Question on the probabilistic nature of QM

[Wormaldson]

Question on the "probabilistic" nature of QM

I read very recently something that I interpreted as stating that certain quantum-mechanical phenomena are necessarily probability-based: for instance the exact path traversed by a photon/electron in the double-slit experiment.

That's all well and good, but the material seemed to make an implication that I've been having a lot of difficulty reconciling or finding an appropriate analogy for in classical terms: that the phenomenon in question, whatever it may be, is genuinely random. That is to say, the exact, actual result has no identifiable cause.

The notion of randomness, to me, has always seemed like an idealisation: we create a situation in which an event has no actual cause, and therefore the occurrence of which can't be exactly predicted, and apply this model to situations in which we have insufficient information or methodology to obtain a perfect prediction. I wouldn't call such a situation "genuine randomness" because we can identify factors which contribute to causing the result, but the model fits well enough I suppose.

Problem is, I can't think of any classical situations in which this notion of genuine randomness actually applies. If you consider, for example, a computerised random number generator, it can generate numbers that are approximately genuinely random very well in many cases, but it always needs a seed of some kind: an example of the cause-and-effect logic I've come to believe is necessary at a classical level.

So, finally, the question(s): a good place to start would certainly be, am I just interpreting the information wrong? Do we know for sure that quantum mechanics obeys this genuine-randomness-dependent behaviour? If not, then what do we suppose determines the behaviour of quantum mechanical phenomena? If so, then how is it that the behaviour is determined without a cause?

As always, any insight would be much appreciated. This has me quite puzzled.

 

[Hurkyl]

You are having trouble imagining "genuine randomness" because you insist on instead imaging "there's extra stuff that we don't know that determines what's going on".

There's a class of theories called "hidden variable theories", which postulate that the state of a particle includes information beyond the quantum mechanical description, and that this extra information determines the results of measurement.

The point of Bell's theorem is that it is a no-go theorem -- it proves that a vast class of hidden variable theories are mathematically incapable of reproducing the predictions of quantum mechanics even for very simple systems.

Instead, if you want a deterministic version of quantum mechanics, you have to embrace quantum "weirdness" and go in directions such as MWI or Bohmian mechanics.

 

[bhobba]

The fundamental axiom of QM is the superposition principle which trivially shows the possible system states form a vector space. First thing to note is determinism is contained in a statistical theory - but it only allows probabilities of zero or one.

Now there is a Theorem called Gleason's Theorem that shows there is really only one way to define probabilities on a vector space - that being the way QM does it. There is an out - the hidden assumption is states do not depend on other states it may part of a basis with - this is known as non-contextuality - that's how Bohmian Mechanics gets around it - its deliberately concocted to be contextual. Now if we try to only assign zero and one we find a contradiction - you can't do it - this is the celebrated Kochen-Specker Theorem - but it is a simple corollary to Gleason's Theorem. So classically probabilities are all you can have in QM - its implied by its fundamental axiom - the Superposition Principle - no way out of it unless you want to be really sneaky and introduce contextuality - which I personally find unnatural - but to each his/her own.

Thanks
Bill

 

[Jano L.]

Do we know for sure that quantum mechanics obeys this genuine-randomness-dependent behaviour?

Exactly. What is genuine randomness? As you point out, it is hard to find a clear example of it. Perhaps it can be defined mathematically?

Or perhaps "true randomness" is just a belief that probability is the ultimate physical quantity and there is no better theory than Born's rule.

I suspect that people proposing "true randomness" find searching for explanations too difficult but still want to appear as sage thinkers.

 

[the_pulp]

I tend to think all the opposite way. I tend to think that the universe is deterministic and that randomness is apparent and it appears because of insuficient information about the instrument which is making the measure. I gave some details of my point of view in the following link:

https://www.physicsforums.com/showthread.php?t=609087

but nobody said nothing about this. What do the experts think? Is it wrong? Is it against some experiment?

Thanks!

 

[Ken G]

I have heard a lot of people who like "fundamental determinism" but hate "fundamental randomness." I find it curious that they don't see these two as simply opposite sides of the same coin-- the coin of what science has at its disposal with which to make working models. In other words, neither one of those phrases has any business including the word "fundamental" (or "genuine")-- what the heck does that mean anyway? I challenge anyone to supply a scientifically testable (not religious or philosphical) way of saying how you could tell if something is "fundamentally" random or deterministic. It's sheer nonsense, it all stems from an error in understanding what science does. Nothing that science does is "fundamental", never has, never will. Once you understand that, the whole problem just goes away-- some models invoke determinism, others invoke randomness, neither is the least bit "fundamental."

Any who doubt that should answer this: what empirical tests has classical physics passed that showed it was "fundamentally deterministic", that I could not devise a "fundamentally random" version of classical physics that would pass all those same tests? What empirical tests has quantum physics passed that shows it is "fundamentally random", that I cannot supply a version that passes all the same tests yet is "fundamentally deterministic"?

In other words, I see no justification at all to be bothered by models that are "fundamentally random" but happy with models that are "fundamentally deterministic." A model is what it is: just a model. We layer on interpretations for various reasons, but they are not unique to the theory, and we should not bother with worrying whether or not they conform to how we'd like the universe to be. That's just not the job of the scientist.

 

[bhobba]

Exactly. What is genuine randomness? As you point out, it is hard to find a clear example of it. Perhaps it can be defined mathematically?

Or perhaps "true randomness" is just a belief that probability is the ultimate physical quantity and there is no better theory than Born's rule.

