Quantum randomness vs. dice randomness

[ivan]

quantum randomness vs. "dice randomness"

Can anybody explain what's the difference between quantum randomness and "regular" randomness, please. (say random distribution of dice-faces when throwing a dice)

 

[masudr]

You can, in principle, predict the outcome of a classically random event (e.g. if you knew the moment of inertia of the dice, the initial torque applied on the dice, any wind/movement of air on the dice, the coefficient of restitution of the dice and table it bounces on as a function of the speed at which the dice hits the table and the angle at which it strikes etc.)

 

[ivan]

You can, in principle, predict the outcome of a classically random event (e.g. if you knew the moment of inertia of the dice, the initial torque applied on the dice, any wind/movement of air on the dice, the coefficient of restitution of the dice and table it bounces on as a function of the speed at which the dice hits the table and the angle at which it strikes etc.)

Thank you.
So then quantum randomness is nondeterministic meaning one could not predict outcome just because it is non-computable even in principle. Is this right?

 

[masudr]

When a system is in a superposition of two or more states with definite eigenvalues of a certain operator (corresponding to a measurement), there is, even in principle, no way to determine what the outcome of that measurement would be; all one can determine is the probability that it would be an outcome.

If it is not in a superposition, and is itself an eigenstate, then one can guarantee what the measurement of that observable will be (if the measurement operator commutes with the Hamiltonian, then one can guarantee the measurement outcome at any time, if not then one can only guarantee it for that instant).

 

[peter0302]

The comprehensible answer to his question was yes.

Also, another key difference is that in classical randomness, different "either/or" probabilities add, as in P(A or B) = P(A) + P(B). In quantum randomness, probability _amplitudes_ add, as in P(A or B)) = ||A>+|B>|*. That is how interference patterns emerge.

 

[ThomasT]

Can anybody explain what's the difference between quantum randomness and "regular" randomness, please. (say random distribution of dice-faces when throwing a dice)

In practice, there's no difference. Random means unpredictable. The order of a set of dice-throws is as unpredictable as the order of a set of single photon detections.

So then quantum randomness is nondeterministic meaning one could not predict outcome just because it is non-computable even in principle. Is this right?

In theory, there's a difference. The physical principles of quantum theory preclude anything but a probabilistic accounting of certain experiments.

But to say that this quantum randomness is some sort of real or true randomness as opposed to the more pseudo randomness of dice throws is meaningless.

 

[masudr]

The comprehensible answer to his question was yes.

Perhaps, but I wanted to point out that in some circumstances, we can make definite claims. e.g. when the state is in an eigenstate already. I guess I didn't get the point across too succinctly.

 

[peter0302]

In practice, there's no difference. Random means unpredictable. The order of a set of dice-throws is as unpredictable as the order of a set of single photon detections.

It is not true that there is no difference in practice. The interference pattern results directly from this distinction. A very clear example of this is how if you set up an experiment where it is possible _in theory_ to know the result of a non-commuting measurement, but nonetheless impossible _in practice_, you lose the interference pattern. Nature doesn't care about "in practice" versus "in theory."

But to say that this quantum randomness is some sort of real or true randomness as opposed to the more pseudo randomness of dice throws is meaningless.

Meaningless is a strong word and that is simply not true. Take computer generated "random" numbers. All such algorithms appear random to the "naked eye" in practice, but they all require a "seed" to generate differences with each run of the program. If you have ever played old video games, you will notice that certain "Random" things actually depend on the ticks of a clock and players could cheat by timing things perfectly.

The only perfect random number generator is a quantum one. Anything else is deterministic and subject to tampering or reverse engineering. Every casino owner knows that dice throws are not "perfectly" random as dice manufacturers go through great pains to make each face of the die have as close to an equal probability of landing as possible. They also know that even a hair's weight difference can throw off the results over the long term, and therefore a lot of time and money is spent trying to achieve perfection.

A better example is card shuffling. Everyone knows that bad shuffling results in a bad card game.

