Atom Orbitals: Exploring the Electron Cloud Theory

[PhaseShifter]

Force due to interaction of field potentials is what is causing acceleration and deceleration. If there was any loss or gain of energy due to radiation, then some of the most basics and tested principles in physics would turn out to be invalid, like 'conservation of energy'. So, do you mean to say these equations have error proportional to "synchrotron radiation" or what?

This is because the Bohr model doesn't adequately explain the structure of an atom. A purely classical model would not have quantized energy states. A purely quantum model would not have "acceleration" or "deceleration", but rather an instantaneous jump from one state to another (or possibly a slower transition where the electron occupies both states simultaneously, but we can ignore that for now).

While the equations associated with the Bohr model do a brilliant job of explaining the spectroscopic series that were known at the time (and predicting the Lyman series as well), the model itself is a bundle of contradictions. Orbiting particles would continuously radiate energy, and thus couldn't have quantized energy levels at all without violating conservation of energy.

So while Bohr's concept was brilliant in one sense, in others it was the conceptual equivalent of patching a wrecked car with duct tape and hoping it ran until you bought a new one. People knew it was wrong from the beginning, so it got modified a few times and dumped faster than universities could turn out Ph.D.s.

 

[varga]

If we ignore the radiation, and treat the system completely classically, then at the point to which you refer, it's kinetic energy is 1 eV .. it's velocity is sqrt(2eV/m_e) .. whatever that works out to.

Ok, something like that, but the point is that this radiation IS indeed ignored. Simply because this voltage difference is very specific distance and electron has to have very specific acceleration to get to that point in a very particular and predefined time interval, determined by it's initial position and velocity vector.

There are no equations where this radiation is taken into account as some sort of error correction as with special relativity 'effects'. This radiation exist in physics on its own and is not accounted for anywhere else, I believe, but I'll stand corrected.

Of course, the KE and the velocity are both a bit smaller since some energy has been radiated by the electron.

Ok, that's all I wanted to establish. So, this radiation would actually make Coulomb law inaccurate, and this error would be more prominent with more rapid accelerations and decelerations, right?

See the Larmor formula link I posted earlier to see how to calculate how much .. I am guessing it is small, but I don't really know for sure. I don't have time to work out the answer right now.

Ok, this may be the answer to some questions above.

We are pretty far afield from your original question/point .. are we going to get back there any time soon?

Yes, at this point I'm happy to accept this radiation, though if you don't mind I'd like to secretly hold an opinion mechanics behind it is rather due to some zero-point energy, vacuum disturbances or aether gargoyles, since I find anything else more absurd.
BACK TO THE POINT:
My original line of thought is that if electrons orbited nucleus with continuous trajectories (yes, with angular momentum), then Quantum Mechanics would still stay just the same and all the equations would work just the same, radiation or not. There would still be electron clouds and all the orbitals, electron pairing and everything. All this should theoretically and practically still be possible and there is nothing in Schrödinger equation or any other QM equation that would actually prohibit electrons to move in continuous trajectories.

One of the most compelling reasons for me to believe these electrons indeed circle nucleus and make tiny electric loops is because that is how magnetism in permanent magnets is explained and I do not know about any other suggested theory since this explanation seem to be accepted across all the fields, including SR and QM. Again, this is not discussion against QM, it is about continuous trajectories and possibility that numerical integration and classical electrodynamics equations might be able to model atom after all, TOO. There is this software I came across that claims to be doing molecular and atom dynamics, atom bonding, atom orbital configurations and all that as real-time simulation with forces, velocities and all the kinetics instead of statistics and regular QM equations. Shall I find it again? There is also a paper on this "discovery", as they call it, where they explain all the equations and how it works.

 

[SpectraCat]

Ok, that's all I wanted to establish. So, this radiation would actually make Coulomb law inaccurate, and this error would be more prominent with more rapid accelerations and decelerations, right?

No, it certainly does not make Coulomb's law in any way inaccurate. Coulomb's law describes the electrostatic interaction between charges .. it says nothing about velocities or accelerations of particles (except implicitly by defining the shape of the electrostatic potential). The phenomena of EM radiation being emitted from charges under acceleration is in the domain of electrodynamics.

Yes, at this point I'm happy to accept this radiation, though if you don't mind I'd like to secretly hold an opinion mechanics behind it is rather due to some zero-point energy, vacuum disturbances or aether gargoyles, since I find anything else more absurd.

Ok, we'll just keep on using free-electron lasers for our research, if you don't mind. (we make the graduate students feed the gargoyles) By the way, the vacuum inside such lasers is very good, so there is no chance of the radiation coming from collisions. Just one more little point .. you said you knew about free-electron lasers, so I just was assuming you know that their tuning range extends *continuously* from the microwaves out to hard-UV and x-rays. It's pretty hard to come up with a model based on collisions with gas molecules that could explain that.

BACK TO THE POINT:
My original line of thought is that if electrons orbited nucleus with continuous trajectories (yes, with angular momentum), then Quantum Mechanics would still stay just the same and all the equations would work just the same, radiation or not. There would still be electron clouds and all the orbitals, electron pairing and everything. All this should theoretically and practically still be possible and there is nothing in Schrödinger equation or any other QM equation that would actually prohibit electrons to move in continuous trajectories.

Well, the Schrodinger equation isn't consistent with continuous trajectories for electrons in atoms, because despite your assertion, electron "clouds" are not consistent with continuous trajectories as you claim. This gets back to the angular momentum issue that I mentioned so long ago. However the deBroglie-Bohm (dBB) formulation of quantum mechanics does hold that there are continuous trajectories for all quantum particles, but that there is an associated "Quantum force" that causes fundamentally unknowable perturbations to the initial conditions of the particles, which provides the observed statistical behavior. One very weird conclusion from dBB is that the classical particle representing the electron is actually *stationary* in the dBB interpretation ... I guess this is because otherwise it would have non-zero angular momentum.

One of the most compelling reasons for me to believe these electrons indeed circle nucleus and make tiny electric loops is because that is how magnetism in permanent magnets is explained and I do not know about any other suggested theory since this explanation seem to be accepted across all the fields, including SR and QM.

