Simple QM question

[Kriminal99]

Originally Posted by Erasmus00

I do. Statistics is a study of data. In order to make any useful predictions with statistics we have to make certain assumptions about the data we have in our posession. The nature of those assumptions can fundamentally alter our conclusions.

What you don't understand is that Bell's argument is not statistical. Experimenters deal with statistics and statistical arguments, but theorists usually do not. You are failing to distinguish between probability theory and statistics.

Please answer the following questions: why do you believe Bell's argument has anything do with statistics? If it does not, why do you believe that discussing statistics is relevant?
-Will

All inductive reasoning is based on assumptions. Probability theory is no exception. Experimenters that are not familiar with probability theory are pretty bad at their job IMO, and I don't know where someone would go to get training as a experimental design specialist that wouldn't include probability theory. They are not seperated anywhere that I have seen, but I suppose it could be forgotten by someone who just went through the motions of designing experiments every day and careful analysis would cause them nothing but trouble with their clients.

In any case...

At least some assumptions have already been identified already with regard to bell's inequality even before it is turned into an experiment. And the inequality alone is useless, it has to be used in an experiment before it has meaning. Then of course each experiment has assumptions that go with it. My concerns translate into 2 things with respect to this.

A) There doesn't seem to be a general understanding of the limitations of induction. IE Assumptions required for various experiments on the subject have been identified after the fact. Some of them have been decided to invalidate previous experiments. To state my problem with this most objectively, we do not have such a good understanding of induction in general that we can look at any experiment or reasoning and immediately see all assumptions we are making or all possible situations that could invalidate or reasoning or experiments.

B) My second problem with QM also relates to understanding of the limitations of inductive reasoning. It has to do with the probability that assumptions are violated. I believe that these probabilities are almost always underestimated. To explain what I mean I will use the much more simple example of Descarte's evil deciever, or any global skepticism example.

In this scenario some person or object has created the illusion of the entire world for us. Everything we percieve is part of this illusion. The question is what is the probability that this scenario is false? Obviously noone worries too much about this scenario. But why? Despite what many people think, it is not because the probability of the scenario is small. The probability is .5. If it is true, there is no way you could have any evidence of it, everything would be exactly the same. Most importantly all your reasoning would be based on the illusion not on the real world.

To demonstrate lets say you claim it is unlikely because it would take a consious entity to so decieve another consious entity, as such deception would not be a product of a random system. And you think the idea of an "evil deciever" is silly. But even such a creation as simple as a maze for a mouse should allow you to recognize that we sometimes do this type of thing and imagine the moust wondering if the maze is not being orchestrated by some intelligent being for some devious purpose. You might then wonder how some one could create an illusion as complex as the whole universe as we see it, but then you must come to the most important realization that everything you think you know would be depedent on the illusionary world in this case and so the probability that global skepticism is false is .5

The defense against global skepticism is to say that we cannot do anything about it unless we had reason to believe it was true (because such reason would consist of information we could act on) not that global skepticism is unlikely.

The idea here is that the probability that alot of the different assumptions in QM are violated is also .5. We are dealing with a new situation, and all of our intuitions and reasoning is based on the macro world.

This objection is best understood when someone creates a possible model of a situation where some assumption is violated. Often times people create such models and scientists look at them and realize they are distinct possibilities and are no longer as sure as they were before that violation of the related assumption is unlikely. This further demonstrates lack of understanding of the limitations of induction. For everyone of these that someone thinks up, who knows how many have yet to been recognized! The probability assumptions are violated is .5

[Erasmus00]

Originally Posted by Kriminal99

Probability theory is no exception.

Probability theory (unlike statistics) is usually deductive, not inductive. There are, of course, exceptions (certain interpretations of Bayesian probability). But, on the whole, probability is an axiomatic and deductive theory. This is the difference I was alluding to earlier. Experimenters do statistics, usually theorists do not.

In this thread, as far as I was aware, we weren't discussing the Aspect experiments, but Bell's inequalities. If you want to discuss where you feel statistical assumptions were violated by any specific experiment then by all means, bring up the experiment and why you feel it was violated.

