Question about Probability

[Membrain]

Hi all, this is my first post.

 

I've come from http://www.ilovephilosophy.com because I had trouble getting answers about the probabilistic nature of quantum mechanics. It had to do with existence of free will, and I realized that I needed to get a better grasp on the nature of quantum indeterminism.

 

One of the things I read was the Wiki page on the "Bohr-Einstein debates":

http://en.wikipedia.org/wiki/Bohr-Einstein_debates

 

as well as numerous double-slit pages, etc.

 

My first question is fairly simple I think:

 

When talking about the probabilistic nature of an electron, WHERE is the electron? And I'm not talking about specifically where it is (since I think this is where the probabilistic nature comes into play), but generally where is it?

 

By this I mean: is it in a shell around a nucleus? Or is if flying towards a slit? Has it passed through a slit? Or are we talking about any incarnation of an electron?

 

Any help would be appreciated, and my apologies in advance for what I'm sure will sound like naive questions!

[Klaynos]

Hi all, this is my first post.

 

I've come from http://www.ilovephilosophy.com because I had trouble getting answers about the probabilistic nature of quantum mechanics. It had to do with existence of free will, and I realized that I needed to get a better grasp on the nature of quantum indeterminism.

 

One of the things I read was the Wiki page on the "Bohr-Einstein debates":

http://en.wikipedia.org/wiki/Bohr-Einstein_debates

 

as well as numerous double-slit pages, etc.

 

My first question is fairly simple I think:

 

When talking about the probabilistic nature of an electron, WHERE is the electron? And I'm not talking about specifically where it is (since I think this is where the probabilistic nature comes into play), but generally where is it?

 

Everywhere where it's probability is not 0.

 

By this I mean: is it in a shell around a nucleus? Or is if flying towards a slit? Has it passed through a slit? Or are we talking about any incarnation of an electron?

 

Well it's a free electron so it's no longer bounded by the probability well of an atom.

 

Any help would be appreciated, and my apologies in advance for what I'm sure will sound like naive questions!

[Membrain]

To clarify: I'm looking for when the electron is considered to be probabilistic (and from what I've heard, it is never probabilistic when it is measured, so I supposed that we are talking about non-measured events).

 

I'll list a few and ask "Probabilistic or Non-Probablistic?"

 

1. An electron in a shell around a nucleus

2. An electron being fired towards a slit

3. An electron going through the slit

4. An electron "just sort of floating around in the air", not attached to a nucleus, not being fired towards nor going through a slit.

 

Is the electron considered probabilistic in all four of these (unmeasured) conditions? And if not, why not?

[Klaynos]

It's always probabilistic, it's just sometimes that the probability wave is over a very small area (depending on the accuracy of your detector).

 

1. Probability wave around the orbital of the energy level that the electron is in.

2. There is an uncertainty about both it's x and y positions, it will have a quite well definined x, wavefront though.

3. When it is in a slit if it is double slits, it has a probability that it is in both slits.

4. A probability function based on what is around it. Other charge carriers.

[Membrain]

It's always probabilistic, it's just sometimes that the probability wave is over a very small area (depending on the accuracy of your detector).

 

1. Probability wave around the orbital of the energy level that the electron is in.

2. There is an uncertainty about both it's x and y positions, it will have a quite well definined x, wavefront though.

3. When it is in a slit if it is double slits, it has a probability that it is in both slits.

4. A probability function based on what is around it. Other charge carriers.

OK thanks.

 

Concerning electrons going around the nucleus of atoms:

 

Via the periodic table, we define atoms by how many electrons (and protons and neutrons) they have, right? Well, lets take silver: atomic weight 47, five energy levels, with electron quantities-per-level being 2,8,18,18, and 1.

 

My understanding is that when we measure the electrons, the wave collapses and we are able to measure them, and that's how we know have many electrons there are at each energy level.

 

Before I go on, can I get some affirmation that I am on the right track here? I want to continue with probability as it refers to measurement and as it refers to reality, but I'd better make sure I'm on track first. Thanks.

[gib65]

Hey Membrain,

 

I've got an account on http://www.ilovephilosophy.com as well. What's your username there?

