QM and Stability

[foodchain]

This is a thread from another thread in which a member thought I should make a thread out of the question I posed in the other thread.

 

So here is the question.

 

From what I understand of QM there seems to be a lot of chaos in general. So what I would like to know is basically how does something orderly, such as chemistry derive from what appears to be such an random system. In that I don’t know of bonded elements arbitrarily dissociate for unknown reasons, and bonding in general seems to be rather regular. Now I know that QM is a rather small domain overall(subatomic), but I think it would apply very easily to chemistry.

[swansont]

What do you mean by "chaos?"

[insane_alien]

well, in many random systems we can see patterns emerge given a large enough sample size.

 

take rolling dice as an example. if we use a large number of dice (say 100) over a large number of throws (say 10000) and record the total value we well end up with a good normal distribution.

 

the patterns in QM are just a bt more complicated and the number of factors greater.

[foodchain]

well, in many random systems we can see patterns emerge given a large enough sample size.

 

take rolling dice as an example. if we use a large number of dice (say 100) over a large number of throws (say 10000) and record the total value we well end up with a good normal distribution.

 

the patterns in QM are just a bt more complicated and the number of factors greater.

 

Yes, but recently a women won the lottery in the news in which she bought the ticket on her dead boyfriends grandmas credit card or something and then lost the money because it was theft of the credit card. Now statistically I don’t even know how you would go about associating those odds, or even what the odds are against something like that occurring or if simply that states statistics only go so far and quite frankly are far removed from being natural.

 

Away from statistics, which I know that for various reasons statistics are employed in QM, but if the system is random overall, how could any order ever arise or for that matter persist? I guess what I am asking is how does QM validate the existence of say any particular element, and the persistence of said element in time? Is it simply just the strong or weak forces at play with that and the fact electrons and protons like each other that lends to elements being stable?

 

The following is cited from the article on QM from wiki. Now I know wiki does not have to be flawless, but from what I can understand of QM again I just miss the point on how stability is achieved through it.

 

"Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly inventive in his field, he did not accept the more exotic corollaries of quantum mechanics, such as the lack of deterministic causality and the assertion that a single subatomic particle can occupy numerous areas of space at one time. He also noticed some of the more exotic consequences of entanglement and used them to formulate the Einstein-Podolsky-Rosen paradox, in the hope of showing that quantum mechanics has unacceptable implications. The Einstein-Podolsky-Rosen paradox shows that measuring the state of one particle can instantaneously change the state of its entangled partner, although the two particles can be an arbitrary distance apart. However, this effect does not violate causality, since no transfer of information is possible."

 

http://en.wikipedia.org/wiki/Quantum_mechanics

[BenTheMan]

From what I understand of QM there seems to be a lot of chaos in general. So what I would like to know is basically how does something orderly, such as chemistry derive from what appears to be such an random system. In that I don’t know of bonded elements arbitrarily dissociate for unknown reasons, and bonding in general seems to be rather regular. Now I know that QM is a rather small domain overall(subatomic), but I think it would apply very easily to chemistry.

 

I think you're a bit confused.

 

First, I wouldn't say that there is a lot of ``chaos'' in a quantum system. The thing to remember is that quantum mechanics says that you cannot know the outcome of a single experiment, but if you preform many experiments, you know very well what should happen. Think of it like socks in drawers---suppose you have ten blue socks and one white sock in your drawer. Now suppose you draw one sock from the drawer. Will it be white or blue? There's no way to tell before you preform the experiment.

 

Now suppose you repeat the experiment many times. You would (rightly) predict that MOST of the time (91%), you would draw a blue sock.

 

This is the way I understand quantum mechanics in terms of macroscopic phenomena. While INDIVIDUAL molecules will ``arbitrarily dissociate for unknown reasons'', chances are that you'll never notice, because you are made from 10^25 ish individual molecules, and 10^25 - 1 = 10^25 (check on your calculator).

 

So don't worry. You're safe.

[foodchain]

I think you're a bit confused.