To state my problem with this most objectively, we do not have such a good understanding of induction in general that we can look at any experiment or reasoning and immediately see all assumptions we are making or all possible situations that could invalidate or reasoning or experiments.

First, good physics "reasoning" proceeds from certain hypotheticals and goes deductively. If an experiment agrees with certain conclusions, those hypotheticals are considered more likely to be true.

Keep in mind, complicated experiments do not need to be done to assess many areas of quantum mechanics. The very fact that atoms are stable is testament to the failures of classical physics.

The probability is .5. If it is true, there is no way you could have any evidence of it, everything would be exactly the same. Most importantly all your reasoning would be based on the illusion not on the real world.

First, the evil deciever isn't a solid example. Even the "illusion" world can be modeled, and so science is doable. Second, even if you truly and firmly believe you are being misled at every step by an intricatly crafted illusion, you have no choice to but to "play by the rules." You can't do anything to "dispel" the illusion.

Next, why would you claim the probability is 1/2? As far as I can tell, you can't set any limit on the probability at all. You can't do multiple trials, you have no data that isn't sensory,etc. Hence, there is simply no way to determine the likelihood of either event.

The idea here is that the probability that alot of the different assumptions in QM are violated is also .5. We are dealing with a new situation, and all of our intuitions and reasoning is based on the macro world.

First, what assumptions in quantum mechanics do you believe are violated? You make these sweeping, general arguments, and never get into details. The arguments you have made thus far can just as well be applied to any scientific theory.

Remember that the experimental facts seem to, thus far, weigh in heavily on the side of quantum mechanics. Given the tremendous amount of experimental evidence, not all the experiments can be flawed by bad statistics.

Second, setting the probability that assumptions are violated is the same misuse of probability you used to assert the probability of global skepticism is 1/2. Just because you can only think of two cases (assumptions violated, or they are not) does not mean those cases are equally likely.
-Will

[Qfwfq]

I have always been perfectly aware of the idea that, if I were a virtual creature in a simulated "reality" I would have no way of knowing it, as long as the simulation was coherent. I don't understand, though, why the probability should be stated as 1/2. On what basis Krim?

I'm also thinking that this discussion should have been started in Philosophy of Science, and perhaps with a slightly different title.

[Kriminal99]

Originally Posted by Qfwfq

I have always been perfectly aware of the idea that, if I were a virtual creature in a simulated "reality" I would have no way of knowing it, as long as the simulation was coherent. I don't understand, though, why the probability should be stated as 1/2. On what basis Krim?

I'm also thinking that this discussion should have been started in Philosophy of Science, and perhaps with a slightly different title.

Maybe- It really depends what kinds of people were on the science forum imo. It seems to me this is more of a "science fan" forum.

.5 Just represents the probability of something when you have no clue what the answer is or evidence one way or the other. Many people claim that scenario unlikely or say that the probability of assumptions being violated is unlikely. For the global skepticism example where it is impossible, by design of the example, to have any evidence for or against it then the probability is
.5.

Short of that, it is not so black and white- You might say that any situation that is so different from anything you have previously experienced that you don't know if any of your past experience applies to it has great uncertainty attached to it. But then you might want to start trying to apply basic truths to that new situation that you have seen to be true with great frequency across many different experiences - and then you wish to use those basic truths to infer more things about the new situation. But of course even those things you consider to be basic truths can be violated as well.

So to give some kind of example, say you drive through what appears to be a ghost town. You can only see so much from the road, but from what you see you infer that there are ruined buildings around you probably left from a previous settlement. You see a saloon and attach a high probability to the belief that behind the door you see there is a bar.

With only this much information, the assertion that it is probably a bar makes sense. Even though it could be a set for a movie, most of the time they probably aren't so the probability makes sense. But suppose you saw a movie company insignia on a box in the street? Then you might say that it probably is a movie set and rightly so.

But now let me ask what would you think if you went to another planet that had no contact with humans and saw the same thing? You would probably be trying to figure out how in the heck it got there. But maybe you would reason that since it looks like a human bar, even though you are fairly certain no human from earth could have built it, that it is either a trap to entice humans or something to make humans feel at home. You might reason this because the probability that another sentient race would create the exact same type of establishment that looked so similar is about 0, so it must have some connection to humans. So maybe you wouldn't place .5 probability exactly to any given thing being behind the saloon front.