I suspect that people proposing "true randomness" find searching for explanations too difficult but still want to appear as sage thinkers.

Yes it can be defined mathematically - see the works of Kolmogorov for example.

It's not a belief and its not that people find searching for explanations too difficult - some of the greatest minds in history tried and failed to get around it in QM. And indeed powerful mathematical theorems such as Gleason's Theorem exists showing it is pretty much impossible if the superposition principle holds - and many many experiments show it does.

Thanks
Bill

 

[Ken G]

Yet there are two problems that trouble me about the language that is often used, along the lines that quantum mechanics is "genuinely random" and classical mechanics is "genuinely deterministic":
1) Things like Gleason's theorem apply to the postulates of some theory (or some version of some theory), not to the universe. Nor does it follow that, simply because our theory has not been falsified by experiment, it must be a correct way to say what the universe is actually doing. We always have to keep separate what the universe is doing, from how we construct our theories, or we fall into the unending fallacy of mistaking our own current best understanding with the way things actually are. Haven't we learned yet the error in doing that? The map is not the territory.
2) Even once we recognize that we are discussing a particular model, not the universe itself, it still isn't clear if we can unambiguously label one theory as "determinstic" and another as "random." As you said yourself, quantum mechanics can be interpreted either way, because Gleason's theorem requires assumptions that go farther than what has actually been experimentally justified. Same for classical mechanics-- deterministic theorems in classical mechanics also invoke assumptions that go beyond what is necessary to get experimental confirmation of the theory, which is exactly the reason that people thought the Newtonian paradigm was correct long before we discovered quantum mechanics. It's high time we recognized that "is the universe random or deterministic" is simply not a scientific question, and nothing that science does ever gives us a definitive or unambiguous answer to that question. It will always be a matter of interpretation, or better yet, a question that is best dispensed with as being outside the purvey of scientific investigation.

The real question for science is, "what mastery and understanding do we obtain by imagining the universe is deterministic, or random?" Anyone addressing that question would have a very hard time dismissing either one of those analysis tools, they are both quite essential to the everyday practice of science, no matter what interpretation we paint over it.

 

[zonde]

The real question for science is, "what mastery and understanding do we obtain by imagining the universe is deterministic, or random?" Anyone addressing that question would have a very hard time dismissing either one of those analysis tools, they are both quite essential to the everyday practice of science, no matter what interpretation we paint over it.

I believe the question is not about universe being deterministic, or random but about some rather limited part of the universe being deterministic, or random.

 

[zonde]

Yes it can be defined mathematically - see the works of Kolmogorov for example.

You have seen works of Kolmogorov, right? So can you provide mathematical definition for genuine randomness?

It's not a belief and its not that people find searching for explanations too difficult - some of the greatest minds in history tried and failed to get around it in QM. And indeed powerful mathematical theorems such as Gleason's Theorem exists showing it is pretty much impossible if the superposition principle holds - and many many experiments show it does.

Do you say there are many many experiments showing that QM applies to single particle?

 

[Ken G]

I believe the question is not about universe being deterministic, or random but about some rather limited part of the universe being deterministic, or random.

But is there any such thing as a "limited part of the universe"? Seems to me you are talking about models, not the universe-- it is only models that are limited, the universe just is.

 

[Jano L.]

...some of the greatest minds in history tried and failed to get around it in QM

They did not fail, they just did not explain everything satisfactorily yet. There were genuine developments in explanations of QT after the Bohr paper refuting EPR in 30's - Bohm's theory, stochastic QT, stochastic electrodynamics/optics, classical models of light detection con-incidence experiments. This development occurs mainly because there are physicists that are not satisfied by "true randomness".

In my opinion, these are contributing to understanding of the phenomena that were before described merely as random quantum jumps. I would not call that a failure, but rather partial success. The quest, of course, continues.

 

[Ken G]

What's more, you can certainly like or hate the deBroglie-Bohm approach, but at least for nonrelativistic QM, it seems clear that this approach has refuted the claim that you must view QM as "fundamentally" random. So we now can pick and choose however we wish to think of QM-- whether random, or deterministic, or best of all in my view: not fundamentally either one, because neither are ever fundamental descriptions. Models just don't have "fundamental" descriptions, and the universe certainly doesn't-- all descriptions are both subjective and provisional to the current state of knowledge and cultural preferences.

 

[Jano L.]

My words, Ken G. Regarding your previous post, I am curious though, do you think it possible to simulate every known deterministic model by a probabilistic model? I think this is hard. Equation of diffusion is easily simulated by random walk process, but think of, say, Schroedinger's time dependent equation for a molecule. It would be great to replace such complicated PDE by some variation of the monte carlo method or so, but is this possible?

 

[Ken G]

Regarding your previous post, I am curious though, do you think it possible to simulate every known deterministic model by a probabilistic model?

It won't be formally the same model, but it can agree with all the same observations, so it will be an equivalent model. One can only use other kinds of ways to select models like that, subjective issues like preferred interpretations or different ways to apply Occam's razor. For example, many people are quick to point out that classical chaos theory is a deterministic model, but I say, how can you tell? The model achieves predictions that quickly become nondeterministic, so even if it is deterministic in some mathematical sense, it is functionally not deterministic whenever used as a physical theory, i.e, whenever tested by observation. This also means that a random model, like statistical mechanics, will achieve the same degree of agreement with observation, so the models cannot be distinguished by anything empirical when applied to general situations.

