Why doesn't the electron fall into the nucleus?

[alxm]

If an electron inside of the bohr radius (53pm) no longer feels an attraction to the proton, then presumbably there is no need to radiate energy. Doesn't it basically just sit around somewhere inside "about" this radius "most" of the time?

Now that's just crazy talk.

 

[granpa]

what radiates energy outside?

 

[feynmann]

Wrong. |\psi(\mathbf{x},t)|^2 is a particle's spatial probability density in quantum mechanics. Regardless of the interpretation. .

Wrong! It's deterministic in Bohm's version of QM. That's why Einstein says that "God does Not play dice with the universe". Bohm believed in "Copenhagen Interpretation", but after talking to Einstein, He changed his mind to "Hidden Variable" interpretation

--Note: pay attention to item #2;

<Principles of Copenhagen Interpretation> http://en.wikipedia.org/wiki/Copenhagen_interpretation

1. A system is completely described by a wave function ψ, which represents an observer's knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic. The probability of an event is related to the square of the amplitude of the wave function related to it. (Born rule, due to Max Born)
3. Heisenberg's uncertainty principle states the observed fact that it is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities.
4. Complementarity principle: matter exhibits a wave-particle duality. An experiment can show the particle-like properties of matter, or wave-like properties, but not both at the same time.(Niels Bohr)
5. Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.
6. The correspondence principle of Bohr and Heisenberg: the quantum mechanical description of large systems should closely approximate the classical description.

 

[malawi_glenn]

Wrong! It's deterministic in Bohm's version of QM. That's why Einstein says that "God does Not play dice with the universe". Bohm believed in "Copenhagen Interpretation", but after talking to Einstein, He changed his mind to "Hidden Variable" interpretation

--Note: pay attention to item #2;

<Principles of Copenhagen Interpretation> http://en.wikipedia.org/wiki/Copenhagen_interpretation

1. A system is completely described by a wave function ψ, which represents an observer's knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic. The probability of an event is related to the square of the amplitude of the wave function related to it. (Born rule, due to Max Born)
3. Heisenberg's uncertainty principle states the observed fact that it is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities.
4. Complementarity principle: matter exhibits a wave-particle duality. An experiment can show the particle-like properties of matter, or wave-like properties, but not both at the same time.(Niels Bohr)
5. Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.
6. The correspondence principle of Bohr and Heisenberg: the quantum mechanical description of large systems should closely approximate the classical description.

Let me then post what is said about Bohm interpretation on Wiki:

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

* The particles form a statistical ensemble, with probability density \rho(\mathbf{x},t) = |\psi(\mathbf{x},t)|^2

Although we don't know the position of any individual particle before we measure them, we find after the measurement that the statistics conform to the probability density function that is based on the wavefunction in the usual way.


You have still not said "thank you" to me for telling you the truth about atom sizes and Yukawa theory :-D

 

[alxm]

Wrong! It's deterministic in Bohm's version of QM.

You continue to confuse something being described statistically, i.e. as a probability with something being indeterministic. They're not the same thing, and assuming it is is simply wrong.

In fact, it's not only wrong, it's a completely bizarre mistake to make. Because the probabilities as viewed in the Copenhagen interpretation are the only example of truly non-deterministic probabilities anywhere. The probability of rolling a 7 on a pair of dice is 1/6. That doesn't mean that dice move indeterministically.

And again, |psi|^2 is a probability, regardless of your interpretation. Go read about the Bohm interpretation. The fact that |psi|^2 is a probability is fundamental postulate of quantum mechanics, from which the entire theory is derived. The normalization condition, for instance, follows immediately and trivially from it.

I'll have to concur with malawi_glenn here, I think you need to read an textbook on Quantum Mechanics. Popular-scientific accounts are not a substitute. Einstein quotes aren't a physical argument.

 

[Dadface]

Can somebody clarify something please?I just Wikigoogled to get a feeling of what Mr Bohm is all about and was informed that his interpretation gives the same theoretical predictions as other interpretations such as Copenhagen.Is that the case because the article had sort of disclaimers at the top including expressing the need for an expert on the subject.For a brief moment I thought I was that expert but then I came back to reality.

 

[malawi_glenn]

Can somebody clarify something please?I just Wikigoogled to get a feeling of what Mr Bohm is all about and was informed that his interpretation gives the same theoretical predictions as other interpretations such as Copenhagen.Is that the case because the article had sort of disclaimers at the top including expressing the need for an expert on the subject.For a brief moment I thought I was that expert but then I came back to reality.

we have zillions of old threads about Bohm Interpretation here.

 

[malawi_glenn]

I'll have to concur with malawi_glenn here, I think you need to read an textbook on Quantum Mechanics. Popular-scientific accounts are not a substitute. Einstein quotes aren't a physical argument.