 

I'm very interested in quantum mechanics also. I'd answer your questions except for the fact that Klaynos seems to be doing a fine job already, and that all my knowledge comes from asking question about it on SFN just like you, not from any expertise or formal education. I'm going to stick around and read the answers as I am very interested in this topic as well.

[Membrain]

Hey Membrain,

 

I've got an account on http://www.ilovephilosophy.com as well. What's your username there?

 

 

"Membrain"!

[fredrik]

Hello Membrain,

 

I'm new here as well.

 

Quantum mechanics is on one hand a defined formal mathematical framework, and there has been and I guess is still some debate over it's interpretation from the philosophic point.

 

To put it briefly, the way I interpret it is that quantum mechanics deals with measurements, and in a certain sense, only what is measured is real. Quantum mechanics deals more with our knowledge of reality, rather than reality itself, whatever that is by the way.

 

First of all, what is an electron? We picture it in our mind as a little charged bullet. However this view is not consistent as it will lead to odd things. In particular the electrons odd spin magnetic makes is peculiar. No classical body can have such a spin. Suggesting already there something is wrong with this picture. An object can only be defined in terms of interactions.

 

If one make a distinction between some abstract reality, and the observed reality I'd say the abstracted reality has more to do with our brains and minds and our amazing desire to understand, simplify and reduce. We would go nuts to see only scattered datapoints and sporadic input. Inventing patterns and logical causal relation in data is as it seems spontaneous and also intuitive. The fact we succed in finding beautiful patterns that repeat, of course suggests that there is something absolute... but in my opinion such an assumption does not make a difference.

 

I think first of all one has to let go of the concept that the electron is a little ball. Sometimes it behaves like one, but sometimes it does not.

 

And when dealing with sensitive details. Small things for example. The differece between reality and the observed reality is blurred.

 

To me the world is fundamentally fuzzy. It's chaos. Our minds and biology all suggests that there is sponatenous formation of associations. I haven't figured it out yet... but as far as quantium mechanics goes... and your electron case I'd say that... your presupposition that the electron is some kind of ball is probably what causes you to wonder "where it is" - assuming that a ball by definition has a definite position. Wich is a meaningless question until something interacts with it. And the type of interaction affects it's position too. If it's not a "ball" after all... maybe the question of "where is it" is simply wrong.

 

/Fredrik

[gib65]

To put it briefly, the way I interpret it is that quantum mechanics deals with measurements, and in a certain sense, only what is measured is real. Quantum mechanics deals more with our knowledge of reality, rather than reality itself, whatever that is by the way.

 

I've never heard it put that way before. Sounds like you've got a unique view of QM.

[fredrik]

Hmm I don't think it's that awfully unique. But others may choose to think otherwise, without contradictions. The interpretation is a choice, and is nothing you prove or disprove. My view is that whatever interpretation that makes your subjective understanding better is right for You. That said, I don't think it's a conincidence that many share the same interpretation.

 

While QM contains is a mathematically well defined framework to calculate alot of things, that is proven to be consistent with experimental input, it's full philosophical interpretation is not defined in the theory. Interpretations doesn't change how you do calculations, neither do they change probability distribution of measured values. But it may change how a subject would attempt to expand the theory by comtemplation or extrapolation.

 

So in a certain sense, from an application point of view or engineering point of view, you can ignore these philosophical aspects of interpretation. For me personally, I just can not allow myself to do so because it happens to be the interesting parts. Taking to abstraction, the rest of it is just "computing" according to set rules. I am interesting in seeing how rules form, not make automated computations based on already acquired rules.

 

But there are problems in QM, as I'm sure has been discussed over and over on this forum before (I'm new here so I'm just guessing). In the domain where you mix QM and General realativity things get hairy. Some people tend to look for technical answers using new mathematical exploits, like string theory and leave the interpretation for later. Others try to rework the basic interpretation in order to find a more natural way out.

 

I've studied QM, and I was annoyed by the official ignorance of important philosophical aspects. But yes, usually one says that some parts of the interpretation isn't "physics", it's "philosophy" or metaphysics or something like that. That maybe true but, well I never allowed myself to get hung up of choice of words. Whatever it is called, it is not less important for my reality and I can not ignore it.

 

I'm sorry if this comes out offensive, but when scientists sometimes reject philosophical questions as baloney on the basis that it's not science, is to me similar to when your doctor diagnosing a sick patient and takes all the tests, and finds them good, completely ignoring the phsycological aspects of things.

