Is a-causality necessary for randomness?

[San K]

What is the relationship between a-causality and randomness?

Let's look at the argument below:

For something to be (truly/inherently) random there cannot be a cause.

Because, if there is a cause then the cause can be studied and the result/output can be predicted and hence there would no randomness.

True Randomness means something that cannot be predicted.

We can predict whether will be an interference pattern or not, however we cannot predict the location of any individual/single photon/electron on the screen.

We can, in principle, predict the results of a roll of a dice (or toss of a coin) if we took into account all the factors such initial forces on the dice during the toss, effect of air molecules etc. Since the roll of a dice has a cause its predictable.

 

[bhobba]

An observation causes a quantum system to change state - we just can't predict what that state will be - but 100% for sure it caused it to change state - the change was not a-casual.

In classical 100% deterministic systems chaotic behaviour abounds meaning since it is impossible to know with 100% accuracy the initial conditions there will always be some imprecision in knowledge that will grow to the point prediction is meaningless.

Thanks
Bill

 

[VortexLattice]

This seems a tad philosophical but... at the very least, it seems like you could have a perfectly reasonable "cause" for a "random" process, but the cause is necessarily hidden. I think that's the same as Hidden Variable Theory, which is I guess wrong because of Bell's Theorem, but I don't know exactly why.

 

[JPBenowitz]

This isn't true. Nothing is truly random, even quantum mechanics. Although QM may seem completely random it isn't, it's just that we can never acquire the necessary information to determine precisely how the system will evolve.

 

[Zarqon]

This isn't true. Nothing is truly random, even quantum mechanics. Although QM may seem completely random it isn't, it's just that we can never acquire the necessary information to determine precisely how the system will evolve.

This is not known. All we can say is that we measure what appears to be a truly random phenomena when we measure quantum states. Although there exists deterministic explanations these are just speculations and have not been proven. At this point it is still an open question on whether the universe is really random or deterministic.

 

[bhobba]

This isn't true. Nothing is truly random, even quantum mechanics. Although QM may seem completely random it isn't, it's just that we can never acquire the necessary information to determine precisely how the system will evolve.

What can be said is a process that passes all tests for randomness may be truly random but of course we can never know if its the result of some deterministic process that has not been discovered yet and that process just happens to mimic randomness - tests for true randomness are pretty good these days and only some very sophisticated algorithms can actually pass it. If you believe nature just happens to be that 'good' - well it is a logically valid position - but I do not ascribe to it. Occams razor would suggest if we know of no underlying deterministic process and it passes randomness tests then the simplest explanation is it really is random.

And as far as we can tell today QM is utterly and truly random eg random number generators based on thermal noise which is quantum in origin I am pretty sure pass every known test for randomness that even some reasonably sophisticated pseudo generators fail - although pseudo generators do exist that do pass those tests.

Thanks
Bill

 

[Maui]

Shouldn't 'truly random' be regarded as the approximately 50/50 distribution of outcomes of hundreds of trials? If you toss a coin 222 times and it lands on tails approximately 111 times, it means it is truly random because nothing unobservable can be said to be affecting its 50/50(1 of 2) possibile outcomes. Does anyone object to this definition?

Electrons and other fundamental particles do not obey the 50/50 statistics so they cannot be truly random. For reference, just look at the interference pattern from single electrons in a double slit experiment. I don't see how we could observe a Newtonian(-like) universe based on a truly random quantum foundation. It would fall apart immediately, wouldn't it?

 

[San K]

Electrons and other fundamental particles do not obey the 50/50 statistics so they cannot be truly random. For reference, just look at the interference pattern from single electrons in a double slit experiment. I don't see how we could observe a Newtonian(-like) universe based on a truly random quantum foundation. It would fall apart immediately, wouldn't it?

Each of the fringes has a fixed probability of the electron/photon landing up on it, I thought...for a given experimental setup (slit width and distance, electron distances etc).

So conceptually the 50/50 i.e. fixed probability (totaling to 1), concept applies.

 

[Maui]

Each of the fringes has a fixed probability of the electron/photon landing up on it, I thought...for a given experimental setup (slit width and distance, electron distances etc).

So conceptually the 50/50 i.e. fixed probability (totaling to 1), concept applies.