Take the slot machines too. It's only a matter of time before these contain quantum randomizers. I promise you casinos will buy them because they know the enormous importance of achieving perfect randomness and the dangers of leaving such things to pseudo-random algorithms.

There is most certainly a real difference between deterministic pseudo-randomness, and quantum randomness. *No* deterministic process is truly random. That's the very definition of deterministic.

 

[ivan]

In practice, there's no difference. Random means unpredictable. The order of a set of dice-throws is as unpredictable as the order of a set of single photon detections.

Then this must be most important thing since theories may be wrong. If I can't even in principle set up an experiment where dice throwing can be shown to be deterministic then how does it matter what I call it(deterministic randomness vs. nondeterministic randomness)?

In theory, there's a difference. The physical principles of quantum theory preclude anything but a probabilistic accounting of certain experiments.

Could you translate that in a language of cause-effect please. This is what I mean. One could conceptualize the outcome of "dice throwing" randomness as being caused by many different causes. Here we say we can't predict outcome because these causes are numerous and change all the time. All these causes and there change is hard to predict.

What about quantum events? Are they random (at least in theory as you say) because they don't have a cause(s)? I understand that quantum theory is very good predicting things and one could stop asking these questions. But I'm just curious what some of the metaphysical thoughts are about this.

Regards to all

 

[Razzor7]

All this quantum stuff confuses the hell out of me. I thought the randomness was due to the fact that the act of taking the measurement changes the particle in a way we can't predict. That seems to me that it doesn't make it truly random. My question is basically does quantum theory contradict determinism?

 

[Mentz114]

We have to consider initial conditions. In a deterministic process, if we know the initial conditions, we can predict the final state. In theory, given the initial state of a coin about to be flipped, we can determine the outcome, and also with the dice.

In the Bohmian model, randomness is somewhat like this - the success of the prediction depends on knowledge of the initial conditions. The crucial difference is that it is in principle not possible to know the initial conditions at the quantum level. This would require simultaneous knowledge of the position and momentum.

Ironically, the probability amplitude of the Copenhagen model, evolves deterministically.

 

[peter0302]

I thought the randomness was due to the fact that the act of taking the measurement changes the particle in a way we can't predict.

Taking the measurement limits what we can say about the particle. (Call it wave function collapse, or whatever else you want). By taking a measurement, another measurement which doesn't commute with the first (like position vs. momentum) becomes random and unpredictable. Thus, if we measure this second property, it is impossible, even in principle, to predict an outcome with precision.

Ironically, the probability amplitude of the Copenhagen model, evolves deterministically.

I don't really see the irony. :) The amplitudes are deterministic but the measurement outcome is non-deterministic. In that way it is similar to a dice throw - there is a known amplitude to obtain a certain result which is deterministic from the initial conidtions, but the result obtained is unpredictable. The only difference between the quantum and classical worlds is how you add probabilities and whether it is possible, even in theory, to make a prediction.

 

[reilly]

In practice, dice or electrons; it's the same deal. Probability deals with events; and these can be classical or quantum events. I's written into the very basics of probability theory that this is so. The only difference between classical and quantum probability spaces is in their dynamics -- examine how the Poisson probability law emerges from coherent states in QM. Interference is just one of the ways that QM generates probability structures. And recall, say from the Coulomb problem that there are no interference terms in Coulomb scattering solutions done with parabolic coordinates.

In practice, random means you get your best results with probability theory, not with causal or deterministic theories. And, note that there are all sorts of statistical tests for determining randomness.

Regards,
Reilly Atkinson

 

[Fra]

But I'm just curious what some of the metaphysical thoughts are about this.

Doing the dice analogy I personally like to think of it like this in the QM case:

Your initial information and choice of questions/measurements, allows you to predict your dice which contains the probabilities for each possible answer/outcome.

So in QM, the evolution of the dice is deterministic, but each time you USE the dice, throw it, and collect the outcome, the your information is changed and the dice is remodelled. So one can say that the dice is "recalibrated" each time you use it.