 

phsycology vs medicine, philosophy vs physics? Is one inferior of the other? IMO, they are both needed in the real world.

 

That said I don't have all the answers, but I have some questions which I feel is a decent first step

 

I recall from old discussions of mine that these things are hard to dicuss for obvious reasons. So some of these things are I think best solved my individual contemplation, but can be stimulated by intermittent dicussions between different individuals.

 

Btw, I am impressed by this forum. Unlike other forums I visited where mosts posts are about people posting their homework, this seems to harbor alot of good things. Glad I found this.

 

/Fredrik

[fredrik]

> To put it briefly, the way I interpret it is that quantum mechanics deals with measurements, and in a certain sense, only what is measured is real. Quantum mechanics deals more with our knowledge of reality, rather than reality itself, whatever that is by the way

 

Not that is has much relevance to the topic, but my personal philosophy is that reality originally is simply "uknown". This is in my mind the "least implausible" starting point. The image or illusion of a definite reality is I think created by associative processing of our experience interacting with it. So on one hand, I would say that reality is an illusion or creation (choose the appropriate word), OTOH I'd say that interactions are the only "real" basis for reality. In that context, it is obvious that the concept of measurement is absolutely central. Central is also the concept of an observer / subject.

 

"Reality" to me is an image, creative by the subject in question (to talk about reality without considering an specific observer or subject is also akward to me, they are central to me at least).

 

The mind boggling parts to me is the problem that that the observer is part of the system. The observer is not an abstraction, the observer also has a physical nature, possessing mass etc. So there is a certain level of self-observation that really gives something to chew on. I've been chewing on that for at least 10 years, and still chewing

 

Many dismiss these things as metaphysics. I can't. It is too painful. My mind begs for a solution. While I am sure that I will never find the ultimate solution, I am sure I will make progress.

 

This philosophy has served me well, and makes me fell good. That is my experimental support for my philosophy. I would reject any philosophy that is detrimenal to my brain as wrong

 

/Fredrik

[Membrain]

I think first of all one has to let go of the concept that the electron is a little ball. Sometimes it behaves like one, but sometimes it does not.

 

And when dealing with sensitive details. Small things for example. The differece between reality and the observed reality is blurred.

 

To me the world is fundamentally fuzzy. It's chaos. Our minds and biology all suggests that there is sponatenous formation of associations. I haven't figured it out yet... but as far as quantium mechanics goes... and your electron case I'd say that... your presupposition that the electron is some kind of ball is probably what causes you to wonder "where it is" - assuming that a ball by definition has a definite position. Wich is a meaningless question until something interacts with it. And the type of interaction affects it's position too. If it's not a "ball" after all... maybe the question of "where is it" is simply wrong.

I have let go of the electron being "a ball".

 

The question of "where it is" seems crucial. I'm attempting to learn whether the electron is considered to be localized at all.

[Membrain]

OK thanks.

 

Concerning electrons going around the nucleus of atoms:

 

Via the periodic table, we define atoms by how many electrons (and protons and neutrons) they have, right? Well, lets take silver: atomic weight 47, five energy levels, with electron quantities-per-level being 2,8,18,18, and 1.

 

My understanding is that when we measure the electrons, the wave collapses and we are able to measure them, and that's how we know have many electrons there are at each energy level.

 

Before I go on, can I get some affirmation that I am on the right track here? I want to continue with probability as it refers to measurement and as it refers to reality, but I'd better make sure I'm on track first. Thanks.

Getting back to this question:

 

Does anyone consider this to be untrue?

[fredrik]

I have let go of the electron being "a ball".

 

The question of "where it is" seems crucial. I'm attempting to learn whether the electron is considered to be localized at all.

 

Ok, maybe I didn't understand your question. I really didn't mean to give you a "stupid answer". Your questions are good ones, I asked myself the same ones in that past except we all think a bit differently.

 

You seem to accept the probability concept, but you still ask "where is it" when it it not measured? I suspect, though I may misunderstand you, that you still have an deterministic reference. Like, ok we don't know exactly where it is until it's measured, but still where is it, while not beeing measured?

 

People may choose to put this, or interpret this, a bit differently:

 

The probability distribution in quantum mechanics represents our complete knowledge of the system. What is not in there, doesn't exist.