Intrinsic angular momentum, or spin, of the electron, and it's coupling to orbital angular momentum, is the QM explanation for how magnetism arises at the atomic and molecular level. I guess the "tiny loops" refers to the orbital angular momentum contribution, but you can still observe magnetism when that contribution is zero, due to the electron spin.

Again, this is not discussion against QM, it is about continuous trajectories and possibility that numerical integration and classical electrodynamics equations might be able to model atom after all, TOO.

Do you really think that Bohr, Heisenberg, Einstein, Dirac, and a host of other BRILLIANT physicists from the early 1900's would have missed that? Rutherford proposed the "planetary" model for the atom after observing that atoms were mostly empty space in his famous "gold foil" experiment. Almost immediately it was realized that this couldn't be right in the context of the KNOWN electrodynamic laws, because the electrons in classical orbits would be under continuous acceleration, and would thus lose energy and slow down due to emission of EM radiation, eventually crashing into the nucleus. That is the context from which QM was born, and it was subjected to incredibly harsh scrutiny, because it seemed so weird to these brilliant scientists who already understood the context of classical physics. QM blew their minds, but they were eventually forced to accept its correctness, and by inference, the fact that atoms can't be understood in the context of classical electrodynamics.

There is this software I came across that claims to be doing molecular and atom dynamics, atom bonding, atom orbital configurations and all that as real-time simulation with forces, velocities and all the kinetics instead of statistics and regular QM equations. Shall I find it again? There is also a paper on this "discovery", as they call it, where they explain all the equations and how it works.

I would be interested to see it .. my guess it is based on dBB formulation.

 

[ZapperZ]

One of the most compelling reasons for me to believe these electrons indeed circle nucleus and make tiny electric loops is because that is how magnetism in permanent magnets is explained and I do not know about any other suggested theory since this explanation seem to be accepted across all the fields, including SR and QM.


Again, this is not discussion against QM, it is about continuous trajectories and possibility that numerical integration and classical electrodynamics equations might be able to model atom after all, TOO. There is this software I came across that claims to be doing molecular and atom dynamics, atom bonding, atom orbital configurations and all that as real-time simulation with forces, velocities and all the kinetics instead of statistics and regular QM equations. Shall I find it again? There is also a paper on this "discovery", as they call it, where they explain all the equations and how it works.

These two point of view is self-contradictory. If you claim that this is not a discussion against QM, then you must have never derived the wavefunction for a hydrogen atom. I don't see how you can reconcile these "tiny electric loops" around the nucleus with the wavefunction of hydrogen atom.

Please note that you are edging on promoting your own personal theory and with no valid references to support your views. This is against the https://www.physicsforums.com/showthread.php?t=5374" that you had agreed to. Unless you are able to provide ample valid evidence and references, this line discussion cannot continue.

Zz.

 

[varga]

I'll cut your post to two pieces to show the contradiction. Later I'll respond to rest, but this here is the most important thing and should be established before we continue with anything else.

No, it certainly does not make Coulomb's law in any way inaccurate. Coulomb's law describes the electrostatic interaction between charges .. it says nothing about velocities or accelerations of particles (except implicitly by defining the shape of the electrostatic potential). The phenomena of EM radiation being emitted from charges under acceleration is in the domain of electrodynamics.

Electric: ma= k*q1q2/r^2

Gravity: ma= k*m1m2/r^2

Have you people forgotten about basic physics when you engaged with QM? Of course it is directly related to acceleration it EXPLAINS it, describes the cause and effect. The point is, if there is no any correction needed and you numerically model this interaction with Coulombs' equations, electrons WILL orbit forever, i.e. they will not loose energy, hence we call those forces 'conservative forces'.

Rutherford proposed the "planetary" model... Almost immediately it was realized that this couldn't be right in the context of the KNOWN electrodynamic laws, because the electrons in classical orbits would be under continuous acceleration, and would thus lose energy and slow down due to emission of EM radiation, eventually crashing into the nucleus. That is the context from which QM was born...

And so we go back to electron radiation. It does not matter to me what final conclusion will be, but you must decide between the two. In REALITY, do electrons radiate and loose energy or not? If they do, as I agreed, then the Coulomb's law has an ERROR, because according to Coulomb's law they should not radiate and they should orbit long time, just like planets do. Please decide whether Coulomb's law is inaccurate, or there is no radiation?ALSO VERY IMPORTANT,
please tell me these basic things, so I can make another point:a) we say electron in orbit with constant velocity still "accelerates" due to change in direction, but is this really 'acceleration' or 'deceleration'?

b) when electron speeds up towards proton, does it radiate or absorb radiation?

c) when electron flies away from proton and it slows down, does it radiate or absorb?

d) how did we managed to measure angular momentum of some atom's electron?

 

[varga]

These two point of view is self-contradictory. If you claim that this is not a discussion against QM, then you must have never derived the wavefunction for a hydrogen atom. I don't see how you can reconcile these "tiny electric loops" around the nucleus with the wavefunction of hydrogen atom.

True, I have never derived the wavefunction for any atom and I do not know about QM much more than what they told me some 15 years ago, but QM was not my field of study.

As I said I only know one explanation, the one with electric loops. So, this is the question directed to everyone else but me, how do you explain what SpectraCat calls "orbital angular magnetic momentum"? (not spin dipole moment)

Please note that you are edging on promoting your own personal theory and with no valid references to support your views. This is against the https://www.physicsforums.com/showthread.php?t=5374" that you had agreed to. Unless you are able to provide ample valid evidence and references, this line discussion cannot continue.

What do you mean, what part exactly?

I do not have "personal theory" my references are Wikipedia pages on classical electrodynamics. I'm looking for explanation. I think I need to explain my current understanding so people can better explain and point to my misunderstandings, if any.

In other words, you obviously believe I lack knowledge and/or understanding. That's fine, I admit that and that's why I'm asking questions, just please point out more directly what are you talking about so I can eventually learn. Thank you.