So, the answer you get from QM is a dice! For you to throw. Ie. it gives you some odds, as a guide for placing bets.

This is consistent with the different that classical mechanics deals with what nature is. Quantum mechanics deals with what we can say about nature. (Bohr's way of putting it)

Thus, the fact that the answer beeing a dice, makes perfect sense.

The irony I think Mentz was referring to is that the predicting to is that, it is natural to try to apply the same trick again, and question wether we instead of asking what the dice is, we could ask what we could say about our dice? Then the "irony" is that QM says that the dice evolves deterministically and is exactly known.

The problem is that the deterministic rule that determines the dice, are not acquired. They are pulled/postulated. And indeed they have been successful, but this treatment is IMO not in like with the humble ideal of Bohr, if you apply them to the rules of reasoning as well. What can we SAY about the rules of reasoning? And this leads possible to the question of wether it's a difference what I can say, or what anyone can say? IE. does the information capacity of the observer matter?

So what's the value of making upp odds, for bet placing? Obviously it's of high value for your survival, as investing your acquired resources randomly (without intelligent rating) may mean death. So it's a trait to develop a good, fit machinery to assist making choices. Incidently this is also how the human brain seems to work, before making a decision the brain evaluates a probability for each option. Note that it's irrelevant wether the probability is RIGHT. Because that tuning is the task of the learning. Insuccessful choices are fed back to the system, and your probability generator is slowly learning.

Of course in a way the rules of QM ARE acquired, in the sense of scientific progress, but this progress perhaps isn't as systematic and formal as is we've made the "measurement process" in QM. THIS is to me the "irony" :)

And I personally suspect this irony will persist until we have a more full version of QM, including gravity. Until then we may have to live with the confusion and the sea if interpretations.

/Fredrik

 

[krimianl99]

It is not true that there is no difference in practice. The interference pattern results directly from this distinction. A very clear example of this is how if you set up an experiment where it is possible _in theory_ to know the result of a non-commuting measurement, but nonetheless impossible _in practice_, you lose the interference pattern. Nature doesn't care about "in practice" versus "in theory."

In defense of Thomas's claim, I ask a question. Is there any way to replicate the interference pattern situation with a classical random situation by manipulating the passage of time.

For example, if you roll a dice that is designed such that it hitting the side of the table now will affect the dice previous to that. (Or at least, as best as we can observe...)

 

[peter0302]

In defense of Thomas's claim, I ask a question. Is there any way to replicate the interference pattern situation with a classical random situation by manipulating the passage of time.

For example, if you roll a dice that is designed such that it hitting the side of the table now will affect the dice previous to that. (Or at least, as best as we can observe...)

No you cannot design a classical die that would behave that way.

You could of course design a (bad) die that lost small amount of its mass every time it landed, which would skew subsequent throws.

I'm not sure what you mean by manipulate the passage of time though...

 

[masudr]

In practice, dice or electrons; it's the same deal.

Not quite, because of superposition, surely?

 

[krimianl99]

No you cannot design a classical die that would behave that way.

You could of course design a (bad) die that lost small amount of its mass every time it landed, which would skew subsequent throws.

I'm not sure what you mean by manipulate the passage of time though...

Then you missed the point of my question. I am not talking about a strictly classical die. I am talking about a dice in which present and future events affect past events.

 

[peter0302]

Well there is no known way to affect past events. The best we do is find non-causal correlations, like with entangled particles. Take a delayed choice quantum eraser. Some more liberal people interpret that experiment to say that an event had an effect on the past, but the only thing that can be said with certainty is that an event affected what we could _say_ about the past, but we cannot be sure, by definition, that the past would have been any different, and therefore cannot say there was an "effect" on the past.

 

[ThomasT]

It is not true that there is no difference in practice. The interference pattern results directly from this distinction. A very clear example of this is how if you set up an experiment where it is possible _in theory_ to know the result of a non-commuting measurement, but nonetheless impossible _in practice_, you lose the interference pattern. Nature doesn't care about "in practice" versus "in theory."