Even pure Newtonian physics can be used to spawn a probabilistic theory by simply noting the highest precision that Newtonian physics has been tested with, even in situations of very high quantum numbers, and notice that the theory cannot be said to apply to exact inputs, since no such thing ever exists anywhere in physics. All theories must be able to work on inexact initial conditions, and have never been tested in any other context, so they are all statistical, automatically. No theory asserts or requires that the theory must still work if the input data uncertainty is reduced arbitrarily, that never happens in physics so it is no kind of requirement of any model. Purely deterministic models are simply a class of model that don't tell you the level of precision at which they become physically impossible to test.

Equation of diffusion is easily simulated by random walk process, but think of, say, Schroedinger's time dependent equation for a molecule. It would be great to replace such complicated PDE by some variation of the monte carlo method or so, but is this possible?

I would imagine that a Monte Carlo treatment of the Feynman path integral formulation would suffice nicely. The path integral can be viewed as a formally mathematical exact structure, but it doesn't need to be viewed that way, nor has it ever been tested to be so. Why should we assume that any "slop" in a theory based on path integrals could be arbitrarily reduced by arbitrarily more precise measurements? When is that ever possible to demonstrate, and when is it ever likely to be true? Determinism could easily be a complete illusion of insufficiently precise measurements, as any probabilistic theory can be made to look deterministic with poor enough resolution.

 

[bhobba]

You have seen works of Kolmogorov, right? So can you provide mathematical definition for genuine randomness?

This is well known to math students:
http://en.wikipedia.org/wiki/Probability_axioms

Do you say there are many many experiments showing that QM applies to single particle?

Thats not what I said - I said many many experiments support the superposition principle.

Thanks
Bill

 

[zonde]

This is well known to math students:
http://en.wikipedia.org/wiki/Probability_axioms

Just to be sure that we are talking about the same thing. Do you mean "genuinely random" in the same sense as OP?

... that the phenomenon in question, whatever it may be, is genuinely random. That is to say, the exact, actual result has no identifiable cause.

 

[zonde]

But is there any such thing as a "limited part of the universe"? Seems to me you are talking about models, not the universe-- it is only models that are limited, the universe just is.

Well yes, I am talking about models. We can't meaningfully discuss reality (if that's what you mean with universe). It's always models.

 

[yoda jedi]

I read very recently something that I interpreted as stating that certain quantum-mechanical phenomena are necessarily probability-based: for instance the exact path traversed by a photon/electron in the double-slit experiment.

That's all well and good, but the material seemed to make an implication that I've been having a lot of difficulty reconciling or finding an appropriate analogy for in classical terms: that the phenomenon in question, whatever it may be, is genuinely random. That is to say, the exact, actual result has no identifiable cause.

The notion of randomness, to me, has always seemed like an idealisation: we create a situation in which an event has no actual cause, and therefore the occurrence of which can't be exactly predicted, and apply this model to situations in which we have insufficient information or methodology to obtain a perfect prediction. I wouldn't call such a situation "genuine randomness" because we can identify factors which contribute to causing the result, but the model fits well enough I suppose.

Problem is, I can't think of any classical situations in which this notion of genuine randomness actually applies. If you consider, for example, a computerised random number generator, it can generate numbers that are approximately genuinely random very well in many cases, but it always needs a seed of some kind: an example of the cause-and-effect logic I've come to believe is necessary at a classical level.

So, finally, the question(s): a good place to start would certainly be, am I just interpreting the information wrong? Do we know for sure that quantum mechanics obeys this genuine-randomness-dependent behaviour? If not, then what do we suppose determines the behaviour of quantum mechanical phenomena? If so, then how is it that the behaviour is determined without a cause?

As always, any insight would be much appreciated. This has me quite puzzled.

in concise terms:


how is it that the behaviour is determined without a cause?

actual result has no identifiable cause.

forget 'genuine determinism' 'fundamental' cos we need zero ramble.

 

[Ken G]

Well yes, I am talking about models. We can't meaningfully discuss reality (if that's what you mean with universe). It's always models.

Yes, and that helps answer-- if we are talking about models, then it doesn't have to be an either/or proposition, deterministic or random is not necessarily uniquely specified, it might just be how we are interpreting our models. For example, the OP connects randomness with lacking a cause, but the concept of cause is also a kind of interpretation. The exact same physical phenomenon could be accurately predicted using language that avoids causation, or language that embraces it, and yet it's still the same "happening."

 

[bhobba]

Just to be sure that we are talking about the same thing. Do you mean "genuinely random" in the same sense as OP?

Hmmmmm. Well of course there is no way to determine a random process from some pseudo random process by standard randomness tests - it's simply not possible. For example the random number generators in computers pass all the tests for randomness such as Kolmogrov axioms and they are deterministic - well they are supposed to be anyway - those that actually use them in simulation like I have done can find problems (I remember simulating a bank with queues etc and the results stubbornly refused to conform to theory - I was pulling my hair out then in exasperation did some randomness tests on the computers random number generator - random it wasn't) - the ones implemented in hardware using some quantum process such as the photoelectric effect are better - but still in principle it is possible.

Its actually quite hard to come up with pseudo random processes outside QM that pass randomness tests:
http://www.math.umbc.edu/~rukhin/papers/talk.pdf

Thanks
Bill

 

[bhobba]

how is it that the behaviour is determined without a cause?