The subtlety lies in the fact that the fringes are formed by the accumulation of thousands of single dots(landings). It's as if the electron travels as a wave through the slits but lands on the detection screen as a particle. After many many landings accumulate, we get the interference pattern and this is anything but random. It's so much more on the holistic side, that calling it random seems to require a re-definition of "randomness".

 

[audioloop]

What is the between a-causality and randomness?

Let's look at the argument below:

For something to be (truly/inherently) random there cannot be a cause.

Because, if there is a cause then the cause can be studied and the result/ can be predicted and hence there would no randomness.

Randomness means something that cannot be predicted.

We can predict whether will be an interference pattern or not, however we cannot predict the location of any individual/ photon/electron on the screen.

We can, in principle, predict the results of a roll of a dice (or toss of a coin) if we took into all the factors such initial forces on the dice during the toss, effect of air molecules etc. Since the roll of a dice has a cause its predictable.

unpredictability does not imply the lack of a cause, we can't confound determinism with predictability (or indeterminism with unpredictability)
a-causality have to do with indeterminism but indeterminism does not have a relationship with randomess.

by the way there are deterministic theories without being computable i.e. nopredictable outcomes and indeterministic process can produces a non-random sequence of outcomes.

 

[JPBenowitz]

What can be said is a process that passes all tests for randomness may be truly random but of course we can never know if its the result of some deterministic process that has not been discovered yet and that process just happens to mimic randomness - tests for true randomness are pretty good these days and only some very sophisticated algorithms can actually pass it. If you believe nature just happens to be that 'good' - well it is a logically valid position - but I do not ascribe to it. Occams razor would suggest if we know of no underlying deterministic process and it passes randomness tests then the simplest explanation is it really is random.

And as far as we can tell today QM is utterly and truly random eg random number generators based on thermal noise which is quantum in origin I am pretty sure pass every known test for randomness that even some reasonably sophisticated pseudo generators fail - although pseudo generators do exist that do pass those tests.

Thanks
Bill

My position isn't necessarily that QM isn't "truly random" but what it means to be truly random. For instance we cannot know both the position and momentum of a particle precisely because observing it changes it; in other words the very act of observation constrains the observer to how much information can possibly be extracted from any given system. Because of this information constraint we cannot know precisely the initial conditions of any system to predict a precise outcome. Does this mean that the universe is intrinsically deterministic? Not necessarily because no observer could possibly compute the future--the future remains completely hidden. The universe isn't exactly deterministic or truly random in this sense.

 

[JPBenowitz]

unpredictability does not imply the lack of a cause, we can't confound determinism with predictability (or indeterminism with unpredictability)
a-causality have to do with indeterminism but indeterminism does not have a relationship with randomess.

by the way there are deterministic theories without being computable i.e. nopredictable outcomes and indeterministic process can produces a non-random sequence of outcomes.

Randomness is really just chaos. Where predicting the outcome in a chaotic system requires hefty computation. True Randomness is where a chaotic system cannot have a predicted outcome because of a fundamental computational limit.

 

[audioloop]

Randomness is really just chaos. Where predicting the outcome in a chaotic system requires hefty . True Randomness is where a chaotic system cannot have a predicted outcome because of a fundamental computational limit.

another confusion,
Chaos involves deterministic process i.e. no random.

A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error*, these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved**.*Casdagli, Martin. "Chaos and Deterministic versus Stochastic Non-linear Modelling", in: Journal Royal Statistics Society: Series B
**Kellert, Stephen H. (1993). In the Wake of Chaos: Unpredictable Order in Dynamical Systems. University of Chicago Press.
Lorenz, Edward N. (1963). "Deterministic non-periodic flow". Journal of the Atmospheric Sciences 20 (2): 130–141

 

[JPBenowitz]

another confusion,
Chaos involves deterministic process i.e. no random.

A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error* these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved**.


*Casdagli, Martin. "Chaos and Deterministic versus Stochastic Non-linear Modelling", in: Journal Royal Statistics Society: Series B
**Kellert, Stephen H. (1993). In the Wake of Chaos: Unpredictable Order in Dynamical Systems. University of Chicago Press.
Lorenz, Edward N. (1963). "Deterministic non-periodic flow". Journal of the Atmospheric Sciences 20 (2): 130–141

That's literally what I am saying. Randomness is really just a deterministic system with an error that increases exponentially. True Randomness is when that error exceeds all computational possibilities on a fundamental physical level.