 

First, I wouldn't say that there is a lot of ``chaos'' in a quantum system. The thing to remember is that quantum mechanics says that you cannot know the outcome of a single experiment, but if you preform many experiments, you know very well what should happen. Think of it like socks in drawers---suppose you have ten blue socks and one white sock in your drawer. Now suppose you draw one sock from the drawer. Will it be white or blue? There's no way to tell before you preform the experiment.

 

Now suppose you repeat the experiment many times. You would (rightly) predict that MOST of the time (91%), you would draw a blue sock.

 

This is the way I understand quantum mechanics in terms of macroscopic phenomena. While INDIVIDUAL molecules will ``arbitrarily dissociate for unknown reasons'', chances are that you'll never notice, because you are made from 10^25 ish individual molecules, and 10^25 - 1 = 10^25 (check on your calculator).

 

So don't worry. You're safe.

 

Well that’s not much to postulate, of course I don’t know what’s going to happen tomorrow. I can use statistically what I do to make a guess but of course I don’t know for sure, I don’t think that really helps me with my question. Is QM really just that then?

 

As for the idea that molecules will simply just dissociate themselves from a system, is that to say if I have a molecule of CO2 in some "vacuum" for instance that at any time it could just break apart into C and O2, or for that matter C could just break apart, or is there were the strong and weak forces come into play? I would like to ask what implications this has on the early universe but that’s probably way off topic huh?

[BenTheMan]

As for the idea that molecules will simply just dissociate themselves from a system, is that to say if I have a molecule of CO2 in some "vacuum" for instance that at any time it could just break apart into C and O2, or for that matter C could just break apart, or is there were the strong and weak forces come into play

 

I think you're missing the point... Sure, there is a finite chance that one molecule of carbon dioxide will pop apart into carbon and oxygen (ignoring the violation of the second law of thermodynamics, of course). But when was the last time you saw just one molecule of carbon dioxide?

 

The point of having all of the carbon dioxide atoms in, say, your body spontaneously dissociate would be the same as drawing a white sock from the drawer 10^23 times in a row. (Actually, it's even smaller.)

 

The point is, the quantum world is inherintly random, and inherintly governed by the laws of probability, just like your spontatneously dissociating carbon dioxide molecule. But when you are dealing with very large numbers, the effect of one molecule matters very little in the grand scheme of things (like people back home in Texas who voted for Kerry).

[foodchain]

I think you're missing the point... Sure, there is a finite chance that one molecule of carbon dioxide will pop apart into carbon and oxygen (ignoring the violation of the second law of thermodynamics, of course). But when was the last time you saw just one molecule of carbon dioxide?

 

The point of having all of the carbon dioxide atoms in, say, your body spontaneously dissociate would be the same as drawing a white sock from the drawer 10^23 times in a row. (Actually, it's even smaller.)

 

The point is, the quantum world is inherintly random, and inherintly governed by the laws of probability, just like your spontatneously dissociating carbon dioxide molecule. But when you are dealing with very large numbers, the effect of one molecule matters very little in the grand scheme of things (like people back home in Texas who voted for Kerry).

 

Right, so how do the laws of probability dictate what is what? Say I have a million sided dice somewhere in a computer program, basically a random number generator, going from just random numbers, I am not going to get anything back but random numbers, so how does a probably random number generator produce say equations then, in retrospect to how did probability produce atoms?

[swansont]

Yes, but recently a women won the lottery in the news in which she bought the ticket on her dead boyfriends grandmas credit card or something and then lost the money because it was theft of the credit card. Now statistically I don’t even know how you would go about associating those odds, or even what the odds are against something like that occurring or if simply that states statistics only go so far and quite frankly are far removed from being natural.

 

The probability is 1, since the event already occurred. You're applying the "Texas Sharpshooter" fallacy — drawing the bulleseye after you've shot at the target, making the result seem unlikely.

 

 

Away from statistics, which I know that for various reasons statistics are employed in QM, but if the system is random overall, how could any order ever arise or for that matter persist? I guess what I am asking is how does QM validate the existence of say any particular element, and the persistence of said element in time? Is it simply just the strong or weak forces at play with that and the fact electrons and protons like each other that lends to elements being stable?

