# Help on Chaos theory

## Main Question or Discussion Point

Hello
I am a new member of this forum and I have very limited math knowledge. My only experience in Physics is a thirty page thesis on the question, What is Light? I am doing a follow up science fair project concerning the significance of the establishment of String theory on chaos theory. My logic behind this is that since the hisenberg uncertainity priciple is basically based on the idea that the electrons postion is chaotic, wouldn't string theory if proven denounce the idea of the choatic electron in favor of a wave viewed electron.

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matt grime
Homework Helper
that isn't what chaos theory is.

Thank you very much for your assistance.

matt grime
Homework Helper
chaos theory is, approximately, the study of non linear systems that display certain properties. it isn't things that behave "at random" and is actually to do with things that are deterministic ie if we knew the system at time t exactly we ould know it at all future times, but given two starting configurations of the system at time t, then at some point in the future the system would form two configurations as far apart as we wish (sensitive dependence) and that all possible configurations can be obtained from a "small" set of starting configurations (topological transitivity). there are other variations on these.

an example would be the map from the interval I={x : 0<=x<=1} (the real numbers between 0 and 1 inclusive) f_k that sends x to kx(1-x)where k is some constant between 0 and 4. this is the so called logistic map and is the fundamental example of a dynamical system. it gives rise to the famous pitchfork bifrucation and feigenbaum's constant. (i think smale's horse shoe map is more intersesting).

string theory, being a phsyical one, cannot be proven, only ever disproven (or shown to be inadequate). i know of nothing it predicts that would contradict the heisenberg principle but i know nothing about string theory at all.

what is it that makes you think string theory would end the quantum nature of electrons? (or presumably photons too, things that are provable wave-particle and such. how about the doulbe slit experiment?)

if you want something to ponder, how about this: why is it that quantum mechanics hasn't found a way to account for gravity, and that relativty doesn't take quantum effects into consideration. ie what is the state of the attempt to unify the very large behaviour and the very small behaviour of the universe? "chaos theory" incidentally deals almost exclusively with the middle ground of the macroscopic world around us, though there is also quantum choas).

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HallsofIvy
Homework Helper
A lot of people confuse "chaos theory" with random behavior. In a certain sense, it is the exact opposite. Every one has seen the simple experiment where you drop a lot of marbles or bbs onto a board with nails so that each marble goes either left or right randomly. Even though there is no way of telling which way a given marble will go at a given nail, at the end you have all the marbles nicely filling out the region below a previously drawn curve- the famous "bell shaped" curve. That is, in the long run, the result of random action can be accurately forecast.

Chaos theory shows that result of completely non-random behaviour can be impossible to forcast accurately. A simple example: start with x0 equal to any number between 0 and 1 and apply the recursion xn= 2n (mod 1) where "mod 1" simply means "if the result is larger than 1, drop the integer part". For example, if x0= .4= 2/5, x1= 2(2/5)= 4/5, 2(4/5)= 8/5 which is larger than 1 so x2 = 8/5-1= 3/5. 2(3/5)= 6/5 which is larger than 1 so x3= 6/5-1= 1/5. x4= 2(1/5)= 2/5 and the sequence starts again. The result is the "periodic" sequence 2/5, 4/5, 3/5, 1/5, 2/5, 4/5, 3/5, 1/5,...
Every number in the sequence is completely determined by the first number- there is no random behavior at all.

An even simpler sequence is 1/3, 2/3, 1/3, 2/3, ... But suppose you chose to use a calculator or computer to do the calculation instead. You can't actually put "1/3" into a finite computer, you would have to approximate it by, say, 0.33333333333333333333333. It's easy to see that after relatively few iteration (15 or 16 say), your sequence is nowhere near "1/3, 2/3, 1/3, 2/3". The slightest change in the initial value results in huge changes (relatively- obviously we stay between 0 and 1 in this example). So the idea of chaos theory is that completely "determined" operations can give results that might as well be random.

The reason I thought this disproved chaos theory, I was in the random state of mind at that time, is because string theory gives rise to the idea that there is no longer such a thing as a point particle. So essentially by eliminating the idea of the point particle you could say that the structure of the atom takes on more wave characteristics. The question is no longer where can the particle possibly be, it is already there. I suppose it struck me by eliminating the idea of random motion in an atom it made no room for chaotic patterns(could be full of errors).