 

[Zarqon]

That's literally what I am saying. Randomness is really just a deterministic system with an error that increases exponentially. True Randomness is when that error exceeds all computational possibilities on a fundamental physical level.

You have to be careful with your statements. I don't think this has been shown at all. It might work like that but you can't make a statement saying it's certain that it does work like that because it has not been proven (and if you think it has been proven could you find some sources for your claim?).

 

[bhobba]

You have to be careful with your statements. I don't think this has been shown at all. It might work like that but you can't make a statement saying it's certain that it does work like that because it has not been proven (and if you think it has been proven could you find some sources for your claim?).

Indeed.

Thanks
Bill

 

[JPBenowitz]

You have to be careful with your statements. I don't think this has been shown at all. It might work like that but you can't make a statement saying it's certain that it does work like that because it has not been proven (and if you think it has been proven could you find some sources for your claim?).

You are correct I do not think it has been proven. Which is precisely why I am going to explore this avenue. I'll get back to you on what I find :)

 

[QuantumHop]

What is the relationship between a-causality and randomness?

Let's look at the argument below:

For something to be (truly/inherently) random there cannot be a cause.

Because, if there is a cause then the cause can be studied and the result/output can be predicted and hence there would no randomness.

True Randomness means something that cannot be predicted.

We can predict whether will be an interference pattern or not, however we cannot predict the location of any individual/single photon/electron on the screen.

We can, in principle, predict the results of a roll of a dice (or toss of a coin) if we took into account all the factors such initial forces on the dice during the toss, effect of air molecules etc. Since the roll of a dice has a cause its predictable.

"Random" is a thirteenth century word, it was never brought into human language to be used in science. Randomness cannot be created using mathematics and I don't believe it takes place in nature, all my spidey senses say its impossible.

If a radioactive particle decays and you say it just happened "randomly" then it would be an effect without a cause, that's insane. I don't know what gave the signal for the particle to decay but it makes more sense to me to say I'm unable to see what gave the signal and therefore (to me) its unpredictable.

Mathematics produces statistically random numbers so why wouldn't nature just use them instead of performing a magic trick. If they would just throw away the word random and replace it with unpredictable or unknowable I could sleep at night.

Pseudo randomness is real, random is a figment of the human imagination.

Either that or I'm just a nut job

 

[bhobba]

If a radioactive particle decays and you say it just happened "randomly" then it would be an effect without a cause, that's insane.

You are not a nut job - simply very ingrained in classical thinking. It has a cause - the act of interacting with the environment causes it to decohere and for the particle decay to manifest in some kind of observational apparatus. This is exactly the same as any other quantum observation with decoherence taken into account. It has a property before observation such as a particle present or not present - the theory simply does not predict it with certainty - only probabilities. Do you consider flipping a coin insane because you can't predict if its heads or tails - but you know its a head or tail. I don't and most people (actually everyone) I know doesn't. This is purely a matter of getting used to a world view that is slightly different - that's all - nothing mind boggling weird to the point its insane weird - weird yes - insane - no.

Thanks
Bill

 

[QuantumHop]

You are not a nut job - simply very ingrained in classical thinking. It has a cause - the act of interacting with the environment causes it to decohere and for the particle decay to manifest in some kind of observational apparatus. This is exactly the same as any other quantum observation with decoherence taken into account. It has a property before observation such as a particle present or not present - the theory simply does not predict it with certainty - only probabilities. Do you consider flipping a coin insane because you can't predict if its heads or tails - but you know its a head or tail. I don't and most people (actually everyone) I know doesn't. This is purely a matter of getting used to a world view that is slightly different - that's all - nothing mind boggling weird to the point its insane weird - weird yes - insane - no.

Thanks
Bill

I can accept that 13.7 billion years ago space and time sprang into existence even though it didn't have a place to happen. I can believe that every time the universe needs to make a decision it splits in two. And I can believe in the existence of multiple realities just so long as none of them can generate a random number

Imagine a universe where a small plastic computer is in charge of creating motion in some particles, the computer runs its program and instructs all the various particles to start moving. It gets so hot with all this movement that the computer melts. From that moment in time it would look like the particles were moving randomly. In reality the motion would be pseudo random and the cause no longer exists.

