effect support the idea. We do NOT know the position or momentum of a virtual photon, yet it appears to interact with the macroscopic universe. Thus, the Univer

## Re: (Score:2)

GHZ contradictions.

Shhh. Intel marketing people start to sweat profusely when you mention this.

## Mandelbrot magnetic fields (Score:2)

Only vaguely related to this story but apparently, the mandelbrot shape has been found in cross-sections of magnetic field borders. I only found the reference from one page a while back though, so I can't say how true it is.

## The coolest thang (Score:2)

From TFA:

"the invariant set of the universe"

Ain't that a nifty idea?

## The theory needs proofreading (Score:3, Informative)

From the author's abstract at http://arxiv.org/abs/0812.1148 [arxiv.org]

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

entirelyanalysis is given of the standard "mysteries" of quantum theory: superposition, nonlocality, measurement, emergence of classicality, the ontology of uncertainty and so on."## Re: (Score:2)

"...entirely

newanalysis..." makes sense to me.## NKS (Score:2)

Palmer and Stephen Wolfram should talk. [wolframscience.com]

## It's not about the math! (Score:2)

.

What we are talking about is the basic concepts in Chaos: self-similarity, superposition, and sensitivity to initial conditions.

.

The article/author is using fractals, cause they look, well, visually appealing to the typical person (it gets the point across). Heck, I can make triangles fit QM to so point (i.e. Math i

## Re: (Score:3, Funny)

## Re: (Score:2)

So maybe all it really takes is a really powerful computer and a m set. On the downside this leaves open the possibility that th

## Re: (Score:3, Informative)