Same holds with R. Feynman quotes, as someone said "In physics, we don't have any prophets".

 

[camboy]

Can somebody clarify something please?I just Wikigoogled to get a feeling of what Mr Bohm is all about and was informed that his interpretation gives the same theoretical predictions as other interpretations such as Copenhagen.Is that the case because the article had sort of disclaimers at the top including expressing the need for an expert on the subject.For a brief moment I thought I was that expert but then I came back to reality.

I attended a course on this at Cambridge which I found very useful. The lectures are online http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" .

 

[alxm]

Dadface, all interpretations give the same predictions because they're not really scientific theories (in the logical-positivist or Popperian sense). They amount to different explanations of what the wave function is.

The wave function is such that it results in a probability distribution of possible states. This is a fundamental postulate from which quantum mechanics is derived, not an interpretation thing. The interpretations amount to why this is the case.

The most obvious assumption (to me at least) would be that there are 'hidden variables'. We're getting a probability, not because the thing is truly random, but because there's a lack of data. A system has some state prior to it being measured, we just don't know what it is. I feel that's the 'obvious' conclusion, because that's the normal state of affairs when something is described probabilistically. As I said, there's a 1/6 chance of rolling a 7 on a pair of dice - but if you knew everything about that dice roll beforehand - then you should be able to predict exactly what the result should be.

The Copenhagen interpretation claims, on the other hand that there are no hidden variables. In other words, the state really is 'undefined' before it's measured. That's what quantum 'weirdness' is largely about, precisely because that's not how probabilities usually work. "Schrödingers Cat" was all about highlighting the weirdness of this interpretation, by taking it to the macroscopic level.

At the moment, nobody has been able to come up with any real experiment to prove (or disprove) hidden variables (much less determine what they are). Many have tried. So the end result is that no interpretation is experimentally testable - or practically significant. There's no practical difference between having a system that's non-deterministic, and one that's deterministic but in terms of things that cannot be measured.

Still, 'hidden variables' is an appealing idea. The problem is with Bell's theorem, which didn't prove or disprove hidden variables, but experimentally (the famous Aspect experiment, etc) showed that if they exist, that they cannot be local. Which is also very weird. (in other words, a kind of faster-than-light interaction is going on).

Personally, I'm mostly an adherent of malawi_glenn's quote: "Only amateurs concern themselves with interpretations". It makes no difference what interpretation you use. I don't even see why you'd bother thinking about it - unless it can be experimentally disproven, it's metaphysics or theology to me, and no more interesting than debating how many angels can dance on the head of a pin.

I'm not entirely certain interpretations are needed. They all hinge on the idea of probabilities that arise from measurement. But that implies a separation into 'measuring' and 'measured' systems which isn't really possible (imho). The wave function of the universe as a whole never gets 'measured' and would have a perfectly deterministic time evolution.

 

[Dadface]

Thank you malawi glen.I should have searched first. I can be so dopey at times.

Thank you camboy.That looks brilliant.I just want a taster of what its all about and I think I have got that already just by looking at the opening bits.When I get time I will look at the rest.

And thank you alxm.I saw your message at the moment I posted this .I have to go now and I look forward to reading it later.

 

[feynmann]

Same holds with R. Feynman quotes, as someone said "In physics, we don't have any prophets".

Suppose you lived in Amazon and you have never heard about Einstein's relativity or Schrodinger Equation. *** Can you figure it out by yourself? I doubt. That why they got Nobel prize but we don't

 

[malawi_glenn]

Suppose you lived in Amazon and you have never heard about Einstein's relativity or Schrodinger Equation. *** Can you figure it out by yourself? I doubt. That why they got Nobel prize but we don't

And the reason for they got Nobel prize was that other physicists can verify their results independently etc. Just because a guy who has got the Nobel Prize does not per automatic make him pass all peer reviews, everything has to be tested.

The person I quoted was Weinberg, if you know who that is ...

and your "analogy" is not even applicable, it is not the amazon tribe guys who give away Nobel Prizes.. LOL

 

[DrChinese]

At the moment, nobody has been able to come up with any real experiment to prove (or disprove) hidden variables (much less determine what they are). Many have tried. So the end result is that no interpretation is experimentally testable - or practically significant. There's no practical difference between having a system that's non-deterministic, and one that's deterministic but in terms of things that cannot be measured.

Still, 'hidden variables' is an appealing idea. The problem is with Bell's theorem, which didn't prove or disprove hidden variables, but experimentally (the famous Aspect experiment, etc) showed that if they exist, that they cannot be local. Which is also very weird. (in other words, a kind of faster-than-light interaction is going on).

