Electron Orbits and Nuclei 2- Rotation vs Orbital Motion

[humanino]

Does a particle have absolute angular momentum or angular momentum in relation to another particle?

I am not sure what "absolute" angular momentum may be, and I don't know what a particle is without any other particle in principle. But a particle has intrinsic angular momentum, which is related to the representation of the Lorentz group it belongs to, and it can also have "orbital" angular momentum.

 

[StandardsGuy]

Today we understand this in terms of Wigner functions

This is some of those mathematical constructs socrates was talking about. A "quasi-probability distribution" is not much of an enlightenment. It doesn't answer the question of what the electron is up to. Just admit it, you have no idea. You also don't know if the electron is a point particle, a cloud, a smaller diameter particle that a proton, or even a particle at all. This is NOT understanding. So when they get higher energy they go into 'higher' "orbitals" but they don't orbit? jtbell had a much better answer in #17.

-S

P.S. I'm not a physicist, so don't be too hard on me.

 

[sokrates]

This is some of those mathematical constructs socrates was talking about. A "quasi-probability distribution" is not much of an enlightenment. It doesn't answer the question of what the electron is up to. Just admit it, you have no idea. You also don't know if the electron is a point particle, a cloud, a smaller diameter particle that a proton, or even a particle at all. This is NOT understanding. So when they get higher energy they go into 'higher' "orbitals" but they don't orbit? jtbell had a much better answer in #17.

-S
P.S. I'm not a physicist, so don't be too hard on me.

They'll never admit it, don't waste your time, resistance is futile... Let them cherish the illusion that they really understand...
JTBell #17 was a jewel in this thread. We must read it over and over again.

 

[sokrates]

Classical intuition is not that mathematically appealing to me. Quantum intuition is much more mathematically rich I think.

Quantum intuition? I hope you really know what you are talking about (considering the fact that all the fuss is really because quantum is utterly non-intuitive).

 

[Phrak]

I am not sure what "absolute" angular momentum may be, and I don't know what a particle is without any other particle in principle. But a particle has intrinsic angular momentum, which is related to the representation of the Lorentz group it belongs to, and it can also have "orbital" angular momentum.

Intrinsic was the word I was searching for, thank you. I don't think any dynamical variables of a particle are provably intrinsic within the scope of quantum mechanics.

As a particle cannot be prepared or measured in isolation, this begs the question: is the state of a particle, or a system of particles, intrinsic or relative?

I've had a tendency to consider--unlike everybody else, it seems--that particle states are not about particles but about what is between particles. Your thoughts?

 

[humanino]

Let them cherish the illusion that they really understand...

I mentioned the fact that you need to write down at least one mathematical symbol before we can discuss the interpretation of anything. You replied "but I'm a PhD student, I am certified to understand so I am allowed to come around with my claims". And then "for instance, I don't understand angular momentum". And then

Just admit it, you have no idea.

Just admit it, YOU do not understand the least beginning of it, so by deduction nobody understand, obviously because you are so smart.

Well bite it, that's flat wrong. There are difficulties with QM, I mentioned at least one (measurement and collapse, the role of unitarity... here is another, possibly related : the links between time and thermodynamics...), but that is not with angular momentum and that is not with Wigner functions. Both of those mathematical objects make perfect sense, they do not suffer from inconsistencies, they are pretty elementary and if they confuse you, just study harder, or do something else. Maybe the reason you do not understand QM is because you insist to apply Newton's laws of billiard collisions. Another news : if QM came first, maybe you would say that Newton does not make sense.

Once again, I admit that there are fundamental difficulties with QM, but not with what you mention. If you want to discuss something, please feel free to bring this discussion to a decent level. Please feel free to not post claims that nobody understand nothing since you do not understand elementary mathematics.

 

[humanino]

Intrinsic was the word I was searching for, thank you. I don't think any dynamical variables of a particle are provably intrinsic within the scope of quantum mechanics.

Intrinsic in the same sense as mass or electric charge of an elementary particle. Not dynamical indeed.

As a particle cannot be prepared or measured in isolation, this begs the question: is the state of a particle, or a system of particles, intrinsic or relative?