How is any behaviour determined without a cause? You find a cause for something, then a cause for that and so on - you must stop somewhere and that doesn't have a cause. If we are ever to find the ultimate laws of nature it must stop somewhere and QM resolves it nicely - especially when decoherendce is included.

Thanks
Bill

 

[yoda jedi]

How is any behaviour determined without a cause? You find a cause for something, then a cause for that and so on - you must stop somewhere and that doesn't have a cause. If we are ever to find the ultimate laws of nature it must stop somewhere and QM resolves it nicely - especially when decoherendce is included.

Thanks
Bill

not my question...

...

you must stop somewhere and that doesn't have a cause.
Thanks
Bill

contentious, your stand.

decoherendce is included.
Bill

a cause ?
you are served !

 

[ThomasT]

I read very recently something that I interpreted as stating that certain quantum-mechanical phenomena are necessarily probability-based: for instance the exact path traversed by a photon/electron in the double-slit experiment.

That's all well and good, but the material seemed to make an implication that I've been having a lot of difficulty reconciling or finding an appropriate analogy for in classical terms: that the phenomenon in question, whatever it may be, is genuinely random. That is to say, the exact, actual result has no identifiable cause.

The notion of randomness, to me, has always seemed like an idealisation: we create a situation in which an event has no actual cause, and therefore the occurrence of which can't be exactly predicted, and apply this model to situations in which we have insufficient information or methodology to obtain a perfect prediction. I wouldn't call such a situation "genuine randomness" because we can identify factors which contribute to causing the result, but the model fits well enough I suppose.

Problem is, I can't think of any classical situations in which this notion of genuine randomness actually applies. If you consider, for example, a computerised random number generator, it can generate numbers that are approximately genuinely random very well in many cases, but it always needs a seed of some kind: an example of the cause-and-effect logic I've come to believe is necessary at a classical level.

So, finally, the question(s): a good place to start would certainly be, am I just interpreting the information wrong? Do we know for sure that quantum mechanics obeys this genuine-randomness-dependent behaviour? If not, then what do we suppose determines the behaviour of quantum mechanical phenomena? If so, then how is it that the behaviour is determined without a cause?

As always, any insight would be much appreciated. This has me quite puzzled.

Insightful posts by everybody. I agree with those who said that the term genuine randomness is meaningless. So, no need to be puzzled about it, imo.

Wrt the level of our sensory apprehension, randomness refers to unpredictability, which is subjective. The term fundamental randomness implies the absence of fundamental laws governing the evolution of our universe, which, it would seem, would preclude the formulation of viable dynamical laws wrt any scale of behavior. Yet viable laws of behavior applicable to many different scales of behavior exist.

 

[bhobba]

not my question...

I beg to differ - you just didn't like the answer.

contentious, your stand.

Just to be clear - in your opinion.

a cause ? you are served !

Decoherence is caused by loss of phase in coherent states by an external environment. Basically it causes random changes in phase so that any original phase is lost and averages out to a big fat zero.

Served for what?

Thanks
Bill

 

[bhobba]

Insightful posts by everybody. I agree with those who said that the term genuine randomness is meaningless. So, no need to be puzzled about it, imo.

Abso-friggen-lutely

Thanks
Bill

 

[yoda jedi]

I beg to differ - you just didn't like the answer.

no, just limiting the original question. this way a concise argumentation from all the people.

Just to be clear - in your opinion.

right, a democracy of opinions.

Decoherence is caused by loss of phase in coherent states by an external environment. Basically it causes random changes in phase so that any original phase is lost and averages out to a big fat zero.

Served for what?

great, you have a cause.

 

[zonde]

Hmmmmm. Well of course there is no way to determine a random process from some pseudo random process by standard randomness tests - it's simply not possible. For example the random number generators in computers pass all the tests for randomness such as Kolmogrov axioms and they are deterministic - well they are supposed to be anyway - those that actually use them in simulation like I have done can find problems (I remember simulating a bank with queues etc and the results stubbornly refused to conform to theory - I was pulling my hair out then in exasperation did some randomness tests on the computers random number generator - random it wasn't) - the ones implemented in hardware using some quantum process such as the photoelectric effect are better - but still in principle it is possible.

Its actually quite hard to come up with pseudo random processes outside QM that pass randomness tests:
http://www.math.umbc.edu/~rukhin/papers/talk.pdf

Thanks
Bill

It seems like you have quite uncommon view on what is determinism.

Anyways question is about examples of randomness that is not deterministic.

 

[bhobba]

It seems like you have quite uncommon view on what is determinism.

I am surprised you think so.

Anyways question is about examples of randomness that is not deterministic.

Examples that can be proven non-deterministic are zero - because in principle even if a process passes all the tests for randomness such as those outlined in the article (and very few man made one actually do - like the article says 75% of random number generators fail the test - although I think that is conservative - but they do exist) you can not say its underlying cause is not deterministic. I wish that wasn't the case because I truly and utterly believe QM is fundamentally random without any underlying deterministic process giving the appearance of randomness - but my wishes and personal beliefs do not change facts.

Thanks
Bill

 

[zonde]

Yes, and that helps answer-- if we are talking about models, then it doesn't have to be an either/or proposition, deterministic or random is not necessarily uniquely specified, it might just be how we are interpreting our models. For example, the OP connects randomness with lacking a cause, but the concept of cause is also a kind of interpretation.

Yes, cause is part of interpretation.

The exact same physical phenomenon could be accurately predicted using language that avoids causation, or language that embraces it, and yet it's still the same "happening."