Now what if you saw something that only somewhat looked like a saloon front on another planet. Hopefully then at least you would attach .5 probability to any given thing being behind it.

So in summary seeing a saloon front on earth makes you think that certain things are probably behind it. But you must realize that your experience that this is the case was all gained on earth, so on a different planet you wouldn't know what to expect although many people without realizing this might walk into it looking for a drink.

Both of these issues apply to quantum physics. The fact that we affect the system by observing it is a big warning sign for the possibility that we cannot really see what is going on. From this you should imagine a potentially infinite number of scenarios where all the information we gain on small particles is heavily biased by the fact that we were able to gain that information.

The saloon front on mars analogy applies equally well. Any reasoning as to what is or what is not taking place in a model regarding small particles should be suspect and be supported by only information we have gotten from other interactions with small particles.

I believe that if both of these problems with inductive reasoning were well understood by everyone involved then there would not be reasoning coming out years after expensive experiments were conducted that invalidates them, because the would be experimenters would realize right off the bat that there was pontential reasoning as to why their experiment might not give any relevant information.

[Kriminal99]

Originally Posted by Erasmus00

Probability theory (unlike statistics) is usually deductive, not inductive. There are, of course, exceptions (certain interpretations of Bayesian probability). But, on the whole, probability is an axiomatic and deductive theory. This is the difference I was alluding to earlier. Experimenters do statistics, usually theorists do not.

In this thread, as far as I was aware, we weren't discussing the Aspect experiments, but Bell's inequalities. If you want to discuss where you feel statistical assumptions were violated by any specific experiment then by all means, bring up the experiment and why you feel it was violated.



First, good physics "reasoning" proceeds from certain hypotheticals and goes deductively. If an experiment agrees with certain conclusions, those hypotheticals are considered more likely to be true.

Keep in mind, complicated experiments do not need to be done to assess many areas of quantum mechanics. The very fact that atoms are stable is testament to the failures of classical physics.



First, the evil deciever isn't a solid example. Even the "illusion" world can be modeled, and so science is doable. Second, even if you truly and firmly believe you are being misled at every step by an intricatly crafted illusion, you have no choice to but to "play by the rules." You can't do anything to "dispel" the illusion.

Next, why would you claim the probability is 1/2? As far as I can tell, you can't set any limit on the probability at all. You can't do multiple trials, you have no data that isn't sensory,etc. Hence, there is simply no way to determine the likelihood of either event.



First, what assumptions in quantum mechanics do you believe are violated? You make these sweeping, general arguments, and never get into details. The arguments you have made thus far can just as well be applied to any scientific theory.

Remember that the experimental facts seem to, thus far, weigh in heavily on the side of quantum mechanics. Given the tremendous amount of experimental evidence, not all the experiments can be flawed by bad statistics.

Second, setting the probability that assumptions are violated is the same misuse of probability you used to assert the probability of global skepticism is 1/2. Just because you can only think of two cases (assumptions violated, or they are not) does not mean those cases are equally likely.
-Will

You are claiming that 1+1=2 is a mathematical proof that putting 1 quart of liquid with another quart of liquid gives you 2 quarts of liquid, even if one quart is bleach and the other ammonia. Probability theory does not exist in a vacuum. And yes it is still based on inductive reasoning anyways. Bell's inequality is violated if the distributions of the random variables changes over the course of the sampling. Even if you condition the inequality on that not being the case (which of course is an assumption) the inequality is still inductively reasoned from our past experiences - although perhaps only using very solid inductive reasoning. Be aware that some people hold deduction itself as having been demonstrated to us inductively.

But the main part is just that deductive reasoning on its own is useless. Deduction uses inductive reasoning to make premises. Bell didn't make the inequalities just to state a universal truth about independent random variables that maintained the same distribution throughout sampling. And if you were talking about deductive reasoning in a vacuum, be aware that I was not.

The probability is .5 because that is the probability of something you have no evidence one way or the other about. Either is just as likely to be the case.

The conclusions made from all the experiments can very well be flawed. You seem to be implying that the experiments do not share any assumptions.

