quantum randomness vs. "dice randomness"

ivan

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

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

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.

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

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

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."

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

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)?

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 probabilty amplitude of the Copenhagen model, evolves deterministically.

peter0302

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.

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

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 aquired, 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

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

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

Not quite, because of superposition, surely?