Let's say I do not believe you that it is possible, namely that physical phenomenon can be accurately predicted without concept of causation.

Scientific method (testing in particular) is based on concept of causation. As a result anything that can't be interpreted from perspective of causation is non-scientific.

 

[zonde]

Examples that can be proven non-deterministic are zero

Fine, describe hypothetical example that can not be proven deterministic.

 

[bhobba]

Fine, describe hypothetical example that can not be proven deterministic.

A sequence of random numbers created by a hardware random number generator based on random noise or the photo-electric effect which are quantum in origin. Describe to me the test that will prove 100% for sure it was not created by a deterministic process that pass such tests. Although deterministic pseudo random number generators that pass all randomness tests known are not trivial to come up with, they do exist - or so I have been told. Describe to me how you would tell the difference between the two? Exactly what test would you use?

I believe QM processes are fundamentally random and think those that want to resort to Bohmian Mechanics or whatever to regain determinism are whistling in the dark - but as a matter of principle I can't prove them wrong. Indeed another answer to your question is how would you tell the difference between standard QM and Bohmian Mechanics?

Thanks
Bill

 

[ThomasT]

... I truly and utterly believe QM is fundamentally random ...

Not sure what you mean by this. Are you saying that you believe that QM is some sort of probability theory? If so, I agree.

... without any underlying deterministic process giving the appearance of randomness ...

Imo it wouldn't be best phrased as an underlying deterministic process giving the appearance of randomness, but rather our inability to track underlying processes. But the fact that many macroscopic processes on many scales are trackable and in accordance with deterministic laws would seem to indicate that the underlying processes are also deterministic (ie., lawful). Unless there's some reason to believe that the reality underlying instrumental behavior is essentially different from the macroscopic reality of our senses, and that our ignorance thereof is not just a matter of the limitations of our sensory capabilities.

 

[bhobba]

Not sure what you mean by this. Are you saying that you believe that QM is some sort of probability theory? If so, I agree.

I mean its fundamentally a probabilistic theory and not some kind of deterministic process masquerading as such, as say Bohmian Mechanics does. I firmly believe it is a fundamental probabilistic theory - I reject completely Einstein's idea it was incomplete - I have zero problem with God playing dice (although that of course was not Einstein's main objection - he was more concerned with an objective reality independent of observation - but as always his reasoning was subtle). I am simply pointing out as a matter of principle QM may be the limit or approximation or whatever of some deterministic process and there is no way it can be ruled out. I find it slightly puzzling why anyone would doubt it.

Thanks
Bill

 

[ThomasT]

I firmly believe it is a fundamental probabilistic theory...

I learned (what I remember of) QM in the probability interpretation.

... I reject completely Einstein's idea it was incomplete ...

I think Einstein was correct. Qm is an incomplete theory of physical reality.

I am simply pointing out as a matter of principle QM may be the limit or approximation or whatever of some deterministic process ...

I agree. In which case QM is an incomplete theory (in a certain sense), and, in any case, there's not a whole lot that anybody can say about the reality underlying instrumental behavior.

 

[DrChinese]

I mean its fundamentally a probabilistic theory and not some kind of deterministic process masquerading as such, as say Bohmian Mechanics does. I firmly believe it is a fundamental probabilistic theory - I reject completely Einstein's idea it was incomplete - I have zero problem with God playing dice (although that of course was not Einstein's main objection - he was more concerned with an objective reality independent of observation - but as always his reasoning was subtle). I am simply pointing out as a matter of principle QM may be the limit or approximation or whatever of some deterministic process and there is no way it can be ruled out. I find it slightly puzzling why anyone would doubt it.

Thanks
Bill

It is only your last statement I am commenting on, as the rest I agree with pretty well.

You might acknowledge that after 80+ years, there has not been the slightest bit of evidence - nor any plausible hypothesis other than perhaps Bohmian class theories - that any underlying deterministic mechanism exists in nature. In that light, I wouldn't find it surprising to doubt it exists. I doubt it, for instance.

So yes, certainly it is possible, no issue there. On the other hand, newer ideas such as the PBR theorem cast significant doubt that there can be a deterministic solution. If the quantum state is fundamental, then there is no determining factor to uncover.

 

[zonde]

Describe to me the test that will prove 100% for sure it was not created by a deterministic process that pass such tests.

I would say you misunderstood what I asked.
In simple words - you provide hypothetical example that demonstrates non-deterministic randomness and I try to provide test that should demonstrate that it is deterministic (according to our view of physical laws).

And please take into the account that this example should supposedly work as explanation for genuine randomness of QM i.e. I ask this question in context of OP:

Problem is, I can't think of any classical situations in which this notion of genuine randomness actually applies.

 

[danmay]

So, finally, the question(s): a good place to start would certainly be, am I just interpreting the information wrong? Do we know for sure that quantum mechanics obeys this genuine-randomness-dependent behaviour? If not, then what do we suppose determines the behaviour of quantum mechanical phenomena? If so, then how is it that the behaviour is determined without a cause?

As always, any insight would be much appreciated. This has me quite puzzled.

Quantum mechanics--at least the most common type students learn--is statistically determinant, not random.

Do we have deterministic objects following statistical laws or statistical objects following deterministic laws? Does atomic structure quantize energy, or does energy quantize atomic structure? It doesn't matter which is which; any event would involve both aspects, so there is no difference.

Problem is, I can't think of any classical situations in which this notion of genuine randomness actually applies.

