How can chance be non-deterministic?

Zweistein

If I throw a dice the chance that I throw any of the six numbers is 1/6. The dice rolls determined towards its destined number.

Our lack of knowledge gives rise to chances. If we somehow could know the initial state of the dice and the exact interactions with its environment then the final numbeŕ could be known.

Well, that's the naive argument. In practice, it can't be known in priciple. Which doesn't mean that the process is not determined. It is.

You can say that chance is a subjective feature that we project to, for example, the world of dice. A dice has a 1/6 chance of showing one of the six (if the dice is ideal).

Then quantum mechanics shows it face. There nothing is determined except the evolution of the wavefunction. If we throw a quantum dice, each outcome has still 1/6 chance of appearing. But the process leading to an outcome is simply not there. We don't project chances because lack of knowledge but the chances are objective properties. That's the main difference with the classical view.

But how can this be? Einstein ask this question by means of a statement: "Der liebe Herr Gott würfelt nicht". How can there be a pure chance, without a deterministic substrate giving rise to our ignorance? The usual reply is that the quantum world is so much different than the everyday experienced world. But why should that be? That's just a presupposition. The wavefunction might be weird, like the collapse of it. That's true. This gives rise to the "shut up and calculate" attitude. Only math, predictions, and observations (values) and their distributions matter. This attitude doesn't look at the heart of the matter and sometimes even denies its existence.

What's the heart of the matter? The heart is that which is actually going on. How can there be no determined process going on behind the chances? Giving a new kind of chance.

Hermeticus

There nothing is determined except the evolution of the wavefunction. If we throw a quantum dice, each outcome has still 1/6 chance of appearing. But the process leading to an outcome is simply not there. — Zweistein

This is if we look at the quantum dice as an isolated system. There are no isolated systems in reality though (except maybe the universe itself - we don't know).

So when we throw the dice in reality, what we're looking at is not just the wavefunction of the dice - but the wavefunction of our throw, the wavefunction of the air, the wavefunction of the table, etc. interacting with each other, is it not?

Now, I'm a donkey when it comes to math but I'd imagine if we were to add up all those wavefunctions that interact with our dice, the result would be something like the determination of our dice throw, no?

tim wood

What's the heart of the matter? — Zweistein

Consider a Galton board.
https://www.youtube.com/watch?v=6YDHBFVIvIs
How is it that the normal distribution occurs all the time? It seems at the macro-level, at least, the more likely events occur more of the time.

At the scale of the very small, that rule seems violated. Which may be no more than a case of different rules - very different rules. Or no rules at all. Or a third case: rules, but not that we can determine because of fundamental limits to our ability to determine rules - at least so far.

So far it appears we can push the veil aside so far as to reveal likelihood but not discrete certainty. But even "discrete certainty" becomes uncertain at the scale where all is waves. Chance, then, all the way down. But so many chances that at any macro-level, certainty coalesces.

Zweistein

↪Hermeticus

I was talking about a metaphorical quantum dice. Sorry if I wasn't clear. Thanks anyway! :smile:

Zweistein

At the scale of the very small, that rule seems violated. — tim wood

What rule?

tim wood

What rule? — Zweistein

It seems at the macro-level, at least, the more likely events occur more of the time.
At the scale of the very small, that rule seems violated. — tim wood

Zweistein

↪tim wood

Also at the micro-level more likely observations appear more often. Statistical ensembles of measuremeants show you the form of the wavefunction, if all states are prepared the same. This doesn't address my question though.

Hermeticus

It seems at the macro-level, at least, the more likely events occur more of the time.
At the scale of the very small, that rule seems violated. — tim wood

I think that goes along rather well with what I said.