I could invent dozens of ways to create the illusion of randomness but not one to create true randomness.

For the universe to be able to create randomness it has to be capable of making a decision, since I view the universe as mathematical then its impossible for it to make a "choice"

The difference between something being truly random or just unpredictable is colossal.

What possible mechanism could the laws of nature use to make a "choice"

 

[QuantumHop]

Its like asking what came first the chicken or the egg but replacing the chicken and egg with cause and effect.

I would ask what came first cause or effect and you would answer "effect"

 

[bhobba]

For the universe to be able to create randomness it has to be capable of making a decision, since I view the universe as mathematical then its impossible for it to make a "choice"

I view the universe as mathematical as well. But why you think being unable to predict the outcome of an observation with certainly involves the universe making a decision has me beat. Mathematically all randomness means is the long term proportion of some outcome reaches a stable limit - nothing to do with decision making of any type.

I don't believe in the MWI rubbish splitting into different realities etc etc - its mystical nonsense IMHO. But hey - to each their own.

Thanks
Bill

 

[bhobba]

Its like asking what came first the chicken or the egg but replacing the chicken and egg with cause and effect. I would ask what came first cause or effect and you would answer "cause"

Precisely why do you believe the inability to predict something means it has no cause?

Thanks
Bill

 

[QuantumHop]

I view the universe as mathematical as well. But why you think being unable to predict the outcome of an observation with certainly involves the universe making a decision has me beat. Mathematically all randomness means is the long term proportion of some outcome reaches a stable limit - nothing to do with decision making of any type.

I don't believe in the MWI rubbish splitting into different realities etc etc - its mystical nonsense IMHO. But hey - to each their own.

Thanks
Bill

If you also think that the universe is mathematical then why would you allow aspects of it to be random when there's no such thing as random in maths. you could observe a moving particle but you wouldn't know if it was in motion because another particle hit it (cause) or it was in motion because of some particle decaying (effect)

 

[QuantumHop]

Precisely why do you believe the inability to predict something means it has no cause?

Thanks
Bill

Aaaaaaagh I got that the wrong way round, I should have said.

I would ask what came first cause or effect and you would answer "effect"

 

[QuantumHop]

If all the particles were just sat there motionless and then for no apparent reason they started to decay (an effect without a cause) and then all those particles start moving around and bumping into each other the net result is there is more effect in the motion of those particle then the cause of bumping into each other, that's crazy.

 

[QuantumHop]

Sit down and try to make a computer program "guess" the outcome of rolling a dice "without using any random function" and you will find its impossible. This is why I'm making a such a big deal over the difference between truly random and just unpredictable. It sounds the same and it yields the same results but deep down one is possible and the other isn't.

 

[bhobba]

If all the particles were just sat there motionless and then for no apparent reason they started to decay (an effect without a cause) and then all those particles start moving around and bumping into each other the net result is there is more effect in the motion of those particle then the cause of bumping into each other, that's crazy.

QM does not say that. Have you actually studied what QM says from a book like QM - A Modern Development by Ballentine? What it says is the outcome of an observation can't be predicted with certainty. Indeed the idea of particles having a definite position for any length of time is not possible so the idea particles just sitting there motionless is silly.

I suspect your view of QM has been too strongly influenced by pop sci accounts.

Again particle decay has a cause - environmental decoherence. We simply can't predict when the decay will occur.

Thanks
Bill

 

[bhobba]

It sounds the same and it yields the same results but deep down one is possible and the other isn't.

Since it is observationally identical have you considered your discomfiture lies within your classically formed intuition rather than nature? Why not face nature on it own terms rather than how you think it should behave? The only difference between throwing a dice and QM is the outcome of the dice can in principle be predicted with sufficient information (although getting that information with enough accuracy to do it is a challenge) and the outcome of an observation is not - they both have a cause - its simply a matter what in principle can be predicted. The idea everything can be predicted with enough information is not something that a-priori must be true.

Thanks
Bill

 

[QuantumHop]

the outcome of an observation can't be predicted with certainty.

I have no problem with that.

the idea of particles having a definite position for any length of time is not possible so the idea particles just sitting there motionless is silly.

