Coulomb, Quantum Mechanics, Chaos and Determinism

[Dancing David]

It was the discussion between JJ and another, I believe Lucy that led me to these thoughts.

The Coulomb effects states that the repulsive forces between similar positive charges rises as the inverse of the square of the distance between them, I hope that is right.
http://education.yahoo.com/referenc...ulomb's+law;_ylt=AoBqCfP2_qkvPovPak9NU9esgMMF

This became a real problem when people were trying to figure out how hydrogen is fused into helium. You can strip the hydrogen of it’s electron or electrons but you can’t force the two nuclei close enough to fuse because of the Coulomb effect. The pressure and temperatures in the sun are not sufficient to overcome the Coulomb effect.

Enter quantum mechanics and the idea that there is a probability that the two nuclei will appear next to each other because of quantum effects, and now there can be fusion. Please enlighten me if I am ignorant.

Simple chaos theory talks about how simple equations can create very complex interactions. For example a pendulum it is set to swinging and the final result is mapped into which direction the pendulum swings in the circular dimension of clockwise or counter clockwise. The pendulum map is made for each potential starting point. These maps are very complex and show great detail. but there are basically two areas on the map, one color shows one direction, and the other color shows another. Now it can be determined which area the pendulum will be plotted to, the areas are complex and interwoven but they are separate.

So now to the question, quantum shells may be very similar to chaotic systems, in that the area a particle is to be found in is a determined area, the particle will not leave the bounded area and there are varying probabilities the particle will appear in different parts of the area.

So is quantum mechanics a deterministic system ? It seems to be in that you can determine where the area is that the particle can be. But it is not deterministic in the sense that you can state where the particle will be within a certain area.

Does the particle have an equal chance of appearing in it’s determined area, that would be random and therefore not deterministic?

Thanks for the enlightenment.

 

[epepke]

It was the discussion between JJ and another, I believe Lucy that led me to these thoughts.

The Coulomb effects states that the repulsive forces between similar positive charges rises as the inverse of the square of the distance between them, I hope that is right.
http://education.yahoo.com/referenc...ulomb's+law;_ylt=AoBqCfP2_qkvPovPak9NU9esgMMF

This became a real problem when people were trying to figure out how hydrogen is fused into helium. You can strip the hydrogen of it’s electron or electrons but you can’t force the two nuclei close enough to fuse because of the Coulomb effect. The pressure and temperatures in the sun are not sufficient to overcome the Coulomb effect.

Enter quantum mechanics and the idea that there is a probability that the two nuclei will appear next to each other because of quantum effects, and now there can be fusion. Please enlighten me if I am ignorant.

Simple chaos theory talks about how simple equations can create very complex interactions. For example a pendulum it is set to swinging and the final result is mapped into which direction the pendulum swings in the circular dimension of clockwise or counter clockwise. The pendulum map is made for each potential starting point. These maps are very complex and show great detail. but there are basically two areas on the map, one color shows one direction, and the other color shows another. Now it can be determined which area the pendulum will be plotted to, the areas are complex and interwoven but they are separate.

So now to the question, quantum shells may be very similar to chaotic systems, in that the area a particle is to be found in is a determined area, the particle will not leave the bounded area and there are varying probabilities the particle will appear in different parts of the area.

So is quantum mechanics a deterministic system ? It seems to be in that you can determine where the area is that the particle can be. But it is not deterministic in the sense that you can state where the particle will be within a certain area.

Does the particle have an equal chance of appearing in it’s determined area, that would be random and therefore not deterministic?

Thanks for the enlightenment.

You're mixing a few concepts here.

First, it's very easy to mislead by talking about QM and chaos in the same breath. Chaos is really a way that small variations can become sort of "amplified," so to speak. (Purists may object to that word, but you do get chaos in amplifiers with positive feedback, I mean literally, as in the case of Jimi Hendrix.)

As far as electrons go, an electron in a molecule or a crystal has a thing called an electron density. The electron density depends on the other things that are around. This is the absolute value of a quantum field distributed in three dimensions, and for any given volume of the electron density, you can calculate the probability of finding an electron within that volume.

The electron orbitals are really values of the electron density for an atom just sitting by itelf in a vacuum. This is what I think you may be trying to get at with the word "area."

However, it's important to note that the electron density is nonzero everywhere. There is no point where the probability of finding an electron is zero. So, there is no well defined volume in which an electron has to be. There's just an extent of volume where you can decide that the probability is so low that you might as well forget about it.