Randomness is relative. In "classical situations", it's usually so small or uniform that we don't care about it, even though it's there. If the system is sensitive enough, however, we would notice. Of course, it doesn't have to be random in a uniform way, in which case again we might find patterns that appear "deterministic", along with some degree of accompanying "randomness".

 

[bhobba]

It is only your last statement I am commenting on, as the rest I agree with pretty well.

You might acknowledge that after 80+ years, there has not been the slightest bit of evidence - nor any plausible hypothesis other than perhaps Bohmian class theories - that any underlying deterministic mechanism exists in nature. In that light, I wouldn't find it surprising to doubt it exists. I doubt it, for instance.

So yes, certainly it is possible, no issue there. On the other hand, newer ideas such as the PBR theorem cast significant doubt that there can be a deterministic solution. If the quantum state is fundamental, then there is no determining factor to uncover.

I acknowledge and agree with everything you say. I am speaking of a matter of principle - not what I believe. IMHO standard QM is correct - BM etc and other outs are a crock.

Thanks
Bill

 

[bhobba]

I would say you misunderstood what I asked.
In simple words - you provide hypothetical example that demonstrates non-deterministic randomness and I try to provide test that should demonstrate that it is deterministic (according to our view of physical laws).

And please take into the account that this example should supposedly work as explanation for genuine randomness of QM i.e. I ask this question in context of OP:

Please be 100% clear what I am saying. I will repeat it again. I am saying there is no way by any test currently available you can tell a random sequence from one created by a well designed deterministic algorithm. If you want specifics let's say it was created by the Mersenne Twister algorithm. I give you such a sequence and you are required to tell me how you would determine if it is genuinely random or made by the twister.

The last part of your requirement - namely - 'should supposedly work as explanation for genuine randomness of QM' - is trivial because you can simply postulate that some unknown process at the sub quantum level mimics that algorithm. Is such - likely - hell no - it would be a totally silly and laughable hypothesis - but again this is a matter of principle - not of reasonableness. Reason, Occam's Razor, all sorts of stuff tells me QM is genuinely random.

If you think the above is outlandish and physically unreasonable you are correct. If that is your concern about what I am saying then let's pin it down to something more physically reasonable. I give you the results of a double slit experiment - namely the positions of the detected particles. Tell me how you would tell the difference between it being genuinely random and what is predicted by BM which is deterministic but the randomness is a result of factors not under control of the experimenter but that are presumably in principle knowable?

Thanks
Bill

 

[Delta Kilo]

Quantum randomness is tied strongly with wavefunction collapse. It is in the same can of worms. "No-collapse" interpretations such as MWI or BM are automatically deterministic. The "appearance of collapse FAPP" naturally translates into "appearance of randomness FAPP" (where the "apparent randomness FAPP" is indistinguishable from "genuine randomness" by any experimental test, a notion I can comfortable live with). True 'genuine randomness' is equivalent to objective collapse. "Consciousness causes collapse" is translated into "consciousness is the source of randomness" etc. So by making a statement about the nature of randomness one implicitly adopts or rejects particular interpretation. Choose your poison.

Personally I don't see what the fuss is about. We know that quantum randomness only appears during measurement process. We also know that this process necessarily involves interaction of one microscopic system being measured with huge number of interacting microscopic systems making up measuring apparatus and its environment. It is only natural to expect that the initial state of the apparatus and/or the environment influences the outcome. Since we do not know the initial state (and cannot possibly know it all even if we tried, due to no-cloning theorem), it should be no surprise that the outcome appears random.

 

[zonde]

Please be 100% clear what I am saying. I will repeat it again. I am saying there is no way by any test currently available you can tell a random sequence from one created by a well designed deterministic algorithm. If you want specifics let's say it was created by the Mersenne Twister algorithm. I give you such a sequence and you are required to tell me how you would determine if it is genuinely random or made by the twister.

Well that's trivial - take the algorithm, take the same seed and you get the same result.
This of course is not genuine randomness as we can clearly identify cause, it's the seed. And with the same seed (the same cause) algorithm is always going to give the same result i.e. no randomness.

 

[Jazzdude]

It is only natural to expect that the initial state of the apparatus and/or the environment influences the outcome. Since we do not know the initial state (and cannot possibly know it all even if we tried, due to no-cloning theorem), it should be no surprise that the outcome appears random.

Indeed, that's very natural, and I guess nobody has a problem with this. However, the resulting randomness breaks the linearity of the evolution. There is no way a linear evolution can create outcomes that depend on the magnitude of components.

So the problem is quite a bit deeper than just identifying a source of randomness. You have to explain the nonlinearity of the observation and the exact distribution of the random outcomes.

 

[Ken G]

Scientific method (testing in particular) is based on concept of causation. As a result anything that can't be interpreted from perspective of causation is non-scientific.

This is sucn an interesting and important issue that it probably calls for its own thread, but I'll just answer briefly that it is highly debatable that the concept of cause is at all important in physics. I would go so far as to argue that the concept of a cause is not even definable in physics, the definition appears more at the level of human interaction with our environment, which is well separated from the laws themselves.

One simple reason for this is the tendency for the laws of physics to be time-reversible. One key ramification of this is that "what causes what" is very much a kind of sociological construct, that has a lot more to do with what we use science for that it has to do with the laws of physics. So I would agree that "causation is important in science", but that's because human interaction with, and involvement in, our environment is indeed important in science. Science is a human endeavor. But the laws can still be expressed in language that is completely devoid of "causes", and the laws are still the same laws-- it is just a popular way of interpreting the laws because it gibes well with what we use science to do.

