Atom Shape: Experiments, Spheres & Cubes in Physics

[Chaos' lil bro Order]

Hello,

Is there any reason to believe an atom, say Hydrogen, is spherical via experiments, or is this merely a model for us to visualize with?

Furthermore, can one prove that an atom is not a cube?

Finally, is there any model in physics that can account for how a photon is emitted from a deexcited electron? Or do we still simply say that the photon is equal to the energy level drop and leave it at that?

Thanks.

 

[HallsofIvy]

First you will have to say exactly what you mean by "the shape of an atom" at the quantum level.

 

[ghostmonkey]

Is there any reason to believe an atom...is spherical...? ...can one prove that an atom is not a cube?

The sphere is a perfect distribution. Anything otherwise would require a greater amount of energy to create, and would therefore deviate from equilibrium.

 

[ZapperZ]

The sphere is a perfect distribution. Anything otherwise would require a greater amount of energy to create, and would therefore deviate from equilibrium.

You may want to look at the geometry of the p,d,f, etc. orbitals before you say that.

Zz.

 

[Manchot]

Is there any reason to believe an atom, say Hydrogen, is spherical via experiments, or is this merely a model for us to visualize with?

There's no reason to believe that it's spherical: even the ground state wavefunction, while spherically symmetric, is not spherical.

Furthermore, can one prove that an atom is not a cube?

Well, none of the energy eigenstates of the hydrogen atom are cubes, but if you chose the appropriate linear combination of states, you should be able to find a cube-shaped one.

Finally, is there any model in physics that can account for how a photon is emitted from a deexcited electron? Or do we still simply say that the photon is equal to the energy level drop and leave it at that?

Well, from a logical standpoint, if you're only considering electromagnetic potentials, conservation of energy says that an electron falling to a lower energy state has to give its energy up somewhere. In this case, it goes to the EM field in the form of a photon. More formally, quantum electrodynamics (QED) describes the emission of a photon.

 

[Chaos' lil bro Order]

Well, from a logical standpoint, if you're only considering electromagnetic potentials, conservation of energy says that an electron falling to a lower energy state has to give its energy up somewhere. In this case, it goes to the EM field in the form of a photon. More formally, quantum electrodynamics (QED) describes the emission of a photon.

So there is no physical model of geometry that can show how an electron's energy drop is transferred into a photon then?

 

[Manchot]

So there is no physical model of geometry that can show how an electron's energy drop is transferred into a photon then?

QED is the physical model, but it's not really a geometric one.

 

[Ubern0va]

QED is the physical model, but it's not really a geometric one.

I think he was looking for the formal description. I too was wondering the same thing: When we say "a human eats a sandwich", there are a lot of details that we don't include but it still makes sense to us. Saying, "an electron emits a photon", may make sense to the electron itself (if we personified it), but that understanding doesn't necessarily transfer to humans. This happened often for me when I took High School Physics, because it isn't advanced enough to provide common sense answers for these more complex areas (I use "common sense" loosely of course) - a lot of it just "magically happened". QED seems like the best bet, do you have any good resources on the subject Manchot (or anyone)?

 

[Chaos' lil bro Order]

I just read Feynman's book 'QED the Theory of Light and MAtter' and there was no mention of how the photon is emitted. The book mostly covers feynman diagrams showing the probability amplitudes of a photon taking route A vs. B, etc. I have always wanted a physical geometric explanation, is that asking too much of physicists?

 

[Farsight]

I think you're missing something about the shape of an atom, Chaos. The thing is, if you say something is spherical, that would imply that it has a spherical surface. That then implies that it has a surface. But you know this isn't right if you think of a black hole. All that's really there is some singularity. It's like a point particle. Sure, the event horizon is spherical, but there's nothing at this event horizon, it's just a place where gravity exceeds a particular measure. And it doesn't make much sense to say the black hole is a sphere. Or any other shape.

 

[jtbell]

I just read Feynman's book 'QED the Theory of Light and MAtter' and there was no mention of how the photon is emitted. The book mostly covers feynman diagrams showing the probability amplitudes of a photon taking route A vs. B, etc. I have always wanted a physical geometric explanation, is that asking too much of physicists?

At this point in time, yes, that is asking too much of physicists. QED is as far as we know how to go. Maybe someday physicists will agree on a "deeper" theory that underlies QED (more precisely the unified electroweak theory that includes it) and QCD (for quark-gluon interactions). It might be string theory. It might be something else.

