# How to tell the difference between randomness and chaos?

Found this question while think of determine&random. If a system if very complex, it may looks like random. Even GUT is found, it is still impossible to tell what a determined system will be after a long period because of Heisenberg's uncertainty principle. An error in initial conditions, even it's smaller than any number which can be imagined, will be zoom out to be seen very soon in a chaotic system.
Then what is the difference between chaos and randomness? Or, are they exactly the same thing since uncertainty principle kills any experiment to tell the difference?

phinds
Gold Member
2021 Award
Found this question while think of determine&random. If a system if very complex, it may looks like random. Even GUT is found, it is still impossible to tell what a determined system will be after a long period because of Heisenberg's uncertainty principle. An error in initial conditions, even it's smaller than any number which can be imagined, will be zoom out to be seen very soon in a chaotic system.
Then what is the difference between chaos and randomness? Or, are they exactly the same thing since uncertainty principle kills any experiment to tell the difference?

http://www.math.tamu.edu/~mpilant/math614/chaos_vs_random.pdf

which is just the first hit I got when I asked your question of google. It IS, after all, exactly the kind of question that Google generally will give you decent answers on.

http://www.math.tamu.edu/~mpilant/math614/chaos_vs_random.pdf

which is just the first hit I got when I asked your question of google. It IS, after all, exactly the kind of question that Google generally will give you decent answers on.
This is not the case! I'm sorry if I didn't make myself understood clearly enough. This file provides the difference between the two mathematical structures, which is useless. My question is, if one says the world is completely determined, which kind of experiment can I do to make him believe real world is random.

NascentOxygen
Staff Emeritus
As unforeseeable as much in the real world may seem, it isn't random. It is difficult to find events which are truly random; for a start, how to prove (i.e., demonstrate to 100% certainty) that something has a truly random outcome? For most apparently-unpredictable events we end up saying, well, as far as we are concerned we'll regard it for our purposes as essentially random. But that doesn't mean it is.

I'm sure cow pat lotto just looks random.

Any experiment needs initial conditions, but uncertainty principle forbids giving the same initial conditions to two systems. So it is never possible to check weather a system is chaotic or random. By Occam's Razor principle(let me just call it a principle), it's better to say there aren't two separated concerpt named random and chaos but a single one.
But a determined theory will allow me to do the following experiment:
I can take a determined process, which is as complex as possible. With supercomputers, I can compute how the system will be after a while with every initial condition. In the process, very small difference will be zoomed out that I can see them. By this method, I can measure position and momentum simultaneously as exactly as I want, because the error I will make will be compressed to be any finite small number by the inverse process(not necessary able to do physically, but I can compute), exponentially.
Is determined theory itself against the uncertainty principle?

I believe randomness is the measure of chaos.

anorlunda
Staff Emeritus
Don't forget that quantum mechanics is as the base of all physics. The randomness in quantum physics is not chaos based.

Don't forget that quantum mechanics is as the base of all physics. The randomness in quantum physics is not chaos based.
Remember that quantum mechanics is much earlier than the chaos theory. At that age, no one of the world knows about chaos. They might think randomness exist everywhere like dice game. I may predict what will the result be for a dice game if I know enough information. They didn't do any experiments to show the randomness, but just guessing. We may or may not believe real world is random, there's no proof,

Nugatory
Mentor
My question is, if one says the world is completely determined, which kind of experiment can I do to make him believe real world is random.

No experiment can settle that question, so this discussion doesn't belong here. Thread closed.