We define particles as representations of the Lorentz group because we want to be able to apply the symmetry to them. I do agree that the state of knowledge is always relative (Rovelli brought that to a new interpretation), but independently of the observer, all of them will make use of some representation of the Lorentz group since we assume relativity. You can not continuously deform one representation into another, but you can continuously go from one observer to the other, so you have quantum numbers for your particle.

 

[Phrak]

Thanks for responding. I hope you don't think I am combative as others here. I would really like to know your thoughts on this.

Intrinsic in the same sense as mass or electric charge of an elementary particle. Not dynamical indeed.

I know this is the usual understanding, but is it provable--or disprovable for that matter--again, within any given set of premises of quantum mechanic?

We define particles as representations of the Lorentz group because we want to be able to apply the symmetry to them. I do agree that the state of knowledge is always relative (Rovelli brought that to a new interpretation), but independently of the observer, all of them will make use of some representation of the Lorentz group since we assume relativity. You can not continuously deform one representation into another, but you can continuously go from one observer to the other, so you have quantum numbers for your particle.[/QUOTE]

This is a convenient image I found searching on trees_discrete_algebra.

Or this one, with thanks to lisab,

that I hijacked from a comoving thread. ()

Everyone talks about the nodes (particles). What can be said of the Lorentz representation of the lines?

 

[sokrates]

Just admit it, YOU do not understand the least beginning of it, so by deduction nobody understand, obviously because you are so smart.
Please feel free to not post claims that nobody understand nothing since you do not understand elementary mathematics.

Calm down. It’s alright. If this is going to chill you, I admit it, I don’t understand elementary mathematics. Please don’t go crazy. Let's try to keep it at the intellectual level, shall we? I don’t write “at least one mathematical symbol”, although it's really an idiotic way to judge knowledge because I can’t write it…! I have kept this as a secret for so many years… But amusingly, just because you probably have skimmed a few elementary books, you think you are an authority. I revealed my 'real life' profession. Could you enlighten us as to why we should take 'your deep understanding' more seriously?
We are not claiming we are smart. You know nothing about us because this is internet (so you shouldn't be so fierce to prove a point - this is not APS March Meeting, seriously it looks funny), and what we claim has nothing to do with your unwarranted attacks (on the lack of our mathematical knowledge which you know nothing about). That said, I am more than sure I’d beat your seemingly half-baked introductory understanding in any platform, but I am content and I don’t care at all.

I can see how your obsession with mathematics gets in the way, maybe you are a mathematician and you feel bad about it because you seem to have no idea what physics is really about. I suggest you start reading ‘lay’ books of Feynman, Gell-Mann instead of learning new tricks on ‘linear algebra’. That’ll do you more good.

The debate is not spinning around specific functions (Wigner) or concepts (momentum), so please don't desperately hold on to those to deliver a message, the point is whether we can really say we understand Quantum Mechanics as well as we understand billiard balls. Being able to write down the mathematical formalism is not enough! And don't make sharp remarks on things you don't know (billiard balls) - Boltzmann equation solves a lot of applied problems. The semiconductor CAD industry (i,e the laptop you are using) is based on 'billiard balls'.

A prime example on how interpretation changes the WAY we think about is non-locality. To explain EPR - MWI does not require the dubious spooky action at a distance. Can you see how much of a difference a MERE interpretation ( no math difference ) can cause? You are welcome to fool yourself that you already know the answer, but physicists BOTHER about PHYSICAL implications a theory suggests. We are not satistified when we fit an experimental curve with some fancy function. You HAVE to explain why it works. We NEED to know the machinery, and it must MAKE SENSE. The ramifications of different interpretations are HUGE. And the theory is not over yet. And no matter how much you elaborate on the subject, NO, you HAVE NO IDEA what the electron is up to inside an atom. Get over it!

Edit: Nobody didn't complain about angular momentum, I am just clarifying this for others who haven't followed the discussion, you are frantically trying to bring the argument down to the so-called elementary level, but it's not about that.Follow the discussion and read #17.

Edit:

Another news : if QM came first, maybe you would say that Newton does not make sense.

Sweet dreams...