 

[Chaos' lil bro Order]

I cannot accept any theory as complete until it can be represented geometrically. I am frustrated that some people are posting scientific dogma without seriously contemplating my question. Is there no theory or white paper outlining how photons and electrons interact in the real, 'physical' terms of geometry?

Are we still stuck at Feynman's 'Magic bag' analogy?

 

[Epicurus]

What is real and physical. These are simply models that agree with experiment. No one has ever seen a photon!

We cannot not say that the hydrogen atom is spherically symmetric, no one has or ever will observe a wavefunction. We may only say things about observables. The only observables are transition energies in the form of detected photons. This leads to certain conclusions about transition probabilities between the possible 'states' an electron may be in in a coulomb field. Observation supports the lowest state being one with zero angular momentum (when the inherent angular momentum of the elctron is taken into account).

 

[RogerPink]

An accelerating electron produces EM radiation. In quantum mechanics, when an electron shifts energy levels it's moving to a lower (or higher) angular momentum, which is an acceleration.

 

[ZapperZ]

An accelerating electron produces EM radiation. In quantum mechanics, when an electron shifts energy levels it's moving to a lower (or higher) angular momentum, which is an acceleration.

Er... what you are saying are highly incompatible with each other.

1. An accelerating electron produces EM radiation

This is fine.

2. In quantum mechanics, when an electron shifts energy levels it's moving to a lower (or higher) angular momentum, which is an acceleration.

While this is also true, you cannot equate this with "accelerating electron produces EM radiation". This is because (i) an electron in an "orbital" is not accelerating; if it is, it would be radiating (ii) an electron making an energy transition is also not "accelerating" - there is no dynamics describing such a transition. So you or I cannot say that this electron is undergoing an acceleration.

Note that I can also produce light without having to make any atomic transition. I can do that simply by having an electron in a conduction band recombine into a hole in the valence band. That is, primitively, what is going on when light is created in your LED's.

Zz.

 

[Careful]

** an electron making an energy transition is also not "accelerating" - there is no dynamics describing such a transition. So you or I cannot say that this electron is undergoing an acceleration. **

Huh ?? Of course there is a description of the transition. ``Just'' start with a stationary state, make a full non perturbative calculation within QED (or Barut self field - there will be agreement up to fifth order in alpha) with this state as initial data and the EM field in the vacuum state (say) and you can perfectly follow what is happening (if you interpret psi^2 as a density).

In the same way you could study photon formation within Barut Self field (lets do that, it is easier, well defined and agrees up to high accuracy) during such transition. Of course this is a LOCAL phenomon, since QFT as well as BSF are local theories (the only non-local thing is this idiotic Von Neumann postulate). The problem is that this is hard to do and that the Feynman plane wave scattering diagrams are obscuring the local character of the dynamics.

The same comments apply to your so called ``non local´´ phonons in lattice theory.

Careful

 

[ZapperZ]

** an electron making an energy transition is also not "accelerating" - there is no dynamics describing such a transition. So you or I cannot say that this electron is undergoing an acceleration. **

Huh ?? Of course there is a description of the transition. ``Just'' start with a stationary state, make a full non perturbative calculation within QED (or Barut self field - there will be agreement up to fifth order in alpha) with this state as initial data and the EM field in the vacuum state (say) and you can perfectly follow what is happening (if you interpret psi^2 as a density).

There is no dynamics during the transition. Could you give me the equation of motion during the instant that the atom went from one energy state to another?

The same comments apply to your so called ``non local´´ phonons in lattice theory.

Careful

Er... what "comment" about "non local phonons in lattice theory"? Are you back to your habit of putting words into people's mouths again?

Zz.

 

[Son Goku]

I cannot accept any theory as complete until it can be represented geometrically. I am frustrated that some people are posting scientific dogma without seriously contemplating my question. Is there no theory or white paper outlining how photons and electrons interact in the real, 'physical' terms of geometry?

Are we still stuck at Feynman's 'Magic bag' analogy?

What do you mean by "physical terms of geometry"?

What kind of explanation do you desire?