 

It is essential to make the distinction of intrinsic uncertainty, and incompletness that is simply due to the ignorance of the observer which is of course a completely different story.

 

Quantum mechanics describes the instrinic uncertainty as would be experience by a hypothetical "super observer". With super observer

I don't mean anything like God, I mean a normal observer, but that

is superperceptiv and superintelligent.

 

In an extension, I think the concept of measurement and the fundamental

concept of interaction are the side. With measurements we often

consider an artificial, external observer that doesn't interact with the

system, it's just a "passive" observer. Quantum mechanics suggest

that is impossible. A passive observer, that makes no measurements,

does not interact with the system and there is now way any information

about the system can be transferred to this imaginary observer.

I think imaginary observers that follow reality from distance without disturbing

it is inherently inconsistent with the concepts of quantum mechanics.

 

In essence, an electron "interacting" with a proton, can be said

to perform mesurements on the field, or communicate.

 

I'd say reality defines itself through interactions.

 

About where it is, as in whereabout is it likely to be detected, that is given by the probability distribution. And the different energy states in an atom gives various wavelike orbitals or shells around the atom. The different orbital shapes are mathematically different solutions to a resonance problem.

 

I had a big time digesting this picture when I started to study QM, I desperatly tried to "invent" an underlying classic picture. But it couldn't be done in a consistent way.

 

In my view the quantum mechanical framwork moves the focus from actualy objects to communication/interactions. We get to konw objects through

interaction/communication, and thus interactions/measurements are more fundamental that the object itself. When taking some time to digest this, I find that it is far better philosophical starting point than is the old deterministic ideals. This change of base really have some profound impact on things and I consider it a significant improvement over old days. It does seem screwed up and wrong at first, but if one thinks about it again again, I wonder how I did ever could think otherwise.

 

I'm still not sure if it helps answer your question?

 

/Fredrik

[fredrik]

> With measurements we often consider an artificial, external observer that doesn't interact with the system, it's just a "passive" observer. Quantum mechanics suggest that is impossible.

 

Ok, I should add that this is my personal abstraction of the essence if QM. It's often disrespected in many treatments, which I consider to be something that need to be fixed.

 

Also, I can't comment on wether others may disagree.

 

So this is my attempt to answer your question.

Perhaps others have alternative answers.

 

The wave concepty can be used of course, but then the question arises as to what the heck this wave *is*, in the context of a determinisitc classic reference. This is why, even the wave-particle duality is sort of semi-classical IMO, because the wave is really a half imaginary wave.

 

/Fredrik

[gib65]

Getting back to this question:

 

Does anyone consider this to be untrue?

 

I'm no expert in QM, but everything I've been taught about it says that you're on the right track.

[Membrain]

OK, so it sounds like the electrons (47 of them) are considered to exist within each silver atom.

 

So that if one had an ingot of silver, all of the atoms would be considered to have 47 electrons.

 

Now my understanding of "probabilities" is that when you measure the electron you can't measure the whole wavy/liquidy/smeared-out thing; you can only measure it once it is collapsed into a point.

 

Is this where the probability comes in? I can see how the electron can seem probabilistic since the electron is in all places within the shell at the same time.

[fredrik]

> Now my understanding of "probabilities" is that when you measure the

> electron you can't measure the whole wavy/liquidy/smeared-out thing; you

> can only measure it once it is collapsed into a point.

>

> Is this where the probability comes in? I can see how the electron can

> seem probabilistic since the electron is in all places within the shell at the

> same time

 

That seems like a decent description.

 

One can imagine the similariy between the statistical concepts from thermodynamics.

 

In a gas, we don't know the position of every single molecule. And if we try to detect a single molecule, it's energy will vary. But the temperature defines a statistical distribution, that says that there is a mean energy and certain % of the "population" has another energy etc. So when we know the temperature of a gas, we know it's mean temperature, and the probability that any randomly chose molecule has a given energy.

 

Quantum mechanics can be interpreted in the same way, except that we picture an imaginary enseble, like suppose we repeated this experiment a trillion times or had a trillion side by side systems, quantum mechanical propability density gives the probability for detecting the system in a certain state.

 

The concept of quantisation OTOH, is something else. It has to do with that the concept of energy and momentum in QM are have different meanings that in classical mechanics. The energy state for example taken to define the energy transformations of the system.

