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Does Randomness Really Exist?

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I can predict that you will lose the lottery 999/1000 (if the odds of winning are /1000) despite the outcome being random.

 

I can predict that if I flip a coin 500 times it will be heads about 250 times, despite the outcome on each throw being random.

 

And these predictions will be pretty much true all the time.

 

When we talk about predicting the outcome of probabilistic systems, we consider an ensemble of systems (a whole set of identical systems). Predicting the outcome of a single experiment that relies heavily on probability is hard - even if we know the probability distribution. For instance, I know the outcome of heads and tails is 50/50. But I can't really predict heads will turn up on the next throw. However I can quite easily predict what will happen over a whole ensemble of throws (ie a million throws). I can say for the next 1million throws Heads will occur approximately 500 thousand times.

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I can predict that you will lose the lottery 999/1000 (if the odds of winning are /1000) despite the outcome being random.

 

I can predict that if I flip a coin 500 times it will be heads about 250 times, despite the outcome on each throw being random.

 

And these predictions will be pretty much true all the time.

 

When we talk about predicting the outcome of probabilistic systems, we consider an ensemble of systems (a whole set of identical systems). Predicting the outcome of a single experiment that relies heavily on probability is hard - even if we know the probability distribution. For instance, I know the outcome of heads and tails is 50/50. But I can't really predict heads will turn up on the next throw. However I can quite easily predict what will happen over a whole ensemble of throws (ie a million throws). I can say for the next 1million throws Heads will occur approximately 500 thousand times.

 

Yeah the likelihood of heads or tails is equal in that case.

 

However, I'm thinking more about the physics of the coin throw itself, not a whole ensemble of throws.

 

For instance, before each individual throw, if you had a perfect knowledge of physics, and if you knew the relationship between the positioning of your fingers and the positioning of the coin, the exact force used for the toss, the weight of the coin, the amount of friction the coin encounters as it flips in the air, and all such related factors and combine them in exactly the right way in order to make a prediction, then you'll be able to predict correctly from one throw to the next.

 

Of course, you'd have to be an omniscient mathematician and have all these information in your fingertips in order to make such a prediction, which is impossible. But the point of this idea is that it shows that predictability is a measure of how much information is available to you at any moment in time and how well you are able to utilize that information. If you had a great deal of information about a process, and about the surrounding environment, then what seemed "random" to you (when you had less information) would become pseudo-random. The fact that we lack all this information is what produces randomness.

 

So more simply, randomness is not a property of the universe, it is a property of our knowledge of the universe. As for the probability distributions, these are just mathematical constructs that express our degree of certainty about the outcome of a process, based on the information that are available to us, at any given time. So you can't say that probability distributions are a property of nature itself. These are subjective measurements, i.e. based on our own incomplete understanding.

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Ok i meant a truly random coin flip that doesn't rely on initial conditions/ hidden variables. All i wanted to demonstrate was that you can have true randomness and predictability. And QM has proven to be random, so honestly if you insist things can't really be random you are saying QM is wrong. Thing is nothing works better than QM when predicting stuff.

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On 4/21/2017 at 0:50 AM, Spider said:

Yeah the likelihood of heads or tails is equal in that case.

 

However, I'm thinking more about the physics of the coin throw itself, not a whole ensemble of throws.

 

For instance, before each individual throw, if you had a perfect knowledge of physics, and if you knew the relationship between the positioning of your fingers and the positioning of the coin, the exact force used for the toss, the weight of the coin, the amount of friction the coin encounters as it flips in the air, and all such related factors and combine them in exactly the right way in order to make a prediction, then you'll be able to predict correctly from one throw to the next.

 

Of course, you'd have to be an omniscient mathematician and have all these information in your fingertips in order to make such a prediction, which is impossible. But the point of this idea is that it shows that predictability is a measure of how much information is available to you at any moment in time and how well you are able to utilize that information. If you had a great deal of information about a process, and about the surrounding environment, then what seemed "random" to you (when you had less information) would become pseudo-random. The fact that we lack all this information is what produces randomness.

 

So more simply, randomness is not a property of the universe, it is a property of our knowledge of the universe. As for the probability distributions, these are just mathematical constructs that express our degree of certainty about the outcome of a process, based on the information that are available to us, at any given time. So you can't say that probability distributions are a property of nature itself. These are subjective measurements, i.e. based on our own incomplete understanding.

 

I get your point but read my post again. I'm just saying even if things are truly random and not pseudo random you can still predict phenomena.

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On 4/21/2017 at 4:52 AM, superman said:

I get your point but read my post again. I'm just saying even if things are truly random and not pseudo random you can still predict phenomena.