 

[Ken G]

But the fact that many macroscopic processes on many scales are trackable and in accordance with deterministic laws would seem to indicate that the underlying processes are also deterministic (ie., lawful). Unless there's some reason to believe that the reality underlying instrumental behavior is essentially different from the macroscopic reality of our senses, and that our ignorance thereof is not just a matter of the limitations of our sensory capabilities.

But there is a very good reason to believe that-- it is almost inevitablly true! Why on Earth would our senses, which are presumably derived from a huge amalgamation of microscopic processes that we are trying to understand, not be essentially different from those processes? Are not the actions of an ant colony essentially different from what an individual ant is doing? Is not what a violinist is doing essentially different from what the particles in a violin are doing? I disagree with the implication that the default assumption is that our way of thinking about and interacting with reality should be the same as what reality is "actually doing", it seems clear to me that the default assumption should be that we are filtering reality to get it to serve our needs, needs that are extremely dependent on what humans are and what we want to do.

So when our filters give us results that allow deterministic interpretations of macro phenomena, we should always expect that to be emergent behavior, just as we expect the way a fluid flows through a nozzle to be emergent from what the atoms are actually doing, and what atoms are actually doing to be emergent from what quarks and fields are doing, and so on ad infinitum (and I say this without necessarily committing to the idea that the universe is built entirely bottom-up). We don't get to know what it is "emergent" from, because even that could also be emergent. We just have to recast what it is we are trying to know about reality.

The key point is that we have no difficultly interpreting seemingly deterministic behavior as emergent from random behavior, that's pretty much the field of statistical mechanics. Also, we have no difficulty interpreting seemingly random behavior as emergent from deterministic behavior, that is what Delta Kilo described so succinctly. These are all just interpretations, but we can't "reason by interpretation." Reality is just not going to give up these secrets, all we can do is make good models and interpret them however it works for us. Sometimes that leads to a consensus interpretation, sometimes it doesn't, but reality is not beholden to our interpretations, any more than you are limited to be what your dog thinks you are.

 

[ThomasT]

But there is a very good reason to believe that-- it is almost inevitablly true! Why on Earth would our senses, which are presumably derived from a huge amalgamation of microscopic processes that we are trying to understand, not be essentially different from those processes? Are not the actions of an ant colony essentially different from what an individual ant is doing? Is not what a violinist is doing essentially different from what the particles in a violin are doing?

It depends on what one is referring to by "essentially". In the context of this thread, I'm supposing that "essentially different" refers to lawful vs nonlawful (ie., deterministic vs nondeterministic) processes or evolutions. Ants, ant colonies, violins, violinists, orchestras, and everything else I can think of, all seem to evolve deterministically.

Beyond that, quantum experimental phenomena, and the theories and models associated with them, seem to me to indicate that the underlying physical world is composed of a vast hierarchy of particulate media. Since I can characterize the macroscopic world of my sensory experience in that way also, and since our sensory machinery is, afaik, vibratory ( that is, we detect frequencies wrt various media), and since there are so many examples of strikingly similar phenomena on so many different scales, then it seems logical to me to suppose that any and all behavior at any and all scales has a common ancestor or fundamental dynamical law(s) governing everything.

... when our filters give us results that allow deterministic interpretations of macro phenomena, we should always expect that to be emergent behavior ...

I agree, and the notion of encompassing fundamental laws (ie., a fundamentally deterministic universe) is compatible with emergence.

... I say this without necessarily committing to the idea that the universe is built entirely bottom-up ...

If you mean from small to large, then I agree. But the bottom, ie., the most fundamental, might also refer to behavioral principles or dynamical laws.

The key point is that we have no difficultly interpreting seemingly deterministic behavior as emergent from random behavior, that's pretty much the field of statistical mechanics. Also, we have no difficulty interpreting seemingly random behavior as emergent from deterministic behavior, that is what Delta Kilo described so succinctly.

Yes, that seems to be the case.

These are all just interpretations, but we can't "reason by interpretation." Reality is just not going to give up these secrets, all we can do is make good models and interpret them however it works for us.

So, aren't we reasoning, regarding the nature of reality, via interpretation?

 

[zonde]

This is sucn an interesting and important issue that it probably calls for its own thread, but I'll just answer briefly that it is highly debatable that the concept of cause is at all important in physics. I would go so far as to argue that the concept of a cause is not even definable in physics, the definition appears more at the level of human interaction with our environment, which is well separated from the laws themselves.

Basic concepts are not definable. Are you familiar with axiomatic systems and what are undefined terms in them?

One simple reason for this is the tendency for the laws of physics to be time-reversible.

This is because we use math for formulation of laws a lot. Math works when quantities are conserved. When quantities are not conserved we combine different quantities so that combination is conserved. This is the bias introduced by extensive usage of math.

One key ramification of this is that "what causes what" is very much a kind of sociological construct, that has a lot more to do with what we use science for that it has to do with the laws of physics. So I would agree that "causation is important in science", but that's because human interaction with, and involvement in, our environment is indeed important in science. Science is a human endeavor.

Any experimental test starts with things that we can do (cause) then from this point we can go further. So it's not just important it's the basis of science.

But the laws can still be expressed in language that is completely devoid of "causes", and the laws are still the same laws-- it is just a popular way of interpreting the laws because it gibes well with what we use science to do.