I realize that, Its just the easiest way I could think of to explain that the sum total of all motion of all particles is more the result of effect than cause. (although you now clear things up a few lines down)

I suspect your view of QM has been too strongly influenced by pop sci accounts.

Absolutely, the 60's were simple. When they put Armstrong on the moon I was wondering why they didn't just pile cardboard boxes on top of each other and climb up.

Again particle decay has a cause - environmental decoherence. We simply can't predict when the decay will occur.

Now you hit the nail on the head and I can sleep, the particle didn't just decay randomly it has a cause, randomness has been replaced with unpredictability and the universe is behaving itself.

Random means something happened without any clear instruction or cause, unpredictable means it appears random but only because the cause is unknown. The idea of randomness gives me nightmare

 

[bhobba]

Random means something happened without any clear instruction or cause, unpredictable means it appears random but only because the cause is unknown. The idea of randomness gives me nightmare

Within what I think your conception of randomness is (being something that just happens spontaneously) I am inclined to agree but without going into the details that would not be my view about randomness which I equate with unpredictability.

Thanks
Bill

 

[Zarqon]

Random means something happened without any clear instruction or cause, unpredictable means it appears random but only because the cause is unknown. The idea of randomness gives me nightmare

Also you have to acknowledge the difference between what you want to be true and what has actually been established with experiments. Science is not based on your nightmares or on spidey senses.

All we see is that if you put an atom into a superposition state of 0 and 1 and then make a measurement in the computational basis, there is no way of predicting if the outcome will be 0 or 1. Although there are potential deterministic explanations, at this point, it is simply not possible for us to scientifically choose between true randomness or determinism + additional stuff (such as many worlds). Both are possible and no known experiment can set them apart, so for all practical purposes, true randomness does exist.

If you don't like it, feel free to pick one of the deterministic interpretations to believe in, but you can't go around claiming that true randomness is "figment of the human imagination", because that is simple a false statement, since no such thing has been established.

 

[Maui]

Precisely why do you believe the inability to predict something means it has no cause?

Thanks
Bill

To play devil's advocate - why do you believe that in a quantum universe best described by fields and operators, causality plays a fundamental role(except for ordering events so that they seem to make some sense to you)?

 

[bhobba]

To play devil's advocate - why do you believe that in a quantum universe best described by fields and operators, causality plays a fundamental role(except for ordering events so that they seem to make some sense to you)?

Without posting the detail non relativistic QM follows from observations of invariance of observational outcomes when expressed in the language of linear algebra and Gleasons Theorem which shows, again from invariance, the outcomes of observations must be probabilistic - determinism is not possible. So the answer is I believe nature is at rock bottom simple and the outs of such things as Bohmian Mechanics is ugly because it is contrived, contextual and not invariant. Fields follow from the desire to treat space and time on equal footing which means position operators must also be a label like time is ie is a field.

But aside from such theoretical considerations physics is an experimental science and QM and QFT are fully in accord with experiment.

Why do people want to have nature working in ways that conform to their intuition and want to introduce mathematically ugly things like non contextuality rather than simply assume the outcome of measurements is invariant to other things you happen to be measuring at the same time and go for something like BM?

Actually I don't expect you to answer that - its because they have pre-conceived ideas on how they think nature should work just as I do. That's all discussions in this vein are about - each side airing their prejudices and why they never get anywhere - except to possibly clear up misconceptions.

So let's turn it around again - why don't you - assuming of course you don't.

Thanks
Bill

 

[JPBenowitz]

Since it is observationally identical have you considered your discomfiture lies within your classically formed intuition rather than nature? Why not face nature on it own terms rather than how you think it should behave? The only difference between throwing a dice and QM is the outcome of the dice can in principle be predicted with sufficient information (although getting that information with enough accuracy to do it is a challenge) and the outcome of an observation is not - they both have a cause - its simply a matter what in principle can be predicted. The idea everything can be predicted with enough information is not something that a-priori must be true.

Thanks
Bill

This is the position I was presenting. What it means to be be truly random is not well defined and may very well be a causal event which does not commute enough information to determine which event took place first. If it is impossible for an observer to distinguish causality that QM will appear to be perfectly random. This is an interpretation of hidden variable theory where the information of the system is effectively hidden from the observer.

 

[JPBenowitz]

To play devil's advocate - why do you believe that in a quantum universe best described by fields and operators, causality plays a fundamental role(except for ordering events so that they seem to make some sense to you)?