Ok, let's consider the sort of interference pattern that emerges after tens of thousands of individual detections -- as in the 1989 Tonamura et.al. experiment.
What I was saying was that, insofar as the word random means unpredictable, then an individual quantum detection is as randomly registered as, say, the result of a coin flip.
There's no difference in the unpredictability of either sort of event until you consider them in terms of quantum vs. classical theory. Then it can be said that the principles (most importantly the uncertainty relations vis the existence of a fundamental quantum) of quantum theory prohibit anything but a probabilistic account of where and when an individual detection will be registered. Nothing deeper is allowed by the theory. No precise causal account (of the sort that would allow the precise prediction of individual results) is possible according to the theory.

There is most certainly a real difference between deterministic pseudo-randomness, and quantum randomness.

*No* deterministic process is truly random.

Quantum theory doesn't tell us that nature is random or deterministic. It only tells us that, as far as the theory is concerned, there's no way to know.

Random means unpredictable. To say that an event is truly random is superfluous. To say that nature is either random or deterministic is meaningless. While somebody's apprehension of natural processes might champion determinism or chance as nature's hallmark, we can't know the answers to questions about the deep realities of nature. Our deepest physical theory tells us so.

 

[peter0302]

I don't see your point. Is it that "we cannot in practice predict the outcomes of chaotic events lile dice throws"? If so, then I suppose I agree with you, but since you can "in theory" this is different from quantum randomness.

Quantum theory doesn't tell us that nature is random or deterministic. It only tells us that, as far as the theory is concerned, there's no way to know.

Not exactly. Any deterministic quantum theory would have to be non-local. So either we're violating the HUP or relativity. So I think current theory tells us that nature is non-deterministic.

Random means unpredictable. To say that an event is truly random is superfluous

The OP wanted to know whether there was a difference between classical and quantum randomness. Clearly there are differences, and they've been talked about. Your only point is that "in practice" there is no difference. That is also wrong. The only thing I agree with you on is that chaotic events like dice throws are very very difficult to prediict but I do not accept that any differences are "meaningless."

 

[ThomasT]

Then this must be most important thing since theories may be wrong. If I can't even in principle set up an experiment where dice throwing can be shown to be deterministic then how does it matter what I call it(deterministic randomness vs. nondeterministic randomness)?

I don't think it matters much what you call it.

What about quantum events? Are they random (at least in theory as you say) because they don't have a cause(s)?

Random means unpredictable. Quantum events that are called random are called random because they're unpredictable. The specific causal chain (assuming such a thing exists) that produces the random event is unknown, and, according to the principles of quantum theory, unknowable.

My guess is that a working assumption among physical scientists, including quantum physicists (I would suppose), is that nature is deterministic. But quantum theory isn't a causal theory.

 

[CaptainQuasar]

Any deterministic quantum theory would have to be non-local.

Sorry to interrupt, but is that really true? I'm not a physicist but my amateur reading of the Bell's Inequality experiments that examined locality is that it seems they were primarily trying to prove that QM is not equivalent to Classical physics. Which isn't the same thing as proving that QM is not deterministic, is it?

Would locality due to any form of determinism whatsoever really violate the Bell's Inequalities? It just seems to me that you could easily have a wacky nonsensical probably-untrue deterministic theory that would reproduce the experimental results due to (completely hypothetical and undetectable) factors present within the locality of the experiment.

As an aside to the conversation, this paper: http://arxiv.org/PS_cache/quant-ph/pdf/0609/0609163v2.pdf" has a section on randomness. Subjective to the author on at least some counts, I'm sure.

⚛​

 

[vanesch]

The only perfect random number generator is a quantum one. Anything else is deterministic and subject to tampering or reverse engineering. Every casino owner knows that dice throws are not "perfectly" random as dice manufacturers go through great pains to make each face of the die have as close to an equal probability of landing as possible. They also know that even a hair's weight difference can throw off the results over the long term, and therefore a lot of time and money is spent trying to achieve perfection.

Ok, I think we have now three categories of "randomness", or at least, of the apparent randomness that occurs in certain processes.