 

I got that. I know that by "random" you meant truly random. I was just telling you that "randomness" is self-referential because it is a product of our lack of knowledge, not a property of the universe itself.
 
Also, I'm not sure exactly why anyone would rule out the existence of hidden variables in QM. If there are no hidden variables, then you are logically implying that QM is the most fundamental and ultimate layer of reality. In other words, there is nothing deeper beyond quantum mechanics. But the question is, how do you know that? Isn't that just a belief?
 
 
Now let's say that the letters below are analogous to quantum events:
 
 

auhishni/ashdf/uivmhduifvghntyrgnfwauice/yrguyen/sagcynghw/uaet/gynmuaey/csgnrueamwhycute/wrktmvgnuC/Ngheruy/tgnm/cheuyngmc/uyesmr/cghuy/ancng/haktmhgu/ewryhtvnu/cnerah/fcnteawhgntmcu/ymawnchgctyv/unmvh/guraeycnhm/guiya/nmtghyuichmyai/ulvmnthluiy/enftuimtr/vayut/vwauie/nmctrgnuaewiyhncyjtrehgw/nvytungakmhquia/wnghw/iueacvhrttc/yuagbsdyvgtfy/euachzmrfuyawegncy/rtumahsiuyegtvnw/aiyehmciuytaltvhg/yiu/aezscnuitmah/zgiygvn/tryiuazngctuiyazmghwiv/umhizl/amahcqy/osiaemvrowetvm/lupaHMuhmawie/ygryuimhroihhi/aghipqpawa/epiumapiuqipug/aipwuzguiuwa/eghnyicmwaiy/tgvpuiawhntv/iyawmhytv/uygewi/runhweauywqiwryegtn/uaeiwtvnomiawet/iovneuyiuhguv/maqm/vroiqhnawyemvuw/iaethqoiyn/tmurvboewa/pmubtiomv/pimqxoiuqwgeny/ruwaqoojnoy

 
 
How sure can you be that the string of letters doesn't have a hidden pattern behind it?
 
You might try to devise various randomness tests to determine whether it is truly random or not. However, if all your tests repeatedly indicate randomness (i.e. no pattern), then you can't distinguish the possibility that your own tests were lacking information and the possibility that the letters are truly random. The two possibilities are equally likely.
 
So if you think that it's truly random, then that's a belief, not a proven fact. Maybe it simply reflects your own lack of knowledge. So there is no way to conclusively prove that the letters above were generated randomly, even though they appear random.

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On 4/21/2017 at 5:31 PM, Spider said:

I got that. I know that by "random" you meant truly random. I was just telling you that "randomness" is self-referential because it is a product of our lack of knowledge, not a property of the universe itself.

 
Also, I'm not sure exactly why anyone would rule out the existence of hidden variables in QM. If there are no hidden variables, then you are logically implying that QM is the most fundamental and ultimate layer of reality. In other words, there is nothing deeper beyond quantum mechanics. But the question is, how do you know that? Isn't that just a belief?
 
 
Now let's say that the letters below are analogous to quantum events:
 
 

auhishni/ashdf/uivmhduifvghntyrgnfwauice/yrguyen/sagcynghw/uaet/gynmuaey/csgnrueamwhycute/wrktmvgnuC/Ngheruy/tgnm/cheuyngmc/uyesmr/cghuy/ancng/haktmhgu/ewryhtvnu/cnerah/fcnteawhgntmcu/ymawnchgctyv/unmvh/guraeycnhm/guiya/nmtghyuichmyai/ulvmnthluiy/enftuimtr/vayut/vwauie/nmctrgnuaewiyhncyjtrehgw/nvytungakmhquia/wnghw/iueacvhrttc/yuagbsdyvgtfy/euachzmrfuyawegncy/rtumahsiuyegtvnw/aiyehmciuytaltvhg/yiu/aezscnuitmah/zgiygvn/tryiuazngctuiyazmghwiv/umhizl/amahcqy/osiaemvrowetvm/lupaHMuhmawie/ygryuimhroihhi/aghipqpawa/epiumapiuqipug/aipwuzguiuwa/eghnyicmwaiy/tgvpuiawhntv/iyawmhytv/uygewi/runhweauywqiwryegtn/uaeiwtvnomiawet/iovneuyiuhguv/maqm/vroiqhnawyemvuw/iaethqoiyn/tmurvboewa/pmubtiomv/pimqxoiuqwgeny/ruwaqoojnoy

 
 
How sure can you be that the string of letters doesn't have a hidden pattern behind it?
 