So when we throw the dice in reality, what we're looking at is not just the wavefunction of the dice - but the wavefunction of our throw, the wavefunction of the air, the wavefunction of the table, etc. — Hermeticus

It's obvious then that a higher number of influencing factors (more particles interacting at macro-level) is more determinable than very few, or no influencing factors (micro-level, singular particles).

tim wood

This doesn't address my question though. — Zweistein

Well, I suppose that while your question is addressable, it does not appear to be willing - and perhaps not able - to give an answer anytime soon, if ever. Determinism or randomness may seem at first reasonable to think about as exhaustive of alternatives. After all, of any thing, it either is or is not, no middle. But at the level of the very small, "thing" itself becomes problematic. Waves suggest themselves, though as metaphors. But "where" is a wave? What is "it" "doing" at a "given" "moment"? All these concepts that have already broken down by the time they're applied at the smallest scales. That is, maybe the language of the question is rendered defective in application, a new language needed, and apparently a work in progress since the 1920s

Neoconnerd

↪tim wood

In fact, we can know. An experiment has been planned to discern between hidden variable and pure chance. It's a though experiment and not yet possible to actually perform, but the idea is to measure arrival times.

sime

If I throw a dice the chance that I throw any of the six numbers is 1/6. The dice rolls determined towards its destined number.

Our lack of knowledge gives rise to chances. If we somehow could know the initial state of the dice and the exact interactions with its environment then the final numbeŕ could be known.

Well, that's the naive argument. In practice, it can't be known in priciple. Which doesn't mean that the process is not determined. It is.

You can say that chance is a subjective feature that we project to, for example, the world of dice. A dice has a 1/6 chance of showing one of the six (if the dice is ideal). — Zweistein

The subjective interpretation of probabilities as representing ignorance which you appear to be assuming, is a logical fallacy in my understanding. Lack of knowledge should give rise to possibilities only. Moreover, it is impossible for anyone to distinguish ignorance from objective uncertainty before the fact. Such distinctions can only be drawn after the fact.

To represent uncertainty in terms of probabilities isn't to assign a particular distribution, but to assign a set of distributions, which is sometimes referred to as assigning "imprecise probabilities". In the case of complete ignorance of a thrown die, one should assign the entire set of distributions with six possible outcomes, which amounts to saying that one only knows that there are six possible outcomes.

Furthermore, having described one's state of ignorance by using a set of distributions, one shouldn't then average over the set, as Bayesians often do, to obtain a precise "ignorance prior", for this fallacious practice amounts to an attempt to extract information from ignorance.

tim wood

It's a though experiment and not yet possible to actually perform, but the idea is to measure arrival times. — Neoconnerd

Why not possible yet to perform the question. As it sits, an if-question. And these of proven utility, but one has to get past the fact that given any if, any question can be resolved. Or the question, will fundamental physics ever reach an end, and will it be due to insurmountable limitation, or the end of things to be known?

Neoconnerd

Why not possible yet to perform the question. — tim wood

What do you mean? Perform the question? Untill now it's just a thought experiment, like all experiments are first.

tim wood

↪sime

Hmm. Could you make all that a little clearer - if you have the ambition? E.g.,

which is sometimes referred to as assigning "imprecise probabilities" — sime

What is imprecise about assigning 1 - 6 as possible outcomes of the throw of a die?

tim wood

What do you mean? Perform the question? Untill now it's just a thought experiment, like all experiments are first. — Neoconnerd

It doable or it is not doable, which matters. As a thought experiment, all outcomes share likelihood.

Neoconnerd

↪tim wood

It's doable but not yet. Work in progress.

tim wood

It's doable but not yet. Work in progress. — Neoconnerd

It have a website?

Neoconnerd

It have a website? — tim wood

Dunno. I read it on a physics forum.

tim wood

↪Neoconnerd

Anything you yourself can describe in a few well-crafted sentences?

Neoconnerd

Anything you yourself can describe in a few well-crafted sentences? — tim wood

I'll give it a try. A deterministic reality behind QM (like van 't Hooft or Bohm suggest and me too) will lead to different trajectories of particles. This results in different arrival times than pure chance gives you. If you start with pure chance calculations and from this result different times are measured, then there is a process behind the chances, as is more reasonable.

sime

What is imprecise about assigning 1 - 6 as possible outcomes of the throw of a die? — tim wood

It is imprecise because probability intervals are assigned to outcomes, rather than numbers.

e.g. P ( dice throw = six) = (0,1)

Which only express the fact that throwing a six is possible, but not certain.

Neoconnerd

e.g. P ( dice throw = six) = (0,1) — sime

What does this mean? In words?

sime

What does this mean? In words? — Neoconnerd

It is saying that the physical propensity for obtaining the respective possible outcome, is above zero and less than 1. Without additional information, or assumptions, a more precise set cannot be assigned to the outcome.