Randomness is of course epistemologically the lack of knowledge, but the question is in how much we could, if we wanted, in principle, fill in that lack of knowledge, and it is on this basis of principle that our different categories reside.

The first category is a pseudo-random number generator as in a computer. This is in fact a finite-state machine that is perfectly predictable, but which has low-order correlation functions which make it look like random numbers. But there's nothing "difficult" in predicting the outcome of a pseudo-random number generator: you have a finite set of outcomes, and the next outcome is determined by the previous one, an internal state (which is also taken from a finite set), and eventually an external input, also taken from a finite number of possibilities. If you know that input (say, the clock), you know the internal state and you know the previous output, then the algorithm of the finite-state machine computes the next output.
If there's no external input, then these generators are always cyclic: they go through a certain cycle of outputs, and then repeat again the same series.

The second category is "deterministic chaos". You have a deterministic system (described by, say, a hamiltonian flow), but the Liapounov exponents are positive. Now, this is much harder to predict over a longer time, simply because you need infinite precision in the initial conditions. As your precision is ALWAYS going to be finite, sooner or later the output will be sensively dependent on the "part after the comma" beyond where your precision went. So here the randomness is dependent on the inherent uncertainty by which one can measure/know a quantity which is a genuine real number. No matter how precise one knows a real number, there will always be a remaining uncertainty (even if it is after 200 digits), and in a chaotic system, this uncertainty is sooner or later blown up to a sizeable part of the phase space. So although the *dynamics* may be "deterministic", if your system is determined by a state given by real numbers, there will ALWAYS be a randomness in the initial conditions, no matter how small. It is THIS unavoidable randomness that "shows its ugly face" in chaotic processes.

The third category are quantum phenomena. Here, it is *in principle* impossible to know what will happen: the dynamics (at least, the *observed* dynamics) is random, and not deterministic. (unless this is proven false one day)

 

[ThomasT]

I don't see your point. Is it that "we cannot in practice predict the outcomes of chaotic events lile dice throws"? If so, then I suppose I agree with you, but since you can "in theory" this is different from quantum randomness.

I agree with your succinct answer to the original poster's original question. The only reason I entered into the discussion was because these considerations seem to often lead to statements regarding determinism in nature, and this is something that I don't think we can (and quantum theory, according to at least one interpretation, tells us that we can't) make any meaningful (i.e. testable) statements about.

Quote from ThomasT:
Quantum theory doesn't tell us that nature is random or deterministic. It only tells us that, as far as the theory is concerned, there's no way to know.

Not exactly. Any deterministic quantum theory would have to be non-local. So either we're violating the HUP or relativity. So I think current theory tells us that nature is non-deterministic.

With regard to the calculation of observable quantities (the need for a nonclassical superposition of states, because of, on the one hand, the deficiency of classical representations to account for observed quantum phenomena, and, on the other hand, the uncertainty relations vis the fundamental quantum) the theory can be interpreted as nonlocal. But, this is not a statement about nature. Quantum nonlocality isn't real nonlocality.

Quote from ThomasT:
Random means unpredictable. To say that an event is truly random is superfluous.

The OP wanted to know whether there was a difference between classical and quantum randomness. Your only point is that "in practice" there is no difference. That is also wrong. The only thing I agree with you on is that chaotic events like dice throws are very very difficult to prediict but I do not accept that any differences are "meaningless."

You explained the difference between classical and quantum randomness quite ok I think. These are theoretical differences. Quantum theory isn't based on some apprehension of deep reality. It's based on material and instrument specifications and responses. Statements about whether nature is nondeterministic or deterministic are outside of quantum theory, and outside of science.