 

[Phrak]

Calm down. It’s alright. If this is going to chill you, I admit it, I don’t understand elementary mathematics. Please don’t go crazy. Let's try to keep it at the intellectual level, shall we? I don’t write “at least one mathematical symbol”, although it's really an idiotic way to judge knowledge because I can’t write it…! I have kept this as a secret for so many years… But amusingly, just because you probably have skimmed a few elementary books, you think you are an authority. I revealed my 'real life' profession. Could you enlighten us as to why we should take 'your deep understanding' more seriously?
We are not claiming we are smart. You know nothing about us because this is internet (so you shouldn't be so fierce to prove a point - this is not APS March Meeting, seriously it looks funny), and what we claim has nothing to do with your unwarranted attacks (on the lack of our mathematical knowledge which you know nothing about). That said, I am more than sure I’d beat your seemingly half-baked introductory understanding in any platform, but I am content and I don’t care at all.

I can see how your obsession with mathematics gets in the way, maybe you are a mathematician and you feel bad about it because you seem to have no idea what physics is really about. I suggest you start reading ‘lay’ books of Feynman, Gell-Mann instead of learning new tricks on ‘linear algebra’. That’ll do you more good.

The debate is not spinning around specific functions (Wigner) or concepts (momentum), so please don't desperately hold on to those to deliver a message, the point is whether we can really say we understand Quantum Mechanics as well as we understand billiard balls. Being able to write down the mathematical formalism is not enough! And don't make sharp remarks on things you don't know (billiard balls) - Boltzmann equation solves a lot of applied problems. The semiconductor CAD industry (i,e the laptop you are using) is based on 'billiard balls'.

A prime example on how interpretation changes the WAY we think about is non-locality. To explain EPR - MWI does not require the dubious spooky action at a distance. Can you see how much of a difference a MERE interpretation ( no math difference ) can cause? You are welcome to fool yourself that you already know the answer, but physicists BOTHER about PHYSICAL implications a theory suggests. We are not satistified when we fit an experimental curve with some fancy function. You HAVE to explain why it works. We NEED to know the machinery, and it must MAKE SENSE. The ramifications of different interpretations are HUGE. And the theory is not over yet. And no matter how much you elaborate on the subject, NO, you HAVE NO IDEA what the electron is up to inside an atom. Get over it!

Edit: Nobody didn't complain about angular momentum, I am just clarifying this for others who haven't followed the discussion, you are frantically trying to bring the argument down to the so-called elementary level, but it's not about that.


Follow the discussion and read #17.

Edit:

Sweet dreams...

You can use this opportunity to learn or teach or rant or in a combination of your choice.

 

[humanino]

Nobody didn't complain about angular momentum

Your very first post in this thread :

Modern interpretations are vague when it comes to these issues. (angular momentum, electron "movement" in atom etc.)

QM is everything but vague. The rules as exposed for instance in von Neumann's book are crystal clear. The major issues remaining are such as e.g. that of the measurement, the non-unitarity of the collapse. The answer provided by statistical decoherence due to large thermodynamical environments is actually more compelling physically than mathematically ! That still leaves open a couple of other points. In due time.

Being able to write down the mathematical formalism is not enough!

I already agreed that it was not sufficient, but I will not let go on the fact that it is necessary."Not enough" as you say, but there is still not a single piece of mathematical idea in what you convey.

A prime example on how interpretation changes the WAY we think about is non-locality. To explain EPR - MWI does not require the dubious spooky action at a distance. Can you see how much of a difference a MERE interpretation ( no math difference ) can cause?

No, I do not see a difference indeed. I am very glad to learn that you prefer MWI to non-locality. For me it is more interesting to understand Bell's theorem and the various people who still study it. So let us go into what you say. You are happy about adding an infinity of possible Universe, an hypothesis which seems hopelessly non-falsifiable. Sure Everett was truly a remarkable fellow, and however bright his MWI, right now it is poetry. On the other hand, you just take for granted that what you consider locality is correct and should not be questioned. Penrose for instance proposes that locality holds in twistor space, where the entangled light-like separated pair would in fact be a point. As a matter of fact, he has very good practical down to Earth reasons to use twistors in the first place. They are already used from dirty QCD calculations to GR where they allow results to be obtained which we do not know how to obtain otherwise. They also seem to provide interesting results for string theory, and non-commutative geometry as well. So on one hand, technical developments allowing concrete calculations, based on reflections about the very nature of space and time, on the other a neat logical sterile trick. Your pick.

you HAVE NO IDEA what the electron is up to inside an atom.