I wouldn't agree with this statement. There are a number of very powerful experiments which disprove ALL hidden variable interpretations. Please keep in mind that advocates of some of these interpretations do not accept this evidence, and in some cases those same advocates assert they do not apply (for example Bohmians generally class BM/dbb theory as contextual and therefore these No-Go theorems don't apply). So I will let you form your own opinion. However, these are some of the recent proofs:

Experimental test of quantum contextuality in neutron interferometry: Test of the Kochen-Specker theorem.

http://www.iop.org/EJ/article/1367-2630/11/3/033011/njp9_3_033011.html: Hardy's.

Leggett's theorem without inequalities: Leggett's.

Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system: Don't forget the GHZ theorem!

Mermin's 1990 summary on No-Go Theorems

So all of these are completely independent of Bell, and do not require the assumption of locality. Not trying to bait the Bohmians with these, as we know already they don't acknowledge any of it.

 

[feynmann]

I wouldn't agree with this statement. There are a number of very powerful experiments which disprove ALL hidden variable interpretations. Please keep in mind that advocates of some of these interpretations do not accept this evidence, and in some cases those same advocates assert they do not apply (for example Bohmians generally class BM/dbb theory as contextual and therefore these No-Go theorems don't apply).

So, in your opinion, what is the way to go? What are we to do with Schrodinger's cat?

 

[granpa]

If the whole electron cloud is spinning, this means the orbital angular momentum in the ground state of hydrogen is not zero. And it also radiates energy outside.

I'm not sure you understood me. here is what I was talking about:
https://www.physicsforums.com/showpost.php?p=1287217&postcount=8

 

[ytuab]

I'm not sure you understood me. here is what I was talking about:
https://www.physicsforums.com/showpost.php?p=1287217&postcount=8

(if we could think of the electron in the H atom as a continuous distribution of charge, it shouldn't radiate.)

--- Your above hydrogen atom model is so interesting, and points out an important thing.

But you forget one thing.
If the whole hydrogen atom is stopping still, it does not radiate as you say.
But actually the whole hydrogen atom is oscillating and moving about, So it loses energy by emitting electromagnetic waves in your model.

 

[granpa]

the electron doesn't have to be motionless to not radiate. it just has to be smeared out over the whole orbit.

whether the hydrogen atom as a whole is moving or oscillating or not is irrelevant to the topic at hand which is 'why doesn't the electron fall into the nucleus'. I have no idea why you would even bring it up.

a mass of warm hydrogen atoms will indeed radiate heat radiation until it cools and the atoms are no longer moving. so what?

 

[alxm]

the electron doesn't have to be motionless to not radiate. it just has to be smeared out over the whole orbit.

Only electrons just don't act like that.

To begin with, the Thomas-Fermi model, and by extension, any such simple electrostatic model that assumes electrons have constant momentum, cannot form chemical bonds and stable molecules. That's even been rigorously mathematically proven. (The Thomas-Fermi theory of atoms, molecules and solids, EH Lieb, B Simon - Adv. Math, 1977)

There is no classical or semi-classical model of atoms that comes even close to being useful, even as an approximation.

 

[granpa]

I don't know anything about the Thomas-Fermi model and I very much doubt its anything like what I'm describing.

what on Earth do you mean by 'constant momentum'? do you mean constant angular momentum?

and yes I am sure that chemical bonds (electron pairing) require a quantum mechanical explanation. so what? my point was simply to show how the electron can keep from falling into the nucleus

and now that I think about it, what do you mean 'electrons don't act like that'? that's pretty much what quantum mechanics is all about. the electron becomes smeared out over the whole atom due to the uncertainty principle.but these discussions go round and round and nothing is ever resolved. whatever your answers are there is nothing I can add at this point that others can't plainly see for themselves.

 

[Vanadium 50]

Personally, I'm mostly an adherent of malawi_glenn's quote: "Only amateurs concern themselves with interpretations". It makes no difference what interpretation you use. I don't even see why you'd bother thinking about it - unless it can be experimentally disproven, it's metaphysics or theology to me, and no more interesting than debating how many angels can dance on the head of a pin.

It was originally me. And I agree - until you can measure it, arguing about something can be many things, but science is not one of them.

I'd go further and say that fundamental question interpretations are asking is "what is happening when we aren't measuring anything"? Of course, by construction, this is unanswerable.

I wouldn't agree with this statement. There are a number of very powerful experiments which disprove ALL hidden variable interpretations.

I agree with this.

 

[alxm]

I don't know anything about the Thomas-Fermi model and I very much doubt its anything like what I'm describing.

what on Earth do you mean by 'constant momentum'? do you mean constant angular momentum?