 

[Frame Dragger]

True, I have never derived the wavefunction for any atom and I do not know about QM much more than what they told me some 15 years ago, but QM was not my field of study.

As I said I only know one explanation, the one with electric loops. So, this is the question directed to everyone else but me, how do you explain what SpectraCat calls "orbital angular magnetic momentum"? (not spin dipole moment)




What do you mean, what part exactly?

I do not have "personal theory" my references are Wikipedia pages on classical electrodynamics. I'm looking for explanation. I think I need to explain my current understanding so people can better explain and point to my misunderstandings, if any.

In other words, you obviously believe I lack knowledge and/or understanding. That's fine, I admit that and that's why I'm asking questions, just please point out more directly what are you talking about so I can eventually learn. Thank you.

Just in case s/he's offline for a while, please let me clear the air here. There are rules, literally, against proposing a "pet" theory, or "Against The Mainstream" theories. It can be hard to tell the difference between (someone like you) a person struggling to grasp these concepts, and someone trying to be sneaky about pushing some nutty theory.

Clearly, what you're saying is that you're just off-base in terms of the science, but not promoting a particular theory of your own. He wasn't trying to be snide or question your knowledge, but literally was checking for crackpots. I think you'll find he and others here are more than helpful if you give them a chance to teach you the way they best know how.

 

[varga]

Ok, we'll just keep on using free-electron lasers for our research, if you don't mind. (we make the graduate students feed the gargoyles) By the way, the vacuum inside such lasers is very good, so there is no chance of the radiation coming from collisions. Just one more little point .. you said you knew about free-electron lasers, so I just was assuming you know that their tuning range extends *continuously* from the microwaves out to hard-UV and x-rays. It's pretty hard to come up with a model based on collisions with gas molecules that could explain that.

I'm fine with radiation being there, I'm unhappy with the cause-effect explanation for it.

Intrinsic angular momentum, or spin, of the electron, and it's coupling to orbital angular momentum, is the QM explanation for how magnetism arises at the atomic and molecular level. I guess the "tiny loops" refers to the orbital angular momentum contribution, but you can still observe magnetism when that contribution is zero, due to the electron spin.

Yes, I mean what you call "orbital angular momentum". How do you explain it?

Do you really think that Bohr, Heisenberg, Einstein, Dirac, and a host of other BRILLIANT physicists from the early 1900's would have missed that?

Missed what? Having computers and ability to actually model all the forces? Yes, even with today computers is hard to model n-body problem and even with only a singe field per particle like gravity orbits, because of the numerical precision and similar time/precision related problems.

Do you think they even tried to model any of the magnetic forces, either due to spin or due to spatial velocity? I do not think so, it would take them years just to trace a few seconds of this interaction and they would hardly manage to do it with double floating point precision of today computers. Then, there is the problem of simultaneity of orientation of magnetic moments, which makes magnetic field interaction kind of impossible to correctly simulate even today. My field is kinetics and numerical modeling by the way.

I would be interested to see it .. my guess it is based on dBB formulation.

Ok, I'll look for it. Let me just say that all their formulas looked more like QM than classical to me, they surely seemed to use a lot of QM, but then I did not understand any of that, I just noticed they were claiming "something new" and that they use forces instead of statistics, which I interpreted as 'continuous trajectories', and that's all I know about it.

 

[ZapperZ]

True, I have never derived the wavefunction for any atom and I do not know about QM much more than what they told me some 15 years ago, but QM was not my field of study.

Then how are you able to claim that you're not violating QM? Here's news for you: you are!

As I said I only know one explanation, the one with electric loops. So, this is the question directed to everyone else but me, how do you explain what SpectraCat calls "orbital angular magnetic momentum"? (not spin dipole moment)

Orbital angular momentum is part of the solution to the wavefunction. Again, solving the Schrodinger equation for the hydrogen atom will give you exactly that for the angular part of the solution. This is not a mystery. However, these are NOT "electric loops", because if you look at the symmetry (or geometry) of the solution, it resembles nothing like any classical orbits.

What do you mean, what part exactly?

I do not have "personal theory" my references are Wikipedia pages on classical electrodynamics. I'm looking for explanation. I think I need to explain my current understanding so people can better explain and point to my misunderstandings, if any.

In other words, you obviously believe I lack knowledge and/or understanding. That's fine, I admit that and that's why I'm asking questions, just please point out more directly what are you talking about so I can eventually learn. Thank you.

Please note that there have been several attempts at trying to straighten you out. However, when you strenuously hang on to these "loops" of current as somehow being the valid explanation for atomic description, then this is no longer a process of learning but rather a process of denial.

We have an entry in the FAQ thread in the General Physics forum that tackled the question on why an electron doesn't crash into the nucleus. There are relevant parts in that entry that can address some of your misconception about how we describe an atom. Rather than making shots in the dark to see which one sticks, you might want to start turning on the light first and see what's there.

Zz.

 

[Frame Dragger]

@SpectraCat: You seem to be very knowledgeable about free electron lasers... this is purely for the sake of a bit of fantasy writing: could you in theory construct (and I mean that in an imagined sense) a Phase-Conjugate FEL, using the best of the ability to "tune" as you say, and the PC array would compensate for bloom, material, distance, etc.

Again, this is obviously not currently possible, and I understand some of the challenges in actually BUILDING phase arrays for one wavelength in the radio frequency, never mind a fictional tuner to sweep from UV to IR or even more. Anyway, I just wanted to get a grasp of the energy involved (efficiency, etc) for an idealized FEL at a given output.

 

[SpectraCat]

I'll cut your post to two pieces to show the contradiction. Later I'll respond to rest, but this here is the most important thing and should be established before we continue with anything else.

Electric: ma= k*q1q2/r^2

Gravity: ma= k*m1m2/r^2

Have you people forgotten about basic physics when you engaged with QM? Of course it is directly related to acceleration it EXPLAINS it, describes the cause and effect. The point is, if there is no any correction needed and you numerically model this interaction with Coulombs' equations, electrons WILL orbit forever, i.e. they will not loose energy, hence we call those forces 'conservative forces'.