The probability is not .5 because there are two cases. It's .5 when there are 2 cases and none of your reasoning as to which one is more likely applies. You are claiming a saloon front on mars is likely to have a bar behind it.

The point is not that a given assumption regarding quantum mechanics is violated in a certain way. The point is that any of them could be violated in an infinite number of possible scenarios.

This doesn't apply to all experimentation. In classical physics, you have experimentation supported by billions of experiences by billions of people. And by supported I don't mean just that unofficial experiments are conducted every day by people just living their lives. I mean for example that we know that apples don't randomly change mass over time because we interact with apples in our normal lives often enough to see this. If they did change mass, then physics experiments conducted on them which assumed uniform mass during the course of the experiment would be invalidated. Are things like this tested for? No, they are just assumed.

But there is no such experience to support quantum physics experiments. They are done in a vaccuum of knowledge regarding the subject. Dozens of experiments in quantum physics is nothing in the way of evidence.

[Qfwfq]

Originally Posted by Kriminal99

Maybe- It really depends what kinds of people were on the science forum imo. It seems to me this is more of a "science fan" forum.

Except that it isn't you tha's running this outfit!

This discussion is essentially about epistemology, which is philosophy but not Natural Philosophy. In today's terms, it is philosophy of science rather than Physics, or scientific fact. It's also where I stared the Schrödinger's Cat thread, long ago.

Originally Posted by Kriminal99

.5 Just represents the probability of something when you have no clue what the answer is or evidence one way or the other.

Equiprobability is an assumption that makes sense on premises slightly stronger than "when you have no clue what the answer is or evidence one way or the other". If you roll a die you suppose equiprobability, as long as it doesn't cross your mind that it might be weighted, but apart from cheating there's a lot more than just having no clue. IMV the Monty Hall paradox is an excellent illustration of how subtle the matter is. Another consideration: Suppose you're a contestant in a quiz, you can bet on any of two or three suggested answers. If the topic of the question is something you have no expertize on and on which you really can't judge by common sense or plausibility, you might equate that with equiprobability. Is it really equiprobability? Suppose you know nothing about the topic but there is something absurd about one answer, although you can't rule it totally out because there's always a possibility that the quiz poser might have been very crafty in devising the questions to catch non-experts off guard. How would you actually calculate a probability? In such cases, it may make more sense to talk about plausibility than probability.

In the case of casting the die, the six possibilities are essentially alike, apart from the mere labels. For a weighted die, they aren't alike but the difference is quantitative, there is a definite probability for each outcome although you may not know it. Subtle question: Someone has a die, of their own, and offers you to bet on a roll of it. It does cross your mind that it could be weighted. What is the probability of each outcome?

As for the "probability" of the reality that I percieve being a simulation, it can be driven into a purely semantic issue. What does the word 'reality' actually mean? To me, it means what I percieve, ever since I can remember, so the answer becomes "Mu".

Originally Posted by Kriminal99

The fact that we affect the system by observing it is a big warning sign for the possibility that we cannot really see what is going on. From this you should imagine a potentially infinite number of scenarios where all the information we gain on small particles is heavily biased by the fact that we were able to gain that information.

Now that is a mighty long step to take in argument!

All serious investigation is conducted in a manner quite in line with the quantum formalism and isn't invalidated by it. I don't see a bias, there are limitations on what we can measure and how, but what we can according to the formalism certainly isn't biased by it.

Originally Posted by Kriminal99

I believe that if both of these problems with inductive reasoning were well understood by everyone involved then there would not be reasoning coming out years after expensive experiments were conducted that invalidates them, because the would be experimenters would realize right off the bat that there was pontential reasoning as to why their experiment might not give any relevant information.

I can't quite follow you here, sorry.

[Kriminal99]

The thread has turned into an epistomology thread, but that wasn't what it was supposed to be. I actually was just asking why there nesseccarily has to be faster than light communication between entangled particles as opposed to just prior communication.

I have an answer to your die problem but it is somewhat circular. I would say that because you don't know how it might be weighted, the probability of each face coming up is still 1/6. If you consider a 1/6 chance that each face is twice as likely to come up as the others, you would arrive at a

1/6 * 2/7 + 5/6 * 1/7 = 7/42 chance of each face coming up.