 

[Careful]

**There is no dynamics during the transition. Could you give me the equation of motion during the instant that the atom went from one energy state to another? **

There is no ``instant'' that the electron jumps from one energy level to another (otherwise you exclude the logical possibility of dynamics in the same way that dr Chinese proves the existence of entanglement); that is a simplified QM picture for kids emerging from better calculations in QFT. You could calculate the wave function and then set up a Bohmian interpretation, or you could be smarter and take a self interacting Dirac soliton-like solution (in which the coulomb wave functions would be solutions of the linear equation) and follow the ``center of mass trajectory´´ of the latter...

**
Er... what "comment" about "non local phonons in lattice theory"? Are you back to your habit of putting words into people's mouths again? **

And you are in self denial again ? I and others have seen you make plenty of comments about phonons being non local lattice vibrations which is clearly nonsense (I know, they teach you that in the QM courses, but still ...).

Careful

 

[ZapperZ]

There is no ``instant'' that the electron jumps from one energy level to another (otherwise you exclude the logical possibility of dynamics in the same way that dr Chinese proves the existence of entanglement); that is a simplified QM picture for kids emerging from better calculations in QFT. You could calculate the wave function and then set up a Bohmian interpretation, or you could be smarter and take a self interacting Dirac soliton-like solution (in which the coulomb wave functions would be solutions of the linear equation) and follow the ``center of mass trajectory´´ of the latter...

Again, you did not answer my question. Please show me the "dynamics" of the equation of motion of such a transition to allow one to conclude that, yes, the electron was accelerating during the transition.

**
Er... what "comment" about "non local phonons in lattice theory"? Are you back to your habit of putting words into people's mouths again? **

And you are in self denial again ? I and others have seen you make plenty of comments about phonons being non local lattice vibrations which is clearly nonsense.

Careful

I'm not in self-denial. You are self-delusional. What phonons? I'm looking over this thread and I see no "phonons" being mentioned by me. Please point to me explicitly where I mentioned phonons in here till you brought it up. I only made two postings in messages #4 and #15 before you stepped in. Where did I mentioned anything about phonons?

Zz.

 

[J77]

Hello,

Is there any reason to believe an atom, say Hydrogen, is spherical via experiments, or is this merely a model for us to visualize with?

Furthermore, can one prove that an atom is not a cube?

Finally, is there any model in physics that can account for how a photon is emitted from a deexcited electron? Or do we still simply say that the photon is equal to the energy level drop and leave it at that?

Thanks.

By the shape of the atom, do you mean the nucleus?

The shape distribution of the protons and neutrons?

Or do you include the orbits of the electrons also?

Or, more exactly, the electron orbitals?

 

[RogerPink]

While this is also true, you cannot equate this with "accelerating electron produces EM radiation". This is because (i) an electron in an "orbital" is not accelerating; if it is, it would be radiating (ii) an electron making an energy transition is also not "accelerating" - there is no dynamics describing such a transition. So you or I cannot say that this electron is undergoing an acceleration.

I said If you go from one angular momentum to another (one orbital to another), it's an acceleration. I never said an electron in an orbital produces a photon.

 

[Careful]

**Again, you did not answer my question. Please show me the "dynamics" of the equation of motion of such a transition to allow one to conclude that, yes, the electron was accelerating during the transition.**

I DID anwser your question ! You demand that I should type in the formula is ridiculous:
(a) every one who understand this can do it (and the formula in the self field case takes a line or two)
(b) to really make the calculation, I should do a perturbative expansion and an infinite mode renormalization in each step.
(c) So what one really should do is a finite element analysis and be careful about convergence, mass and charge renormalization and so on.

So, duh, sorry that I do not type that out here However, that does not take away that YOUR answer basically is wrong.

**
I'm not in self-denial. You are self-delusional. What phonons? I'm looking over this thread and I see no "phonons" being mentioned by me. Please point to me explicitly where I mentioned phonons in here till you brought it up. I only made two postings in messages #4 and #15 before you stepped in. Where did I mentioned anything about phonons? **

Not here of course you silly boy, you did that some while ago in another thread. Let's not just get involved again because simply I do not deem it useful for neither of us.

So let's concentrate on the content:
(a) are phonons local objects or not , or better is interactions with phonons local ?
(b) do you believe that QFT implies an immediate jump from one orbital level to another ?