I suggest you very quickly drop the attitude that all of the people who are trying to help you are somehow ignorant drones who have been "dazzled by QM" at the expense of common sense. It is *you* that have the misconception; we are trying to help you to understand that, by explaining the mainstream, established, and accepted physical theory to you.

Coulomb's law says *nothing* about motion, or orbiting particles. It *only* establishes the shape and magnitude of the electrostatic potential. In order to understand the *motion of particles* in this potential, you need to solve the *dynamical* equations of motion, taking into account the forces. Everything we have said is consistent with the laws of physics. Your argument is equivalent to saying that, "because air drag changes the trajectory of a particle, based on what would be expected exclusively from the law of gravity, gravitation must be wrong".

And so we go back to electron radiation. It does not matter to me what final conclusion will be, but you must decide between the two. In REALITY, do electrons radiate and loose energy or not?

Yes.

If they do, as I agreed, then the Coulomb's law has an ERROR, because according to Coulomb's law they should not radiate and they should orbit long time, just like planets do. Please decide whether Coulomb's law is inaccurate, or there is no radiation?

Please decide if you are going to carefully consider our counterarguments and explanations concerning your misconception, or continue to dismiss them.

ALSO VERY IMPORTANT,
please tell me these basic things, so I can make another point:a) we say electron in orbit with constant velocity still "accelerates" due to change in direction, but is this really 'acceleration' or 'deceleration'?

What is the difference? Google centripetal acceleration.

b) when electron speeds up towards proton, does it radiate or absorb radiation?

c) when electron flies away from proton and it slows down, does it radiate or absorb?

I don't know if these questions have meaningful answers in the classical context you are insisting on. They certainly have meaningful answers in the context of quantum electrodynamics (QED), which takes into account the quantum nature of the electrostatic field, as well as the particles.

My take on the classical case is, if we consider the proton to be stationary, then there is no source of radiation, so we can ignore absorption and only consider emission. Since the electron is always accelerating in your picture, then it is always emitting radiation. Thus its classical kinetic energy and velocity is always a bit smaller than would be expected if you ignore the radiation.

d) how did we managed to measure angular momentum of some atom's electron?

By measuring the probability distribution for that electron around the atom. The symmetry of the probability distribution provides information about the angular momentum. Spherical symmetry means the angular momentum is zero .. to understand this, consider a planet in an orbit around a star .. what is the probability distribution of finding the planet around the star? How similar is it to spherical? Furthermore, consider that the probability distribution for the ground state of an atom is distributed over a spherical *volume*, not a spherical shell with a well-defined radius. Can you explain how an electron in a classical orbit with non-zero angular momentum could generate such a distribution?

Also, there is a phenomenological justification in terms of atomic spectra. When an electron relaxes from a higher to a lower energy state, it emits a photon that carries (at least) on unit of angular momentum. By conservation of angular momentum, this must mean that the orbital angular momentum of the electron must [STRIKE]decrease[/STRIKE] change by one unit in the transition. No emission of photons has ever been observed from ground state electrons in an atom, suggesting that their orbital angular momentum has some minimum value, which is less than Planck's constant divided by 2*pi (the quantum unit of angular momentum). The mathematical formalism of QM predicts that this value is exactly zero, which is consistent with experiment.

 

[SpectraCat]

Do you really think that Bohr, Heisenberg, Einstein, Dirac, and a host of other BRILLIANT physicists from the early 1900's would have missed that?

Missed what? Having computers and ability to actually model all the forces? Yes, even with today computers is hard to model n-body problem and even with only a singe field per particle like gravity orbits, because of the numerical precision and similar time/precision related problems.

Who said anything about computers? Some of the systems we have been discussing (such as one electron atoms) have analytical solutions, and in cases where analytical solutions aren't possible, there are mathematical approximation methods that are accessible to pencil and paper. Computers are a convenient tool for allowing more and more accurate approximate calculations, but the theory for all this stuff was worked out back in the 1920's or earlier.

Do you think they even tried to model any of the magnetic forces, either due to spin or due to spatial velocity? I do not think so, it would take them years just to trace a few seconds of this interaction and they would hardly manage to do it with double floating point precision of today computers. Then, there is the problem of simultaneity of orientation of magnetic moments, which makes magnetic field interaction kind of impossible to correctly simulate even today. My field is kinetics and numerical modeling by the way.

As I said, they tried (and succeeded) to understand the problem, not to model it. Models are useful for developing or improving understanding of physical systems in deeper detail. But in this case, the problem is simple, and they understood it just fine without needing to model anything.

Ok, I'll look for it. Let me just say that all their formulas looked more like QM than classical to me, they surely seemed to use a lot of QM, but then I did not understand any of that, I just noticed they were claiming "something new" and that they use forces instead of statistics, which I interpreted as 'continuous trajectories', and that's all I know about it.

Thanks.

 

[SpectraCat]

@SpectraCat: You seem to be very knowledgeable about free electron lasers... this is purely for the sake of a bit of fantasy writing: could you in theory construct (and I mean that in an imagined sense) a Phase-Conjugate FEL, using the best of the ability to "tune" as you say, and the PC array would compensate for bloom, material, distance, etc.

Again, this is obviously not currently possible, and I understand some of the challenges in actually BUILDING phase arrays for one wavelength in the radio frequency, never mind a fictional tuner to sweep from UV to IR or even more. Anyway, I just wanted to get a grasp of the energy involved (efficiency, etc) for an idealized FEL at a given output.

I'll need a little more info on what you mean by "phase-conjugate". This may already be incorporated into the design of the lasers, since there is a "re-bunching" effect that helps to keep the bunches of electrons in-phase.

My knowledge of FEL's is rather applied .. I have used them for my research in spectroscopy, but I have not designed or modified them. I have a basic understanding of the physical principles involved, but there are certainly many details of which I remain ignorant.

 

[varga]

I suggest you very quickly drop the attitude that all of the people who are trying to help you are somehow ignorant drones who have been "dazzled by QM" at the expense of common sense. It is *you* that have the misconception; we are trying to help you to understand that, but explaining the mainstream, established, and accepted physical theory to you.