Back in the day when I used to do visualization of quantum chemistry, we often did isosurfaces of 95% electron density. That's an arbitrary number, but it gave a good idea of the overall shape of a molecule.

In summary, no, you can't save determinism this way.

 

[Dancing David]

You're mixing a few concepts here.

First, it's very easy to mislead by talking about QM and chaos in the same breath. Chaos is really a way that small variations can become sort of "amplified," so to speak. (Purists may object to that word, but you do get chaos in amplifiers with positive feedback, I mean literally, as in the case of Jimi Hendrix.)

As far as electrons go, an electron in a molecule or a crystal has a thing called an electron density. The electron density depends on the other things that are around. This is the absolute value of a quantum field distributed in three dimensions, and for any given volume of the electron density, you can calculate the probability of finding an electron within that volume.

The electron orbitals are really values of the electron density for an atom just sitting by itelf in a vacuum. This is what I think you may be trying to get at with the word "area."

However, it's important to note that the electron density is nonzero everywhere. There is no point where the probability of finding an electron is zero. So, there is no well defined volume in which an electron has to be. There's just an extent of volume where you can decide that the probability is so low that you might as well forget about it.

Back in the day when I used to do visualization of quantum chemistry, we often did isosurfaces of 95% electron density. That's an arbitrary number, but it gave a good idea of the overall shape of a molecule.

In summary, no, you can't save determinism this way.

Thank you, BTW, I am not one who would save determinism, I am too much a fan of Steven Gould for that.

I asked about chaos in the mix, because it demonstrates a predictable system with seemingly random distribution. I feel that QM has yet to be proved to be deterministic, so I was curious if the electron position effect were similar to chaotic effect. In other words, which I think you answered, it is determined where an electron might be, but the system may not be strictly deterministic.

 

[epepke]

I asked about chaos in the mix, because it demonstrates a predictable system with seemingly random distribution. I feel that QM has yet to be proved to be deterministic, so I was curious if the electron position effect were similar to chaotic effect. In other words, which I think you answered, it is determined where an electron might be, but the system may not be strictly deterministic.

Where an electron is determined to be is only somewhere in the universe.

 

[Ziggurat]

I feel that QM has yet to be proved to be deterministic,

This is a misunderstanding. Quantum mechanics IS deterministic, and completely so. There's no proof required: all you need to do is look at the actual math.

Sometimes people TREAT it like it's probabilistic (ie, "collapse" of the wavefunction), but what's really going on is you're deciding that you don't want to deal with quantum mechanics anymore (you want to know a particle's position instead of its wave function), and you brush under the rug all the complexity of the quantum state of your measurement instrument because it's simply too hard to work out. But the theory itself is completely deterministic.

It is a SEPARATE question of whether or not REALITY is completely deterministic. Despite the excellent experimental support for quantum mechanics, it is possible that it's just a really good approximation (as Newtonian mechanics is known to be a fairly good, but not exact, approximation in many circumstances).

 

[Schneibster]

Ziggurat, an admirable brief summation.

 

[Paul C. Anagnostopoulos]

How does the randomness of the vacuum fluctuations figure into it?

~~ Paul

 

[hammegk]

This is a misunderstanding. Quantum mechanics IS deterministic, and completely so.

If you feel predicting that a specific entity-described-by-QM exists somewhere in this universe, I'd agree.

It is a SEPARATE question of whether or not REALITY is completely deterministic.

If REALITY is not a local phenomena, who is to say one way or the other?

 

[Ziggurat]

If you feel predicting that a specific entity-described-by-QM exists somewhere in this universe, I'd agree.

I don't know what the hell you're trying to say, but you're not making any sense to me. Quantum mechanics is a theory. Whether or not it is deterministic depends ONLY on what that theory actually is. And the theory of quantum mechanics is deterministic, meaning that if you give it an initial state, there is one and ONLY one way that quantum mechanics predicts the system will evolve. It is a COMPLETELY separate question as to how well the theory corresponds to reality (whether the predictions of that theory are accurate).

If REALITY is not a local phenomena, who is to say one way or the other?

Non-locality doesn't remove determinism.

 

[Ziggurat]

How does the randomness of the vacuum fluctuations figure into it?

~~ Paul

I'm not well versed in QED (quantum electrodynamics), but my impression is that the vacuum, while "fluctuating" in the same way that the ground state of a quantum harmonic oscillator is still "vibrating", isn't actually random. Throw on top of it lots of particles interacting at high energies, as well as the impossibly large number of particles in any detector set, and the problem of particle-antiparticle pair creation (where the idea of a fluctuating vacuum becomes important) starts to look random, but as far as I know, just like in the case of wave function "collapse", the apparent randomness is still the result of not being able to model it all.