Some simple example, please.

 

[zonde]

Indeed, that's very natural, and I guess nobody has a problem with this. However, the resulting randomness breaks the linearity of the evolution. There is no way a linear evolution can create outcomes that depend on the magnitude of components.

So the problem is quite a bit deeper than just identifying a source of randomness. You have to explain the nonlinearity of the observation and the exact distribution of the random outcomes.

I would agree that the problem is a bit deeper.
I would say that it's certain lack of randomness that is puzzling when we speak about interference rather than excess randomness. And it's similar with entanglement.

 

[Ken G]

It depends on what one is referring to by "essentially". In the context of this thread, I'm supposing that "essentially different" refers to lawful vs nonlawful (ie., deterministic vs nondeterministic) processes or evolutions. Ants, ant colonies, violins, violinists, orchestras, and everything else I can think of, all seem to evolve deterministically.

I see you are not fan of "systems" thinking, but rather are a strict reductionist? For myself, I see a lot of value in the "systems" viewpoint (that the action of complex systems is best understood as an interplay between top-down coupling constraints and bottom-up independent processes, than it is with a purely reductionist approach that the whole is understood purely by considering the elementary parts). But more to the point, I would certainly not say that what an orchestra is doing is strictly deterministic! It certainly cannot be demonstrated in detail to be deterministic, nor precisely predicted as a deterministic process, so the issue must boil down to whichever one views as the "default" assumption. I think many physicists are way too quick to picture determinism as the default, there really isn't any solid reasons to adopt that stance-- it's simple overinterpretation, in my view.

Beyond that, quantum experimental phenomena, and the theories and models associated with them, seem to me to indicate that the underlying physical world is composed of a vast hierarchy of particulate media.

But what do we mean "composed of"? Strictly composed of that? There's no question the particulate model is vastly important and successful, but so is the fields model, so at the very least we might wish to say the physical world is composed of particles and fields. But I wouldn't even say that-- I would just say our models invoke particles and fields, and what the "underlying physical world" is composed of is simply not a concept that physics needs, and we never get to know that, not even using physics.

Since I can characterize the macroscopic world of my sensory experience in that way also, and since our sensory machinery is, afaik, vibratory ( that is, we detect frequencies wrt various media), and since there are so many examples of strikingly similar phenomena on so many different scales, then it seems logical to me to suppose that any and all behavior at any and all scales has a common ancestor or fundamental dynamical law(s) governing everything.

Yes, the rationalistic view that laws "govern" reality, rather than reality "governs" what we will interpret as laws. That debate has raged as long as there has been thought about our environment, let me just say that an extremely unlikely proposition, and it has never stood the test of time, a fact we all too easily overlook.

I agree, and the notion of encompassing fundamental laws (ie., a fundamentally deterministic universe) is compatible with emergence.

Not really-- not unless you think that some phenomena emerge and other, more fundamental ones, don't. But if you hold, as I do, that all phenomena are emergent, and that there is never going to be any such thing as a fundamental process (nor does there need to be to do physics exactly as we do it), then the notion of encompassing fundamental laws is not compatible with emergence, because even the laws must emerge from something else (given that no law deals in the currency of something fundamental, but rather only in emergent phenomena). It seems a more natural "default" assumption, being the only one that actually has stood the test of time!

If you mean from small to large, then I agree.

I do, the common idea is that large phenomena emerge from small phenomena. But I'm not claiming that to be true, I think emergence can also cascade from large to small (as in the case of a violinist manipulating the instrument in a way that ultimately affects its atoms). But it is no longer important to specify what emerges from what if there is nothing fundamental that is "at the bottom" anyway.

So, aren't we reasoning, regarding the nature of reality, via interpretation?

I would argue no-- not if we are being precise about what we are doing. When we get a little casual about expressing what physics does, we often frame it as reasoning about the nature of reality, but Bohr had it right-- physics is what we can say about nature. I believe he meant that this means physics is not about nature herself, it is about our interaction with nature. We can interpret what we are doing around our interaction with nature, because we need to interpret our goals and objectives, but we are not interpreting the "nature of reality"-- as soon as you interpret that, it ain't the nature of reality any more.

 

[Ken G]

Basic concepts are not definable. Are you familiar with axiomatic systems and what are undefined terms in them?

If you hold that a "cause" is an axiom in physics, please specify a theory, any theory, that requires that in its axiomatic structure. I'm not aware of any, causes are sociological constructs we add on top of our theories to help us interpret them, no laws of physics refer to causes that I've ever heard of. This is clear from the simple fact that you would need to immediately remove from consideration any laws that are time reversible, so gone are Newton's laws, the Schroedinger equation, and general relativity.

Any experimental test starts with things that we can do (cause) then from this point we can go further. So it's not just important it's the basis of science.

No, you don't need to imagine you are causing something to do a scientific experiment. That we often do that is indeed our sociology, but it's not a requirement. If I drop a mass in my experiment, I never need to imagine that I "caused the mass to fall", or that gravity did, I am just setting up an experiment and watching what happens. No causation necessary, indeed causation brings in significant philosophical difficulties (around free will and so on). But I agree that we do invoke causation concepts constantly when we do science, and that's because science is a human endeavor, and humans use causation concepts in our daily lives all the time-- it's part of our sociology.

Some simple example, please.

Give me any phenomenon of your choosing that you feel must be described in terms of causes and effects, and I will offer a perfectly successful way to describe that same phenomenon without invoking those concepts at all.