Careful

 

[ZapperZ]

**Again, you did not answer my question. Please show me the "dynamics" of the equation of motion of such a transition to allow one to conclude that, yes, the electron was accelerating during the transition.**

I DID anwser your question ! You demand that I should type in the formula is ridiculous:
(a) every one who understand this can do it (and the formula in the self field case takes a line or two)
(b) to really make the calculation, I should do a perturbative expansion and an infinite mode renormalization in each step.
(c) So what one really should do is a finite element analysis and be careful about convergence, mass and charge renormalization and so on.

Er.. you call this the answer to my question? It isn't. All you did was claim to have the equation of motion for such a transition, which I haven't seen. You are more than welcome to cite a specific equation of a text or a paper, and I will try to go find it. Or if you want, give me the exact equation of motion of a hydrogenic transition from n=2, l=1 to n=1, l=0, including the time scale for such a transition that has been verified.

Not here of course you silly boy, you did that some while ago in another thread.

Point to me WHERE. You'll understand if I do not believe or trust your "perception" of what has been said.

Let's not just get involved again because simply I do not deem it useful for neither of us.

Then YOU shouldn't have brought this up in the first place, or are you attempting to re-interpret that too?

So let's concentrate on the content:
(a) are phonons local objects or not , or better is interactions with phonons local ?
(b) do you believe that QFT implies an immediate jump from one orbital level to another ?

Careful

What does this have anything to do with the topic? For some WEIRD reason, out of the blue, you decided to take a swipe at me and bring out some mumbo-jumbo phonon stuff that is irrelevant to this thread. Are you attempting to derail this thread by resurrecting another one of those "local" and "non-local" thread?

Zz.

 

[ZapperZ]

I said If you go from one angular momentum to another (one orbital to another), it's an acceleration. I never said an electron in an orbital produces a photon.

Then you may need to show me where in the textbooks that is mentioned.

Remember that if you open your standard QM text, the "transition" is only given via the Fermi Golden Rule. All you get out of that are info about the initial and final states and probability of transition from the matrix element.

Zz.

 

[RogerPink]

Then you may need to show me where in the textbooks that is mentioned.

Are you implying that an electron that is in L=1 and then transitions to L=2 experiences no angular acceleration? Do we really need a textbook for this?

 

[Careful]

**Er.. you call this the answer to my question? It isn't. All you
did was claim to have the equation of motion for such a transition,
which I haven't seen. You are more than welcome to cite a specific
equation of a text or a paper, and I will try to go find it. Or if
you want, give me the exact equation of motion of a hydrogenic
transition from n=2, l=1 to n=1, l=0, including the time scale for
such a transition that has been verified. **

Sorry Zapper, but if you understood BM or BSF (which you did not if
I read your comments about SED) then you know that these numbers
come out right by DEFINITION of the single event dynamics. Now I
presume that you have the intelligence to write down the Dirac
equation for an electron coupled to an external spherical potential
(from the nucleus ) and self coupled by a maxwell field
determined by the current of the latter spinor field. If this is
too difficult, you might want to look up any text on BSF. Now in
the case of BM, you only second quantize the radiation field as a
first approximation and study the current equation for the latter.
So basically I GIVE the equation to you.

*** What does this have anything to do with the topic? For some
WEIRD reason, out of the blue, you decided to take a swipe at me and
bring out some mumbo-jumbo phonon stuff that is irrelevant to this
thread. Are you attempting to derail this thread by resurrecting
another one of those "local" and "non-local" thread? **

Now, now ... anyone knows that this ultimately goes about the
measurement problem, it is like that when you want to talk intelligently about something.
However, the other interactions involved are all
local in QFT, as well as the decaying of the atomic states.
Therefore, it does matter wether you consider this mumbo jumbo
phonon-phonon interaction to be local or not -since this goes about basic
understanding of QFT. So, what is it going to be ??

Careful

 

[Careful]

Are you implying that an electron that is in L=1 and then transitions to L=2 experiences no angular acceleration? Do we really need a textbook for this?

Right, Zapper needs textbooks ...

Careful

 

[ZapperZ]

Are you implying that an electron that is in L=1 and then transitions to L=2 experiences no angular acceleration? Do we really need a textbook for this?

There is a change in angular momentum quantum number. That is what your textbooks tell you. But you are using a purely classical analogy and making an inference that this is what is going on in such a transition. My point here is that your standard QM doesn't tell you such a thing. There isn't even a clear definition of what an "acceleration" is in QM.

