QM randomness vs chaotic determinism?

[lukephysics]

TL;DR

Random vs chaotic?

Can you swap out the RNG that is the wave function collapse with a suitable deterministic chaotic process that matches the wave function (squared)?

I can picture a multi leg pendulum swinging around drawing out the wave function. The point where you measure is the point the pendulum was at.

Is there any measurable difference between the two?

 

[PeterDonis]

the RNG that is the wave function collapse

What does this even mean?

 

[lukephysics]

RNG is random number generator. Ie true random, pseudo random, quasi random etc.

 

[Nugatory]

Is there any measurable difference between the two?

Yes.
Google for "Bell's theorems quantum mechanics" and check out the web page maintained by member @DrChinese. This theorem shows that any deterministic mechanism, even one that is too complicated to analyze (which is what chaotic systems and good PRNGs are) will produce results in some experiments that are statistically different than the results predicted by quantum mechanics. These experiments have been done and they match the quantum mechanical predictions.

(Strictly speaking, the word "any" above is an overstatement - Bell's theorem does not apply to mechanisms that are "superdeterministic". However, a discussion of superdeterminism is irrelevant for the sorts of mechanisms that your question is considering)

 

[Nugatory]

@lukephysics You might want to go back and reread some of the references from your older thread about this: https://www.physicsforums.com/threads/why-isnt-quantum-entanglement-just-correlation.1007029

 

[PeterDonis]

RNG is random number generator.

Yes, I know that. That's not what I asked you. I asked you about the specific claim you made in your OP, that I quoted. I can't even make sense of it.

 

[lukephysics]

This theorem shows that any deterministic mechanism

No, bell only eliminates local deterministic mechanisms. Not non-local deterministic mechanisms.

Either god is rolling a dice in a cup, or god is glancing at his multi leg pendulum toy. Either way god is non local here. Either are interchangeable from what I can tell.

 

[Nugatory]

No, bell only eliminates local deterministic mechanisms. Not non-local deterministic mechanisms.

Yes, but the stuff you’re describing (chaotic processes, RNG, multi-keg pendulum,…) are all local unless you are adding some non-local mechanism on top of them.

 

[LittleSchwinger]

Even if one added stochasticity atop of a chaotic evolution you would still not replicate quantum theory. Classical Probability and Quantum Probability are simply different mathematical structures.

 

[lukephysics]

Classical Probability and Quantum Probability are simply different mathematical structures.

Could you please explain that a little more? As far as I know there is no such thing as quantum probability. It is simply the born rule which gives you a pdf which is classical.

So if your chaotic process evolves to give you a pdf that matches the wave function pdf they are the same thing.

Even if one added stochasticity atop of a chaotic evolution

The trick is here you can only collapse the wave function once, so it doesn’t matter what the chaotic process is, you are only ever taking one sample, so need zero stochastic element to it.

 

[PeterDonis]

you can only collapse the wave function once, so it doesn’t matter what the chaotic process is, you are only taking one sample, so need zero stochastic element to it

This is wrong. For one particular quantum system at one particular time, you can only make one measurement and apply the wave function collapse rule one time. But you can do the same experiment on a large number of identically prepared systems and get a large number of wave function collapse rule applications and do statistics on them.

You still have not answered my question in post #2. You already have had one thread discussing something that looks very, very similar to what you are asking now. If this is just a rehash of that already closed thread, that is off limits here and this thread will be closed as well.

 

[GarberMoisha]

TL;DR Summary: Random vs chaotic?

Can you swap out the RNG that is the wave function collapse with a suitable deterministic chaotic process that matches the wave function (squared)?

I can picture a multi leg pendulum swinging around drawing out the wave function. The point where you measure is the point the pendulum was at.

Is there any measurable difference between the two?

Did you understand that in classical mechanics identical systems always behave the same while in QM this does not hold?
There is a limit to the threshold of determinancy that cannot be overcome.

 

[lukephysics]

This is wrong. For one particular quantum system at one particular time, you can only make one measurement and apply the wave function collapse rule one time. But you can do the same experiment on a large number of identically prepared systems and get a large number of wave function collapse rule applications and do statistics on them.

yes this would be correct if they were identical runs. perhaps the elementary particles interact with a non-local field that evolves chaotically, which makes each run non-iid.

this field might be truely random or it might be chaotic and appear random to us. maybe we can never know how it evolves.

the purpose of my quest is to hunt for sources of the randomness in the collapse. as a programmer i know you can code an RNG to spit out random numbers even if they are not truely random. If i know the seed I can predict the numbers. i am not sure what you could do with this information if you can perfectly predict the result of a wave function collapse, might be important to humankind (!)

You still have not answered my question in post #2. You already have had one thread discussing something that looks very, very similar to what you are asking now. If this is just a rehash of that already closed thread, that is off limits here and this thread will be closed as well.