Interesting. I do not see the point of discussing anything else before we make this clear. I'll go step by step and I would like to know exactly at what point do we start to disagree, ok?


1.) Do you agree with the following statements from Wikipedia:

http://en.wikipedia.org/wiki/Force#Conservative_forces

A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms... Conservative forces include gravity, the electromagnetic force, and the spring force.

For gravity:

For electrostatic forces:

2.) Do you agree "F= m*a", and so:

Electric: F= m*a= k*q1q2/r^2

Gravity: F= m*a= k*m1m2/r^2


3.) Are you familiar with:
http://en.wikipedia.org/wiki/N-body_problem
http://en.wikipedia.org/wiki/N-body_simulation


4.) Do you agree Newton's law of universal gravitation can be used to describe planetary motion?
(That was the whole point I'd say.)


5.) Do you agree Coulomb's law equation will describe very similar orbits as gravity one, only smaller?


6.) Do you agree that to make orbits spiral to proton, like they would as you say, we need to add "correction" (radiation) into the equation?


7.) If equation needs correction to accurately describe the real world, then it's not completely accurate, right?

Coulomb's law says *nothing* about motion, or orbiting particles. It *only* establishes the shape and magnitude of the electrostatic potential.

8.) Do you agree motion is 'change of position over time' and so acceleration IS description of motion - that is, if you know acceleration vector of some object in any given instant in time, then you know EVERYTHING about its MOTION and you can precisely draw its trajectory, right?


9.) Do you agree: F= m*a= k*q1q2/r^2, and therefore Coulomb's law says EVERYTHING about motion (not necessarily accurate) by defining the force and therefore defining the acceleration, which defines velocity, which defines position, which integrated over time is called trajectory?


10.) If you still disagree with 9, then please tell me what 'dynamical' equations of motion do you suggest?


Sometimes gravity force is even referred to as simply "acceleration", and acceleration is derivative of position, so of course it says a lot about motion, since motion is defined as 'change of position over time'... and this is all true for Coulomb's force too as equations are almost the same.

In order to understand the *motion of particles* in this potential, you need to solve the *dynamical* equations of motion, taking into account the forces.

It's called 'kinematics equations', I call it kinetics, it is also known as dynamics... but 'dynamical', no, I don't think so. Yes, forces, that is why I'm talking about Coulomb's FORCE and gravity FORCE equations.

 

[Oudeis Eimi]

Interesting. I do not see the point of discussing anything else before we make this clear. I'll go step by step and I would like to know exactly at what point do we start to disagree, ok?1.) Do you agree with the following statements from Wikipedia:

http://en.wikipedia.org/wiki/Force#Conservative_forces

A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms... Conservative forces include gravity, the electromagnetic force, and the spring force.

For gravity:

For electrostatic forces:

I'm afraid there's an important misconception on your part regarding electrostatic forces: strictly, they can only be used to model a static scenario, ie, no movement.

2.) Do you agree "F= m*a", and so:

Electric: F= m*a= k*q1q2/r^2

Gravity: F= m*a= k*m1m2/r^2

The gravitational example is correct (within the domain of validity of Newtonian
physics and assuming the masses can be considered as puctual).

The electric example, OTOH is WRONG in general. IOW, it is generally NOT
TRUE that $$m a = k q_1 q_2 / r^2$$.

Classical electrodynamics is rather more complicated than classical gravitation,
because, unlike Newtonian gravity, it's described as a non instantaneous interaction
from the onset. So, in order to describe moving charges in an electromagnetic field
you generally need to resort to the full machinery of electrodynamics. Google Maxwell's
equations.

Sometimes you can indeed use Coulomb's equation to study a non static problem,
as a way of simplifying the treatment, but you have to know when such simplification
is justified.

3.) Are you familiar with:
http://en.wikipedia.org/wiki/N-body_problem
http://en.wikipedia.org/wiki/N-body_simulation4.) Do you agree Newton's law of universal gravitation can be used to describe planetary motion?
(That was the whole point I'd say.)5.) Do you agree Coulomb's law equation will describe very similar orbits as gravity one, only smaller?

They would if they described the whole of electrodynamics, which they don't.

6.) Do you agree that to make orbits spiral to proton, like they would as you say, we need to add "correction" (radiation) into the equation?

Maxwell's equations do correctly predict radiation b accelerating charges.

7.) If equation needs correction to accurately describe the real world, then it's not completely accurate, right?

8.) Do you agree motion is 'change of position over time' and so acceleration IS description of motion - that is, if you know acceleration vector of some object in any given instant in time, then you know EVERYTHING about its MOTION and you can precisely draw its trajectory, right?

Another misconception. Newton's equations are NOT universally valid. In particular
they don't apply in Quantum Mechanics.

9.) Do you agree: F= m*a= k*q1q2/r^2, and therefore Coulomb's law says EVERYTHING about motion (not necessarily accurate) by defining the force and therefore defining the acceleration, which defines velocity, which defines position, which integrated over time is called trajectory?

10.) If you still disagree with 9, then please tell me what 'dynamical' equations of motion do you suggest?

Again... for a classical point particle, Maxwell's equations.

Sometimes gravity force is even referred to as simply "acceleration", and acceleration is derivative of position, so of course it says a lot about motion, since motion is defined as 'change of position over time'... and this is all true for Coulomb's force too as equations are almost the same.

It's called 'kinematics equations', I call it kinetics, it is also known as dynamics... but 'dynamical', no, I don't think so. Yes, forces, that is why I'm talking about Coulomb's FORCE and gravity FORCE equations.

 

[SpectraCat]

Interesting. I do not see the point of discussing anything else before we make this clear. I'll go step by step and I would like to know exactly at what point do we start to disagree, ok?1.) Do you agree with the following statements from Wikipedia:

http://en.wikipedia.org/wiki/Force#Conservative_forces

A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms... Conservative forces include gravity, the electromagnetic force, and the spring force.