You might try to devise various randomness tests to determine whether it is truly random or not. However, if all your tests repeatedly indicate randomness (i.e. no pattern), then you can't distinguish the possibility that your own tests were lacking information and the possibility that the letters are truly random. The two possibilities are equally likely.
 
So if you think that it's truly random, then that's a belief, not a proven fact. Maybe it simply reflects your own lack of knowledge. So there is no way to conclusively prove that the letters above were generated randomly, even though they appear random.

 

I have told you so many times that there is really good evidence that there are no classical hidden variables in quantum mechanics. (you know, the French dude I was on about?) In fact, I don't think anyone really believes in Einstein's theory on QM anymore (maybe a few guys here and there). So no, it is not just a belief. There are experiments that have been done on this. Again, https://en.wikipedia.org/wiki/Bell%27s_theorem

 

If you want I can link you the paper, I'm sure you won't understand the maths but the discussion section may be of interest to you.

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On 4/21/2017 at 5:31 PM, Spider said:

I got that. I know that by "random" you meant truly random. I was just telling you that "randomness" is self-referential because it is a product of our lack of knowledge, not a property of the universe itself.

 
Also, I'm sure exactly why anyone would rule out the existence of hidden variables in QM. If there are no hidden variables, then you are logically implying that QM is the most fundamental and ultimate layer of reality. In other words, there is nothing deeper beyond quantum mechanics. But the question is, how do you know that? Isn't that just a belief?
 
 
Now let's say that the letters below are analogous to quantum events:
 
 

auhishni/ashdf/uivmhduifvghntyrgnfwauice/yrguyen/sagcynghw/uaet/gynmuaey/csgnrueamwhycute/wrktmvgnuC/Ngheruy/tgnm/cheuyngmc/uyesmr/cghuy/ancng/haktmhgu/ewryhtvnu/cnerah/fcnteawhgntmcu/ymawnchgctyv/unmvh/guraeycnhm/guiya/nmtghyuichmyai/ulvmnthluiy/enftuimtr/vayut/vwauie/nmctrgnuaewiyhncyjtrehgw/nvytungakmhquia/wnghw/iueacvhrttc/yuagbsdyvgtfy/euachzmrfuyawegncy/rtumahsiuyegtvnw/aiyehmciuytaltvhg/yiu/aezscnuitmah/zgiygvn/tryiuazngctuiyazmghwiv/umhizl/amahcqy/osiaemvrowetvm/lupaHMuhmawie/ygryuimhroihhi/aghipqpawa/epiumapiuqipug/aipwuzguiuwa/eghnyicmwaiy/tgvpuiawhntv/iyawmhytv/uygewi/runhweauywqiwryegtn/uaeiwtvnomiawet/iovneuyiuhguv/maqm/vroiqhnawyemvuw/iaethqoiyn/tmurvboewa/pmubtiomv/pimqxoiuqwgeny/ruwaqoojnoy

 
 
How sure can you be that the string of letters doesn't have a hidden pattern behind it?
 
You might try to devise various randomness tests to determine whether it is truly random or not. However, if all your tests repeatedly indicate randomness (i.e. no pattern), then you can't distinguish the possibility that your own tests were lacking information and the possibility that the letters are truly random. The two possibilities are equally likely.
 
So if you think that it's truly random, then that's a belief, not a proven fact. Maybe it simply reflects your own lack of knowledge. So there is no way to conclusively prove that the letters above were generated randomly, even though they appear random.

 

 

Again, being random does not indicate there is no pattern. That is just one distribution (everything is equally as likely). If there is a distribution of probabilities then we will see patterns in the data.

 

Anyway, certain inequalities (known as Bell inequalities) were found to be violated that are impossible to violate*

 

this is mathematically proven

* if we consider a pseudo random system - ie randomness occurs due to a lack of information.

 

Now you can say two things really:

 

The experimental set up is dodgy - Possible, but time and time again these inequalities have been violated to death. There are still a few loopholes that people mention but it really looks like QM is actually random. It isn't a belief anymore, pretty much every experiment violates these inequalities. The evidence favours true randomness in QM. You can still believe that if the loopholes were patched up then we would find out that QM is classically random - but the evidence isn't on your side.

 

QM is wrong - It is possible that the framework of QM is itself is wrong, in which case we need a better theory to explain reality. But tell that to your smartphone.