 

[peter0302]

The second category is "deterministic chaos". You have a deterministic system (described by, say, a hamiltonian flow), but the Liapounov exponents are positive. Now, this is much harder to predict over a longer time, simply because you need infinite precision in the initial conditions. As your precision is ALWAYS going to be finite, sooner or later the output will be sensively dependent on the "part after the comma" beyond where your precision went. So here the randomness is dependent on the inherent uncertainty by which one can measure/know a quantity which is a genuine real number. No matter how precise one knows a real number, there will always be a remaining uncertainty (even if it is after 200 digits), and in a chaotic system, this uncertainty is sooner or later blown up to a sizeable part of the phase space. So although the *dynamics* may be "deterministic", if your system is determined by a state given by real numbers, there will ALWAYS be a randomness in the initial conditions, no matter how small. It is THIS unavoidable randomness that "shows its ugly face" in chaotic processes.

The line between quantum and classical starts to blur at this level though. Precision of 200 digits, for example, is impossible because the entire universe is smaller than 10^200 Planck lengths.

Now if we're talking about something as simple as a dice throw, I think you can, in theory, know enough about the initial conditions to predict the outcome. Commander Data, for example, would be able to cheat at Craps without much difficulty. If that's true, then a dice throw is not random. Heck, I could simply turn my hand over and let the dice fall flat and have a good idea of what side they'll land on (even though I'll get my legs broken).

So the question whether something is truly random or unpredictable really depends on how much precision you are capable of having, and how much precision you need. If a system is so complex and runs for so long that precision greater than a Planck length would be required to make an accurate prediction, then I agree that chaotic randomness would be, in principle, unpredictable. But if the accuracy required is less, then the outcome is predictable.

And, again, I'd emphasize that this is in stark contrast to quantum randomness, which is unpredictable no matter HOW much precision you have or how simple and non-chaotic the system is.

 

[basePARTICLE]

\theta

You can, in principle, predict the outcome of a classically random event (e.g. if you knew the moment of inertia of the dice, the initial torque applied on the dice, any wind/movement of air on the dice, the coefficient of restitution of the dice and table it bounces on as a function of the speed at which the dice hits the table and the angle at which it strikes etc.)

Those are the initial conditions (\upsilon,\theta). After, you study the boards.

> One thing not random about QM, is it guarentees an interaction/experience...

> Can anyone be a sharpshooter, when aiming protons at a target?

 

[krimianl99]

I don't see your point. Is it that "we cannot in practice predict the outcomes of chaotic events lile dice throws"? If so, then I suppose I agree with you, but since you can "in theory" this is different from quantum randomness. Not exactly. Any deterministic quantum theory would have to be non-local. So either we're violating the HUP or relativity. So I think current theory tells us that nature is non-deterministic.The OP wanted to know whether there was a difference between classical and quantum randomness. Clearly there are differences, and they've been talked about. Your only point is that "in practice" there is no difference. That is also wrong. The only thing I agree with you on is that chaotic events like dice throws are very very difficult to prediict but I do not accept that any differences are "meaningless."

If a person asks this question, they are likely to be interested in whether or not Quantum Mechanics disproves Determinism. As Thomas points out, it does no such thing. Any claim to the contrary is an argument from ignorance. We are not throwing out determinism because some people don't understand the concept of limited applicability of any theory.

The options for explaining entangled particles are basically:

No reality apart from observation
No Cause and effect, logic, etc
Locality

The mere thought that the first two could be wrong is utterly absurd. The third is a complex human created scientific theory that seems to accurately explain behavior WITHIN A CERTAIN REALM.

Seeing this list, it is all I can do to not laugh out loud at the thought of God holding two tablets labeled "Objective reality" and "Cause and effect" then a silly human with a poster board and a stick labeled "relativity" trying to redirect our investigations to god to find the failing assumption. A metaphor to be sure, but that is how I picture it.

Every science buff I talk to says that a different one of the 3 assumptions is believed to be false and all cite someone who agrees with them. It seems to me the scientific community has not come to a consensus on this at all.

A philosopher from 2000 years ago could have pointed out that Relativity's ability to explain everything from electrons up says absolutely nothing about it's applicability to smaller particles. That is because no theory can ever be sure to apply to a realm outside that which the theory was sampled from. There can always be some reason why the new realm is different.