 

As with "chaos" before, you need to explain what you mean by "random" (and also "stability"). QM is stochastic, and you can use statistics to tell you about events, but not all outcomes are equally probable.

 

The following is cited from the article on QM from wiki. Now I know wiki does not have to be flawless, but from what I can understand of QM again I just miss the point on how stability is achieved through it.

 

"Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly inventive in his field, he did not accept the more exotic corollaries of quantum mechanics, such as the lack of deterministic causality and the assertion that a single subatomic particle can occupy numerous areas of space at one time. He also noticed some of the more exotic consequences of entanglement and used them to formulate the Einstein-Podolsky-Rosen paradox, in the hope of showing that quantum mechanics has unacceptable implications. The Einstein-Podolsky-Rosen paradox shows that measuring the state of one particle can instantaneously change the state of its entangled partner, although the two particles can be an arbitrary distance apart. However, this effect does not violate causality, since no transfer of information is possible."

 

http://en.wikipedia.org/wiki/Quantum_mechanics

 

(the emphasized word is wrong, it should be "determine")

 

An electron is bound to a proton, forming hydrogen; it takes 13.6 eV to separate them. The electron's position is governed by QM, and is thus given by a probability, but the ionization energy is part of that calculation, too. The electron is simply not likely to be found too far from the nucleus.

 

I think the issue here is largely one of vocabulary. You are using words that have certain definitions within physics, but are using different ones.

[BenTheMan]

Right, so how do the laws of probability dictate what is what? Say I have a million sided dice somewhere in a computer program, basically a random number generator, going from just random numbers, I am not going to get anything back but random numbers, so how does a probably random number generator produce say equations then, in retrospect to how did probability produce atoms?

 

But the system isn't just a ``random number''... It's a weighted random number, just like my sock example. Certain outcomes are more likely than others, and over very large numbers, the classical outcomes are the most likely ones.

 

If your ``million sided die'' had 900,000 sides that said `1', then if you threw that die enough times, you would expect to see a 1 come up most of the time.

 

You must have heard that the quantum world is ``random'', which I think you have misinterpretted. We are choosing from a range of options---for example, when you make a random choice at a resturaunt, it is from food that is actually on the menu.

[fredrik]

Right, so how do the laws of probability dictate what is what? Say I have a million sided dice somewhere in a computer program, basically a random number generator, going from just random numbers, I am not going to get anything back but random numbers, so how does a probably random number generator produce say equations then, in retrospect to how did probability produce atoms?

 

Hmmm maybe you are trying to understand the concept of self organisation in the context of a probabilistic model. That is I think a good perspective, and on that part I think we are still looking for good answers.

 

I think one should then view things in a bigger perspective. Given a menu, and we are to make a choice. If we have no reason to prefer any item over the other, we might as well consider that we make a "random choice". But of course, where did the menu come from in the first place? Suppose we don't quite know the menu either, then we have to first guess the menu, before we can make a choice.

 

I think of self organisation as structures as emerging as per a learning rule, successful structures become self-stabilized, because they are more in phase with the environment. This self-organisation I picture taking place at all levels, starting with spacetime formations. Perhaps one could say that a perfectly random chaos might not be stable. And perhaps there is an aswer in terms of probability, that strucutres are simply more likely to appear, then it is for a "perfect chaos" to be conserved.

 

But there is as far as I know, not yet a complete understanding of this. But when the modern physics is better understood I expect alot along these lines, including much better answers to your questions.

 

We can't yet answer everything.

 

/Fredrik

[BenTheMan]

Given a menu, and we are to make a choice. If we have no reason to prefer any item over the other, we might as well consider that we make a "random choice". But of course, where did the menu come from in the first place? Suppose we don't quite know the menu either, then we have to first guess the menu, before we can make a choice.

 

I'm not sure if I agree with some of the things in the post. For example, ``where does the menu come from?'' I am not sure what this means. Physics gives us a very good idea of why things should be as they are. In fact, I can't think of any examples of quantum systems that we don't understand in the sense which I think you think we don't understand them.

 

So perhaps you can clarify what you mean by this.