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Wait till spider finds about many world interpretation of QM, where QM is deterministic after all (only, not in this universe)

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On 4/21/2017 at 6:47 PM, Haku said:

Wait till spider finds about many world interpretation of QM, where QM is deterministic after all (only, not in this universe)

 

My professor says there's no point to such theories because they're un testable so you never know if it's true or not

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On 4/22/2017 at 9:52 AM, superman said:

My professor says there's no point to such theories because they're un testable so you never know if it's true or not

 

Traditionally, discouraged thinking about the philosophical implications of QM, but that was a historical mistake.

 

There are some proposed methods to test many-world-interpretation with use of a quantum computer. Not possible for now, but who knows.

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On 4/22/2017 at 9:54 AM, superman said:

I have a feeling spider favours determinism because he read that our futures are already written

 

Is freewill tied to determinism or causality?

 

Dunn Dunnn DHUUUNNNNNNN

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On 4/21/2017 at 6:17 PM, superman said:

I have told you so many times that there is really good evidence that there are no classical hidden variables in quantum mechanics. (you know, the French dude I was on about?) In fact, I don't think anyone really believes in Einstein's theory on QM anymore (maybe a few guys here and there). So no, it is not just a belief. There are experiments that have been done on this. Again, https://en.wikipedia.org/wiki/Bell%27s_theorem

 

If you want I can link you the paper, I'm sure you won't understand the maths but the discussion section may be of interest to you.

 

The idea that that there are no hidden variables in quantum mechanics is supported by the Copenhagen interpretation of QM. That's considered as the standard interpretation but there are other interpretations as well (and not just a few but multiple). I think you know that already. One alternate interpretation is called the de Broglie-Bohm theory or the pilot-wave theory (or Bohmian mechanics). Unlike the Copenhagen interpretation, this is a deterministic interpretation and it says that there are hidden variables in quantum mechanics.
 
The pilot-wave theory is one of the interpretations that have been left by the wayside as science marched on. It hasn't caught on like the Copenhagen view and the Many Worlds view of QM. Recently, however, some new experiments have fueled some interest in the pilot-wave theory and so it is possibly poised to make a comeback:
 
 
 
 
Who is the French dude, btw? Are you thinking of John Stewart Bell? If so, then he is Irish, not French.

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I have told you so many times that there is really good evidence ​that there are no classical hidden variables in quantum mechanics. (you know, the French dude I was on about?) In fact, I don't think anyone really believes in Einstein's theory on QM anymore (maybe a few guys here and there). So no, it is not just a belief. There are experiments that have been done on this. Again, https://en.wikipedia.org/wiki/Bell%27s_theorem

 

If you want I can link you the paper, I'm sure you won't understand the maths but the discussion section may be of interest to you.

 

I'm not sure if Einstein even had a theory on QM.

 

What I know is that Einstein was unsatisfied with almost every interpretation of quantum mechanics. He had no issues with the statistical interpretation of quantum mechanics, but he maintained that the quantum probabilities are epistemic and not ontological in nature. In other words, the quantum probabilities exist only as mental constructs (epistemic), not as a property of reality (ontic). Einstein didn't agree with the pilot-wave theory either, even though it claimed to explain quantum mechanics in deterministic terms.

 

"It seems that Einstein, who was unsatisfied with the Copenhagen approach, did not like the pilot wave approach either because both interpretations have this notion of action at a distance: particles that are far away from each other can profoundly and instantaneously affect each other. As the father of the theory of relativity, he believed that action at a distance cannot travel faster than the speed of light." (Source)

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I have told you so many times that there is really good evidence ​that there are no classical hidden variables in quantum mechanics. (you know, the French dude I was on about?) In fact, I don't think anyone really believes in Einstein's theory on QM anymore (maybe a few guys here and there). So no, it is not just a belief. There are experiments that have been done on this. Again, https://en.wikipedia.org/wiki/Bell%27s_theorem

 

If you want I can link you the paper, I'm sure you won't understand the maths but the discussion section may be of interest to you.

 

I've looked at the those experiments and what they imply about randomness and hidden variables.

 

Well, here is a quote, from one of the links above (Quanta Magazine), which states that the idea that Bell's theorem rules out hidden variables in QM is a misinterpretation:

 

"Later, the Northern Irish physicist John Stewart Bell went on to prove a seminal theorem that many physicists today misinterpret as rendering hidden variables impossible. But Bell supported pilot-wave theory. He was the one who pointed out the flaws in von Neumann’s original proof. And in 1986 he wrote that pilot-wave theory “seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored."

 

I have more things to say about the Bell's inequality experiments. I had fun deconstructing them. And unsurprisingly I still do not see how they prove that true randomness exists. On the contrary, they seem to suggest that proving randomness is an impossible task, as I've been saying all along. But it's going to be a longer post, so I'll write that stuff later.

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