Sounds like a hasty conclusion if you don't know anything about it. And yes, it means both momentum and angular momentum. Such as would be the case with an electronic 'cloud' at a fixed distance, which seemed to be what you envisioning.

and yes I am sure that chemical bonds (electron pairing) require a quantum mechanical explanation. so what? my point was simply to show how the electron can keep from falling into the nucleus

But if you use an un-physical model to do so, it doesn't actually show anything.

and now that I think about it, what do you mean 'electrons don't act like that'? that's pretty much what quantum mechanics is all about. the electron becomes smeared out over the whole atom due to the uncertainty principle.

And that's part of the point I was making. If you think a quantum mechanical description of an bound electron simply means replacing a point charge with a static charge-density 'cloud', then you're simply wrong, because you have to account for the complicated dynamics of motion of the electrons. Even though the charge-density distribution is constant, electrons move, dynamically and have substantial kinetic energy. Any model based soley on electrostatic interactions is going to fail badly.

 

[WaveJumper]

And that's part of the point I was making. If you think a quantum mechanical description of an bound electron simply means replacing a point charge with a static charge-density 'cloud', then you're simply wrong, because you have to account for the complicated dynamics of motion of the electrons. Even though the charge-density distribution is constant, electrons move, dynamically and have substantial kinetic energy. Any model based soley on electrostatic interactions is going to fail badly.

This isn't suggesting that electrons "move" continuously, right?

 

[RonL]

I find this very interesting, and the term electron cloud, I really like.

Because I only have a limited understanding of all this, I try to build a picture in my mind of something large enough to interact with, in this case I see the atom the size of a golf ball. At this size if we take an atom (say copper) with a single electron in the outer shell, the speed of the outer electron circling the nucleus, by rough math, is over 120 billion revolutions per second. At this size the electron and nucleus will still be too small to see, in fact the outer shell would be invisible, but feel like a solid object.

The question I have is, has anyone ever purposed a therory of air or a gas like substance being bound inside the valence shell, and equally divided between the other shells, I see this like compressed air inside a basketball. Heat would have an effect and an expansion and contraction would take place.
At the speed an electron moves, it seems a seal barrier might exist, and all shells would react to any energy change.

Just a thought that popped into my brain as I was reading through the thread, I did look at some other threads that had been linked by Marlon (I think). One of those threads mentioned "Kato's Theorem" but I have not found anything yet.

Don't worry, I'm sure this will be my only post here.

Ron

 

[malawi_glenn]

It was originally me. And I agree - until you can measure it, arguing about something can be many things, but science is not one of them.

That is one of my favourite quotes of all times :!)

 

[WaveJumper]

The question I have is, has anyone ever purposed a therory of air or a gas like substance being bound inside the valence shell, and equally divided between the other shells, I see this like compressed air inside a basketball. Heat would have an effect and an expansion and contraction would take place.
At the speed an electron moves, it seems a seal barrier might exist, and all shells would react to any energy change.

Ron

Hi RonL,

The thing you appear to have overlooked is that "air" is made of molecules, which are themselves composed of atoms.

It's counter-intuitive but a bound electron is not stationary. And it's not moving either.

 

[Matterwave]

I wouldn't agree with this statement. There are a number of very powerful experiments which disprove ALL hidden variable interpretations.

You don't mean to say local hidden variable? Even unlocal hidden variable interpretations have been disproven? I was unaware of this.

 

[RonL]

Hi RonL,

The thing you appear to have overlooked is that "air" is made of molecules, which are themselves composed of atoms.

It's counter-intuitive but a bound electron is not stationary. And it's not moving either.

Thanks for the reply,
The mention of "air or gas like substance" was only to help build a thought.

I'm a long way from knowing enough to throw anything else out, but when I read about density of black holes, my little pea brain thinks something has to fill the voids from the nucleus to the outer shell.

Guess I better get back to things i can see.

 

[feynmann]

Hi RonL,

The thing you appear to have overlooked is that "air" is made of molecules, which are themselves composed of atoms.

It's counter-intuitive but a bound electron is not stationary. And it's not moving either.

What about particle in a box? http://en.wikipedia.org/wiki/Particle_in_a_box
<Particle in a box> is a bound state and its potential energy is all zero.
It's absurd to suggest that it's Not moving in the box. What else can it do in the box, just sit there?

 

[Count Iblis]

What about particle in a box? http://en.wikipedia.org/wiki/Particle_in_a_box
<Particle in a box> is a bound state and its potential energy is all zero.
It's absurd to suggest that it's Not moving in the box. What else can it do in the box, just sit there?

You have to define pecisely what you mean by "moving". So, you need to write down some observable, e.g. the momentum operator, and look at the expectation value. In case of a particle in a box in some energy eigenstate, the expectation value of the momentum is zero. The particle in an energy eigenstate is in a superposition of two states with opposite momenta.