Causality plays a fundamental role as an emergent property on the macroscopic level as the arrow of time. The laws of physics are for the most part time-symmetric with the weak force and second law of thermodynamics being exceptions. QM is not entirely free from T-asymmetry. The larger question at hand is why is there an arrow of time on large scales but not on small scales?

 

[bhobba]

What it means to be be truly random is not well defined

I think you need to study some math - in math it is very well defined indeed - so well defined tests to determine randomness exist that are actually quite hard to pass for pseudo random number generators that try to mimic randomness. It can be done - but it aren't easy - even some highly sophisticated pseudo random number generators fail it. That's why those seriously into computer simulation use hardware random number generators based on QM and not pseudo generators - they are more reliable. I have done some simulation in the past and obtained some results in a queuing problem clearly at odds with theory - it took a while to sort out but the random number generator was not random - not random at all. You can choose to believe the randomness in QM is the result of some underlying deterministic process - no doubt about it such is an unassailable position - but it must be really good to pass the tests they have these days - I simply do not believe nature is that devious.

Thanks
Bill

 

[bhobba]

The larger question at hand is why is there an arrow of time on large scales but not on small scales?

In QM the arrow of time is a result of decoherence which is the interaction with the environment. Studies have shown it actually doesn't take much to do it - for example a collision with a dust particle - just one collision - is evidently enough to irreversibly decohere a quantum particle. Because of that it is there at small scales as well - which is why its actually hard to demonstrate quantum effects eg to demonstrate superconductivity you generally need very low temperatures so its not in thermal contact with the environment.

Thanks
Bill

 

[JPBenowitz]

I think you need to study some math - in math it is very well defined indeed - so well defined tests to determine randomness exist that are actually quite hard to pass for pseudo random number generators that try to mimic randomness. It can be done - but it aren't easy - even some highly sophisticated pseudo random number generators fail it. That's why those seriously into computer simulation use hardware random number generators based on QM and not pseudo generators - they are more reliable. I have done some simulation in the past and obtained some results in a queuing problem clearly at odds with theory - it took a while to sort out but the random number generator was not random - not random at all. You can choose to believe the randomness in QM is the result of some underlying deterministic process - no doubt about it such is an unassailable position - but it must be really good to pass the tests they have these days - I simply do not believe nature is that devious.

Thanks
Bill

Randomness in mathematics is defined only statistically not formally.

 

[JPBenowitz]

In QM the arrow of time is a result of decoherence which is the interaction with the environment. Studies have shown it actually doesn't take much to do it - for example a collision with a dust particle - just one collision - is evidently enough to irreversibly decohere a quantum particle. Because of that it is there at small scales as well - which is why its actually hard to demonstrate quantum effects eg to demonstrate superconductivity you generally need very low temperatures so its not in thermal contact with the environment.

Thanks
Bill

There is not apparent arrow of time on QM scales precisely because of the energy-time uncertainty principle which does not mean it requires a Δt to measure ΔE with a accuracy but means that the system with a ΔE requires Δt =\pih/2ΔE to evolve into a distinguishable state; in other words there are time intervals where no information is present and thus causality cannot be determined, hence no arrow of time. Just as there exists discrete energy levels there also exists discrete information levels.

 

[bhobba]

Randomness in mathematics is defined only statistically not formally.

That makes no sense, since statistically is itself a concept involving probability. Can I ask exactly what books on probability theory you have studied? Can you explain the non formal nature of Kolmogorov’s axioms?

Books on axiomatic probability theory are extremely formal going to great lengths to prove things that are pretty obvious so they can rigorously prove things that are not such as the existence of a Wiener process - which actually has applications in QFT eg Hida distributions.

Tanks
Bill

 

[bhobba]

There is not apparent arrow of time on QM scales

I think you need to be clearer exactly what you mean by QM scales - usually decoherence occurs very very quickly - so quick that only under special contrived circumstances such as temperatures near absolute zero can it even be measured. Are you talking of time scales even below that - time scales so short present technology can't measure it? If so then I agree.

Thanks
Bill

 

[audioloop]

Randomness is really just chaos.

to be precise and concise:

chaos is highly sensitive to initial conditions, randomess is independent of initial conditions.