 

[hammegk]

Quantum mechanics is a theory. Whether or not it is deterministic depends ONLY on what that theory actually is. And the theory of quantum mechanics is deterministic, meaning that if you give it an initial state, there is one and ONLY one way that quantum mechanics predicts the system will evolve.

Yup.

It is a COMPLETELY separate question as to how well the theory corresponds to reality (whether the predictions of that theory are accurate).

Here's the point of disagreement. QM is by acclaim the most accurate theory ever, yet in one sense it does predict that a specific QM entity is located 'somewhere in this universe'. I don't find that statement as determining anything of value.

Non-locality doesn't remove determinism.

Agreed, nor does it imply it to be true. Do you consider Cramer's TI deterministic? Or the results to date of 'quantum eraser' etc experiments?

 

[Dancing David]

Where an electron is determined to be is only somewhere in the universe.

Thank you. Is it bounded by the speed of light?

 

[Dancing David]

This is a misunderstanding. Quantum mechanics IS deterministic, and completely so. There's no proof required: all you need to do is look at the actual math.

Sometimes people TREAT it like it's probabilistic (ie, "collapse" of the wavefunction), but what's really going on is you're deciding that you don't want to deal with quantum mechanics anymore (you want to know a particle's position instead of its wave function), and you brush under the rug all the complexity of the quantum state of your measurement instrument because it's simply too hard to work out. But the theory itself is completely deterministic.

It is a SEPARATE question of whether or not REALITY is completely deterministic. Despite the excellent experimental support for quantum mechanics, it is possible that it's just a really good approximation (as Newtonian mechanics is known to be a fairly good, but not exact, approximation in many circumstances).

Thanks, I used to understand easy math, I assume that this would be beyond CALC II.

 

[Tez]

This is a misunderstanding. Quantum mechanics IS deterministic, and completely so. There's no proof required: all you need to do is look at the actual math.

Sometimes people TREAT it like it's probabilistic (ie, "collapse" of the wavefunction), but what's really going on is you're deciding that you don't want to deal with quantum mechanics anymore (you want to know a particle's position instead of its wave function), and you brush under the rug all the complexity of the quantum state of your measurement instrument because it's simply too hard to work out. But the theory itself is completely deterministic.

I suppose you have a proof of this assertion?

Orthodox quantum mechanics IS probabilistic. Some people believe by adding something to the theory they can make it deterministic (e.g. decoherence to pointer basis states, existence of many-worlds etc.) These suggestions have problems of their own. Anyone who has taught you otherwise is full of it.

Interestingly there is a way of finding a deterministic theory underlying quantum mechanics I became aware of only recently. And it involves chaos! In simple form the story is this: There are 3 main ways of quantizing a (deterministic) classical theory: Canonical quantization, path integral quantization and stochastic quantization. The latter of these involves adding a fictitous temporal dimension, and evolving the fields under a stochastic equation in this fictive time - this is done by adding "white noise" to a deterministic part of the equation. What someone realized was that you can generate this white noise with a chaotic process (which is also deterministic). If you do it on a small enough scale (say the planck scale) then the fact this chaotic noise deviates slightly from white noise won't be observable in any current experiments.

Once again, this is something added to QM. I don't believe it per se, its just an interesting idea which serves as a useful philosophical tool.

 

[Dancing David]

I suppose you have a proof of this assertion?

Orthodox quantum mechanics IS probabilistic. Some people believe by adding something to the theory they can make it deterministic (e.g. decoherence to pointer basis states, existence of many-worlds etc.) These suggestions have problems of their own. Anyone who has taught you otherwise is full of it.

Interestingly there is a way of finding a deterministic theory underlying quantum mechanics I became aware of only recently. And it involves chaos! In simple form the story is this: There are 3 main ways of quantizing a (deterministic) classical theory: Canonical quantization, path integral quantization and stochastic quantization. The latter of these involves adding a fictitous temporal dimension, and evolving the fields under a stochastic equation in this fictive time - this is done by adding "white noise" to a deterministic part of the equation. What someone realized was that you can generate this white noise with a chaotic process (which is also deterministic). If you do it on a small enough scale (say the planck scale) then the fact this chaotic noise deviates slightly from white noise won't be observable in any current experiments.