 

I think of self organisation as structures as emerging as per a learning rule, successful structures become self-stabilized, because they are more in phase with the environment.

 

It seems like you are talking of some sort of coherence---many atoms together in an ``environment'' will behave the same way.

 

I think that it is dangerous to think this way. Particles in a quantum system don't necessarily know that they're in a quantum system. Take photons in a laser beam, for example. The photon doesn't know that it's surrounded by tons of OTHER photons. It just knows that it has a very specific frequency and direction.

 

Another example is blackbody radiation---there, a large number of non-interacting particles behave the same way. How can one say that a photon obeys any sort of ``learning rule'' when it is quite clear that this cannot be the case?

 

The correct interpretation of macroscopic phenomena is simply a numbers game, as I said earlier.

 

This self-organisation I picture taking place at all levels, starting with spacetime formations.

 

Again, it is not clear that this is true at all. At least at the sub-Planck scale, we expect the space-time formations to be completely random, as there are (in principle) no symmetries for the space-time to obey. Quantum Gravity doesn't respect ANY symmetries. So I'm not sure how you can claim this.

 

Perhaps one could say that a perfectly random chaos might not be stable.

 

We are mixing vocabularies here. Either way, could you clarify this?

 

And perhaps there is an aswer in terms of probability, that strucutres are simply more likely to appear, then it is for a "perfect chaos" to be conserved.

 

Fredrik---I'd point you to my previous posts. If everything is based on probability, then the fact that large lumps of atoms behave in a predictable way was EXACTLY the point I tried to make. If you believe in Statistical Mechanics, then this is trivially true.

 

Take an ideal gas, for example. Quantum mechanically, one cannot define, say, the temperature of a single atom. But if one takes a large collection of such atoms, and writes down a partition function (which is defined in terms of the hamiltonian of all of the individual atoms), then macroscopic phenomena emerge. Now one can take derivatives of the partition function to define temperature, pressure, entropy, etc. This is exactly what foodchain is talking about. At the quantum level, we can't know what one atom of a gas is doing from one instant to the next. Statistically, however, we have a very good idea about what is going on.

[fredrik]

Quantum mechanically, one cannot define, say, the temperature of a single atom. But if one takes a large collection of such atoms, and writes down a partition function (which is defined in terms of the hamiltonian of all of the individual atoms), then macroscopic phenomena emerge. Now one can take derivatives of the partition function to define temperature, pressure, entropy, etc. This is exactly what foodchain is talking about. At the quantum level, we can't know what one atom of a gas is doing from one instant to the next. Statistically, however, we have a very good idea about what is going on.

 

What you say make perfect sense here of course. I don't disagree with any of this.

 

But the reason for my comment is that I got the feeling(?) foodchain didn't get a satisfactory answer to this question. So I guess I questioned if this was really what he meant? I sure don't know, I'm just guessing and this was in bold on my menu, I can't see foodchains menu with his eyes But if that's really what he meant, my comments was misdirected in the first place.

 

About the other things, spacetime formations, the question seems to boil down to what spacetime is, how can we induce spacetime structures from a starting point when all blurs? It's alo easier to do it the other way around, to consider how given structures "dissolve"... but the other way around seems to be more tricky? How do structures emerge when we do not have any given expectations to what they will be? Everyone knows it's easier to rip something apart, than to put it back together, and the reason is a probabilistic one (entropy).

 

I don't have the answers to all the questions, and to my knowledge nonone else has either. But I'm sure alot of people have ideas. But if this was not even near what foodchain talke about we could leave this at this point.

 

/Fredrik

 

About uncertainty of the menu, what I meant was that there is always idealisations. Any experiment has a finite duration, and collects finite data, so there is always a uncertainty even in the statistical structures. Like in statistics, you make a long experiment, and get a mean and a standard deviation. But there is always an uncertainty in the mean too. We consider infinite measurement series but that's where we leave reality. In some cases, like particle physics this idealization is clearly decent enough! But if we are talking about logical structures of the theory, it's not acceptable in general. An infinite measurement series would require infinite information capacity and infinite time probable. So at some point, some domains, our "menus" remains inherently uncertain as well, unless we appeal to idealisations. This was what I meant with that. The menus evolve as well. Sometimes new items appear on the menu, that wasn't there before, I want a clean logic to cope with that without breakdown of the formalism. Becuase that happens in reality, and reality doesn't break down. It finds new ways.