 

[Darwin123]

What is the relationship between a-causality and randomness?

Let's look at the argument below:

For something to be (truly/inherently) random there cannot be a cause.

Because, if there is a cause then the cause can be studied and the result/output can be predicted and hence there would no randomness.

True Randomness means something that cannot be predicted.

We can predict whether will be an interference pattern or not, however we cannot predict the location of any individual/single photon/electron on the screen.

We can, in principle, predict the results of a roll of a dice (or toss of a coin) if we took into account all the factors such initial forces on the dice during the toss, effect of air molecules etc. Since the roll of a dice has a cause its predictable.

The word “random” is not always used as meaning without a cause. Random is used in the sense that the correlation of two sets of numbers is zero. Random usually refers to the correlation between future events and a set of measurements. Nonzero correlation has a very precise meaning in mathematics, but loosely corresponds to a practical level of predictability. It has nothing to do with “cause”.
There is no such thing as an absolute measure of randomness. There is only randomness relative to a set of measurements or experiences. Events can be random with respect to one set of measurements, but not random with respect to another set of randomness. You are making the error of thinking there exists and absolute randomness.
I think this is the way physicists, mathematicians and actuaries define random. In the case of insurance, they use statistics on sickness and accidents. They know that each sickness and accident has a cause. In fact, two accidents on opposite sides of the globe may be connected by a series of causes. However, the actuary still considers these random events if the correlation between two sequences of such events is zero.
It really doesn’t matter to the actuary if that there are causes that can be uncovered with great difficulty. That is the job of the insurance detective. The insurance detective may be using a different criteria for random than the actuary. However, the actuary and the insurance detective have access to different types of measurement and experience. So “random” has to be defined relative to their job, not metaphysical causes.
Zero correlation occurs just as often in classical physics as in quantum physics. If there is no correlation between the numbers one can measure and future events, then it doesn’t matter if there is a perfectly understandable cause for the events. The events are random with respect to those measurements.
If there are other measurements that hypothetically can be made which have a nonzero correlation with future events, then the events are not random with respect to those other hypothetical measurements. However, not all hypothetical measurements can be done.
What I am referring to as random is related to what an electronics engineer calls noise. The electronics engineer can have problems with a fluctuating voltage, which he knows is “caused” by other users of electricity on the electronic grid. If he could know precisely what everybody in the world is doing with their electrical devices at the same time, and know the atmospheric electrical conditions all over the world, then he probably could predict electronic noise. He could subtract it. However, he can’t. The most that he could do is characterize the statistical moments of his electronic noise. What makes it noise is that it doesn’t correlate with itself given any sort of time delay. Whether it has a cause or not is irrelevant.
Here is a link concerning the definition of random as used by an electronic engineer.
http://en.wikipedia.org/wiki/White_noise
“A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following:


That is, it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation.”

Let me play devils advocate here. Suppose that we are using a definition of random that includes the concept of “cause”. Quantum mechanics is still a random theory even though there may be a hidden variables theory which is better.
Quantum mechanics is still a random theory because it does not include the hidden variables with which the calculations can be made. The final cause can not be measured. The final results relative to the measurements that can be made consistent with quantum mechanics can’t be used to calculate future events precisely. Therefore, quantum mechanics calculations are random with respect to all known measurement techniques. It may not be random with respect to measurement techniques that may be developed in the future. However, it is still random with respect relative to currently known causes.

Basically, acausal does not mean random. I think the concept of cause is not as well mathematically defined as the concept of random. As a physicist, I generally hear the word "acausal" referring to logical paradoxes or to hysteresis. If "history" can be "changed" in some fashion in a system, the system is considered acausal.
For instance, I often hear "acausal" referred to when discussing time travel. I also hear the word acausal referred to in terms of the Cramers-Kronig relations in optics. If a system is acausal, then supposedly the Kramers-Kronig relations are invalid. It turns our that the Kramers-Kronig relations are invalid if the system shows hysteresis. Hysteresis refers to a sensitivity to past history.
Cause has more to do with time ordering than to randomness. If the time ordering of a series of events is important, the earlier events are said to be the cause of the later events. However, there are hypothetical ways of creating a correlation even when the time ordering is not important.
<Spoiler for "A Sound of Thunder>
<Anyone who reads this should read the story anyway. It is more suspense than mystery.>