I have as much of an idea about what an electron does as quantum mechanics allow us to know in principle. In fact, my professional activity is not mathematics since you ask, it is about figuring out what quarks and gluons do inside the proton, and I did spend quite a bit of time to think and read about what the electron does.

Follow the discussion and read #17.

Very well, let me repost for anybody who would still read

There is no generally accepted answer to this question. The mathematics of QM allows us to calculate the probabilities of getting various values for physical quantities when we measure/observe them, but it does not address the question of what is "really going on" when we don't measure/observe them. This is the subject of interpretations of QM, about which people argue vigorously (in this forum and elsewhere). We cannot as yet distinguish between these interpretations experimentally, even in principle, as far as I can tell.

QM does not tell you what specifically is going on when you are not measuring. I agree that this is not to say we can not try to imagine things. I claim it is unlikely that progress will be achieved by trying to go backwards and re-establish billiard games. It is more likely that there is something fundamental about space-time that we are missing or not taking seriously enough in our assumptions. We can and will understand, I reckon that. But if you agree that we need to improve something fundamental, we will need to convince a community and that goes through putting forward testable, practical, precise mathematical statements, calculation toolboxes, anything that allows some form of significant progress. Not MWI.

 

[sokrates]

Sure Everett was truly a remarkable fellow, and however bright his MWI, right now it is poetry.

This is the deal breaker for me. I won't even talk to you anymore. This is why you cannot be taken seriously at all, you are considering MWI "poetry"... I advise you to keep this piece of treasure with you, and not to spell it out anywhere, especially in a place full of physicists, because people will give you a sad smile and turn back... This is not about MWI being the answer or not, this is about your attitude. By saying things like this, you only reveal your physics understanding is similar to that of a poet.

You are attacking MWI as if it was MY very own theory, parroting some very old criticisms you have learned from this forum (MWI being non-falsifiable and so forth) and you are hopelessly trying to crush it... You still desperately take the single word angular momentum out of its context and use it even though I explained clearly, the argument has nothing to do with that.

Your reply to jtbell is even more interesting. You are not even listening what he has to say. Instead, you are valiantly detailing the 'missing ingredient' in Quantum Mechanics, the 'magic thing' that has been elusive to physicists for hundred years... And that is

something fundamental about space-time that we are missing

This looks by the way, spectacularly mathematical, and thank you for sharing this with the rest of the community. You know what? Don't keep it here, please publish this. You will reach a broader audience.

I am sure everybody will be convinced and a few theoretical groups will start investigating that in no time.
----------------------------
Anyway, you can rant all day about MWI being worthless and waste of time, (although I find it ironic that YOU were the first person pedantically pointing out that "FEELINGS" towards interpretations must be carried over to the philosophy section) , or you might believe that you KNOW everything that's KNOW-ABLE about the electron, but since this is my last post I'll try to be friendlier.

Carve some round edges to your biased personal views on understanding QM for your own sake.(You are not even working in the field). Because these cloud all the other "important things" that you try to convey. We won't even listen. You need to put your FEELINGs and personal preferences out of the way before you hope to see people give the slightest attention to your ideas.

Good luck in your studies.

 

[humanino]

...

Still not a single scientific contribution in your post.

 

[StandardsGuy]

Just admit it, YOU do not understand the least beginning of it, so by deduction nobody understand, obviously because you are so smart.

Well bite it, that's flat wrong. There are difficulties with QM, I mentioned at least one (measurement and collapse, the role of unitarity... here is another, possibly related : the links between time and thermodynamics...),

I don't know who this was intended for, but rest assured we are not as ignorant as you think (we knew what you didn't know!). I don't claim to have your understanding. I'll admit a mathematical understanding is better than none. I'm here to learn, so could you enlighten me as to what you meant by "measurement and collapse". A non-mathematical explanation is prefered, but any is better than none. Thanks.

-S

 

[GreyBadger]

I'm here to learn, so could you enlighten me as to what you meant by "measurement and collapse". A non-mathematical explanation is prefered, but any is better than none.