Once again, this is something added to QM. I don't believe it per se, its just an interesting idea which serves as a useful philosophical tool.

Interesting , thank you.

 

[Ziggurat]

I suppose you have a proof of this assertion?

Look at any equation in standard quantum mechanics to describe the evolution of a wave function, and you will see that it is deterministic. For example, take the Schrodinger equation:

[latex]H \Psi = i \hbar \frac{\partial \Psi}{\partial t}
[/latex]

There's no probability in that at all: it's completely deterministic, and there is only ever ONE possible solution for the time evolution of a given initial state.

Orthodox quantum mechanics IS probabilistic.

No, it's not. People think it is because of the problem of "collapse" of the wave function. But as I said, that's NOT really part of the theory. That's what you get when you want to STOP dealing with the theory, and that's where all the "interpretations" (many-world idea, Copenhagen interpretation, etc) come in, but at that point you're no longer really dealing with quantum mechanics.

 

[Ziggurat]

Here's the point of disagreement. QM is by acclaim the most accurate theory ever, yet in one sense it does predict that a specific QM entity is located 'somewhere in this universe'. I don't find that statement as determining anything of value.

I'm sorry, but I really don't know what you mean by that.

Agreed, nor does it imply it to be true. Do you consider Cramer's TI deterministic?

Can't say I've looked at it in depth, but as far as I can make out, the Transactional Interpretation is precisely that: an interpretation. In that sense, whether or not it's deterministic becomes irrelevant: it does not make any new or different predictions. The Copenhagen interpretation, for example, is certainly probabilistic, but it too is just an interpretation, it is not a testable theory.

Or the results to date of 'quantum eraser' etc experiments?

This is again simply the problem of wave function "collapse": we cannot accurately model the quantum state of our measurement device, and so we brush it under the rug by assuming a "collapse" of the wave function upon interacting with it. The collapse in treated as a probability process, but there is no real evidence that this probability represents anything other than our uncertainty about the quantum state of our measurement device.

 

[Tez]

Look at any equation in standard quantum mechanics to describe the evolution of a wave function, and you will see that it is deterministic. For example, take the Schrodinger equation:

[latex]H \Psi = i \hbar \frac{\partial \Psi}{\partial t}
[/latex]

There's no probability in that at all: it's completely deterministic, and there is only ever ONE possible solution for the time evolution of a given initial state.



No, it's not. People think it is because of the problem of "collapse" of the wave function. But as I said, that's NOT really part of the theory. That's what you get when you want to STOP dealing with the theory, and that's where all the "interpretations" (many-world idea, Copenhagen interpretation, etc) come in, but at that point you're no longer really dealing with quantum mechanics.

Your understanding of what is and isn't quantum mechanics is woeful.

How about next time you say something like "since I, Ziggurat, choose to ignore the primary part of quantum mechanics which gives it predictive power and a connection with experimental observation, I can claim that it is deterministic."

Thats your choice, but it sure isn't science and its irresponsible to promugate such silly memes to peopel who may not know better.

For anyone who is interested, the part of quantum mechanics which "touches base" with experiments that doesn't make use of projection valued measures (the "non-deterministic part") is the computation of energy spectra of Hamiltonians. There are some indications this part can actually be done within a (psuedo-)classical theory anyway (SED, Gutzweiler trace formula etc).

 

[Tez]

This is again simply the problem of wave function "collapse": we cannot accurately model the quantum state of our measurement device, and so we brush it under the rug by assuming a "collapse" of the wave function upon interacting with it. The collapse in treated as a probability process, but there is no real evidence that this probability represents anything other than our uncertainty about the quantum state of our measurement device.

In case anyone cares, this too is speculation. I have seen numerous attempts to prove this rigorously within the framework of QM itself, and all have failed badly. Similar things can be proven by adding something to QM (GRW for example). Educate yourself.

 

[Schneibster]

If REALITY is not a local phenomena, who is to say one way or the other?

Show an experiment that shows that reality is not a local phenomenon. Don't say "Aspect" or "EPR," because neither of those shows that anything non-local occurs; what they do show is that local realism, that is, the statement that all parameters have values all the time that conform to conservation laws if they are constrained by them, is incorrect. What YOU are asserting is not the absence of local realism; you are asserting non-locality, and non-locality is impossible under SRT. It is therefore much more likely that the lack of local realism is due to lack of causality rather than non-locality. There is no experiment that shows that there MUST be non-locality; there are only experiments that show that there must EITHER be non-locality OR lack of causality.