For gravity:

For electrostatic forces:

2.) Do you agree "F= m*a", and so:

Electric: F= m*a= k*q1q2/r^2

Gravity: F= m*a= k*m1m2/r^23.) Are you familiar with:
http://en.wikipedia.org/wiki/N-body_problem
http://en.wikipedia.org/wiki/N-body_simulation4.) Do you agree Newton's law of universal gravitation can be used to describe planetary motion?
(That was the whole point I'd say.)

Yes to all of the above

5.) Do you agree Coulomb's law equation will describe very similar orbits as gravity one, only smaller?

Basically yes ... although it depends on the magnitudes of the charges, and the initial conditions (i.e. relative positions and velocities)

6.) Do you agree that to make orbits spiral to proton, like they would as you say, we need to add "correction" (radiation) into the equation?

The correction is not to Coulomb's law equation, it is an additional term that needs to be incorporated to more completely and accurately describe the physical reality of the problem.

7.) If equation needs correction to accurately describe the real world, then it's not completely accurate, right?

Hmmm ... there is some dangerously loose context there I think. Coulomb's law is accurate, but there may be other factors in play that need to be included in order to describe real physical trajectories in nature.

8.) Do you agree motion is 'change of position over time' and so acceleration IS description of motion - that is, if you know acceleration vector of some object in any given instant in time, then you know EVERYTHING about its MOTION and you can precisely draw its trajectory, right?

I think I agree with what you are trying to say, but the above doesn't seem quite right. I would say that if you have the initial position and velocity of a particle, and you know all of the forces acting on the particle, and how they change with position and time, then you have enough information to accurately predict its trajectory. If any of that information is missing, you can of course still make a prediction, but it will probably be wrong.

9.) Do you agree: F= m*a= k*q1q2/r^2, and therefore Coulomb's law says EVERYTHING about motion (not necessarily accurate) by defining the force and therefore defining the acceleration, which defines velocity, which defines position, which integrated over time is called trajectory?

No, I do not agree. See my previous comments. As I said before, your assertion here is like stating that the law of gravitation in inaccurate, just because someone told you about air drag or friction, and how they can cause the decay of a trajectory that is predicted to be stable using just the law of gravitation.

10.) If you still disagree with 9, then please tell me what 'dynamical' equations of motion do you suggest?

See above.

Sometimes gravity force is even referred to as simply "acceleration", and acceleration is derivative of position, so of course it says a lot about motion, since motion is defined as 'change of position over time'... and this is all true for Coulomb's force too as equations are almost the same.

And yet people never claim that gravity is wrong because of friction ...

It's called 'kinematics equations', I call it kinetics, it is also known as dynamics... but 'dynamical', no, I don't think so. Yes, forces, that is why I'm talking about Coulomb's FORCE and gravity FORCE equations.

Whatever, the point was that you needed some equations of motion in there. Coulomb's law is not an equation of motion, although of course it can be used to describe the contributions of electrostatic forces to the trajectory of a charged particle. There is no stipulation anywhere in physics that it provides a complete description of everything that matters for a charged particle, as you are so doggedly asserting.

 

[PhaseShifter]

Interesting. I do not see the point of discussing anything else before we make this clear. I'll go step by step and I would like to know exactly at what point do we start to disagree, ok?


1.) Do you agree with the following statements from Wikipedia:

http://en.wikipedia.org/wiki/Force#Conservative_forces

Why do you keep repeating this?
You're forgetting that nonconservative forces are also involved, due to the rotating dipole. (At least that's what it looked like at first. Now it's looking more and more like you expect everyone else to forget them if you shout about coulomb forces enough.)

You need to consider Maxwell's equations as well as coulomb attraction, because the charges are in motion. These predict energy loss by radiation.

 

[jfy4]

2.) Do you agree "F= m*a", and so:

Electric: F= m*a= k*q1q2/r^2

Gravity: F= m*a= k*m1m2/r^2

As the two previous posters said, No. $$\mbox{Force}\not= ma$$

rather

$$F_{net}=ma$$ if you want to be concerned with the radiation reaction and be as accurate as possible, then you must consider the radiation reaction force. Applying $$F_{net}=ma$$ is physics, so you must write down what physics you want to happen. Here is the equation for the radiation reaction force so you can adjust your electric equation

$$\mathbf{F}_{rad}=\frac{\mu_{0}q^{2}}{6\pi c}\mathbf{\dot{a}}$$

when you set those two equations equal, you are saying what is happening, not the theory. Electrostatics is fine, and so is electrodynamics, insofar as they are classical. it is the physicist who have to be careful.

Does this help?

 

[varga]

Ok, except for Oudeis Eimi, I conclude we are all saying the same thing, though from different aspects and making emphasis on different relations so our conclusions seem to differ, but I'm happy to leave that particular issue as it is, since I see general agreement. I'm going back to where I left off.


@ZapperZ

Orbital angular momentum is part of the solution to the wavefunction. Again, solving the Schrodinger equation for the hydrogen atom will give you exactly that for the angular part of the solution. This is not a mystery. However, these are NOT "electric loops", because if you look at the symmetry (or geometry) of the solution, it resembles nothing like any classical orbits.

Please tell me more about 'angular part of the solution', that sounds a lot like 'continuous trajectory' to me. And if it looks like a loop, then what is the difference with classical loop?

If this "electric loop" does not have 'internal' velocity there will be no magnetic field there according to electrodynamics (magnetic field of moving charge), but to have velocity you have to have continuous trajectory. If electron was not actually moving by "sliding", but was appearing and disappearing at different locations then there would not be any velocity vector and no magnetic field which would in any case be random at best in such situation. So, how do you reconcile all this with all that?

I'm strictly talking about CONTINUOUS TRAJECTORIES, I'm not talking about Classical vs QM or Bohr vs Schrodinger, it is not important to me what equations and what physics is actually true or more correct, all I care is whether the trajectories are continuous or not.




@SpectraCat

a) we say electron in orbit with constant velocity still "accelerates" due to change in direction, but is this really 'acceleration' or 'deceleration'?

What is the difference? Google centripetal acceleration.