I'm sure Humanino will put me right, but this is the problem. In the Schrödinger picture, all quantum mechanical systems are described by the wavefunction and the Hamiltonian, which describes the total energy of the system. These are then tied together by Schrödinger's equation, which describes how the wavefunction changes as a function of time. It is very simple, figuring out the Hamiltonian for an arbitrary quantum system isn't!

One side of the equation has the wavefunction laid bare and the other has the rate of change of the wavefunction with respect to time. So far, so good - the rate of change of the wavefunction is related to the Hamiltonian.

Note that this doesn't include anything about determining the state of the system (i.e. measuring it). The wavefunction is, at any point in time, a combination of all possible states (say, spin up and spin down for a fermion). If a measurement is made, the wavefunction instantaneously becomes only one of these possible states.

Stop to think about this - if the wavefunction can take only '1' or '0', you then have an instantaneous change from 'something' to '1' or '0'. Remember the Schrödinger equation has the rate of change with respect to time of the wavefunction? In this, instantaneous case, this is infinite. So, the equation states that the total energy of the system becomes infinite at the point a measurement is made.

This is glossing over a whole lot of detail, but I hope it makes sense.

 

[mccoy1]

Your very first post in this thread :
QM is everything but vague. The rules as exposed for instance in von Neumann's book are crystal clear. The major issues remaining are such as e.g. that of the measurement, the non-unitarity of the collapse. The answer provided by statistical decoherence due to large thermodynamical environments is actually more compelling physically than mathematically ! That still leaves open a couple of other points. In due time.

I already agreed that it was not sufficient, but I will not let go on the fact that it is necessary."Not enough" as you say, but there is still not a single piece of mathematical idea in what you convey.No, I do not see a difference indeed. I am very glad to learn that you prefer MWI to non-locality. For me it is more interesting to understand Bell's theorem and the various people who still study it. So let us go into what you say. You are happy about adding an infinity of possible Universe, an hypothesis which seems hopelessly non-falsifiable. Sure Everett was truly a remarkable fellow, and however bright his MWI, right now it is poetry. On the other hand, you just take for granted that what you consider locality is correct and should not be questioned. Penrose for instance proposes that locality holds in twistor space, where the entangled light-like separated pair would in fact be a point. As a matter of fact, he has very good practical down to Earth reasons to use twistors in the first place. They are already used from dirty QCD calculations to GR where they allow results to be obtained which we do not know how to obtain otherwise. They also seem to provide interesting results for string theory, and non-commutative geometry as well. So on one hand, technical developments allowing concrete calculations, based on reflections about the very nature of space and time, on the other a neat logical sterile trick. Your pick.

I have as much of an idea about what an electron does as quantum mechanics allow us to know in principle. In fact, my professional activity is not mathematics since you ask, it is about figuring out what quarks and gluons do inside the proton, and I did spend quite a bit of time to think and read about what the electron does.
Very well, let me repost for anybody who would still read
QM does not tell you what specifically is going on when you are not measuring. I agree that this is not to say we can not try to imagine things. I claim it is unlikely that progress will be achieved by trying to go backwards and re-establish billiard games. It is more likely that there is something fundamental about space-time that we are missing or not taking seriously enough in our assumptions. We can and will understand, I reckon that. But if you agree that we need to improve something fundamental, we will need to convince a community and that goes through putting forward testable, practical, precise mathematical statements, calculation toolboxes, anything that allows some form of significant progress. Not MWI.

mm I'm not an expert so excuse me if I seem 'ignorant' but what does QM says about electron when we are measuring? You said QM can't tell us anything if we're not measuring, which means it can tell us what an electron does in the atom when we measure it...so what does it say?Sometines I wonder though how scientists come up with a sensible and complete theory about electrons if they don't have an idea of what electrons do in the atom!
I'm now doing a diploma in physics, just started and my bro(younger) came to me with a book that says QM explain most physics and all of chemistry.He asked me some weird questions on Complex Chemistry (on electronic spectras etc), but i said i don't know QM.So If he ask me next time what electrons doe in atom, then I think it would be safe to tell him "QM doesn't explain all of the chemistry mate".
Moreover, why do you think nothing in Qm can't make sense unless you're a genius in maths? Newtons' lwas make sense without math, you can understand why protons split each other without maths...so what's all this maths thing about?
I think if you can't explain a theory in words so that it makes sense without resorting to maths as an explanation, then that theory must be incomplete if not nonsense. Well I'm a fun of Qm but I'd appreciate if people admit that it's a baby(an incomplete theory) and it may be improved as time goes and that some interpretaions and assumptions may be revisited on the way.So don't get mad when a layman come over and ask what electron does in the atom.Just tell him we don't know!