If you read the Ray Bradbury's story, a "Sound of Thunder", you will know what I mean. A time traveler votes for a certain candidate who wins. He then steps on a butterfly in the Mesozoic. When he gets back to his own time, the other candidate has won.
The choice of which candidate won is random with respect to the lifespan of butterflies in the Mesozoic. There was no way to tell that stepping on that butterfly will cause the other candidate to win. However, killing the butterfly was obviously the cause of the other candidate winning. If he stepped on another butterfly, maybe the first candidate would have won. Or maybe he would have come back to a kingdom rather than a democracy. The butterfly in this case is definitely a cause, but it still has a random effect on the election.
Note that the hunter who steps on the butterfly is still responsible for his actions. He didn't know what the consequences would be. However, he knew that it would cause something. The fact that he had no way to predict what would happen makes him MORE responsible for doing it because it could have been a lot worse. Therefore, randomness is NOT free will at least in this story.

 

[JPBenowitz]

That makes no sense, since statistically is itself a concept involving probability. Can I ask exactly what books on probability theory you have studied? Can you explain the non formal nature of Kolmogorov’s axioms?

Books on axiomatic probability theory are extremely formal going to great lengths to prove things that are pretty obvious so they can rigorously prove things that are not such as the existence of a Wiener process - which actually has applications in QFT eg Hida distributions.

Tanks
Bill

Of course there are formal proofs in probability what I am saying is that no pure mathematical equation can generate a truly random number. All true random number generators utilize a random physical system.

 

[JPBenowitz]

to be precise and concise:

chaos is highly sensitive to initial conditions, randomess is independent of initial conditions.

I am making a speculation that there exists an error in computing the initial conditions of a chaotic system that exceeds a fundamental physical computational limit thereby rendering it impossible to compute the initial conditions of the system. This "true randomness" is not independent of initial conditions but at the time of the initial conditions to the time it reaches this limit we can say no information has survived.

 

[Maui]

But aside from such theoretical considerations physics is an experimental science and QM and QFT are fully in accord with experiment.

Thanks
Bill

I agree about the BI but my point about causality, which seems to have been lost, was that you get 'causaility' after solving the equations of motion, i.e. there are no pre-existing classical Lagrangians. In this view, both causality and classicality are emergent(and also the apparent randomness), the trade-off is that there appears to be just one possible worldview(if one must have such) - reality probably has to be a projection?

 

[bhobba]

I think this is the way physicists, mathematicians and actuaries define random. In the case of insurance, they use statistics on sickness and accidents

Formally they define it usually by Kolmogorov's axioms. Intuitively it is usually thought of as the limiting proportions of a long sequence of trials.

Thanks
Bill

 

[bhobba]

I agree about the BI but my point about causality, which seems to have been lost, was that you get 'causaility' after solving the equations of motion, i.e. there are no pre-existing classical Lagrangians. In this view, both causality and classicality are emergent(and also the apparent randomness), the trade-off is that there appears to be just one possible worldview(if one must have such) - reality probably has to be a projection?

You get causality in the following way. The fundamental principle is an infinitesimal change in time leads to an infinitesimal change in state. From this, probability invariance and Wigners theorem the transformation must be unitary. Stones theorem implies it has a generator that by definition is called energy. Thus knowledge of energy uniquely determines the time evolution of a quantum system. Galilean invariance of probabilities implies the form of the energy operator has exactly the same form as the Hamiltonian in classical mechanics which in fact is Schrodinger's equation - for a proof of this see Chapter 3 of Ballentine.

Thanks
Bill

 

[JPBenowitz]

You get causality in the following way. The fundamental principle is an infinitesimal change in time leads to an infinitesimal change in state. From this, probability invariance and Wigners theorem the transformation must be unitary. Stones theorem implies it has a generator that by definition is called energy. Thus knowledge of energy uniquely determines the time evolution of a quantum system. Galilean invariance of probabilities implies the form of the energy operator has exactly the same form as the Hamiltonian in classical mechanics which in fact is Schrodinger's equation - for a proof of this see Chapter 3 of Ballentine.

Thanks
Bill

Which is why the time-energy uncertainty principle is correctly interpreted as the energy required to drive the evolution of a quantum system to an orthogonal and hence distinguishable state.