 

I find some of these mathematically extremely basic things philosophically unsatisfactory. In the formalism, they can be taken to be axioms or definitions or the parameters and you get a mathematically sensible thing that can produce numbers. But the nature of these axioms or coulping of defined quantities to real observations are somewhat fuzzy. Here is room for improvement from philosophical sides.

 

In a logical formulation there are a number of postulates of classical quantum mechanics that by no means are self evident for a philosopher. So their nature are ad hoc stuff that are invented to make it logically self consistent at lest. The problem is of course if the set of axioms make sense from a realistic point of view. They most probably don't IMO.

 

/Fredrik

[fredrik]

Students of quantum mechanics are taught the "system". Ie. here are the axioms, and here are it's implications, and here is how we apply it and compare with experiments.

 

If you take it that way, isolated "classical" quantum mechanics is quite crystal clear.

 

However what is not part of the education is to question the philosophical validity of the axioms. This is often completely ignored, by the motivation that whatever the origin of these axioms, experience has taught us that when we apply them, we tend to det lucky, so there is got to be something to it, which is indeed correct, but the whole thing is still inherently fuzzy.

 

Learning QM, is to learn the axioms and what they imply. And they learn the formalism.

 

As for reality, it just isn't that easy of course. My conviction that many students and engineers learns quantum mechanics and then later forgets that it's all build upon a number of assumptions or axioms that really isn't obvious. As an engineer it could even be "easier" on your mind, to just accept the axioms and learn the formalism, given the acioms. But from the philosophers point of view, one typically studies not an abitrary sytems of axioms, but rather reality.

 

Roughly speaking it seems you are on the right idea thouhg. If you still find some things are odd, I'd that's part of the current construction.

 

/Fredrik

[fredrik]

I have to add this.

 

> In a gas, we don't know the position of every single molecule.

 

A fundamental difference is of course, is that in classical statistical mechanics, the reason we don't know the position of every molecule can technically be kind of said to be due to "ignorance" of the observer.

 

This is not so in quantum mechanics, where the reason we don't know everything is an intrinsic uncertainty, that is beyond even a "superobserver".

 

/Fredrik

[gib65]

Now my understanding of "probabilities" is that when you measure the electron you can't measure the whole wavy/liquidy/smeared-out thing; you can only measure it once it is collapsed into a point.

 

Is this where the probability comes in? I can see how the electron can seem probabilistic since the electron is in all places within the shell at the same time.

 

Yes, what is probable is where the electron will be when the wave function collapses - and it collapses because of the measurement.

[swansont]

OK, so it sounds like the electrons (47 of them) are considered to exist within each silver atom.

 

So that if one had an ingot of silver, all of the atoms would be considered to have 47 electrons.

 

Now my understanding of "probabilities" is that when you measure the electron you can't measure the whole wavy/liquidy/smeared-out thing; you can only measure it once it is collapsed into a point.

 

Is this where the probability comes in? I can see how the electron can seem probabilistic since the electron is in all places within the shell at the same time.

 

 

What about the electron are you measuring? "measure the electron" is pretty wide-open. There are a lot of measurements you can make.

[Membrain]

What about the electron are you measuring? "measure the electron" is pretty wide-open. There are a lot of measurements you can make.

Mass and velocity I believe are the common ones. Are there any measurements that we make where the electron does NOT collapse?

[Membrain]

I have to add this.

 

> In a gas, we don't know the position of every single molecule.

 

A fundamental difference is of course, is that in classical statistical mechanics, the reason we don't know the position of every molecule can technically be kind of said to be due to "ignorance" of the observer.

 

This is not so in quantum mechanics, where the reason we don't know everything is an intrinsic uncertainty, that is beyond even a "superobserver".

 

/Fredrik

How is our being unable to measure all of the electron in the electron shell not a limitation of measurement? Didn't we just agree that our method of measurement collapses the electron?

[swansont]

Mass and velocity I believe are the common ones. Are there any measurements that we make where the electron does NOT collapse?

 

If you make these measurements you will not have localized the electron's position. You "collapse" the wave function in a velocity measurement, in that you now know the velocity so there are values it can't have, but not in a charge or mass measurement — those values can't be any different.