Sorry if I come across rude!

 

[GreyBadger]

Moreover, why do you think nothing in Qm can't make sense unless you're a genius in maths?

QM is a model. Physics is a model. Nobody (well, few) claim that 'The world IS this'; the claim is that 'The world looks like this to the best of our experimental knowledge'. I would point out that aspects of QM are the most well measured of any theory ever (look up the electron magnetic moment, or g-2 measurement). This model is expressed in the language of mathematics as it is a predictive theory (i.e. we can compute probabilities, cross-sections, decay rates, etc etc), and not hand-having.

So Newton's laws in words. Let's pick one:

"The net force on a particle is equal to the rate of change with respect to time of its linear momentum"

This is just maths writ down:

<br /> F=\frac{dmv}{dt}=ma<br />

One could happily express QM in such terms, but we'd be here for years and years and years. Langauge is the key to communication, and QM (and, indeed, all Physics ever) is communicated in the language of mathematics.

 

[StandardsGuy]

The wavefunction is, at any point in time, a combination of all possible states (say, spin up and spin down for a fermion). If a measurement is made, the wavefunction instantaneously becomes only one of these possible states.

Thanks GreyBadger for your reply. The piece above is sufficient, and doesn't contain any mathematics. So let's see I am on track. All matter in the universe is in the form of waves until they are 'looked at' or measured. At that time they instantly become particles. So why does humanino call this a problem for QM? It seems to be the basis of it. Or was he talking about the mathematics of computing ("understanding") it being the problem?

 

[humanino]

why does humanino call this a problem for QM?

I did not come up with that. There are more books on the measurement problem than anybody alive will ever read seriously. There are two contradictory postulates in quantum mechanics. One of them is unitarity (the evolution of the wavefunction is given by a Schroedinger equation), and the other is the measurement postulate (which is not unitary as has been mentioned simply above). If you formulate QM in terms of density matrices, you'll find out that it is plausible that non-diagonal elements vanish, because large thermodynamical systems are not coherent. But that does not hold mathematically, strictly speaking you obtain infinitely complex, subtle, evermore tiny structures in a huge wavefunction.

 

[maverick_starstrider]

mm I'm not an expert so excuse me if I seem 'ignorant' but what does QM says about electron when we are measuring? You said QM can't tell us anything if we're not measuring, which means it can tell us what an electron does in the atom when we measure it...so what does it say?Sometines I wonder though how scientists come up with a sensible and complete theory about electrons if they don't have an idea of what electrons do in the atom!
I'm now doing a diploma in physics, just started and my bro(younger) came to me with a book that says QM explain most physics and all of chemistry.He asked me some weird questions on Complex Chemistry (on electronic spectras etc), but i said i don't know QM.So If he ask me next time what electrons doe in atom, then I think it would be safe to tell him "QM doesn't explain all of the chemistry mate".
Moreover, why do you think nothing in Qm can't make sense unless you're a genius in maths? Newtons' lwas make sense without math, you can understand why protons split each other without maths...so what's all this maths thing about?
I think if you can't explain a theory in words so that it makes sense without resorting to maths as an explanation, then that theory must be incomplete if not nonsense. Well I'm a fun of Qm but I'd appreciate if people admit that it's a baby(an incomplete theory) and it may be improved as time goes and that some interpretaions and assumptions may be revisited on the way.So don't get mad when a layman come over and ask what electron does in the atom.Just tell him we don't know!

Sorry if I come across rude!

I'm afraid you're basically going to get nowhere with physics then (or, much more likely you'll realize the error in your thinking). All of physics is intensely mathematical and the inability to fully communicate complex mathematical concepts using the english language is 100% the failure of the english language and the average education/understanding of the layman, not the fault of the theory.