 

/Fredrik

[swansont]

What you say make perfect sense here of course. I don't disagree with any of this.

 

But the reason for my comment is that I got the feeling(?) foodchain didn't get a satisfactory answer to this question. So I guess I questioned if this was really what he meant? I sure don't know, I'm just guessing and this was in bold on my menu, I can't see foodchains menu with his eyes But if that's really what he meant, my comments was misdirected in the first place.

 

foodchain hasn't defined what he meant, so the question, thus far, is ill-formed. Chaos, random and stability have certain meanings in physics, and either alternate definitions are being used or the correct ones are being misapplied.

[fredrik]

foodchain hasn't defined what he meant, so the question, thus far, is ill-formed. Chaos, random and stability have certain meanings in physics, and either alternate definitions are being used or the correct ones are being misapplied.

 

Yes I agree with this. The langugage and terminology is always an issue. And I confess that I am pretty sloppy at times too.

 

Sometimes english isn't too bad although informal, sometimes it's ambigous. I guess my estimate of foodchain was based on my subjective understanding of his thinking(beeing bio interested) based on my past reading of his posts and how this is processed in my brain. Which in a nutshell illustrates also my understanding on physical interactions. The menu formed that is sustained/survived for me is the one that harmonises with the interactions I participate in. Sort of analogous to that organisms and lifeforms that grow and survive are those that are in harmony with it's environment. Different environments select different structures. Most yeasts like simples sugars, mold like starches.

 

Foodchain should bring me feedback if I'm wrong, but I was trying to put in a way I think (as per my vision of foodchains relative menu) would be most efficient in a short message.

 

/Fredrik

[foodchain]

Yes I agree with this. The langugage and terminology is always an issue. And I confess that I am pretty sloppy at times too.

 

Sometimes english isn't too bad although informal, sometimes it's ambigous. I guess my estimate of foodchain was based on my subjective understanding of his thinking(beeing bio interested) based on my past reading of his posts and how this is processed in my brain. Which in a nutshell illustrates also my understanding on physical interactions. The menu formed that is sustained/survived for me is the one that harmonises with the interactions I participate in. Sort of analogous to that organisms and lifeforms that grow and survive are those that are in harmony with it's environment. Different environments select different structures. Most yeasts like simples sugars, mold like starches.

 

Foodchain should bring me feedback if I'm wrong, but I was trying to put in a way I think (as per my vision of foodchains relative menu) would be most efficient in a short message.

 

/Fredrik

 

First of all I did not set out to upset anyone’s day or anything, so please don’t go that route I am a certified laymen of physics.

 

What I mean in general by the word selection I guess if I can sum such up is that QM as I understand it is not deterministic. If per say I have a group of different colored spheres, the color of such being the only difference, say 400 of them in a box and I shake the box for an hour, what pattern am I going to get back if the pattern I assign to it is not completely arbitrary, or fault of the observer. So I don’t understand I guess in the terms of cosmic evolution following along from say the big bang on how QM which is a very real part of our universe say lent a hand to the standard model coming into existence or for that matter persisting in time. Odds would have it that if I did my colored spheres enough I might get twenty green ones on the surface, but those are just odds.

 

It just seems to me that from where I sit in regards to understanding QM it basically must then hold the key to understanding a great deal of things. Such as entanglement, is that purely arbitrary and random also, simply if its not can you follow entanglement into the past if not the future? What role did QM play in quarks coming about, or flavors of such for that matter, and why out of a non deterministic system could something so regular as the laws of physics come about, or is it really just a modern probability open to massive change? From what I know of conservation laws they aid me in understanding a great deal of things because I can see how stuff has to work in that deterministic tone, it has no consciousness of course and water will take the easiest path, which I think plays a large role in the various phenomena’s we come to observe from the formation or pattern of galaxies to why I get circles in water if I drop a drip in it, I just get confused when trying to lump something like that up with QM when what I know of such is that QM is non deterministic, the only thing I keep getting back in a loop then is entanglement must play or reflect some larger role, but being a laymen I come here to ask of course people actually “certified” in such endeavors of course.