Well there is no known way to affect past events. The best we do is find non-causal correlations, like with entangled particles. Take a delayed choice quantum eraser. Some more liberal people interpret that experiment to say that an event had an effect on the past, but the only thing that can be said with certainty is that an event affected what we could _say_ about the past, but we cannot be sure, by definition, that the past would have been any different, and therefore cannot say there was an "effect" on the past.

I would think rather the best we could do was a thought experiment.

I was imagining creating a deterministic randomness where future events affected past ones, and then looking at not an absolute time line but rather a point in the time line as us humans would perceive it - a point between the affected past event and the future cause.

Then analyzing the probabilities to see if we could create a similar situation. The only thing preventing anyone from doing this is conceptual difficulty.

Also, future events effecting past ones could simply mean that we are perceiving things out of order because there is a superluminal force at work, rather than there being no true order of events.

 

[vanesch]

The line between quantum and classical starts to blur at this level though. Precision of 200 digits, for example, is impossible because the entire universe is smaller than 10^200 Planck lengths.

This is because you think of a classical universe as some approximation to a quantum universe. But if we assume a truly classical universe, then even there, you would always end up with a finite precision, beyond which randomness is unavoidable.

Of course, your argument is: in a classical universe, although you have finite precision, you can make it arbitrarily high. True, but the idea is that ONCE you have picked your precision, in a chaotic dynamics, after a certain time (which is function of course of this picked precision), the dynamics will become random, as it will depend eventually sensitively on the digits beyond your precision.

Now if we're talking about something as simple as a dice throw, I think you can, in theory, know enough about the initial conditions to predict the outcome. Commander Data, for example, would be able to cheat at Craps without much difficulty. If that's true, then a dice throw is not random. Heck, I could simply turn my hand over and let the dice fall flat and have a good idea of what side they'll land on (even though I'll get my legs broken).

That would then simply mean that a dice throw is not chaotic enough for M. Data. But no matter what he does, M. Data will always have a finite precision of initial conditions, and it is sufficient to use a chaotic process long enough, for him not to be able anymore to do the prediction. Say, a lottery ball machine. You pick the time it mixes the balls. Of course, for the NEXT go, he might increase his precision... only for it to be undone by us having the machine run a bit longer.

So whether something is "truely random" depends on the precision by which one has determined the initial conditions, how "divergent" is the dynamics, and how long we make the process run before "sampling", but we can always find a running time that will make it impossible to make a definite prediction for a given precision.

In some universes, this precision can be in principle limited, in others, maybe not.

 

[vanesch]

Every science buff I talk to says that a different one of the 3 assumptions is believed to be false and all cite someone who agrees with them. It seems to me the scientific community has not come to a consensus on this at all.

But you seem not have understood what Bell's theorem is about: it proves the incompatibility of a set of assumptions with the predictions of quantum mechanics. That's it. As such, we know that we won't find an exact replacement for quantum mechanics that satisfies at the same time the entire set of assumptions. THIS was Bell's result: that certain theories aren't necessary to look after, because they don't exist formally.

It is not necessary to try to find a theory that respects, at the same time the set of assumptions (no superdeterminism, locality the way relativity sees it, statistical regularity, uniqueness of outcome) and that is perfectly equivalent to quantum mechanics, because you won't find such a theory. THAT'S IT.

A philosopher from 2000 years ago could have pointed out that Relativity's ability to explain everything from electrons up says absolutely nothing about it's applicability to smaller particles. That is because no theory can ever be sure to apply to a realm outside that which the theory was sampled from. There can always be some reason why the new realm is different.

Nobody is denying that. Bell simply helped us in stopping to look for a theory that doesn't exist. People would have liked to find (and Einstein was convinced it existed) a classically-looking theory (which hence respects all the basic assumptions) entirely compatible with relativity (hey, it was Einstein, right ?), that would make the same statistical predictions as quantum mechanics.
Bohmian mechanics did this, except that it WASN'T respecting relativity. So people said that one should try better. Bell showed that "Einstein's dream" wasn't possible.