I thought the difference would be whether they are supposed to emit or absorb radiation, but you seem to be saying energy is lost, radiated away, in either case, whether it is acceleration or deceleration, do you confirm?

My take on the classical case is, if we consider the proton to be stationary, then there is no source of radiation, so we can ignore absorption and only consider emission. Since the electron is always accelerating in your picture, then it is always emitting radiation. Thus its classical kinetic energy and velocity is always a bit smaller than would be expected if you ignore the radiation.

I'm not about strictly "Classical" at all, use QED or whatever is supposed to give the best description (most accurate in relation to the real world) and particular issues in question. In any case, can you confirm that electrons in circular motion but with constant velocity would still radiate?

So, if they radiate when they slow down, and they radiate when they speed up, where does the absorption of em radiation come into this?

 

[varga]

By measuring the probability distribution for that electron around the atom. The symmetry of the probability distribution provides information about the angular momentum. Spherical symmetry means the angular momentum is zero .. to understand this, consider a planet in an orbit around a star .. what is the probability distribution of finding the planet around the star? How similar is it to spherical?

Ok, that is reasonable argument.

I wanted to completely ignore magnetic forces for the most part, for the simple reason that I'm certain whomever ever tried to model an atom based on classical electrodynamics (Bohr model is more 'early QM' than classical mechanics and modeling of the electromagnetic forces by time integration as n-body problem) they did so by modeling ONLY the electric forces and by completely ignoring spin magnetic dipole moment and the magnetic field of a moving charge. Again, it is impossible to accurately integrate magnetic forces even today as there is unsolved problem connected to simultaneity which is not present in purely electrical interaction, this has to do with electron "size" and orientation of its dipole magnetic moment.


The point is, n-body problem describes CHAOTIC system. It becomes UNPREDICTABLE with even only 3 bodies interacting having just one field per body. Therefore, the probability of two particle, interacting with both electric AND magnetic forces, to be at some location at any given point in time would most likely indeed be spherical, though really unknown to us if we are unable to simulate it.

We are talking about 'Chaos theory', these 'dynamical systems are chaotic, they have all the familiar properties to QM folks, like lower energy states (strange attractors), and there are geometrical symmetries and relations closely resembling quantum clouds and orbital shapes... There is also a field called 'quantum chaos'.

http://en.wikipedia.org/wiki/Chaos_theory
http://en.wikipedia.org/wiki/Quantum_chaos


This is also closely related to fractals, since basic kinetics integration of these forces is actually 'recursive algorithm' by its functionality, i.e. it is a 'fractal equation' in its very essence as time integral.

Furthermore, consider that the probability distribution for the ground state of an atom is distributed over a spherical *volume*, not a spherical shell with a well-defined radius. Can you explain how an electron in a classical orbit with non-zero angular momentum could generate such a distribution?

Considering above, I'd say that by modeling magnetic forces, not only electric field interaction, electron in this hydrogen atom model would most likely describe very complex and irregular trajectory, and if you set longer exposure on your camera that has a really good chance to look as "cloud".

Also, there is a phenomenological justification in terms of atomic spectra. When an electron relaxes from a higher to a lower energy state, it emits a photon that carries (at least) on unit of angular momentum. By conservation of angular momentum, this must mean that the orbital angular momentum of the electron must decrease in the transition. No emission of photons has ever been observed from ground state electrons in an atom, suggesting that their orbital angular momentum has some minimum value, which is less than Planck's constant divided by 2*pi (the quantum unit of angular momentum).

I do not see how photon can have angular momentum? Perhaps some "spin", but I do not see how some spin angular momentum of photon can say anything whether electron that supposedly emitted it had continuous trajectory or not. Electron can not transmit that information as photons always travel in a straight line, right?

The mathematical formalism of QM predicts that this value is exactly zero, which is consistent with experiment.

It is expect for light to travel the straight line, so please explain again how is circling electron supposed to influence a photon so that later keeps information of former being in a circular or continuous trajectory?

 

[SpectraCat]

I don't have time right now to address all your issues here, so I'm just going to cherry-pick for now

Ok, except for Oudeis Eimi, I conclude we are all saying the same thing, though from different aspects and making emphasis on different relations so our conclusions seem to differ, but I'm happy to leave that particular issue as it is, since I see general agreement. I'm going back to where I left off.

Well, unless you want to revise your earlier statements, I don't see how we are saying the same thing at all. And Oudeis Eimi's content was closer to agreeing with mine (and PhaseShifters, and jfy4's) than anything you have posted.

We are telling you that electrodynamics (i.e. Maxwell's equations) describes radiation from charged particles accelerating in a Coulomb field (or any other potential). You are denying that this radiation exists, in the face of all evidence and arguments to the contrary .. unless you have changed your mind and not informed us of that.

I thought the difference would be whether they are supposed to emit or absorb radiation, but you seem to be saying energy is lost, radiated away, in either case, whether it is acceleration or deceleration, do you confirm?

That is correct, an accelerating charge emits light, whether it is slowing down or speeding up.

I'm not about strictly "Classical" at all, use QED or whatever is supposed to give the best description (most accurate in relation to the real world) and particular issues in question. In any case, can you confirm that electrons in circular motion but with constant velocity would still radiate?

Not quite, because they will slow down from the radiation .. that was the flaw in the planetary model of the atom.

So, if they radiate when they slow down, and they radiate when they speed up, where does the absorption of em radiation come into this?

Where-ever it needs to .. an electron can absorb E/M radiation and either be accelerated or decelerated, depending on the relative velocity vectors. Google compton scattering.

Considering above, I'd say that by modeling magnetic forces, not only electric field interaction, electron in this hydrogen atom model would most likely describe very complex and irregular trajectory, and if you set longer exposure on your camera that has a really good chance to look as "cloud".

Nope, because the angular momentum in the ground state is *exactly* zero .. it does not average to zero.

I do not see how photon can have angular momentum? Perhaps some "spin", but I do not see how some spin angular momentum of photon can say anything whether electron that supposedly emitted it had continuous trajectory or not. Electron can not transmit that information as photons always travel in a straight line, right?