Does Chaos theory pretain to the evolution of a population?

chaos theory(i prefer to think of dynamical systems)is all about having a basic set of rules and an initial state in a system and watching the system mechanically evolve through what some call a transition table, others may use another term, It can be applied to any field if one can define "the basic set of rules" and the initial state of the environment.

a simple example is cellular automats or the game of life.
OR billiards...if the basic set of rules were the classical mechanics motion equations.
OR neural nets...depending on the learnign rule you use, and growth and prune
structures.
OR strategies in RTS games...in which types of strategies would be the base
OR in FPS...state of emotion of agents
OR in astrophysics...cosmology your fundamental units would be stars and gravity
OR iin linguistics, just building a language cna create complex patterns

Evolution is harder to say but IMO yes it is(well in computer programming GAs are)...but it depends on what you start with...DNA,Xsomes? then one could probably consider it to be.

matt grime
Homework Helper
scott_alexsk said:
The reason I thought this disproved chaos theory, I was in the random state of mind at that time, is because string theory gives rise to the idea that there is no longer such a thing as a point particle. So essentially by eliminating the idea of the point particle you could say that the structure of the atom takes on more wave characteristics. The question is no longer where can the particle possibly be, it is already there. I suppose it struck me by eliminating the idea of random motion in an atom it made no room for chaotic patterns(could be full of errors).

you appear to be confusing what something 'is' (an electron) with a *model* to describe its behaviour.

matt grime
Homework Helper
scott_alexsk said:
Does Chaos theory pretain to the evolution of a population?

not necessarily but a *model* for the evolution of a popultion may be chaotic.

chaos theory pertains to any mathematical system that possesses chaotic properties (mostly taken to mean sensitive dependence on initial conditions and/or topological transitivity). don't confuse what chaos means mathematically with the misusage of it as a label in popular science.

Was not the main idea of the Heisenberg Uncertainty principle to account for supposed clout around a point particle. And to answer your earlier question, the reason neither theories can account for the effects of the other is because neither theories accounted for dealing with opposing large scales or small scales. Quantum mechanics does not deal with multi dimensional stuff and likewise Relativity does not obey the laws of the Heisenberg Uncertainty Principle.

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matt grime
Homework Helper
it accounts for the fact that the momentum and position operators do not commute. electrons are not point particles in a cloud (cloud of what?).

It is not Cloud but clout which I refer to because it means a distorted position. It seems that either the photons around the electron or the electrons speed distort its position. It could be my own flawed view but it appears to me that the speed of the electron stops time for itself but also creates this field of activity around itself. This is where the major debate is on particle-wave duality. The question is whether or not a point particle exsists and are the effects we observe, not distorted, just a continuous wavefront.

matt grime
Homework Helper
"photons around the electron"? Or "clout"? you appear to be inventing you own physics now.

Yes Photons around the electron, they are called messenger particles for the strong magnetic force. Never the less the postion of the electron is unclear and because of this it is hard to settle whether or not the electron is a wave.

Hurkyl
Staff Emeritus
Gold Member
There is no debate about wave-particle duality: both pictures are wrong. The wave picture and the particle picture are just two different approximations to how things really behave.

Incidentally, special relativity and quantum mechanics do mix. There is no fundamental problem using the two together, it's just that the details are much trickier, so it took physicists a while to work it out.

Special relativity is, more or less, simply geometry. You can do classical mechanics in it, or you can do quantum physics in it. There's no problem either way.

Incidentally, I can't imagine what you mean by "Quantum mechanics does not deal with multidimensional stuff"

The famous problem you may have heard about is between general relativity and quantum mechanics. General relativity is also mainly a theory about geometry. However, general relativity is a lot more, well, general than special relativity, and as such has proven to be much harder to work through the details to do quantum general relativity.

However, you should be aware that people do do what is essentially quantum general relativity. The problem is essentially that people haven't been able to show that it resembles the universe we observe.

What I meant when I said multidimensional stuff, I was talking about how general relativity deals with folding of dimensions while, to my knowledge, quantum mechanics provides a completely different picture. Personally I believe wave theory is more correct but it cannot fully address all physical properties. String theory seems to unify the two theories quite well by introducing strings vibrating through the multidimensional calabai-yau shapes.

Gokul43201
Staff Emeritus
Gold Member
scott_alexsk said:
My logic behind this is that since the hisenberg uncertainity priciple is basically based on the idea that the electrons postion is chaotic, wouldn't string theory if proven denounce the idea of the choatic electron in favor of a wave viewed electron.
(1)the Heisenberg Uncertainity Priciple is NOT based on the idea that the electron's position is chaotic,
(2) the electron's position is NOT chaotic
(3) String Theory, if proved, will NOT nullify the mountains of experimental evidence supporting HUP.

Scott, you seem like someone enthusiastic about physics. Unfortunately, there's a whole lot more to the physics and math involved in QM, Relativity, String Theory or Chaos Theory than you can possibly dream of learning from reading a single document. There are members here that have spent several years learning and developing advanced math and physics. They usually have a very good idea of when someone is wasting their time over speculations that are based on ignorance.

I have a suggestion. Learn math and physics the right way - through classes (or from recognized texts) - you will discover a whole lot more beauty that way. Unless you do so, you can not produce any NEW science or math.

If you want to propose your own theories on this Forum, there are a set of requirements that your theory must pass in order to not be considered non-science. https://www.physicsforums.com/showthread.php?t=82301