It will balance out in a similar manner to equiprobability no matter how you complicate the weighting. Of course this depends on there being equal probability each face is weighted as well, but I think the argument still adresses an issue you were bringing up- namely that after many rolls one face would show up more often. If you know which face that is going to be then you apply the stronger probability to that face. If you don't, then you must realize that the stronger probability could be any face. If you want have the guy roll a dice to determine which face to weight at the beginning.

The last quoted paragraph addresses your response to the previous quoted block of text. It isn't the case that scientists address every possible concern before conducting an experiment and accurately determine whether or not the experiment will be useful. People come after these experiments with realizations that there was a possible problem in the experiment that wasn't initially recognized. This clearly demonstrates that there is no perfect understanding of the limitations of the reasoning used among the scientific community.

[Qfwfq]

Originally Posted by Kriminal99

I would say that because you don't know how it might be weighted, the probability of each face coming up is still 1/6.

Exactly.

And your explanation of why boils down to that the six possibilities are essentially alike, in lack of the information about weighting. Even in the case where you know the die is weighted, and even to a given degree, but you do't know towards which face.

Could you say the same, about all cases in which there are two or more possibilities, but you lack information, or it isn't possible to gain it? Specifically, the quiz which offers a very common-sense answer and an apparently absurd or contorted one.

Originally Posted by Kriminal99

The last quoted paragraph addresses your response to the previous quoted block of text. It isn't the case that scientists address every possible concern before conducting an experiment and accurately determine whether or not the experiment will be useful. People come after these experiments with realizations that there was a possible problem in the experiment that wasn't initially recognized. This clearly demonstrates that there is no perfect understanding of the limitations of the reasoning used among the scientific community.

Uh, yeah, nobody's perfect, but people try and there are some sharp minds investigating local realism. It's all very tricky and requires a good understanding of the quantum formalism and the possible interpretations.

[Erasmus00]

A few points:

1. Kriminal,nearly all of your arguements are so broad as to be applicable, with virtually no change, to any scientific theory. This, despite what you may think, is a bit of a weakness. You have no specific examples of errors you believe have been made. Any argument that can be applied with equal validity to ANYTHING is essentially useless.

2. In one of your only specific arguments, you point out that classical physics is less likely to be wrong because it is supported on a daily basis by everyone's common sense experience. I beleive this argument to be flawed.

I wish to draw your attention to the following: most people are geniunely surprised by the (entirely classical) behavior of rotating systems (things like gyroscopes). Classical mechanics in this sense then, is not routinely validated by people's past experience.

Also, classical physics encompasses classical E/M. Hardly anyone has any real everyday intuition for electricity and magnetism. Hence, the validity of classical physics (and any scientific theory) is based on a very similar experimental base to quantum mechanics.

3. Your assertion of a probability of 1/2 to global skepticism is a misuse of statistics that would make a statistics/probability teacher cringe. With no way to take any data (all data comes through our sense, and we are assessing the possibility that we can't trust our senses) we have no knowledge at all of the system. It's like asking "what's the probability to roll a 6?" without telling you the number of sides on the dice or how it is numbered.

As a quick argument: by your assignment of probabilities there is a 1/2 chance that our world is "real" and a 1/2 chance that our senses are being manipulated. This means, logically, by your reasoning, there is a 0 chance that half of us are controlled and half of us are free, or any other "half-way" scenario.
-Will

[Qfwfq]

Furthr to:

Originally Posted by Erasmus00

2. In one of your only specific arguments, you point out that classical physics is less likely to be wrong because it is supported on a daily basis by everyone's common sense experience. I beleive this argument to be flawed.

Indeed, I would add:

How does classical physics explain ferromagnetic materials? How would it explain semconductor properties, in particular the Esaki diode? How does it explain a laser? How does it explain superconductivity and superfluidity? How would you explain the results of the Young experiment performed photon by photon?

If you think these things don't count because they are too far from everyone's common sense daily experience, then how about chemical valence and the stability of atoms? What would the world be like without Pauli's principle? Even worse, if electrons simply radiated their momentum away and fell into the nucleus?

Ooohps, what would the nucleus even be like, without QCD?