Ultimately you're mis-understanding that nature of "uncertainty" in quantum mechanics. It's not a case of "we don't know", it's a case of "the universe doesn't know". A lot of things that you might think extremely impossible are very much possible (and experimentally verified every time you turn on your computer or use anything with a transistor (i.e. anything with a microchip). Now I already posted pretty much the exact same type of comment earlier today so I'll just copy and paste:

"I suppose I can make an attempt at at least conveying some of the difficulty in answering these questions. Imagine superposing two wavefunctions/light EM waves/whatever that are cos(wt) and -cos(wt). The result is a net oscillation of zero. Now in quantum mechanics if we have an area of space that has a zero net probability function (i.e. the wavefunction is zero in that area, i.e. a vacuum) it is not only physically but metaphysically impossible to say that there are zero particles their vs. two particles whose wavefunctions exactly cancel, vs. 4 particles whose wavefunctions exactly cancel or a billion particles whose wavefunctions exactly cancel you just can't tell. But it's not a situation of the form "this is unknowable, we're screwed" it's a situation of the form "it doesn't make a lick of difference, if we measure the net wavefunction in that region it'll be zero, this presents no problem for us in terms of prediction". Often a wavefunction, in general, is a complicated creature and we often deal with it by taking a Fourier transform (I would encourage you to look for a little java applet demonstrating what this is) and represent it as a sum of basis functions. So is there one particle there who has this crazy wave function? Or is there an infinite number of particles there whose summed wavefunction make this total wavefunction? *shrug* the math'll work out no matter what mental image you have in your head and really you can't make a philosophical point towards ANY OF THEM being irrefutably correct.

So I hope I'm conveying a sense of what it is very difficult to say "there is something there or there isn't something there". When we quantize space and essentially slap a quantum oscillator on each "grid point" those oscillators have a ground state energy that is not zero. Where there is energy there is Heisenberg's uncertainty which basically says that as long as the uncertainty in the energy of a system times the uncertainty in the time of measuerment are greater than some value it's all allowed. Which means when you ask "was their an electron-positron there" you can get an answer like "depends how long we take to measure". And if that seems to make no sense well I'd say the problem is the visualization/expectations of particles being these distinct pee like things shooting around and interacting with each other. At the end of the day you could say there's a quantized probability amplitude (or in the language of second quantization a certain energy assigned to) each "grid point". Any attempt to say, "well that amplitude was caused by three electrons with the following wavefunctions" vs. "6 billion electrons with the following wavefunction" is not wrong, it's flat out meaningless."

So do we "know" what an electron is doing around an atom? Well if you want to know how it is going to behave, what result we will get when we measure various aspects of it then yes. yes we do. We can predict it more accurately than any human theory have ever been able to predict anything before. Can you say WHERE is the electron? NO! Not because WE don't know but because an electron ISN'T a little point particle orbitting an accumulation of point particles (the nucleus). It's just not how the universe works. It's like asking "where is the ocean at this second". Had we been born in a universe without decoherence (the reason why the classical realm doesn't behave quantum mechanically) then we would have a much more malleable perspective on things. But yes, there are most certainly computer codes that you tell it the chemical compound and it will give you the EXACT electron distribution to whatever level of accuracy you like (although the more accurate the more computing power/time it takes). These kind of computations are done all the time.

 

[maverick_starstrider]

We can, in fact, prove that the situation ISN'T that there's this little pee-like thing shooting around which DOES have a certain position and momentum we just don't know what it is. This is called a hidden variable theory (i.e. there are actually concrete hidden variables ). (This is due to what is called the bell inequality). Well to be ultimately correct we can prove/have experimentally verified that any hidden variable theory would have to be non-local (nevermind what that means).

 

[DaveC426913]

We can, in fact, prove that the situation isn't that there's this little pee-like thing shooting around

I'm hoping you meant pea-like thing...

 

[maverick_starstrider]

I feel like Feynman probably talked about the relativistic hydrogen atom in his book QED which was written for layman. It might be worth checking out.

 

[maverick_starstrider]

I'm hoping you meant pea-like thing...

Lol. Yes, you would hope. Ah the horrors of stream of consciousness typing without spellcheck or review... I'm not going to fix it though. This thread could use a little levity.

 

[DaveC426913]

...stream of consciousness...

See now you're just making it worse...