This is nothing to do with bell or entanglement which is my other thread, which was 2 years ago. i am perfectly understanding bell and non-local non-real implications. But you did reply in the paragraph above so i think you are on the right track(?)

 

[Nugatory]

yes this would be correct if they were identical runs. They are not identical if you have different starting parameters for the underlying chaotic process. for example, perhaps the elementary particles interact with a field during creation, and that grants them their starting parameters which makes each run non-iid.

OK, let's consider a specific example. We have a laboratory oven heating up and ionizing a bunch of silver atoms, then we send them towards a vertically-oriented Stern-Gerlach device, and an upwards-directed and a downwards-directed beam emerges. We pass one of these through a horizontally-oriented SG device and again two beams emerge. You are suggesting that there some hypothetical field in the oven is setting the state of the ions such that some hypothetical mechanism will cause some of them to be deflected left and other right even though the first SG device has already picked out only the ones that have vertically oriented spin, and even though they were all subject to the same initial conditions within the oven.

Furthermore, the operation of this hypothetical field must either be non-local (to allow for violations of Bell's inequality in other experiments) or some other just as hypothetical field must be at work when entangled pairs are created.

And its not as if you have any candidate theory that might explain the operation of these hypothetical fields, nor observational evidence that they might exist.

 

[PeterDonis]

the purpose of my quest is to hunt for sources of the randomness in the collapse

The best way to do this is to work your way through the voluminous literature that already exists on this topic.

 

[PeterDonis]

perhaps the elementary particles interact with a non-local field that evolves chaotically, which makes each run non-iid.

this field might be truely random or it might be chaotic and appear random to us. maybe we can never know how it evolves.

All of this is personal speculation and is off limits here.

 

[PeterDonis]

This is nothing to do with bell or entanglement which is my other thread

Yes, actually, it does, because whatever you believe "wave function collapse" is in QM (and different QM interpretations make different claims about this--discussion of that belongs in the interpretations subforum, not this one), it has to be able to produce violations of the Bell inequalities. No classical "RNG" mechanism of the kind you appear to have in mind can do that.

 

[lukephysics]

And its not as if you have any candidate theory that might explain the operation of these hypothetical fields, nor observational evidence that they might exist.

Copenhagen takes the probabilities as prima facia. I am looking for causes for those probabilities because no cause is given in Copenhagen.

You are suggesting that there some hypothetical field in the oven is setting the state of the ions

no, sorry. i edited my example. the non-local field might interact upon decoherence, not on creation. sorry to do that to you. maybe its random, maybe its pseudorandom (chaos). maybe we will never know.

i am just skeptical something can be random prima facia. doesnt nature require some engine to produce random numbers? im just looking for the engine based off how humans know how to do it.

 

[vanhees71]

Could you please explain that a little more? As far as I know there is no such thing as quantum probability. It is simply the born rule which gives you a pdf which is classical.

That right and wrong at the same time ;-). Born's rule gives usual probabilities a la Kolmogorov at best for the measurement of a complete compatible (!!!) set of observables, $A_1,\ldots,A_n$, because then the possible outcomes of such a measurement are the n-tupels of eigenvalues $(a_1,\ldots,a_n)$ of the corresponding operators, and the eigenstates are unique up to an irrelevant phase factor and build a complete orthonormal (!!!) basis. That means here you have to usual notion of a probability space a la Kolmogorov, i.e., with the set of "elementary outcomes" given by the $n$-tupels of eigenvalues, and the corresponding probabilities, given by Born's rule,
$$P(a_1,\ldots,a_n) = \langle a_1,\ldots a_n| \hat{\rho}|a_1,\ldots,a_n \rangle,$$
where $\hat{\rho}$ is the statistical operator describing the quantum state the system is prepared in. In this sense the quantum probabilities form a standard realization of Kolmogorov's axioms.

However, there are almose more observables, which are not compatible with all the observables in any complete set. So the probabilities for the entire set of possible observables doesn't form such a Kolmogorovian probability scheme. You can even extent the description of probabilities for measurements involving incompatible observables, where you do "weak measurements", i.e., you gain some probabilistic information about the incompatible observables measured, but it can never be a complete information. That's formalised with positive operator-values measures (POVMs).

 

[PeterDonis]

doesnt nature require some engine to produce random numbers?

Sure: that "engine" is quantum indeterminacy!

As you noted previously, "random" number generators in most computers don't actually generate "random" numbers; if you know the seed you can duplicate the entire sequence of "random" numbers being generated.

However, for some applications that isn't considered sufficient and actual randomness is needed. To get it, such applications sample some real-world process that is not predictable or repeatable. The best such real-world processes known are quantum processes.

 

[Structure seeker]

Sure: that "engine" is quantum indeterminacy!