Now, we CAN test this classically. We know (i.e. we have both theoretical descriptions and experimental observations) what happens when an electron in a cyclotron changes from one circular "orbit" into another. I could even show you the radiation we get when an electron in a Lamour path progressively gets smaller and smaller - this happens all the time when you introduce quadrupole magnets in a particle accelerator to focus a beam of charged particles. There are clear signatures of such a "transition" from the radiation being emitted. You don't get this in a typical "energy" transition, certainly not when an electron anhilates with a hole in the valence band.

You could argue ".. but electron in such a circular path are "classical" particles and cannot be compared with that in stationary orbits in an atom!" To which I would reply : That's My Whole Point! The analogy here in using what we know from classical mechanics doesn't quite fit in here.

Zz.

 

[ZapperZ]

**Er.. you call this the answer to my question? It isn't. All you
did was claim to have the equation of motion for such a transition,
which I haven't seen. You are more than welcome to cite a specific
equation of a text or a paper, and I will try to go find it. Or if
you want, give me the exact equation of motion of a hydrogenic
transition from n=2, l=1 to n=1, l=0, including the time scale for
such a transition that has been verified. **

Sorry Zapper, but if you understood BM or BSF (which you did not if
I read your comments about SED) then you know that these numbers
come out right by DEFINITION of the single event dynamics. Now I
presume that you have the intelligence to write down the Dirac
equation for an electron coupled to an external spherical potential
(from the nucleus ) and self coupled by a maxwell field
determined by the current of the latter spinor field. If this is
too difficult, you might want to look up any text on BSF. Now in
the case of BM, you only second quantize the radiation field as a
first approximation and study the current equation for the latter.
So basically I GIVE the equation to you.

OK, can someone else tells me if he has answered my question?

If appears that something that is so "simple" can't be written down, or even pointed out directly. All I asked for is a silly equation of motion when the electron leaves the n=2, l=1 state and goes to the n=1, l=0 state. I'd like to see that path, and the time it takes to make that path. Your numerous grandstanding here hasn't produced even that.

*** What does this have anything to do with the topic? For some
WEIRD reason, out of the blue, you decided to take a swipe at me and
bring out some mumbo-jumbo phonon stuff that is irrelevant to this
thread. Are you attempting to derail this thread by resurrecting
another one of those "local" and "non-local" thread? **

Now, now ... anyone knows that this ultimately goes about the
measurement problem, it is like that when you want to talk intelligently about something.

No it isn't. This ISN'T about the "measurement problem". Look at the OP, and then look at the post that I responded to. I'm surprised you didn't dig even a little deeper and start proclaiming that this is also about "philosophy".

However, the other interactions involved are all
local in QFT, as well as the decaying of the atomic states.
Therefore, it does matter wether you consider this mumbo jumbo
phonon-phonon interaction to be local or not -since this goes about basic
understanding of QFT. So, what is it going to be ??

Careful

I see you still cannot produce (and have avoided responding) the evidence on where I have said such things about "phonons" being "non-local". If you cannot do such a thing, then all your diatribe directed towards me regarding such issues is MOOT because it is based on a faulty premise.

You have managed to derail what is supposed to be a straightfoward standard QM thread. Since you have continued to refuse to address the two points that I have repeatedly asked [(i) produce an explicit form of the equation of motion for the transition and (ii) where I have said such things about phonons], then I will assume (with good reasons) that such things are not forthcoming. This thread is done.

Chaos and RogerPink: Please PM me if you would like to reopen this thread with your followup or responses.

Zz.

 

[msohl]

interations

I cannot accept any theory as complete until it can be represented geometrically. I am frustrated that some people are posting scientific dogma without seriously contemplating my question. Is there no theory or white paper outlining how photons and electrons interact in the real, 'physical' terms of geometry?

Are we still stuck at Feynman's 'Magic bag' analogy?

two things interacting is not known as a physical phenomenon. so every where we describe it different (interacting two objects). A phenomenon is any observable occurrence.
when in normal scales we say "when a ball hits a wall it folds it to some degree", then the wall being folded is a phenomenon which physics is interested in, and not the interaction which is only an assumption. now not typically something to fold but to change or variant, you know.
now the wall that folds, there is something observable about this folding. having this potential to fold is one of its invariance property and to what degree it is being folded, in another sense, is an observable quantity of the wall.