Why Did We Shift from Electron Orbitals to Electron Clouds?

[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.