Could it be that the unknown quantum states of the particles in the device that does the measurement (and other environment) are part or whole of this engine? They have certain wavefunctions as state (which we can never know exactly) and the deterministic Schrödinger equation makes those influence the outcome of the collapse? I'm a big fan of Einstein, the belief that "God" does not play dice even in quantum mechanics is also my belief (Although I don't like how dark matter is presented as being more Einstein-like than MOND. Einstein never thought his theories were already perfect without question).

It's just a pet thought of mine to retain determinism this way (the other option of superdeterminism I dislike because it feels like superstition to me that deciding what to measure influences the quantum states).

 

[gentzen]

Could it be that the unknown quantum states of the particles in the device that does the measurement (and other environment) are part or whole of this engine? ...

It's just a pet thought of mine to retain determinism this way (...).

Why not Bohmian mechanics, if you are such a fan of determinism?

 

[GarberMoisha]

Could it be that the unknown quantum states of the particles in the device that does the measurement (and other environment) are part or whole of this engine? They have certain wavefunctions as state (which we can never know exactly) and the deterministic Schrödinger equation makes those influence the outcome of the collapse? I'm a big fan of Einstein, the belief that "God" does not play dice even in quantum mechanics is also my belief (Although I don't like how dark matter is presented as being more Einstein-like than MOND. Einstein never thought his theories were already perfect without question).

It's just a pet thought of mine to retain determinism this way (the other option of superdeterminism I dislike because it feels like superstition to me that deciding what to measure influences the quantum states).

It's not like the outcomes are ever random.
It is more about them being indeterminant, as in being impossible to know them in advance even with the best technology ever.
Tough luck. Nature, whatever it is, guards its secrets well.
It is a flat out limit on knowledge. This is what it is.

 

[GarberMoisha]

Scientists sometimes use the term "random" when explaining quantum systems because if they use the term "inderminant", it could evoke a feeling that quantum systems somehow conspire against against knowledge. And this venue is unscientific in its framework. Science assumes that particles cannot evade knowledge. Even though the HUP suggests that this assumption could be wrong.

 

[PeterDonis]

Could it be that the unknown quantum states of the particles in the device that does the measurement (and other environment) are part or whole of this engine?

That would seem to be very likely, yes. There are many treatments of measurement in the literature (including the vast literature on decoherence) that discuss this. However, nobody has yet found a way for quantum interactions of this sort to pick out just one measurement result. The best that can be done thus far is to explain why the different "branches" of the wave function corresponding to different results don't interfere with each other. But the straightforward quantum dynamics of the measurement interaction ends up with all of the "branches" corresponding to all of the possible measurement results being in the final wave function. In other words, something like the MWI. Nobody knows how to get just one of the possible results from the quantum dynamics.

 

[Structure seeker]

Why not Bohmian mechanics, if you are such a fan of determinism?

Whether Bohmian mechanics is true or not seems to me independent of my pet idea. It's not a theory I expect to be true, but that's an opinion.

Nature, whatever it is, guards its secrets well.
It is a flat out limit on knowledge

I'm quite convinced that there is no place where the light of understanding will not reach, once. We'll be mystified and enlightened more and more :-)

In other words, something like the MWI. Nobody knows how to get just one of the possible results from the quantum dynamics.

Thanks for your answer! I'd like to emphasize "something like": not actually the same as the MWI, right?
And indeed nobody knows; perhaps there is some unknown law at work?

 

[PeterDonis]

I'd like to emphasize "something like": not actually the same as the MWI, right?

Correct. What I described is just doing the math of QM to a much greater extent than is usually done (because in most practical cases it's not necessary). The MWI goes beyond that to claim that nothing else happens except what that unitary math describes--i.e., that all of the possible measurement outcomes do happen in reality, not just in the unitary math--there is no physical process that in the end just picks out one outcome to actually happen. Collapse interpretations say there is such a process--we just don't understand (yet) how it works.

 

[lukephysics]

-there is no physical process that in the end just picks out one outcome to actually happen. Collapse interpretations say there is such a process--we just don't understand (yet) how it works.

Thank you for admitting this. This is what this thread is about.

But an NPC in a game will never be able to know the random damage it’s sword is doing is just a deterministic formula.
And that npc will never see outside it’s program because it’s brain is sitting in protected memory walled from the rest of the computer.
It would be sad if no information leaks through on the wall in our universe

 

[PeterDonis]

Thank you for admitting this.

Um, I was not "admitting" anything. I was describing claims made by two different QM interpretations. We do not know if either one of them is "true". Discussion of QM interpretations belongs in the interpretations subforum, not this one.

an NPC in a game will never be able to know the random damage it’s sword is doing is just a deterministic formula.
And that npc will never see outside it’s program because it’s brain is sitting in protected memory walled from the rest of the computer.
It would be sad if no information leaks through on the wall in our universe

At this point you are just wandering around in speculation. That's not what PF discussion is for.

Thread closed.