So im reading up on chaos stuff right now but I have a few questions

So im reading up on chaos stuff right now but I have a few questions.

So essentially there is chaos (deterministic) and real randomness. Chaos is almost everything we declare as random (rolling a dice for example) while real randomness is essentially really rare, for example in radioactive half-life.

Are there any other examples of actual randomness?

>Are there any other examples of actual randomness?
Everything that depends on quantum effects. Tunnelling (radio decay) is the easiest to explain, but basically all of quantum mechanics.

Layman here. Can we prove their randomness or we just don't know what happen behind the scenes and use this approximation?

Thanks, gonna read up on that and try to understand it at least a little bit

Classical mechanics cannot explain quantum phenomena. In tunnelling, for example, a particle that you know for a fact is in the interval (a, b) subject to a potential energy such that it's kinetic energy cannot overcome such potential has a probability of being found outside (a,b); one thing that absolutely cannot happen classically. It's like you put a ball in a bowl, and then you find it has crossed to the other side, even though you gave it no velocity.

It follows that what OP proclaimed as elaborate chaos, i.e. throwing dice, is truly random as well.

It would depend on the mass of the dice, I suppose.

OP here, when im throwing a dice its chaotic because you could theoretically calculate the outcome if you knew all the parameters, am I not understanding that right?

I read up a little bit on tunnelling and I if I understood everything correctly its random because the energy is uncertain so you can't actually calculate it, only probability?

rolling dice has literally nothing to do with chaos.

Chaos is about butterfly-effect like stuff. Small changes in initial conditions => unpredictable mess of changes 10 iterations down the road

And what is rolling a dice? You make a small change in the initial conditions like moving your hand 1mm to the right and you get a completly different result

hm, here

I think your question is ultimately philosophic and hinges on (untestable and therefore unscientific) interpretations of quantum mechanics.

Or maybe its not and I should read the wiki article on determinism right now, but Im lazy.

So I will just ask Veeky Forums:
Is determinism consistent with the current mathematics and observations about QM?
I believe the catchphrase here was hidden variable theories, and iirc "global" hidden variables werent contradictory, albeit useless from a science point of view.

I'm tempted to post the Vsauce & Veritasium videos that deal with this topic but I don't want everyone to go >m-muh popsci

To model rolling a die mathematically, you assume the die can be described by 12 variables (say xyz position, xyz velocity, pitch, yaw, roll and their derivatives) and the environment by a (possibly time dependent) potential energy surface. Then you just apply some mechanical integration technique (ie. Legrangian mechanics). The process returns a 12-vector which has associated error based on the error in the original measurements and/or the error in your integration technique.

Past some theoretical threshold tolerance for initial error your vector will match the actual outcome of the die roll with arbitrarily high confidence.

To model a quantum phenomenon (quantized field BS aside) you assume the system can be described by a wave function of so many variables (say 12 again) and the environment by a (possibly time dependent) potential energy surface. Once again you apply some sort of integration technique (derived from our time dependent Schrodinger equation). The process returns a wave function which has associated error based on the error in the original measurements and/or the error in your integration technique.

Past some theoretical threshold tolerance for initial error your vector will match the """actual""" """wavefunction""" for some arbitrarily high confidence, but at this point you *still* only have a statistical description of physical reality. You can predict discrete outcomes a b and c with associated odds or continuous outcome x with probability distribution p(x), but past that you're blind.

Whether this is true in-determinism or the effect of hidden variables is an open philosophical question. But if we "shut up and calculate" we still recognize a very real difference in the math.

Hmm.. okey thanks. So what im taking from this thread is that we aren't actually sure if its chaotic with some hidden variables or truly random.
This is probably too high for some 12th grade high school papers but I'll include it anyway

Yes

Read about Bell's Theorem. It states that no theory of local hidden variables explains quantum phenomena meaning that it's either random or that particles "know" what's happening everywhere at once. I'm more inclined to go with randomness but some people take issue with it.

>Whether this is true in-determinism or the effect of hidden variables is an open philosophical question.

No it's not

Randomness is just something that cannot be compressed? I am obviously talking about Kolmogorov randomness, but it is worth noting.

OP, Kolmogorov had a lot to do with fluid mechanics + turbulence and the two concepts are inherently related.

Also the term >random< has multiple definitions depending on the field.

You have experimental evidence against De Broglie–Bohm theory?

free will is true random.

>believing the free-will meme

Please, keep believing the reaction you have reading my post is totally under your control.

But for large masses quantum uncertainty becomes vanishingly small. A so called super-astronomically unlikely event. So a dice tunnelling through a wall or rolling from the opposite side you calculated it would is so unlikely it is unlikely to ever happen in the lifetime of the universe.

Like for example a macroscopic amount of entropy reversing by chance (which is possible in a statistical mechanics formulation of entropy )