[BenTheMan]

Odds would have it that if I did my colored spheres enough I might get twenty green ones on the surface, but those are just odds.

 

How many green ones do you have?

 

foodchain---I think you are trying to make big leaps in understanding. First of all, the way quantum mechanics works in the very early universe is just not known. This would require knowledge of how gravity behaves at a quantum level, and this is something that nobody knows. Why we have quarks is another question that no one understands.

 

Second of all---don't try to make such huge leaps. Quantum systems are not deterministic, this is true, however, statistical treatments of such systems are still possible. I gave you several examples of such systems---an ideal gas, for example.

 

Either I am completely misunderstanding the question, or you aren't reading my posts.

[foodchain]

How many green ones do you have?

 

foodchain---I think you are trying to make big leaps in understanding. First of all, the way quantum mechanics works in the very early universe is just not known. This would require knowledge of how gravity behaves at a quantum level, and this is something that nobody knows. Why we have quarks is another question that no one understands.

 

Second of all---don't try to make such huge leaps. Quantum systems are not deterministic, this is true, however, statistical treatments of such systems are still possible. I gave you several examples of such systems---an ideal gas, for example.

 

Either I am completely misunderstanding the question, or you aren't reading my posts.

 

Well, you just answered my questions.

[fredrik]

Foodchain I don't think you upset anyones day Even Einstein used to be a layman.

 

Like Ben has explained, as compared to newtons mechanics QM isn't deterministic in the sense that particle positions can't be predicted to have exact trajectories, and the reason is that while in newtons mechanics the vision is that it's in prininciple no problem to specify complete information in the initial conditions. In quantum mechanics the information concept is taken more serious. And momentum and position are logically related in quantum mechanics. This relation alone, implies logical restrictions on the mutual simultaneous specification of information.

 

But at the statistical or probabilistic level, one can still say that QM is deterministic in the sense that while the evolution of particle positions is not, the probability is.

 

So the evolution of probability distributions is deterministic. At least in the standard QM. This is how we maintain some order still.

 

On this side of things I see things that aren't satisfactory yet. But that belongs to the parts that noone yet fully understands, as it touches gravity and unification issues. I personally find this inconsistent. If you take the information and measurement ideals serious, then I do not like the deterministic treatment of probabilities. I think consistency of reasoning implies not only second quantization but possibly n'th quantization, but we need some rules to control this expansion or we will inflate the model beyond handling, in which case it's useless. At this level, issues that you mention, stability of structures and formalisms will be considered. But alot of this is speculation and matter of opinion of what path to choose. I thought this touched on your questions...

 

If you know how many socks of each you have, you obviously know the probability for drawing a particular colour. But the question of mine, is that if you know that you obviously already performed an infinite measurement series in the past, because how else did we obtain that information in the first place? However none of these objection invalidates current effective models, on the contrary it might suggest the expansion to the domains where we currently don't konw as much.

 

Next we come to the dynamics! Usually it's heuristically derived from the classical equations of motion with some operator substitutions and so one. And that apparently works. Fine. But the question is wether there is a deeper understanding on this? I think so. But that also belongs to the cloudy parts.

 

For example, in QM one usually considers the hamiltonian to be given, outside the initial information and the wavefunction. But in effect I think the ahamiltonian is also information. It's information regards the expected, evolution of the information. This kind of reasoning will lead to relativistic thinking all by itself. This is also something I never liked. In general relativity we have a proper relation between the system and the dynamics, but then it's not a quantum model. So one problem is how to unify them. I think a proper analysis of QM foundations will lead us right to relativity from a much more fundamental information perspective. But this is also speculation and a matter of choice of route to explore.

 

So if your questions touches any of that which noone yet can answer, I think noone should discourage you in asking good questions.

 

/Fredrik