I have no idea what you mean there ... you are the only one talking about continuous trajectories ... I only talked about conservation of angular momentum. When an electron relaxing between energy levels emits a photon, the angular momentum must change by one unit, period. If am not worried if this cannot be explained in terms of classical trajectories for electrons, because those do not give a correct description of physical atoms, as many people have been explaining to you for several pages now.



It is expect for light to travel the straight line, so please explain again how is circling electron supposed to influence a photon so that later keeps information of former being in a circular or continuous trajectory?[/QUOTE]

 

[varga]

You are denying that this radiation exists, in the face of all evidence and arguments to the contrary.

I accepted it long ago, even if no one provided adequate photo. The whole side-argument is around the actual consequences of it being there, so I have been referring to it as a fact for quite some time now. I do not deny radiation is measured in experiments and I appreciate all the applications of this phenomenon, I just don't think anyone explained the causality of it:

a) DECELERATION: does it slow down BECAUSE it radiates, or it radiates because it slows down?

b) ACCELERATION: does it speed up BECAUSE it radiates, or it radiates because it speeds up?

We are telling you that electrodynamics (i.e. Maxwell's equations) describes radiation from charged particles accelerating in a Coulomb field (or any other potential).

Yes, and so everyone confirmed my original question, which is - whether Coulomb's law need any error correction or not, answer is - "yes, so use Maxwell equation".


a) What is this Maxwell equation everyone is talking about?

b) How do you think 'Electron Volt' was calculated and experimentally confirmed, according to some Maxwell equation or Coulomb's law equation?

c) do you think anyone would call Coulomb force "conservative" if they knew there was any loss of energy there?

d) do you think we should still consider Coulomb force as "conservative"?

Q: ..electrons in circular motion but with constant velocity would still radiate?

A: Not quite
(..because they will slow down from the radiation .. that was the flaw in the planetary model of the atom.)

Will they radiate or not, it's yes/no question, what do you mean by "not quite"?

Nope, because the angular momentum in the ground state is *exactly* zero .. it does not average to zero.

I do not think you explained measurement of any angular momentum, you explained some assumption and the lack of confirmation of that particular prediction, that is not actual measurement. As far as I know QM says we CAN NOT measure any such thing, which is different from actually measuring something has zero value. Can you point to this particular experiment with some reference?

- If something was moving left-right in a straight line, making 180 degree turns, what would be its angular momentum?

I have no idea what you mean there ... you are the only one talking about continuous trajectories ... I only talked about conservation of angular momentum.

I would like we all start talking about 'continuous trajectories', in terms of whether electron motion is "continuous-sliding" or "appear-disappear" kind of thing, or something else. If there is anything about this angular momentum experiments that can directly or indirectly prove or disprove "continuous trajectories", not "classical trajectories", then I'd like to talk about that too.

When an electron relaxing between energy levels emits a photon, the angular momentum must change by one unit, period.

I agree about "one unit". But, what angular momentum, of electron or photon? How it must change?

If am not worried if this cannot be explained in terms of classical trajectories for electrons, because those do not give a correct description of physical atoms, as many people have been explaining to you for several pages now.

A.) "Classical trajectories" described by Bohr model

B.) "Classical trajectories" described by Coulomb's law

C.) "Classical trajectories" described by Maxwell equation


These are all different things and do not represent the general concept I'm talking about. What I'm talking about is CONTINUOUS TRAJECTORIES, this is COMPATIBLE with statistical measurements of QM (assertion for the sake of argument), and I do not care if it is neither A, B, C or anything similar... I'm fine with QED and QM, or whatever, I just want to know whether or not trajectories are *continuous*, I do not care about "classical".

What I'm talking about goes back to Zeno's paradox and the nature of motion in its most essential meaning, in terms unrelated to any physics and equations, it is more abstract and philosophical question of logic in terms of cosmology than about QM or "Classical trajectories", ok? However, evidence I prefer is the one based on experiments as the theories are subject to interpretation, even the most basics and accepted ones, obviously.


Basically, answer to this even if in terms of QM might explain a lot - ORBITAL ANGULAR MOMENTUM (magnetic dipole moment due to charge velocity, not "spin"): If this "electric loop" does not have 'internal' velocity there will be no magnetic field there according to electrodynamics (magnetic field of moving charge), but to have velocity you have to have continuous trajectory. If electron was not actually moving by "sliding", but was appearing and disappearing at different locations then there would not be any velocity vector and no magnetic field which would in any case be random at best in such situation. So, how do you reconcile all this with all that?

 

[ZapperZ]

I accepted it long ago, even if no one provided adequate photo. The whole side-argument is around the actual consequences of it being there, so I have been referring to it as a fact for quite some time now. I do not deny radiation is measured in experiments and I appreciate all the applications of this phenomenon, I just don't think anyone explained the causality of it:

a) DECELERATION: does it slow down BECAUSE it radiates, or it radiates because it slows down?

b) ACCELERATION: does it speed up BECAUSE it radiates, or it radiates because it speeds up?

These make no sense. Both are easily answered because if it radiates BECAUSE it speeds up, it is violating the conservation of energy. Or is that something you question as well?

If it radiates because it slows down, then it is violating causality because it is doing something on its own. While there is such a thing as self-interaction, this is not the case here. I have to slam a bunch of electrons into a stainless steel wall, i.e. I have to force it decelerate to produce Bremsstrahlung radiation. Bremsstrahlung does not happen automatically and spontaneously to slow down the electrons. No such cases have ever been observed, unless you have one to share with us.

a) What is this Maxwell equation everyone is talking about?

Oh my goodness! After all this debacle and a thread this lengthy, we now have a confirmation that you really don't know what you're discussing?

Unless the OP has lingering question related to the original question, I think this thread is going nowhere fast because we keep having to make several steps back to explain basic physics. If you don't understand basic E&M (i.e. these "Maxwell equations"), then we'd be more than happy to answer specific questions on it. This is not the way to do it.

Questions on the origin of "spin" and magnetic moment of atoms have been answered in many other threads in the Quantum Physics forum. One is welcomed to do a quick browse.

This thread is done.

Zz.