AlienFromEarth

↪Zweistein

Quantum fluctuations. Quantum theory has already proven that while we can certainly make good estimates of things that may happen in the future, you can't really predict the future.

Quantum interactions are physical, therefore, they affect the physical world, therefore they affect you and me, in turn making us ultimately not truly predictable.

Again, being able to guess that someone is going to do something and they actually do it at about the same time you thought they would and in the same manner, that's just a good estimation. Some things are eventualities because nature has laws and it works a certain way. You can't change the fundamental laws. So yes, you can "predict" if you will, that eventually this and that will happen, because that's natural law. But you CANNOT predict EXACTLY how and EXACTLY when it will occur. Beyond that though, lies the abyss of uncertainty and chance.

IT works like this. If logic says A + B = C. Then we must first figure out how we got to A and then B in the first place. And so on, and so on. A never ending chain of questions, which leads us back to the only answer - that is: You cannot predict the future. Yes, logic can help you understand things, but you cannot perfectly control or predict how or when you are going to use it

Hooman

I think the Quantum dice and normal dice are quite different. If I drop a ball it certainly falls and ends up at a predictable place, no blow up of location owing to Quantum mechanic. For the dice, the physical process and the final variable that you are observing are very sensitive to the initial conditions and accuracy of calculations in a non-continuous way. This is like what is observed in chaotic dynamic systems when even round-off errors change the outcome.

AlienFromEarth

↪Hooman

no that's just a good estimation. YOu can't predict quantum fluctuations, therefor eyou can't predict *exactly* what the ball is going to do at any given time. These fluctuations can vastly affect the trajectory of the ball. Yes, most of the time it's kinda estimatable perhaps, but even then it's not the same every single time. Those fluctuation are ALWAYS HAPPENING.

tim wood

A deterministic reality behind QM (like van 't Hooft or Bohm suggest and me too) will lead to different trajectories of particles. This results in different arrival times than pure chance gives you. If you start with pure chance calculations and from this result different times are measured, then there is a process behind the chances, as is more reasonable. — Neoconnerd

Sounds interesting. Please don't infer I actually understand it. Might this be like in some very distant way predicting the arrival times and thus the trajectories of the balls on a Galton board? Is there a name associated with this experiment so that one might search it?

tim wood

What is imprecise about assigning 1 - 6 as possible outcomes of the throw of a die?
— tim wood
It is imprecise because probability intervals are assigned to outcomes, rather than numbers.
e.g. P ( dice throw = six) = (0,1)
Which only express the fact that throwing a six is possible, but not certain. — sime

Are we saying the same thing only you maybe more technically correctly? Or something different?
All I'm saying is that if I throw that fair die, I shall get any of 1 through 6, and that I shall expect each to occur about 1/6th of the time.

TheMadFool

↪Zweistein

The Achilles' heel of determinism is the problem of induction.

Determinsim seems wedded for all eternity with the so-called laws of nature (go to the science section) but, for better or worse, all causal patterns are, it seems, severely undermined by Hume's coup de grâce, delivered mid-18th century. I don't know what the fuss is all about! Determinism is predicated on the laws of nature but the laws of nature have no leg to stand on.

T Clark

Well, that's the naive argument. In practice, it can't be known in priciple. Which doesn't mean that the process is not determined. It is. — Zweistein

The pragmatists rebuttal to this is that if a specific outcome is not predictable, even in principle, then it is meaningless to call the phenomenon determined. I think this is a good way of looking at things. This argument can be extended to include phenomena that are completely impractical to predict accurately, e.g. the winner of the 2024 Super Bowl. I think the dice example is somewhere in the middle - highly impractical in most cases, but not impossible.

And this is all before quantum mechanics and chaos theory are taken into account.

T Clark

Hume's coup de grâce, delivered mid-18th century. I don't know what the fuss is all about! Determinism is predicated on the laws of nature but the laws of nature have no leg to stand on. — TheMadFool

Apparently you haven't gotten the word. Hume was full of it. Of course induction works. This is probably not the right thread to discuss it further.

How can chance be non-deterministic?

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